𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, January 10, 2023
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Generated Wed 11 Jan 02:42:40 GMT 2023
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Gemini index for the day: gemini://gemini.techrights.org/2023/01/10/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
  Previous bulletins in IPFS (past 21 days, in chronological order):

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QmcYNvBka24tu2hBsNQvBVNcTjpuUCQEfzcyW15SJLsr1Y
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QmcoTd9cdz13ZUiXpFN832GoD59aNm8naY18eRHZ8th4bc


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

⦿ When the Employer Doesn’t Understand or Grossly Underestimates AWS Capacity Issues (and a Story of Lost E-mail in Clown Computing) | Techrights

⦿ IRC Proceedings: Monday, January 09, 2023 | Techrights

⦿ [Meme] Censorship of Self-Incriminating Evidence | Techrights

⦿ Microsofters Stabbing People in Debian | Techrights

⦿ More Than Half a Dozen Copyright Litigation Threats Sent to Techrights in Less Than Six Months Over EPO and UPC Articles (Misusing Copyrights for Censorship/Intimidation) | Techrights

⦿ Like Elon Musk at Twitter, Sirius is Passing Financial Liabilities to Suppliers by Not Paying (Sirius Clients Suffer as a Result) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2023/01/10/aws-trap/#comments
		http://techrights.org/2023/01/10/irc-log-090123/#comments
		http://techrights.org/2023/01/10/judge-grabinksi-hiding-from-critics/#comments
		http://techrights.org/2023/01/10/microsoft-backstabbing/#comments
		http://techrights.org/2023/01/10/suepo-video-and-video-on-copyright-trolling/#comments
		http://techrights.org/2023/01/10/video-sirius-management-to-blame/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2023/01/10/easyos-dunfell-series-4-5-5/#comments
		http://techrights.org/2023/01/10/john-deere-big-news/#comments
		http://techrights.org/2023/01/10/more-twitter-departures/#comments
		http://techrights.org/2023/01/10/yet-more-security-issues-in-rust/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 65

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/10/aws-trap/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/10/aws-trap/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ When_the_Employer_Doesn’t_Understand_or_Grossly_Underestimates_AWS_Capacity
Issues_(and_a_Story_of_Lost_E-mail_in_Clown_Computing)⠀✐


Posted in Free/Libre_Software, Servers at 9:41 pm by Dr. Roy Schestowitz


Summary: The Sirius_‘Open_Source’ management was dumb enough to replace the in-
house infrastructure with overpriced (and oursourced) junk that did not even
work as expected


THE report we deposited over a month ago already covered the fiasco of
oursourcing (gradual) where I had worked for nearly 12 years. We don’t want to
repeat what was already covered. I discussed this in person with the main
person responsible for the awful decision. He said they envisioned it would
save money, but based on bills that I saw it was beyond insane to suggest so!
Why would a company throw about 10,000 pounds down the drain every year. A
modest second-hand server can be purchased for just 1,000 pounds and we didn’t
need to buy any. We already had servers!!!


“Who’s going to be held accountable?”When the company’s “cloud” bills keep
blowing upwards (upward to almost a thousand pounds a month), for something
that started very small (the vendor lock-in relies on this sort of illusion,
before exit barriers are raised), you have to wonder about the judgment of
short-sighted decision-makers. Who’s going to be held accountable?


As a reminder, AWS operated at a loss for years and Azure still seems to be
operating at a loss (they just call everything “Azure” now). They are enticing
people to enter the trap. Microsoft loses money and so does Google. Billions in
losses! I brought this up over the phone, speaking to the CEO for about an hour
almost a year ago! But they don’t want to listen!


“As a reminder, AWS operated at a loss for years and Azure still seems to be
operating at a loss (they just call everything “Azure” now).”As a reminder,
Microsoft laying off staff, cancelling and shutting down datacentres, as they
overprovisioned for something that never came (or resulted in massive losses).
Microsoft basically misleads shareholders by rebranding many things “cloud”
and/or “Azure”, so even if it’s not growing Microsoft claim claim otherwise.


On the phone about a year ago I suggested small self-hosted machines (the CEO
called this “hobbyist”). It’s worth reminding ourselves that we lost staff that
looked after our servers. That too was the fault of the management, for reasons
we explains before.


It would be so much cheaper and safer to run our own infrastructure, as we
already did for decades. And yes, we covered this in the report and earlier in
this series. This is a no-brainer.


To give one example of what moving to AWS caused Sirius: OTRS, a ticketing
system, needed us throwing more and more resources at it (partly because of bad
design, partly due to workers sending megabytes of text in E-mails, as they
top-post — the “Microsoft Way” basically — and don’t bother trimming/snipping
what they respond to). Each time you add resources the bills go up by a lot!
That’s the “magic” of “the clown”! It’s getting very expensive very fast!


“To give one example of what moving to AWS caused Sirius: OTRS, a ticketing
system, needed us throwing more and more resources at it…”Remember that we used
to self-host all the E-mail of the company; now the company uses phony
encryption as a tenant on someone else’s servers (Amazon). I challenged my
colleagues about this. I argued with management. They could not even defend
their decision. They saw no need to defend what they had done! We’ve had
arguments over this internally in 2022. Of course it was risky for me to bring
this up, but at this stage it was the moral thing to do, even a moral
obligation. At Sirius, colleagues felt like their efforts and contributions
were ignored/discarded by the cabal (family), so they quit caring. This is how
nepotism dooms companies. Some colleagues left, some remained but without much
desire to go beyond the basics. And this we covered before.


Regarding E-mail hosting in “the clown”, here’s a 2020 story. To quote an
Evening Shift handover: “Spent most of my evening tracking down missing emails.
I was rather perturbed by xxxxx’s handover email disappearing and I’m guessing
that because the server was underpowered it started to behave strangely and
misclassified legitimate emails as viruses and deleted them. Fortunately each
email is given an unique id by the system which is useful for searching the
logs. Managed to get a list of deleted ones and sent it to xxxxx, xxxxx, and
xxxxx suggesting that they identify their clients or ones they recognise and
email them with the time + 1 hour asking to resend. I found one from xxxxx and
emailed and xxxxx kindly sent his email again.”


Wonderful! What a mess.


In some cases useful virtual machines were turned off to “save money”. Even if
they took little space and CPU. If self-hosted, they would cost almost nothing
to leave on.


“Clown computing: it’s here today, but gone tomorrow. You’re not part of the
decision!”Clown computing is a trap. To quote one new (days-old) cautionary
tale (already in Daily Links): “Turns out that Revue is getting shut down. This
means that I won’t be able to use it anymore (and I stopped using it because it
wasn’t getting much traction vs the amount of work I put into it).”


So maybe outsourcing isn’t such a wise long-term strategy after all.


At one point by far our biggest client relied on VMware for clown hosting; of
course VMware shut the whole thing down and in a hurry we need to get all the
servers out of there. Clown computing: it’s here today, but gone tomorrow.
You’re not part of the decision! It does not matter is you have critical
services on there and they give you a very short notice (to vacate). █



                    ䷩ 𝚕𝚒𝚗𝚎 193

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/10/irc-log-090123/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/10/irc-log-090123/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Monday,_January_09,_2023⠀✐


Posted in IRC_Logs at 2:43 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-090123.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-090123.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-090123.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-090123.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
 QmT3ULA19f6oA7M3wZJh1emsuWYNYPFhYp3yJbpdBQMKPW #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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 QmfR4nJWYnHiQYWAK2VqCAfDq2jrFA7tZvjwUnB9F5JKzT (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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                                                 IRC log for
 QmYn3KupxNc4YKz7em7Zg1qRSG1DnDm63rbEJFVjdvkJGE #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
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 QmdjfgfKE6YB9w5cchhkrYu5KJyx7pd2Cjox8fbXJCfQwg (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmcoTd9cdz13ZUiXpFN832GoD59aNm8naY18eRHZ8th4bc



                    ䷩ 𝚕𝚒𝚗𝚎 320

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/10/judge-grabinksi-hiding-from-critics/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/10/judge-grabinksi-hiding-from-critics/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Censorship_of_Self-Incriminating_Evidence⠀✐


Posted in Europe, Patents at 2:32 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇We've_got_the_chief_patent_judge_in_our_pocket..._We've_got
                    the_chief_patent_judge_in_our_pocket⦈_


Summary: EPO and UPC chiefs won't_tolerate people who show evidence of António
Campinos controlling the person who’s supposed to independently assess fake
European_Patents_that_he_has_been_granting


⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣦⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⠐⠀⣿⠀⢸⡆⡇⡄⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠌⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⢩⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣦⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣏⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⢿⣿⡿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠃⣇⡆⢸⢸⠄⡗⡇⢸⠀⠀⠸⣿⠀⢸⡄⡧⡄⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⢡⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣧⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠃⣇⡆⢸⢸⠄⡗⡇⢸⠀⠀⠸⣿⠀⢸⡆⡧⡄⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⣤⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⠰⢸⣿⠀⢸⠀⡇⡍⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣇⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⠀⠈⣿⠀⢹⡇⡧⡅⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⣿⣟⣭⣿⣿⣿⠋⠀⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠃⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠇⢻⡆⡧⡅⡇⠀⡇⡷⡇⢸⢸⢸⢸⢸⣿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠉⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⠟⠉⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣿⣭⣿⣿⣿⠟⠋⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠀⢿⡇⡧⡅⡇⠀⡇⡷⡇⢸⢸⢸⢸⢸⣿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⠉⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠉⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⠿⠋⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠃⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠇⢹⡇⡧⡅⡇⠀⡇⡷⡇⢸⢸⢸⢸⢸⣿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⢩⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠉⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣿⣭⣿⣿⣿⠛⠀⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠀⢹⡇⡧⡅⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⣿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⡍⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⢿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣿⣭⣿⣿⣿⠿⠋⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠀⢹⡇⡧⡅⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⢰⡍⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣯⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣿⣭⣿⣿⣿⠋⠀⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠇⢹⡇⡧⡅⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⢿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⢰⣭⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⠿⠋⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠇⣇⡆⢸⢸⠄⡗⡇⢸⠀⢸⢸⣿⠀⢻⡆⡧⡄⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⣿⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠁⠀⠁⠈⠁⠈⠉⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⢰⡍⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⠆⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣷⣧⣷⣿⣿⣟⣭⣿⣿⣿⠛⠈⡇⠰⡇⢸⠀⢸⢘⢸⢸⢸⢸⠄⡧⠀⠠⠃⣇⡆⢹⢸⠄⡗⡇⢸⠀⢸⢸⣿⠇⢹⡇⡧⡅⡇⠀⡇⡷⡇⢰⢸⢸⢸⢸⣽⠀⢸⠜⡇⡇⡇⠁⢸⡇⠨⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠀⠀⠁⠀⠁⠈⠁⠈⠈⠈⠈⠈⠈⠁⠁⠀⠀⠀⠁⠁⠈⠈⠁⠁⠁⠈⠀⠈⠀⣭⠀⠉⠀⠉⠁⠉⠀⠁⠁⠁⠀⠉⠀⠉⠈⠈⠀⠈⠀⠈⠁⠈⠁⠈⠈⠈⠁⠁⠀⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢧⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⣀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣼⣿⣿⣆⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣾⣥⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⣿⢹⣿⢿⣿⡟⣱⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢰⣿⣿⣇⠀⣿⡇⠀⣿⣿⢰⣿⠃⠸⠁⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠘
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⡇⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣇⠀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠘⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣼⣿⣿⣿⣷⣾⣿⣿⣟⣵⣿⣿⣽⣿⣿⣿⣿⠻⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠘⠿⠇⠿⠿⠟⠻⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠃⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⢿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣷⡍⣿⣿⢸⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⡇⠀⣿⣿⢰⣿⠇⠈⠋⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⡍⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⡇⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⡇⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣇⠀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣥⣿⣿⣽⣿⣧⠁⠀⠸⠿⠀⠀⠀⠀⠿⠿⠀⠿⠿⡸⠿⠇⠿⠿⠟⠻⠿⠘⠿⠇⠀⠿⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠃⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⡿⠿⠿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢹⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢸⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠉⣿⣿⢰⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⡀⣼⣿⢿⣷⢹⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⢻⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣥⣿⣿⡹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠿⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⡀⠛⠿⠿⠋⠀⠸⠿⠃⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⡏⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡟⠁⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣵⣿⣿⣽⣿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠃⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠙⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⡯⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⠃⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣵⣿⣿⣽⣿⡇⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⡀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⠏⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣵⣿⣿⣽⣿⣇⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣝⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠂⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡟⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣽⣿⣏⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠆⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠈⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡟⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣵⣿⣿⣽⣿⣯⠁⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠆⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠈⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡟⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣟⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣽⣿⣏⠁⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⡸⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠆⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡟⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣟⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣵⣿⣿⣽⣿⣯⠁⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⡸⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⡀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠂⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡟⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣟⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⣽⣿⣏⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠸⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡏⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣵⣿⣿⣽⣿⣏⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⢀⠸⠿⢇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⣿⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⡏⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⣽⣿⡇⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⡀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠻⣿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⡯⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⣿⠇⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⣽⣿⡇⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢹⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⡏⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⠈⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡿⠁⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣵⣿⣿⣽⣿⠇⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠟⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⠿⠿⡿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣷⠍⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡏⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣽⡿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⡀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡧⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⣟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠃⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡝⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢾⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣟⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⡽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⠿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢻⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⣸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⡽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠛⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠿⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⠛⠉⠙⠙⠛⠻⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣟⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠟⠉⠉⠉⠉⠛⠻⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢺⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣟⣷⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠏⠉⠉⠉⠙⠛⠟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢹⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢺⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠏⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠀⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⢀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠉⠀⠀⠙⠛⠛⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⠿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣱⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⠀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠏⠁⠀⠀⠉⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣻⣿⣿⣿⡟⣱⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢾⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠿⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⢋⡀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠿⠋⠀⠀⠈⠙⠛⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⣽⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⢋⢀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠙⠿⠁⠀⠀⠀⠙⠛⠋⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣱⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⠸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣟⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⢋⢀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠹⠟⠁⠀⠀⠈⠙⠋⠉⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⣹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⡀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠹⠟⠀⠀⠀⠈⠛⠛⠉⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⡹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠿⠛⠀⠀⠀⠘⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣱⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠇⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠈⢹⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⡹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⡀⠸⠿⠇⠀⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠩⠿⠏⠀⠀⠀⠙⠛⠛⠛⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠁⣿⣿⢸⣿⠃⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⡹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠿⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠩⠿⠋⠀⠀⠀⠘⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣻⣿⢿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠃⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢸⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣵⣿⣿⠹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠿⠋⠀⠀⠀⠘⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡍⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣧⠀⣿⣿⠁⣿⣿⢸⣿⠃⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⡀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢹⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢹⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣟⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣟⣵⣿⣿⠹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠗⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠉⠿⠋⠀⠀⠀⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣿⣿⣿⡟⣵⣿⢿⣿⡝⣿⣿⢹⣿⡿⣿⠿⢿⣿⠿⠇⠀⠿⣿⣿⠿⢸⣿⣿⣇⠀⣿⣿⠉⣿⣿⢸⣿⠃⠀⠀⣿⣿⣿⠀⣿⣿⢿⣷⠀⣴⣿⢿⣷⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠀⢸⣿⠸⢿⣿⡿⠇⣿⣿⠀⠀⠀
⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠉⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⢸⣿⢻⣿⠀⣿⣿⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⡄⣿⣿⣼⣿⠁⣿⣿⢸⣿⢸⣿⡇⣿⣿⢸⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡏⠀⠀⠀
⣿⢹⣿⢿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⣾⣿⣾⣿⡄⣿⣿⡀⣿⣿⢻⣿⡀⠀⢸⣿⣾⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⠸⣿⡇⣿⣿⠘⢸⣿⡇⠀⠀⢸⣿⠀⢸⣿⡇⠀⠿⠇⠀⠀⠀
⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣵⣿⣿⠹⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠿⠟⠀⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠘⠿⠇⠀⠻⠿⠀⠿⠇⠿⠿⠿⠟⠁⠙⠿⠿⠛⠀⠛⠿⠿⠋⣀⠸⠿⠇⠀⠀⠸⠿⠀⠘⠿⠇⠀⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1449

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/10/microsoft-backstabbing/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/10/microsoft-backstabbing/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsofters_Stabbing_People_in_Debian⠀✐


Posted in Debian, Microsoft at 8:58 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Anyway,_good_news_for_today_so_I'm_in_a_good_mood:_https://
lists.debian.org/debian-devel-announce/2023/01/msg00003.html⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Stabbing_debian⦈_


Summary: Hours ago Microsoft_Matt bragged that he had just entered the
technical committee in Debian; he probably doesn’t want people to see what_he
wrote_before (content warning: violence)


⢾⣿⣾⡷⢾⢿⣿⡿⢿⣿⣿⣿⣾⣷⡶⢷⣮⢽⢿⠿⢷⠶⢶⣶⡾⡾⡶⡶⣾⢾⠶⣷⠷⡶⡲⠾⡾⠾⠖⠮⠷⡶⡷⣿⡷⠶⣶⡷⣷⢾⡿⠶⡶⡾⢳⠶⠾⠾⢶⢻⣶⢶⠶⠶⡶⢶⣶⣶⣶⣾⣶⣶⣶⣷⣷⣿⣾⣿
⠼⣷⣷⣷⣾⡿⣿⣶⣿⣿⣿⣿⣿⢿⢿⣶⡧⣦⣦⣼⢴⣧⣧⣽⣤⣮⣮⣮⣿⣦⣼⣤⣧⠧⡮⡼⠧⢶⡤⠤⣴⣧⣮⣿⣷⢿⢿⢶⢼⠤⡧⣤⣦⣦⣼⣤⣴⣴⣴⣼⣿⣭⣥⣬⣤⣥⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣘⣀⣛⣘⣘⣐⣃⣓⣛⣘⣂⣈⣃⣀⣀⣀⣈⣂⣃⣀⣐⣂⣈⣃⣀⣀⣀⣀⣘⣊⣀⣈⣋⣈⣈⣈⣈⣋⣙⣉⣃⣀⣘⣐⣑⣁⣁⣁⣁⣁⣀⣒⣚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣯⣮⣧⣴⣾⣿⣸⣇⣭⣸⣝⣭⣻⣿⣺⣩⣻⣿⣏⣉⣈⣼⣅⣨⣫⣿⣋⣿⣟⣽⣥⣟⣩⣚⣞⣆⢙⣈⣈⣯⣇⣈⣟⣹⣕⣍⣗⣽⣘⣾⣟⣽⣉⣿⣿⣨⣟⣯⣹⣏⣟⣟⣝⣿⣿⣋⣉⣭⣉⣸⣿⣻⣿⣼⣿⣹⣿
⣹⣯⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣽⣽⣽⣿⣭⣋⢩⣜⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⡀⡀⢸⣏⣉⣉⣉⣙⣏⣉⣉⣉⣉⣉⣉⣉⣉⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠈⠁⢸⣿⣭⣭⣭⣽⣭⣿⣭⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⠩⢩⢍⡍⠍⠉⠩⢩⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣬⣬⣥⣥⣥⣤⣬⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣷⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣛⣛⣛⣟⣟⣛⡙⣟⡛⣟⣛⣻⣙⡛⢻⣙⣻⣛⣛⣟⣛⣟⣛⣻⣛⣻⣛⣛⣙⡏⣛⣛⣛⣋⣟⣛⣛⣯⣟⣻⣙⣻⣛⣛⣟⣙⣛⣛⣛⣛⣟⣛⣋⣙⣙⣛⣛⣛⣛⣫⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣻⣛⣛⣟⣻⣿
⣿⣭⣉⣉⣏⣍⣝⣫⣍⣉⣍⣍⣹⣉⣉⣽⣩⣍⣏⣩⣉⣭⣽⣉⣩⣩⣉⣍⣉⣩⣉⣍⣉⣍⣯⣉⣹⣩⣩⣉⣍⣏⣹⣩⣏⣉⣉⣩⣹⣉⣏⣍⣉⣭⣹⣉⣍⣍⣏⣍⣉⣉⣹⣩⣍⣩⣩⣏⣍⣭⣉⣉⣹⣍⣍⣉⣹⣿
⣿⣬⣴⣼⣤⢤⣤⡼⣤⣤⣧⣤⣤⢯⣤⡤⡦⣼⣤⣥⣭⣤⣤⣤⣼⡼⣤⣤⡼⣤⣬⡴⣬⣼⣴⢤⢧⣤⣧⣬⣤⢥⣥⣤⣥⣤⣤⡤⢤⣤⡷⡤⠤⣤⣤⣽⣤⢥⠃⠀⠐⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠘⠀⠁⠀⢠⣼
⣿⠒⠒⠚⠒⠒⠒⠓⠒⠂⠒⠒⠒⠒⠓⠒⠒⠓⠒⠒⠂⠒⠓⠓⠒⠒⠚⠒⠒⠐⠒⠓⠒⠓⠓⠒⢲⠼⠶⠧⠶⠦⠗⡞⠶⠖⠼⠶⠶⠶⠷⠖⠶⠾⢶⠶⠶⠺⠤⢤⠤⠤⣄⠄⠤⠤⠄⠤⠤⠤⠤⠤⡄⠤⠠⠤⢼⣿
⣿⠒⠒⠒⣖⢒⠒⠒⠒⡒⠒⡒⠒⢲⠒⠒⠒⣒⠒⠒⡒⠒⠒⡖⠒⠒⣖⠒⡖⠒⠒⠒⡖⠒⢲⠒⢺⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1497

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/10/suepo-video-and-video-on-copyright-trolling/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/10/suepo-video-and-video-on-copyright-trolling/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ More_Than_Half_a_Dozen_Copyright_Litigation_Threats_Sent_to_Techrights_in
Less_Than_Six_Months_Over_EPO_and_UPC_Articles_(Misusing_Copyrights_for
Censorship/Intimidation)⠀✐


Posted in Deception, EFF, Europe, Patents at 2:30 am by Dr. Roy Schestowitz


Video_download_link | md5sum 4284b6c8bada7f9eec70cb35ae8bb0a4
Censorship by Threats
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-upc-copyright-spiel.webm


Summary: Freedom of speech is under threat; the few who still cover EPO
corruption are routinely subjected to threatening letters, misusing “copyright”
in spite of Fair Use provisions; Europe’s patent system is now dominated by a
bunch of gangsters like the_ones_who_roam_Malta


THE state of the EPO is as dire as it was under Benoît_Battistelli if not a lot
worse (the problem is that the media no longer talks about it!) and we’re being
attacked for covering EPO scandals. We’ve been subjected to copyright trolling
last year [1, 2] and the_start_of_this_year (belatedly).


“Please do not donate to the EFF; it’s money down the drain as the EFF is run
by (and for) the billionaires who pay a lot more.”Regarding the latest example
(only happened about 12 hours ago), I’ve since then spoken to three people. I
told them about this latest example and they’ve ridiculed the censorship
attempts. I also contacted 3-4 people in the EFF and so far they have of course
had nothing to say, let alone do. Even_since_one_co-founder_died_and_another
was_ousted_the_EFF_has_barely_done_anything_about_patents_and_SLAPPed/bullied
bloggers. Please do not donate to the EFF; it’s money down the drain as the EFF
is run by (and for) the billionaires who pay a lot more. The EFF never helped
me; the best it did was, it responded to an E-mail (about 4 years ago). The EFF
was infiltrated a few years ago. It’s not coming back. █



                    ䷩ 𝚕𝚒𝚗𝚎 1552

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/10/video-sirius-management-to-blame/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/10/video-sirius-management-to-blame/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Like_Elon_Musk_at_Twitter,_Sirius_is_Passing_Financial_Liabilities_to
Suppliers_by_Not_Paying_(Sirius_Clients_Suffer_as_a_Result)⠀✐


Posted in Deception, Finance, Free/Libre_Software at 1:51 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 31260807834863dcb60ccf64d9155b42
Sirius Failure to Pay Providers
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/sirius-not-paying.webm


Summary: The Sirius_‘Open_Source’ CEO and other 'management' staff are to blame
for major outages/downtimes clients were experiencing; while they were busy
eating or pretending to be busy it was the technical staff taking 24/7 support
calls and fighting to restore services (after management failed to pay bills,
even repeatedly, in spite of repeated reminders)


THE video above covers a clear (slam-dunk) case of gross incompetence/
negligence by managers at Sirius. We’ll be showing more examples later this
month. From the clients’ perspective, such gross incompetence by Sirius
management may merit a refund (failing to meet SLAs for sure) and would
typically constitute gross misconduct — albeit only in a company that actually
holds managers too accountable (they won’t hold themselves accountable and step
down/resign upon failure; instead they say absurd_things). Mr. "Art_of_the
Deal" is no good role model unless we ran a truly scammy operation. █



                    ䷩ 𝚕𝚒𝚗𝚎 1599

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/01/2023:_EasyOS_Dunfell-series_4.5.5,_CoolerMaster’s_MasterPlus
Liberated⠀✐


Posted in News_Roundup at 8:01 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o Reviews
          o New_Releases
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Events
          o Web_Browsers/Web_Servers
                # Mozilla
          o SaaS/Back_End/Databases
          o Productivity_Software/LibreOffice/Calligra
          o FSFE
          o Programming/Development
    * Leftovers
          o Science
          o Proprietary
          o Transparency/Investigative_Reporting
          o Finance
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Mastering_the_Linux_CLI:_why_GUI_tools_aren’t_enough_–
                  Linux_Careers⠀⇛


                       In today’s world of computer technology, there is a
                       constant battle between graphical user interface
                       (GUI) and command line tools. While GUI tools are
                       often easier to use and have a more intuitive user
                       experience, they can fall short when it comes to
                       more complex tasks. This article will explore why
                       mastering the command line is essential for any
                       computer user, explaining the benefits of using a
                       command line over GUI tools and demonstrating why
                       GUI tools are not enough for certain tasks. By the
                       end, readers will have a better understanding of
                       why command line tools are an important part of
                       their computing experience.


                       Automating repetitive tasks with command line tools


                       Command line tools can be especially beneficial for
                       Linux administrators because of their ability to
                       automate repetitive tasks, which can save time and
                       reduce the risk of errors. This can be especially
                       useful in situations where tasks need to be
                       performed on a regular basis or on multiple
                       systems. In contrast, graphical user interface
                       (GUI) tools may not have the same level of
                       automation capabilities, requiring users to
                       manually perform tasks each time they are needed.


                       This is just one example of the many benefits that
                       command line tools can offer over GUI tools in
                       Linux. While GUI tools may be more user-friendly
                       and easier to learn, command line tools offer a
                       level of power and flexibility that can be
                       essential for tasks such as system administration,
                       data manipulation, and automation.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ 9_Best_Free_and_Open_Source_Linux_Terminal
                  Multiplexers⠀⇛


                       The nuts and bolts of Linux seem destined to be
                       increasingly hidden away from the desktop user. The
                       continuing development of popular desktop
                       environments offering attractive interfaces and
                       fancy features shows no sign of abatement. However
                       intuitive and slick desktop environments become,
                       there is little prospect that the faithful terminal
                       will be consigned to the recycle bin in the near
                       future. There is simply too much power at the hands
                       of a terminal for many experienced Linux users.


                       Users that want to exploit the full power of the
                       terminal may benefit from using a terminal
                       multiplexer. This type of application can be
                       considered to be a text version of a graphical
                       window manager. It enables users to run multiple
                       text programs simultaneously, as well as offering
                       features that allow users to switch seamlessly
                       between these programs in operation. Terminal
                       multiplexers also allow multiple computers to make
                       simultaneous connections.


                # ⚓ Medevel ☛ Open_Note_Scanner:_The_Libre_Doc_Scanner_You_Have
                  Been_Waiting_For⠀⇛


                       Document Scanner app is a commercial paper document
                       scanner app that many had to upgrade from the free
                       version with limited options to the full feature
                       paid one. Yet, many do not have the slightest idea
                       that there is an open source free alternative app
                       that does the same.


                       Open Note Scanner is a free mobile scanner app for
                       Android devices that enables you to scan documents,
                       paper, cards, handwritten notes, art, or even your
                       shopping receipts. Then do all the heavy lifting
                       for you as automatically adjust the image aspect,
                       contrast and save it in a high quality PDF format.
                       It also supports the automatic scan of preformatted
                       pages with QR Code and action indicators. PDF file
                       with the pages are available on the application
                       website, in the releases section.


                       [...]


                       Software licensed under the GPL version 3 available
                       in GPLv3.TXT and online.


          o § Instructionals/Technical⠀➾


                # ⚓ TecAdmin ☛ lsusb_Command_in_Linux_(Display_USB_device
                  Details)_–_TecAdmin⠀⇛


                       The `lsusb` command is a utility in Linux that
                       allows users to list the USB (Universal Serial Bus)
                       devices connected to the system. It is a part of
                       the “usbutils” package, which provides utilities to
                       display information about USB buses in the system
                       and the devices connected to them.


                # ⚓ TecMint ☛ 6_Deprecated_Linux_Commands_and_Alternative_Tools
                  for_Linux [Ed: In this guide, we will highlight 6 deprecated
                  Linux commands and alternative tools that you should be using
                  instead in your Linux system.]⠀⇛


                       Linux provides tons of command-line utilities to
                       perform various tasks. However, with the passage of
                       time, some of these tools have become outdated and
                       replaced by other alternative command-line tools.


                       In this guide, we will highlight 6 deprecated Linux
                       commands and alternative tools that you should be
                       using instead. Most of these commands are
                       networking utilities that are provided by the net-
                       tools package which has not been under active
                       maintenance for quite a while now.


                # ⚓ ID Root ☛ How_To_Install_TeamSpeak_Client_on_Ubuntu_22.04
                  LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       TeamSpeak Client on Ubuntu 22.04 LTS. For those of
                       you who didn’t know, TeamSpeak is a proprietary,
                       cross-platform voice-over-Internet Protocol (VoIP)
                       application that is used for communication in
                       online gaming, education, and business. Its main
                       idea is to allow people to communicate on a
                       channel, similar to other conferencing apps like
                       Zoom, Google Meet, Skype, Slack, Microsoft Teams,
                       etc. TeamSpeak allows users to communicate with
                       each other using voice and text chat, and it
                       includes a range of features, including support for
                       multiple channels, file sharing, and voice activity
                       detection.


                       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 TeamSpeak voice-over-Internet
                       Protocol (VoIP) on Ubuntu 22.04 (Jammy Jellyfish).
                       You can follow the same instructions for Ubuntu
                       22.04 and any other Debian-based distribution like
                       Linux Mint, Elementary OS, Pop!_OS, and more as
                       well.


                # ⚓ LinuxConfig ☛ How_often_do_you_have_to_reboot_your_Linux
                  server?⠀⇛


                       Are you tired of constantly having to reboot your
                       servers to fix issues or apply updates? You’re not
                       alone. Server maintenance and uptime can be a
                       tricky balance, and the decision of when to reboot
                       a server comes with trade-offs. In this article,
                       we’ll take a deep dive into the reasons why servers
                       may need to be rebooted, the potential consequences
                       of not rebooting, and the different approaches to
                       server maintenance and uptime.


                       We’ll also explore tools and techniques that can
                       minimize the need for reboots. Whether you’re a
                       sysadmin, a developer, or a manager, this article
                       will give you a better understanding of the
                       complexities of server maintenance and uptime and
                       help you make informed decisions about when to
                       reboot your servers.


                # ⚓ Red Hat Official ☛ Linux_file_permissions_explained_|
                  Enable_Sysadmin⠀⇛


                       Understanding Linux file permissions (how to find
                       them, read them, and change them) is an important
                       part of maintaining and securing your systems.


                # ⚓ HowTo Forge ☛ Install_Dolibarr_ERP_on_Ubuntu_22.04⠀⇛


                       Dolibarr is an open-source ERP and CRM system
                       written in PHP.


                # ⚓ HowTo Forge ☛ How_to_Install_and_Use_Varnish_Cache_on
                  Debian_11⠀⇛


                       Varnish Cache is an open-source, powerful, and one
                       of the most popular HTTP accelerators used by over
                       3.4 million websites.


                # ⚓ HowTo Forge ☛ How_to_Install_Rust_Programming_Language_on
                  Ubuntu_22.04⠀⇛


                       The Rust programming language has been adopted by
                       hundreds of big companies in production
                       environments.


                # ⚓ Red Hat ☛ How_to_automate_devices_using_the_Ansible_CIP
                  collection_|_Red_Hat_Developer⠀⇛


                       Discover how Red Hat Ansible Automation Platform’s
                       CIP collection allows industrial device automation
                       through YAML configuration files.


                # ⚓ Own HowTo ☛ How_to_Install_Vnstat_on_Linux_Mint⠀⇛


                       Vnstat is a network traffic monitoring tool that
                       you can use to monitor how much bandwidth you are
                       using. If you ever wanted to track the bandwidth
                       usage on desktop then vnstat is the right choice to
                       keep track of bandwidth. This console based app is
                       lightweight, very easy to install and use.


                       In this tutorial you will learn how to install
                       Vnstat on Linux mint via terminal and Software
                       Manager.


                # ⚓ Linuxiac ☛ How_to_Install_VS_Code_on_Linux_Mint_in_5_Easy
                  Steps [Ed: Why is Bobby Borisov helping Microsoft promote
                  proprietary spyware to GNU/Linux users? This is harmful to
                  users' freedom.]⠀⇛


                # ⚓ H2S Media ☛ How_to_install_Telegram_on_Linux_Desktop_in
                  2023_–_Linux_Shout⠀⇛


                       Telegram is a perfect cross-platform alternative to
                       Whatsapp. It is a cloud-based chatting app that
                       keeps giving tough competition to other similar
                       applications. It was developed by Pavel Durov and
                       Nikolai Durov, Russian entrepreneurs.


                       This instant messaging app, apart from chatting
                       also allows sending of photos, videos, documents,
                       and other types of media content. But this is not
                       the reason behind the popularity of Telegram
                       instant its cloud-based technology and focus on the
                       security & privacy of users.


                       To protect the user’s identity and maintain their
                       privacy, Telegram offers end-to-end server-client
                       encryption. So, that hackers won’t be able to read
                       the chats. Further, users can initiate Secret Chats
                       on Telegram that can’t be forwarded and even has
                       self-destruct timer for messages and media.


                # ⚓ H2S Media ☛ Snap_on_Linux-_Installation,_update_and_delete
                  commands_–_Linux_Shout⠀⇛


                       What is a snap? Snap has been introduced as a
                       package management method by Canonical developers,
                       the people behind the popular Ubuntu Linux systems.
                       We can install and use the SNAP on various types of
                       Linux distros such as Redhat, Ubuntu, CentOS,
                       Elementary, Debian, Linux Mint, Manjaro, and more…


                       It is similar to a container with all the files and
                       libraries of an application, and each application
                       is completely independent. So the advantage of
                       using the snap package is that it solves the
                       dependency problem between applications, making it
                       easier to manage between applications. Thus, we can
                       install any Lincu software or packages available in
                       the SNAP repository on any supported Linux distro
                       regardless of its origin, I mean it doesn’t matter
                       what it is. RPM-based or.Deb.


                # ⚓ Beginners_Guide_for_W_Command_in_Linux⠀⇛


                       The w command is a built-in Linux utility that is
                       capable of listing the usernames of all the users
                       that are currently logged-in, locally or remotely.


                       In the output, you can view the information of all
                       the logged-in users, like their username, where
                       they are logged-in from, when they are logged-in,
                       and their activity.


                       In this article, you will learn how to use the w
                       command, including its options (with examples).


                # ⚓ Beginners_Guide_for_Logname_Command_in_Linux⠀⇛


                       The logname command gives you the username of the
                       currently logged-in user by reading the “/var/run/
                       utmp” file, which is identical to the whoami
                       command with one difference.


                       Stick with this article to learn the difference
                       between the logname and whoami commands, the usage
                       of the logname command, and how to use it in shell
                       scripts.


                # ⚓ Trend Oceans ☛ How_to_Resolve_“unable_to_launch_“X_session
                  cinnamon-session-cinnamon””⠀⇛


                       When I boot up my Linux Mint machine, I am greeted
                       with a login screen, and when I press the enter key
                       to complete the login process, I found a simple
                       error message that clearly states, “Unable to
                       launch “cinnamon-session-cinnamon” X session —
                       “cinnamon-session-cinnamon” not found; falling back
                       to the default session.”


                # ⚓ Matthew Garrett ☛ Matthew_Garrett:_Integrating_Linux_with
                  Okta_Device_Trust [Ed: Okta is proprietary, i.e. the very
                  opposite of trust. Linux is gravitating/dragged towards
                  Pentagon trash because of Microsofters such as Matthew
                  Garrett.]⠀⇛


                # ⚓ Linux Capable ☛ Solved:_How_to_List_All_Users_on_a_Linux
                  System_–_LinuxCapable⠀⇛


                       In Linux systems, effective user management is an
                       essential yet challenging task for administrators.
                       Within Linux, all local user information is stored
                       at the path /etc/passwd, with each row representing
                       a single user that contains their name, user ID,
                       directory, and login details.


                       Several different methods are available to list
                       these users in Linux, and in this tutorial, we will
                       cover some of the popular ones utilizing the
                       command line terminal.


                # ⚓ Beginners_Guide_for_Whoami_Command_in_Linux⠀⇛


                       The whoami (concatenated of the strings “who,”
                       “am,”, “i” as whoami) is a Linux command line
                       utility that prints the username associated with
                       the current effective user ID.


                       It comes in handy, especially while writing the
                       shell script, like fetching the username within the
                       script or executing the script for a specific user
                       like root.


                       In this article, you will learn the usage of the
                       whoami command, how to use it in shell scripts, and
                       its alternative commands.


                # ⚓ Beebom ☛ How_to_Update_Your_Chromebook_Easily_(2023_Guide)
                  |_Beebom⠀⇛


                       When users report that their Chromebook is running
                       slow, we recommend they update Chrome OS to the
                       latest version. Google regularly releases update
                       patches that include performance fixes and new
                       features, so it’s important to stay up-to-date.
                       Keeping an update pending for many days is strongly
                       discouraged, as these updates also help keep your
                       Chromebook secure. Additionally, if you happen to
                       use Linux on your Chromebook, it’s also important
                       to keep it updated to the latest version. So if you
                       want to learn how to update your Chromebook, refer
                       to our guide for detailed instructions.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ DebugPoint ☛ Vanilla_OS_22.10_Review:_Ambitious_Linux
                  Distro_for_Tech-Savvy_Users⠀⇛


                       There is joy in trying out a freshly baked Linux
                       distro. And it’s time to have a first distro review
                       of the Vanilla OS.


                       Vanilla OS is a new and unique Linux distribution
                       that has been under development for a year or more.
                       After considerable testing in closed beta, the team
                       announced the maiden release of Vanilla OS 22.10
                       “Kinetic”. It’s based on Ubuntu and its release
                       cycle. Hence the code name “Kinetic”, following the
                       release of Kinetic Kudu in October.


                       This review mainly targets this first release.
                       Let’s dig in while I can give you an idea of the
                       essence of this distribution.


          o § New Releases⠀➾


                # ⚓ Barry Kauler ☛ EasyOS_Dunfell-series_version_4.5.5
                  released⠀⇛


                       Version 4.5.4 was released on January 4, and there
                       has only been one bug-fix since then; however, I
                       decided to release 4.5.5 as woofQ and EasyOS will
                       be undergoing fundamental structural changes, for
                       which it is better to start a new Series — that
                       will be the Kirkstone-series.


                       Hence, 4.5.5 is intended to be the last release of
                       the Dunfell-series.


                       The “fundamental structural change” is mostly about
                       international language support, and the previous
                       couple of blog posts are about the start of that —
                       those changes are not in 4.5.5.


          o § Fedora Family / IBM⠀➾


                # ⚓ Fedora Project ☛ FMN_Replacement_Blog_–_December_–_Fedora
                  Community_Blog⠀⇛


                       Hello and welcome to another installment of the
                       Fedora Messaging Notification (FMN) Replacement
                       blog! It’s been about a month since our last
                       update, and I hope that time was as productive for
                       you as it was for us. We’ve been like Santa’s elves
                       working tirelessly to deliver presents for all the
                       good Fedora users out there.


                # ⚓ Enterprisers Project ☛ New_Ebook:_Build_a_resilient_IT
                  culture_|_The_Enterprisers_Project⠀⇛


                       CIOs are facing no shortage of big challenges in
                       the year ahead – from the Great Resignation, to
                       economic and supply chain issues, to ongoing
                       pandemic-related burnout, and more. While these
                       issues are all complex, there’s one thing that can
                       help IT leaders – and their teams – tackle the
                       unknowns ahead and adapt to changing priorities and
                       obstacles in their way: Resilience.


                       CIOs hoping to build more resilience on their IT
                       teams should focus more on the people elements of
                       culture rather than on the technology, says
                       Shabnoor Shah, principal open leadership global
                       lead and executive coach at Red Hat.


                       [...]


                       A new Ebook explores the key aspects that make up
                       resilience IT culture – as well as the five common
                       obstacles that may be standing in the way. Learn
                       the link between resilience and digital
                       transformation success, how to recruit and retain
                       resilient IT talent, and how CIOs can set the tone
                       for their teams.


                # ⚓ Enterprisers Project ☛ IT_leadership:_Top_5_challenges_to
                  expect_in_2023_|_The_Enterprisers_Project⠀⇛


                       Every year has challenges that impact IT strategy
                       and priorities. Some can be identified and planned
                       for at the start of the year, while others can
                       materialize anytime. As an IT leader, investing in
                       outside-in learning and dialing your active
                       listening skills to identify the signals of the
                       upcoming year’s risks and opportunities is
                       essential.


                       [...]


                       Cybersecurity challenges include a 33 percent
                       increase in ransomware attacks in 2022, and CISOs
                       have ongoing challenges combatting malware,
                       phishing attacks, and security threats related to
                       hybrid work.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu ☛ DIY_chiselled_Ubuntu:_crafting_your_own_chiselled
                  Ubuntu_base_image [Ed: Canonical_is_shilling_Microsoft_and
                  .NET. Canonical has already outsourced chisel to proprietary
                  prison of Microsoft (GitHub), so it’s like in many ways
                  Microsoft already controls Canonical.]]⠀⇛


                       In a previous post, I explained how we made our
                       Ubuntu image 15 times smaller by chiselling a
                       specific slice of Ubuntu for .NET developers.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ reComputer_J4012_mini_PC_features_NVIDIA
                  Jetson_Orin_NX_for_AI_Edge_applications_–_CNX_Software⠀⇛


                       reComputer J4012 is a mini PC or “Edge AI computer”
                       based on the new NVIDIA Jetson Orin NX, a cost-down
                       version of the Jetson AGX Orin, delivering up to
                       100 TOPS modern AI performance.


                       The mini PC is based on the Jetson Orin NX 16GB,
                       comes with a 128GB M.2 SSD preloaded with the
                       NVIDIA JetPack SDK and offers Gigabit Ethernet,
                       four USB 3.2 ports, and HDMI 2.1 output. Wireless
                       connectivity could be added through the system’s
                       M.2 Key E socket.


                # ⚓ CNX Software ☛ MistySoM_Renesas_RZ/G2L_or_RZ/V2L_SoM_and
                  devkit_goes_for_$112_and_up_–_CNX_Software⠀⇛


                       We’ve previously written about several system-on-
                       modules and SBCs based on Renesas RZ/G2L or RZ/V2L
                       Cortex-A55/M33 processors such as Geniatech
                       “AHAURA” RS-G2L100 and “AKITIO” RS-V2L100 single
                       board computers, Forlinx FET-G2LD-C system-on-
                       module, and SolidRun RZ/G2LC SOM and devkit.


                       But most of those are hard to buy, and you need to
                       contact the company, discuss your project, etc…
                       before purchase, except for the SolidRun Renesas
                       RZ/G2LC Evaluation Kit going for $249. Another
                       option is the MistyWest MistySOM module offered for
                       $112 and up on GroupGets with either Renesas RZ/G2L
                       or RZ/V2L processor, as well as an optional carrier
                       board.


          o § Open Hardware/Modding⠀➾


                # ⚓ CNX Software ☛ Maker_Feather_AIoT_S3_–_An_ESP32-S3_board
                  programmable_with_CircuitPython_or_Arduino_–_CNX_Software⠀⇛


                       Cytron Make Feather AIoT S3 is an ESP32-S3 board
                       compatible with the Adafruit Feather form factor
                       and suitable for makers and STEM education with
                       features like LEDs for GPIOs, a buzzer, expansion
                       headers and connectors, and support for
                       CircuitPython & Arduino.


                       The WiFi and Bluetooth LE IoT board also supports
                       LiPo and Li-Ion batteries, includes a USB Type-
                       C port for power/charging and programming, and a
                       few buttons. It’s suitable for machine learning
                       thanks to the vector extensions found in the ESP32-
                       S3 microcontroller.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ How_to_Disable_Apps_on_Android_and_What_Happens_When_You_Do
                  –_Guiding_Tech⠀⇛


                # ⚓ Android Police ☛ This_app_brings_themed_icons_to_most_of
                  your_apps_on_Android_13⠀⇛


                # ⚓ Android Police ☛ Android_13_QPR2_Beta_2_is_available_for
                  Google_Pixel_phones_right_now⠀⇛


                # ⚓ 9to5Google ☛ Here’s_everything_new_in_Android_13_QPR2_Beta
                  2_[Gallery]⠀⇛


                # ⚓ Android Police ☛ Spark_Mail_picks_up_new_Android_13-style
                  personalization_features⠀⇛


                # ⚓ SamMobile ☛ Samsung_Galaxy_A71_5G_gets_Android_13_update_in
                  the_US_–_SamMobile⠀⇛


                # ⚓ Pixel_recents_menu_or_home_screen_freezes_after_Android_13
                  update⠀⇛


                # ⚓ 9 to 5 Toys ☛ Today’s_Android_game_and_app_deals:_Zenge,
                  OXXO,_Transport_INC,_and_more⠀⇛


                # ⚓ 9to5Google ☛ Which_cloud_gaming_services_work_on_Google_TV
                  and_Android_TV?⠀⇛


                # ⚓ Tom’s Guide ☛ My_favorite_phone_from_CES_2023_is_this_big-
                  screen_Android_for_just_$219_|_Tom’s_Guide⠀⇛


                # ⚓ The Tribune IN ☛ Google_bringing_new_features_to_older
                  versions_of_Android_:_The_Tribune_India⠀⇛


                # ⚓ Android_One_UI_5.0_update_released_for_Samsung_Galaxy_Tab
                  A8⠀⇛


                # ⚓ Android Police ☛ Your_Android_phone_could_soon_handle_more
                  than_one_Chrome_window⠀⇛


                # ⚓ TheHinduBusinessLine ☛ Google_announces_new_features_to
                  older_versions_of_Android�OS_–_The_Hindu_BusinessLine⠀⇛


                # ⚓ Android Police ☛ Google_helps_devs_bring_new_Android
                  features_to_older_phones⠀⇛


                # ⚓ XDA ☛ Android_could_soon_make_it_easier_to_transfer_eSIM
                  profiles_to_a_new_phone⠀⇛


                # ⚓ Android Police ☛ The_first_Paranoid_Android_beta_is_live
                  for_the_Nothing_Phone_1⠀⇛


                # ⚓ Android Headlines ☛ This_Android_smartphone_will_stop
                  receiving_updates_after_7_years⠀⇛


                # ⚓ Net2 ☛ 10_Best_Offline_Shooting_Games_For_Android⠀⇛


                       Shooting games are a classic genre in the world of
                       video games and have been popular since the early
                       days of gaming. In recent years, the popularity of
                       mobile gaming has increased significantly, and as a
                       result, there are now numerous offline shooting
                       games available for Android devices. These games
                       range from fast-paced first-person shooters to more
                       tactical and strategic games. In this tutorial, we
                       will explore the 10 best offline shooting games for
                       Android. These games are all available for free,
                       although some may have in-app purchases or ads.


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


          o ⚓ It’s FOSS ☛ Wow!_CoolerMaster’s_MasterPlus_Software_to_Go_Open
            Source!⠀⇛


                 Most gaming/peripheral software suits are either
                 proprietary or not officially available for Linux.


                 As a result, we must constantly look for open-source
                 tools to configure our hardware to get native
                 functionality.


                 The likes of Piper, OpenRGB, Solaar, etc. come in handy
                 in these situations.


                 But, sometimes, even these are not enough.


                 Luckily, CoolerMaster has decided to release an open-
                 source version of its MasterPlus software that aims to
                 work with its coolers and non-CoolerMaster coolers.


          o § Events⠀➾


                # ⚓ OpenSUSE ☛ openSUSE_Conference_Call_for_Papers_is_Open_–
                  openSUSE_News⠀⇛


                       The call for papers for openSUSE Conference 2023 is
                       open!


                       The openSUSE Conference 2023 is scheduled to take
                       place May 26 to May 28. The call for papers will
                       close on April 9, which leaves 89 days to submit a
                       talk.


                       The conference already has two sponsors with Fedora
                       and SUSE. Companies interested in sponsoring the
                       event can view sponsorship information on the
                       project’s wiki page.


                # ⚓ Bootlin ☛ Embedded_Linux_Conference_Europe_2022:_a
                  selection_of_talks_by_Bootlin_engineers_–_Bootlin’s_blog⠀⇛


                       Almost the entire engineering team of Bootlin
                       attended the Embedded Linux Conference Europe 2022
                       in Dublin mid-september, an important event for
                       Bootlin as it helps everyone in the team stay up to
                       date with the latest developments in the Embedded
                       Linux ecosystem, and connect with members of the
                       community.


          o § Web Browsers/Web Servers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Mozilla ☛ Roblox_browser_extensions_for_better_gaming
                        –_Firefox_Add-ons_Blog⠀⇛


                             Every day, more than 50 million people play
                             among millions of user-created games on
                             Roblox. With a massive global audience and an
                             ocean of games, there are vastly different
                             ways users like to interact with Roblox. This
                             is where the customization power of browser
                             extensions can shine. If you’re a Roblox
                             player or creator, you might be intrigued to
                             explore some of these innovative extensions
                             built just for Roblox users on Firefox.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PostgreSQL:_pgDay_Paris_2023_—_Call_for
                  Sponsors_and_Registrations⠀⇛


                       After a successful 2022 edition, we are excited to
                       announce that pgDay Paris is back for 2023 – live
                       and in person on March 23! We’ve had so much
                       interest that this year, we’re planning two tracks
                       of talks and are proposing various half-day
                       training sessions on March 22.


                # ⚓ OpenSource.com ☛ A_guide_to_strings_in_MySQL_|
                  Opensource.com⠀⇛


                       Strings are one of the most common data types you
                       will use in MySQL. Many users insert and read
                       strings in their databases without thinking too
                       much about them. This article aims to give you a
                       bit of a deep dive into how MySQL stores and
                       displays your string variables so that you can have
                       better control over your data.


                       You can break strings into two categories: binary
                       and nonbinary. You probably think about nonbinary
                       strings most of the time. Nonbinary strings have
                       character sets and collations. Binary strings, on
                       the other hand, store things such as MP3 files or
                       images. Even if you store a word in a binary
                       string, such as song, it is not stored in the same
                       way as in a nonbinary string.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ LibreOffice_QA/Dev_Report:_December_2022⠀⇛


                       Rafael Lima continued polishing dark mode features
                       and improved scrolling and zooming in the Basic
                       code editor. He also improved help for ScriptForge


          o § FSFE⠀➾


                # ⚓ FSFE ☛ Promising_news_from_Belgium_and_Dortmund_+++_IT
                  Security_+++_Job_opportunity_–_FSFE⠀⇛


                       In January’s Newsletter: Dortmund embraces Free
                       Software, and Belgium is working to ensure Router
                       Freedom. A cryptographer analyzes IT security. A
                       digital health ecosystem licenses files with the
                       REUSE tool. We are looking for an office
                       coordinator. We look forward to seeing you in
                       FOSDEM and I Love Free Software events.


                       [...]


                       The combination of two ideas, universal access to
                       healthcare and Free Software, gives us GNU Health.
                       Created by GNU Solidario, a non-profit dealing with
                       technology and social medicine, GNU Health is a
                       community-driven Free Software project. While
                       visiting schools in Latin America twenty years ago,
                       the founder, Dr. Luis Falcón, realised that
                       technology needs to support social changes.


                       To make the licensing clear, the project has
                       recently adopted the REUSE specification 3.0 in its
                       components Hospital Management System (both server
                       and client) and Thalamus (the message server for
                       the GH Federation). Luis presented the project and
                       the process of the REUSE implementation in a video
                       interview.


                       Presentation of the digital health ecosystem
                       GNUHealth by founder Dr. Luis Falcón. Becoming
                       REUSE compliant was simple, says Luis in the
                       interview, also available in in our Peertube
                       instance.


          o § Programming/Development⠀➾


                # ⚓ KDAB ☛ On_QVarLengthArray_and_Uninitialized_Storage_in_C++
                  –_KDAB⠀⇛


                       If you’re following our Youtube channel you might
                       have heard me talking about QVarLengthArray.


                       If you’re not… you should follow us! But let me
                       give you a quick recap.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ Smart_watches_won’t_replace_smartphones?_Really?_|_Stop_at
                  Zona-M⠀⇛


                       In conclusion, “lesser screen times, fewer
                       distractions” just thanks to smart watches is
                       likely to remain wishful thinking. It is much more
                       important and necessary to demand the one thing
                       without which no glasses or watches could decently
                       be called “smart”, that is: full interoperability
                       between all watches and all glasses, regardless of
                       who makes them.


          o § Proprietary⠀➾


                # ⚓ Softpedia ☛ Microsoft_Fixes_Windows_11_Bug,_Causes_Another
                  [Ed: Even diehard_Microsoft_shills seem unhappy about
                  Microsoft breaking Windows on the fly]⠀⇛


                       The new glitch in Windows 11 blocks some apps from
                       being installed when using provisioning packages,
                       Microsoft says.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Internet Freedom Foundation ☛ Kerala_High_Court_protects
                  the_right_to_access_court_records⠀⇛


                       A series of petitions before the Kerala HC sought
                       the removal of court orders from the Indian Kanoon
                       website by claiming the ‘right to be forgotten’.
                       Indian Kanoon argued that ‘the right to be
                       forgotten’ is not absolute and that it is
                       inconsistent with the principle of open courts. The
                       Kerala HC ruled in the favour of Indian Kanoon and
                       struck a balance between the right to privacy and
                       the right to freedom of information by holding that
                       the ‘right to be forgotten’ cannot be exercised in
                       criminal law cases and current/recent cases. Though
                       it could be exercised on a case-to-case basis with
                       respect to matrimonial/family cases etc.


                       [...]


                       India Kanoon is a popular open-access search engine
                       that was launched in 2008. Court orders from the
                       website of the Supreme Court, High Courts, district
                       courts and tribunals are automatically uploaded on
                       the Indian Kanoon website. Indian Kanoon reproduces
                       these orders verbatim, after redacting personally
                       identifiable details of victims of sexual violence.
                       No other modifications or edits are made to the
                       court order. India Kanoon’s case removal policy is
                       available here.


                       Several petitioners filed writ petitions before the
                       Kerala HC, seeking the removal of their individual
                       court records online based on a purported right to
                       be forgotten. Of these, two were matrimonial
                       matters and the rest were criminal matters. Indian
                       Kanoon was impleaded as a party in the case as the
                       petitioners sought deletion of these court records
                       from Indian Kanoon’s database as well.


                       Indian Kanoon argued that a right to be forgotten
                       cannot extend to court records. Placing reliance on
                       the Supreme Court’s ruling in R. Rajagopal v. State
                       of Tamil Nadu, Indian Kanoon argued that court
                       records are public documents and that a right to
                       privacy cannot be used to prevent their
                       publication. Further, the only circumstances in
                       which the publication of a court order can be
                       prevented are if the court specifically issues such
                       an order or if there is a statutory prohibition
                       against the publication of certain types of orders.
                       For example, Section 228A of the Indian Penal Code
                       prohibits the disclosure of the identities of
                       victims of sexual violence, and Indian Kanoon
                       removes any personally identifiable information of
                       such victims from the court orders it publishes on
                       its website.


          o § Finance⠀➾


                # ⚓ Being_frugal_was_ALWAYS_expensive_|_Stop_at_Zona-M⠀⇛


                       What is important is to understand the REAL reasons
                       why this happens. I’m sure that many will
                       instinctively answer “I just have NO TIME to do
                       that stuff! Not after being away from home 40 / 50
                       hours a week just to stay a working poor!”


                       [...]


                       One big reason why most of us can’t apply the tips
                       above is that everything with a chip inside is
                       unrepairable at home, or anywhere else. Even
                       without that chip wasn’t really necessary in the
                       first place You may need hard to find tools just to
                       diagnose a fault in your “smart” fridge, TV or
                       dishwasher, and just to find that it’s cheaper to
                       buy a new one.


                       [...]


                       Learning to use a table saw and finding the money
                       to buy it is relatively easy and probably still
                       affordable for most people in western societies.


                       But goods like sewing machines or power tools, let
                       alone vegetable gardens or table saws… are simply
                       not affordable, even if they came for free, when
                       the only place to store them when idle (that is,
                       almost always 99.999% of the time) is the same one,
                       tiny cabinet that is already full of clothes, shoes
                       or suitcases (more on this below).


                       And even if one had access to enough money for a
                       house with an extra room or closet, spending it
                       just to play carpenter or tailor once per decade
                       would hardly make sense, would it now? (*)


                       [...]


                       Here in Rome, the number of people who can afford a
                       weekend in Paris, or a week snorkeling in Sharm El
                       Sheik is way, way higher than that of those who can
                       afford any toolshed where they could build or fix
                       their own furniture with their own tools. And from
                       what I hear, it’s pretty much the same in most of
                       the western world.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ It’s FOSS ☛ Combatting_Academic_Dishonesty:_OpenAI_to
                        Help_Detect_ChatGPT_Text [Ed: Microsoft angling_to
                        become_“market_leader”_in_plagiarism, basically
                        breaking the law as a “service”]⠀⇛


                             ChatGPT has been the talk of the town in
                             recent times as a very interactive chatbot
                             powered by AI. Launched back in November
                             2022, it has caused quite a ruckus in the
                             tech world.


                             Developed by OpenAI as a language model, it
                             interacts with users as if it were having a
                             conversation with them. It can answer follow-
                             up questions, reject inappropriate questions
                             and even admit mistakes!


                             But, as with many things AI, this has also
                             raised a few eyebrows


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Car_Free_Lifestyle⠀⇛


                       When we moved about six months ago we were looking
                       forward to being closer to places we want and need
                       to go. We like to ride our bikes, ebikes and walk
                       so this was a big part of our decision to move
                       where we did. Well after six months I can say that
                       I’m loving it.


                # ⚓ 🔤SpellBinding:_HLYNOTM_Wordo:_CHAIN⠀⇛


                # ⚓ Freezr’s_PEBCAKs:_Happy_New_Pebcak_Year!_😎⠀⇛


                       Another year is gone and a lot of pebcaks good and
                       bad happened and are going to happen again!


                       A good pebcak is the new “Pebcak [DOT] Club” domain
                       has been activated and the capsule transferred on
                       it… A bad one is I already paid for “GeminiSpace
                       [DOT] Club” till 2025… ^^”


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



                    ䷩ 𝚕𝚒𝚗𝚎 2804

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/01/2023:_John_Deere_Surrenders_a_Little_and_Nadella_Drops_Hints_of
Upcoming_Microsoft_Layoffs⠀✐


Posted in News_Roundup at 12:00 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o BSD
          o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
          o Slackware_Family
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o GNU_Projects
          o Programming/Development
                # Perl_/_Raku
                # Rust
    * Leftovers
          o Science
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ 5+_Reason_Wayland_Is_Not_Ready_For_You…_For_Now_–
                  Invidious⠀⇛


                       Wayland is making great headway in improvements but
                       that doesn’t mean that you have to use it today, so
                       today let’s go over some reason why you might want
                       to avoid doing so.


                # ⚓ Late_Night_Linux_–_Episode_211_–_Late_Night_Linux⠀⇛


                       The ultimate ESP system, VoIP & RTC capture and
                       troubleshooting, overpriced keyboards, making
                       arcade cabinets even more fun, some notable distro
                       releases, avoiding CAPTCHAs, and more.


                # ⚓ Video ☛ Python_Dictionaries_Explained_Quickly_–_Invidious⠀⇛


                       Python dictionaries are known as associative arrays
                       or hashmaps in other languages. In this video I
                       explain how python dictionaries work quickly


                # ⚓ Video ☛ KaOS_Linux_|_Beautiful_KDE_Plasma_Distro_–
                  Invidious⠀⇛


                       In this video, I take a quick look at KaOS Linux!
                       KaOS is a free, open-source Linux distribution
                       built from scratch, focusing on KDE software. It is
                       designed to provide a modern, stable, and fully
                       customizable operating system built using the most
                       recent software packages.


                # ⚓ Video ☛ How_to_install_Vanilla_OS_22.10_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Vanilla OS 22.10.


          o § Kernel Space⠀➾


                # ⚓ 9to5Linux ☛ You_Can_Now_Install_Linux_Kernel_6.1_on_Ubuntu,
                  Here’s_How⠀⇛


                       Being the latest stable kernel series, Linux 6.1,
                       which will also be a long-term supported (LTS)
                       series receiving updates for at least two years,
                       brings new features, better performance, and
                       improved hardware support so you can enjoy a safer,
                       faster, and more stable Linux desktop or server
                       experience.


                       It took a while, but Linux kernel 6.1 is now
                       finally available for Ubuntu users and users of
                       Ubuntu-based distros. The latest release, Linux
                       kernel 6.1.4, can be downloaded and installed on
                       Ubuntu 22.10 (Kinetic Kudu), Ubuntu 22.04 LTS
                       (Jammy Jellyfish), or even Ubuntu 20.04 LTS (Focal
                       Fossa).


                # ⚓ Bootlin ☛ Welcome_to_Alexis_Lothoré_–_Bootlin’s_blog⠀⇛


                       Bootlin is really happy to welcome another engineer
                       in its team: Alexis Lothoré, who joined us on
                       January 3, 2023.


                       Alexis graduated in 2016 from INSA Toulouse and
                       built his experience on embedded systems and
                       embedded Linux while working for Smile and then
                       Somfy Protect. In addition his experience on
                       embedded Linux, Alexis has experience on micro-
                       controller based development, with real-time
                       operating systems such as FreeRTOS, and also has a
                       wide knowledge around connected systems: protocols,
                       security, robustness, evolutivity.


          o § Graphics Stack⠀➾


                # ⚓ Turnips_in_the_wild_(Part_3)_–_Danylo’s_blog⠀⇛


                       This is the third part of my “Turnips in the wild”
                       blog post series where I describe how I found and
                       fixed graphical issues in the Mesa Turnip Vulkan
                       driver for Adreno GPUs.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Excellent_Utilities:_Nushell_–_flexible
                  cross-platform_shell_with_a_modern_feel⠀⇛


                       The shell is a program that takes commands from the
                       keyboard and gives them to the operating system to
                       perform. This environment lets users run commands,
                       programs, and shell scripts. The shell is both an
                       interactive command language and a scripting
                       language, and is used by the operating system to
                       control the execution of the system using shell
                       scripts.


                       The first Unix shell was the Thompson shell, sh,
                       written by Ken Thompson at Bell Labs back in the
                       early 1970s. Nowadays, on many Linux systems, bash
                       (which stands for Bourne Again SHell) acts as the
                       shell program. But there are lots of other free and
                       open source shells available for Linux.


                # ⚓ Make Use Of ☛ What_Is_Oracle_VirtualBox_and_What_Can_You_Do
                  With_It?⠀⇛


                       Computers have become so fast and capable that you
                       can run multiple other virtual computers using its
                       internal resources. This idea is known as
                       virtualization, and although it may seem strange,
                       virtualization has many uses. Plus, it can save you
                       a lot of money for tasks that would normally
                       require multiple computers to accomplish.


                       To create these virtual machines, we use a program
                       known as a hypervisor. One of the most recommended
                       hypervisors is Oracle’s VirtualBox. So, what
                       exactly can you do with VirtualBox? And why use it
                       over other hypervisors?


                # ⚓ Video ☛ All_About_htop_–_Invidious⠀⇛


                       Explaining some of the things you can do in the
                       popular interactive process viewer htop


                # ⚓ Medevel ☛ Impressive:_Make_a_Catchy_Presentation_with
                  Style⠀⇛


                       Impressive is a free open source presentation
                       software that enables you to create a catchy
                       beautiful presentation. In another work
                       “Impressive”.


                       It allows smooth alpha-blended slide translation,
                       overview screen, and allows you to add a highlight
                       for your boxes. Moreover, adding spotlight effect
                       that you can browse or navigate through.


                       Smooth alpha-blended slide transitions are provided
                       for the sake of eye candy, but in addition to this,
                       Impressive offers some unique tools that are really
                       useful for presentations.


                # ⚓ Medevel ☛ Spice-up:_Open_source_Standalone_Presentation
                  App⠀⇛


                       Unlike many presentation software programs that
                       resemble Microsoft PowerPoint, and LibreOffice
                       embedded presentation, Spice-up is a standalone
                       presentation software for Linux systems.


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_Google_Chrome_on_Manjaro_21_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Google Chrome on Manjaro 21. For those of you who
                       didn’t know, Google Chrome is a free and open-
                       source web browser developed by Google. The
                       usability and extensive feature list of Chrome
                       attracts users, and therefore a large community of
                       people is using it as their primary web browser.
                       Chrome is available for Windows, Mac, Linux,
                       Android, and iOS operating systems.


                       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 Google Chrome browser on a
                       Manjaro 21.


                # ⚓ TecAdmin ☛ (Resolved)_MySQL_connection_error:_certificate
                  verify_failed⠀⇛


                       The SSL connection error: error:0A000086:SSL
                       routines::certificate verify failed error is
                       usually encountered when establishing an SSL
                       connection to a MySQL server. I was configuring the
                       replication between two MySQL servers running with
                       MySQL version 8.0. After configuring the
                       replication, the “SHOW SLAVE STATUS” command on the
                       slave instance shows me the following error…


                # ⚓ AddictiveTips ☛ Difference_between_Shadowsocksr_vs
                  Shadowsocks_vs_SOCKS5_proxy⠀⇛


                       If you’re looking for different ways to spoof your
                       IP address, you’ll quickly come across proxy
                       protocols like SOCKS5 as well as Shadowsocks and
                       its different variants. What do these protocols do,
                       and how are they different from each other?


                # ⚓ Linux Capable ☛ How_to_Install_QMPlay2_on_Linux_Mint_21_or
                  20_–_LinuxCapable⠀⇛


                       QMPlay2 is an open-source multimedia player
                       designed to provide a simple and feature-filled way
                       to enjoy all media types in one place. Unlike VLC
                       Media Player, QMPlay2 does not require extra
                       plugins or libraries; its features are built and
                       made available from the program’s modern GUI and
                       inbuilt modules.


                # ⚓ Linux Capable ☛ How_to_Install_WoeUSB_on_Linux_Mint_21_or
                  20_–_LinuxCapable⠀⇛


                       WoeUSB is a free, open-source simple tool that
                       enables you to create your own USB stick windows
                       installer from an iso image or an actual DVD. I
                       have used it myself to create bootable USB sticks
                       for installing Windows from ISO images, and it has
                       worked flawlessly every time. The interface is
                       straightforward to use. Select the ISO image or DVD
                       you want to use, select your USB drive, and click
                       “Create.” The process is quick and painless, and
                       the results are always perfect. If you need to
                       install Windows from a bootable USB stick, WoeUSB
                       is the ideal tool for the job.


                       The following tutorial will teach you how to
                       install WoeUSB on the Linux Mint 21/20 desktop
                       release series using a LaunchPAD APT PPA with the
                       command line terminal. This installation method
                       will allow you to run in CLI mode or use the
                       graphical mode interface.


                # ⚓ Linux Capable ☛ How_to_Install_Firefox_ESR_on_Ubuntu_22.04
                  or_20.04_–_LinuxCapable⠀⇛


                       Firefox ESR is the perfect choice for enterprise
                       users who need stability and security updates but
                       may not have access to newer features. The Firefox
                       Extended Support Release (ESR) versions are
                       officially supported by their respective
                       organizations because they do not contain any bugs
                       or unfinished products within their programmed
                       functions! The Firefox extended support release is
                       perfect for university or government networks
                       needing more support than updated software or for
                       users who prefer using Enterprised-based software.


                       The following tutorial will teach you how to
                       install Firefox ESR on Ubuntu 22.04 LTS Jammy
                       Jellyfish or Ubuntu 20.04 Focal Fossa LTS Linux
                       using a recommended Launchpad PPA repository to
                       provide the most up-to-date version using the
                       command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Remmina_on_Fedora_Linux_–
                  LinuxCapable⠀⇛


                       Remmina is a remote desktop client written in GTK+,
                       aiming to be useful for system administrators and
                       travelers who need to work with many remote
                       computers in front of either large monitors or tiny
                       netbooks. It supports the following protocols: RDP,
                       VNC, NX, XDMCP, and SSH. Among its features are
                       Multi-Monitor support, Tabbed sessions, port
                       forwarding, proxy support, and easy access to
                       typical applications like Firefox or LibreOffice.
                       Remmina also has a robust plugin system that can be
                       used to extend its functionality.


                       In the following tutorial, you will learn to
                       install Remmina on Fedora Linux using two different
                       methods: dnf package manager or flatpak package
                       manager, with some tips for maintaining or removing
                       popular remote desktop software in the future.


                # ⚓ UNIX Cop ☛ How_to_install_and_use_Vim_plugins⠀⇛


                       Recently, you learned how to install Vim in Ubuntu
                       22.04. This powerful text editor that emerges as an
                       improvement to the mythical vi also has support for
                       plugins. Today, you will learn how to install and
                       use Vim plugins.


                       One of the most important reasons to use vim is
                       that it is fast, lightweight, efficient and because
                       it supports many important plugins. These plugins
                       further increase the functionality of the editor
                       and turn it into a Swiss army knife that can help
                       us with almost anything.


                       There are two ways to install plugins in Vim. The
                       first one is manually, where we will have to
                       download each one of the plugins. Although this
                       process is safe and very efficient, the truth is
                       that if you are going to install several, it will
                       not be so much.


                # ⚓ Linux Made Simple ☛ How_to_install_Your_Only_Move_Is_HUSTLE
                  on_a_Chromebook⠀⇛


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


                # ⚓ HowTo Forge ☛ How_to_Install_phpBB_Forum_with_Apache_and
                  free_Let’s_Encrypt_SSL_on_Ubuntu_22.04⠀⇛


                       phpBB is free and open-source forum software that
                       provides a space for people to gather and
                       communicate with each other.


                # ⚓ HowTo Forge ☛ How_to_Install_Wireguard_VPN_on_Debian_11⠀⇛


                       Wireguard is a free and open-source VPN protocol
                       alternative to IPSec, IKEv2, and OpenVPN.


                # ⚓ HowTo Forge ☛ How_to_Install_and_Configure_a_JupyterLab
                  Environment_on_Rocky_Linux_9⠀⇛


                       JupyterLab is a next-generation web-based
                       development environment for Project Jupyter.


                # ⚓ Ubuntubuzz ☛ How_To_Switch_Ubuntu_Desktop_Language_to
                  Chinese⠀⇛


                       This tutorial will help you switching Ubuntu user
                       interface language to Chinese (汉语, Hànyǔ or 中文,
                       Zhōngwén). We offer you both choices of Simplified
                       (简化字, Jiǎnhuàzì) and Traditional Chinese (正體字,
                       Zhèngtǐzì). This will change the language of
                       basically everything you see on the screen
                       including login screens, menus and buttons,
                       calendar and locale / regional format. For example,
                       once switched you will immediately see Files,
                       Writer and Clock all turned into Chinese
                       characters. We also included a procedure to revert
                       back to English language in case you need it.
                       Finally, we write this as an aid for our friends
                       Ubuntu computer users whose language is Chinese
                       everywhere including China, Hong Kong, Indonesia,
                       Macau and Taiwan.


                # ⚓ Make Use Of ☛ What_Is_Ubuntu_Remote_Desktop?_How_to_Set_Up
                  and_Use_It⠀⇛


                       If you’re working from home, or are too far from
                       your Ubuntu PC, setting up a remote connection
                       seems smart.


                       Ubuntu features a built-in remote desktop tool.
                       This gives you total control over your desktop from
                       any other computer or mobile device. You’ll see
                       what’s on that screen and be able to move the mouse
                       and even type!


                       The remote desktop feature supports RDP and VNC and
                       is built into Ubuntu by default. Here’s how to use
                       remote desktop software with Ubuntu.


                # ⚓ HowTo Forge ☛ How_to_Install_Strapi_CMS_on_Ubuntu_22.04⠀⇛


                       Strapi is an open-source, headless Content
                       Management System (CMS) built with JavaScript
                       (NodeJS).


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Video ☛ How_to_install_Minetest_on_KDE_Neon_–
                        Invidious⠀⇛


                             In this video, we are looking at how to
                             install Minetest on KDE Neon.


                      # ⚓ Introducing_@tde@floss.social,_the_official_TDE
                        Mastodon_channel!⠀⇛


                             The channel is intended to provide a space
                             for promptly sharing information about new
                             features, bug fixes, announcements and any
                             other thing that may be related to the
                             development of the TDE project.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Linux Magazine ☛ Gnome_44_Now_Has_a_Release_Date_–
                        Linux_Magazine⠀⇛


                             Gnome 44 will be officially released on March
                             22, 2023.


                             Although it’s a bit premature to talk about
                             what features will be found in the 44th
                             iteration of the Gnome desktop, it’s safe to
                             say that the Epiphany web browser will most
                             likely get the GTK4 port we’ve been waiting
                             for as well as WebExtensions support that
                             will be enabled out of the box. There also
                             may be wider libadwaita support in more apps.


                             The big question on my mind is will Gnome 44
                             finally feature the new terminal app,
                             Console, or will it continue on with the
                             current default gnome-terminal?


                             According to 9To5Linux, Gedit is making a
                             comeback, although there is no indication it
                             will return as the default text editor. My
                             guess is that the new default will remain the
                             same with the newly-updated Gedit available
                             as an alternative.


                      # ⚓ OMG Ubuntu ☛ Help_Test_GNOME’s_New_‘Window_Focus’
                        Behaviour_–_OMG!_Ubuntu!⠀⇛


                             A new ‘window focus’ animation for GNOME
                             Shell is available to test.


                             GNOME designers are currently exploring a
                             different way to indicate ‘focus’ in GNOME
                             Shell. One idea is to remove the app icon,
                             name, and menu that appears in the Top Bar
                             (next to Activities button – this was
                             retained to indicate the app in focus) and
                             replace it with a window animation


                             As is, user testing shows the (what’s left of
                             the) app menu confuses users. “They think
                             that it’s a task switcher, a shortcut to a
                             specific app, or don’t understand what it is
                             at all. It seems to be a trip hazard for new
                             users,” explains GNOME design team member
                             Tobias Bernard.


                             Those running GNOME 43 interested to see if
                             the proposed approach would affect their
                             workflow can try it out by installing a new
                             GNOME extension.


                      # ⚓ DEV Community ☛ Reflections_on_GNOME_.Asia_Summit
                        2022_–_DEV_Community⠀⇛


                             Recently, I got an opportunity to attend
                             GNOME Asia Summit 2022 held in Kuala Lumpur.
                             And it was an experience that I’ll never
                             forget.


                             It was my first time attending an in-person
                             conference. I was not quite nervous and
                             unsure of what to expect. However, from the
                             moment I arrived at the conference, I was
                             immediately struck by the welcoming and
                             inclusive atmosphere.


                             [...]


                             I also got an opportunity to meet and connect
                             with other members of the GNOME community. I
                             had the chance to chat with developers,
                             designers, and advocates from different parts
                             of the globe, and it was fascinating to hear
                             about the different ways in which they are
                             using and contributing to GNOME. Along with
                             that, I also got to meet my fellow GSoCers/
                             friends at the event, and they made the event
                             even more fun.


    * § Distributions and Operating Systems⠀➾


          o ⚓ MX Linux ☛ desktop-defaults-mx-common_updates_–_MX_Linux⠀⇛


                 We are fixing an issue in desktop-defaults-mx-common that
                 should allow menu editing tools like menulibre to work
                 without removing the mx-tools category. The fix involves
                 a change is capitalization of the mx-tools.menu file that
                 is hidden from users, but needs adjusted so that
                 menulibre actually populates the category.


                 For some users, you may see a double “mx-tools” menu
                 category after the change. By defaults, those users who
                 did fresh installs with MX-21 iso and those that updated
                 from MX-19 may see the double category. Anyone doing a
                 fresh install with MX-21.1 and later should not see the
                 issue. This has to do with the original way the mx-tools
                 menu entry was setup, by supplying files directly into
                 the user’s home folder at user creation. From MX-21.1 and
                 forward, those files have been moved outside the home
                 folder, which is why only some users will see the issue.
                 Users who successfully updated to desktop-defaults-mx-
                 common 23.01.03 also won’t see the issue, but that
                 package was pulled because it failed for some users. The
                 full changes are in desktop-defaults-mx-common 23.01.04.


          o § BSD⠀➾


                # ⚓ Ruben Schade ☛ Rubenerd:_I_feel_for_the_NetBSD_community⠀⇛


                       We share a common struggle within the BSD
                       community, and more broadly among Unix-like OSs
                       that aren’t Linux. Think Minix, illumos, heck maybe
                       even big iron UNIX. Linux is now perceived as the
                       default, meaning anyone presenting an alternative
                       has to justify their existence on top of its
                       features and capabilities. Linux people with longer
                       memories probably can recall what that used to be
                       like.


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


                # ⚓ Mandriva_Linux_Chronicles:_First_2023_post:_OpenMandriva_Lx
                  ROME_23.01_is_here!⠀⇛


                       Two days ago, Distrowatch published the
                       announcement that OpenMandriva is making its debut
                       into the world of rolling distros with its ROME
                       (Rolling OpenMandriva Edition, I presume) release.


                       I had upgraded the system not long ago, but I
                       wanted to make sure that I am using this release,
                       so I followed ben79′s most detailed walkthrough
                       here. Big thanks, ben79!!!


                       Everything worked perfectly and my system is stable
                       as a rock.


          o § Slackware Family⠀➾


                # ⚓ Eric Hameleers ☛ Mirror_for_slackpkg+_and_slakfinder_|
                  Alien_Pastures⠀⇛


                       For some time now, the slakfinder.org website has
                       been offline. The domain still exists, but the web
                       site just does not respond. Matteo Rossini
                       (zerouno) needed a break from computers, so it is
                       likely that the site won’t return on short notice.


          o § Fedora Family / IBM⠀➾


                # ⚓ CentOS ☛ CentOS_Hyperscale_SIG_Quarterly_Report_for_2022Q4
                  –_Blog.CentOS.org⠀⇛


                       This report covers work that happened between
                       October 1st 2022 and January 8th 2023. For previous
                       work, see the 2022Q3 report.


                       [...]


                       Since the last update, the SIG gained one new
                       member (Jun Wang).


                       We welcome anybody that’s interested and willing to
                       do work within the scope of the SIG to join and
                       contribute. See the membership section on the wiki
                       for the current members list and how to join.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu Fridge ☛ The_Fridge:_Ubuntu_Weekly_Newsletter_Issue
                  769⠀⇛


                # ⚓ Ubuntu News ☛ Ubuntu_Weekly_Newsletter_Issue_769⠀⇛


                       Welcome to the Ubuntu Weekly Newsletter, Issue 769
                       for the week of January 1 – 7, 2023


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_reverse_geocache_gift_box_only_opens_at
                  specific_GPS_coordinates_|_Arduino_Blog⠀⇛


                       Geocaching is a hobby that combines the fun of a
                       scavenger hunt with modern GPS technology. One
                       party will hide a small cache somewhere, then post
                       the general location and the exact GPS coordinates
                       for other parties to find. The goal is to use GPS
                       navigation to find the hidden cache. Often, people
                       will sign a log or leave a small memento in the
                       cache for others to find. Trent Wyatt took that
                       idea and flipped it with this “reverse geocache
                       box” that will only open when someone takes it to a
                       specific GPS location.


                       Wyatt designed this with gift-giving in mind. The
                       box has an internal lock that isn’t accessible from
                       the outside. The only way for the recipient to open
                       the box and get their gift is by pushing the red
                       button when they are at the location set by the
                       giver. If they aren’t at the proper location, the
                       display on the box will show the distance to the
                       proper GPS location and how many tries they have
                       left. The idea is that the giver will tell the
                       recipient the general location and the recipient
                       will have to perform triangulation to find the
                       exact coordinates where the box will open.


                # ⚓ Purism ☛ Phosh_2022_in_Retrospect_–_Purism⠀⇛


                       We’re usually aiming for a phosh release at the end
                       of each month. In 2022, we did 10 releases like
                       that, 7 major releases (bumping the middle version
                       number) and 3 betas. We skipped the April and
                       November releases. We also did one bug fix release
                       out of line (bumping the last bit of the version
                       number).


                       I hope we can keep that cadence in 2023 as it
                       allows us to get changes to users in a timely
                       fashion (thus closing usability gaps as early as
                       possible) as well as giving distributions a way to
                       plan ahead. Ideally we’d not skip any release but
                       sometimes real life just interferes.


                       Those releases contain code contributions from
                       about 20 different people and translations from
                       about 30 translators. These numbers are roughly the
                       same as 2021 which is great. Thanks everyone!


                       In phosh’s git repository we had a bit over 730
                       non-merge commits (roughly 2 per day), which is
                       about 10% less than in 2021. Looking closer this is
                       easily compensated by commits to phoc (which needed
                       quite some work for the gestures) and phosh-mobile-
                       settings which didn’t exist in 2021.


                # ⚓ Adafruit ☛ MIDI_For_Makers⠀⇛


                       MIDI stands for Music Instrument Digital Interface.
                       It’s the standard communication method for all
                       things music. It’s the way an instrument can talk
                       to a computer. Every musician working in the
                       digital space uses MIDI. Laurie Anderson’s violin?
                       MIDI. Chemical Brothers? MIDI. But why might a DIY
                       MIDI project be useful for you?


                # ⚓ Petros Koutoupis ☛ CircuitMess_Spencer:_The_Educational_DIY
                  Voice_Assistant_Hobby_Kit_–_Random_[Tech]_Stuff⠀⇛


                       Around the same time last year, I posted a review
                       of a project where my son and I built a DIY mobile
                       phone: the CircuitMess Ringo. Well, this year, both
                       he and I built a DIY voice assistant: the
                       CircuitMess Spencer.


                       I have to admit, this kit took a bit less time to
                       assemble [than the Ringo]. It also required less
                       soldering which is good for my son, because he
                       needs to spend time practicing before taking on
                       projects such as this. Fortunately, CircuitMess
                       manufactures and sells practicing kits which I will
                       need to purchase for him to build up his soldering
                       skills.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Police ☛ This_Snapdragon_801_phone_running_Android
                  10_is_only_now_getting_its_last_update⠀⇛


                # ⚓ CNX Software ☛ Khadas_VIM1S_(Amlogic_S905Y4)_SBC_review
                  with_Android_11_–_CNX_Software⠀⇛


                # ⚓ Here’s_What’s_New_in_Spark’s_Android_13_Update⠀⇛


                # ⚓ Android Headlines ☛ Google_releases_Android_13_QPR2_Beta_2
                  with_Unicode_15_Emoji_–_more⠀⇛


                # ⚓ The Verge ☛ Google’s_bringing_new_features_to_older
                  versions_of_Android_–_The_Verge⠀⇛


                # ⚓ 9to5Google ☛ Android_13_QPR2_Beta_2_now_available_for
                  Google_Pixel⠀⇛


                # ⚓ The Sun ☛ Millions_of_Android_owners_urged_to_activate
                  setting_now_–_or_it_could_cost_you_|_The_US_Sun⠀⇛


                # ⚓ Make Use Of ☛ 4_Ways_Twitter_Is_Different_on_the_Android
                  App⠀⇛


                # ⚓ Android Central ☛ AC_Podcast_588:_Will_Android_Actually
                  Improve_in_2023?_|_Android_Central⠀⇛


                # ⚓ Google ☛ Chrome_Releases:_Chrome_Beta_for_Android_Update⠀⇛


                       Hi everyone! We’ve just released Chrome Beta 109
                       (109.0.5414.85) for Android. It’s now available on
                       Google Play.


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


          o § GNU Projects⠀➾


                # ⚓ GNU ☛ GNU_Health_–_News:_GNU_Health_Hospital_Management
                  patchset_4.0.5_released_[Savannah]⠀⇛


                       GNUHealth 4.0.5 patchset has been released !


                       [...]


                       We provide “patchsets” to stable releases.
                       Patchsets allow applying bug fixes and updates on
                       production systems. Always try to keep your
                       production system up-to-date with the latest
                       patches.
                       Patches and Patchsets maximize uptime for
                       production systems, and keep your system updated,
                       without the need to do a whole installation.


          o § Programming/Development⠀➾


                # ⚓ Linux Hint ☛ How_to_Uninstall_Boards_from_Arduino_IDE⠀⇛


                       Arduino is a microcontroller-based platform that
                       includes both hardware and software (Arduino IDE)
                       to program. Arduino is an open-source platform
                       which means we can install multiple libraries and
                       different board cores in it. Sometimes we need to
                       uninstall these boards from the Arduino IDE. This
                       article will cover all the methods one can follow
                       to delete Arduino boards from IDE.


                # ⚓ GNOME ☛ Using_the_‘glab’_CLI_tool_with_GNOME_GitLab_–_Will
                  Thompson⠀⇛


                       I like to use the glab command-line tool, which
                       used to be a third-party project but which has
                       apparently now been adopted by GitLab themselves.
                       In particular, the glab mr family of commands to
                       interact with merge requests are invaluable for
                       checking out branches from contributors’ forks.


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ Rakudo_Weekly_News:_2023.02
                        Microfeatures⠀⇛


                             Hillel Wayne wrote an interesting article
                             titled “Microfeatures I’d like to see in more
                             languages“, which caused quite some comments
                             on the interwebs, including many references
                             to the Raku Programming Language. Check out
                             the comments on HackerNews, /r/programming
                             and Lobste.rs. Good to see many people out of
                             the blue mentioning Raku!


                      # ⚓ Perl ☛ Creating_a_Simple_DSL_in_Perl⠀⇛


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ Updating_the_Android_NDK_in_Rust_1.68_|
                        Rust_Blog⠀⇛


                             We are pleased to announce that Android
                             platform support in Rust will be modernized
                             in Rust 1.68 as we update the target NDK from
                             r17 to r25. As a consequence the minimum
                             supported API level will increase from 15
                             (Ice Cream Sandwich) to 19 (KitKat).


                             [...]


                             Going forward the Android platform will
                             target the most recent LTS NDK, allowing Rust
                             developers to access platform features
                             sooner. These updates should occur yearly and
                             will be announced in release notes.


    * § Leftovers⠀➾


          o ⚓ Xe’s Blog ☛ Site_Update:_Revue_backups_are_live⠀⇛


                 Turns out that Revue is getting shut down. This means
                 that I won’t be able to use it anymore (and I stopped
                 using it because it wasn’t getting much traction vs the
                 amount of work I put into it).


          o § Science⠀➾


                # ⚓ SWI ☛ Switzerland_–_where_the_robots_of_tomorrow_are_born_–
                  SWI_swissinfo.ch⠀⇛


                       The Alpine nation is well known for its watches,
                       chocolate and pharmaceutical industry. But in
                       recent years Switzerland has also become a leader
                       in robotics thanks to its top universities,
                       research centres and start-ups.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ [Repeat] Ruben Schade ☛ Time_spent_looking_at_my_phone⠀⇛


                       I gave myself a few goals to meet this year, one of
                       which was to be more aware of how I use my phones.
                       Whenever I reach for them, I take deliberate note
                       and have them justify their intrusion, or their
                       flip cases remain closed.


                       [...]


                       The other observations were a tad unsettling. The
                       most alarming is what I’m dubbing the lucid dream
                       effect. I’ve become more attuned to when I’m
                       reaching for my phone, but I’ve still caught myself
                       mindlessly scrolling well after the fact. It’s
                       become so rote, in some cases I had no recollection
                       of picking it up in the first place. It’s like
                       realising you’ve been in a dream this whole time.


                       Mostly though, I’ve realised just how often I reach
                       for it to fill a spare moment. This is
                       unsurprising; it’s conventional wisdom that we’re
                       hooked on these devices and crave the sugar hit and
                       dopamine that comes from a brief, superficial
                       distraction. But I think we kid ourselves by
                       thinking yeah, but I’m smart, and that doesn’t
                       happen to me! It does.


                       [...]


                       And I’ve already noticed a change, even after just
                       a week. There isn’t a way to talk about these
                       without sounding cliché, but I’ve become more aware
                       of my surroundings. I’ve smiled at more people! I
                       look out the window more.


          o § Proprietary⠀➾


                # ⚓ CNN ☛ LinkedIn_is_having_a_moment_thanks_to_a_wave_of
                  layoffs [Ed: Typical Microsoft propaganda in CNN. LinkedIn
                  itself has layoffs, but Microsoft seems to be eager to
                  googlebomb the topic out of view/sight]⠀⇛


                # ⚓ Axios ☛ Microsoft_CEO:_Next_two_years_will_be_‘most
                  challenging’⠀⇛


                # ⚓ The Register UK ☛ Microsoft’s_Nadella:_Tech_is_in_for_a
                  rough_two_years [Ed: Microsoft CEO uses newspeak for, “Expect
                  many_more_layoffs!”]⠀⇛


          o § Security⠀➾


                # ⚓ LinuxSecurity ☛ Admins_Receive_Automated_Linux_Patch
                  Management_&_Improved_Security_with_ManageEngine_Endpoint
                  Central⠀⇛


                       Patching endpoints is one of the most exhausting
                       and redundant tasks that Linux admins are burdened
                       with, but keeping up with the latest security
                       updates is crucial in maintaining a robust security
                       posture. Failing to keep endpoints up-to-date with
                       critical and recent patches that are released
                       allows for security vulnerabilities to exist in the
                       network that malicious hackers can use to infect
                       endpoints and systems with harmful malware.


                # ⚓ Pen Test Partners ☛ UK_gov_website_being_used_to_phish_porn
                  site_creds_|_Pen_Test_Partners⠀⇛


                       UK Government Environment Agency web site had an
                       open redirect that was actively being used to
                       redirect to various porn sites, including OnlyFans
                       clone sites. Disclosure should have been easy but
                       wasn’t, as the agency haven’t followed wider UK
                       government policy on vulnerability disclosure.


                       [...]


                       Don’t run government sites on old web servers.


                       Check for open redirects.


                       Make vulnerability disclosure easy.


                # ⚓ How_to_Learn_Ethical_Hacking_Online?⠀⇛


                       In order to prevent a data breach, ethical hackers
                       look for loopholes in systems, network
                       architecture, and software. In the contemporary
                       digital age, the internet has helped users to
                       connect with one another on a global scale, but it
                       has also created a number of challenges related to
                       cybercrime and theft. Even large organizations have
                       had substantial financial setbacks and data leaks
                       as a result of security flaws. Over time, there has
                       been an increase in demand for certified ethical
                       hackers due to the growth in online attacks. To
                       protect their data from criminal cyber-attacks,
                       several businesses already use the expertise of
                       ethical hackers.


                       [...]


                       The technique of getting into network or computer
                       systems to check for threats or flaws that a
                       hostile attacker may find and exploit to steal
                       sensitive information, inflict financial loss, or
                       do other major damage is known as ethical hacking,
                       also referred to as penetration testing.


                # ⚓ DISA_Issues_Security_Technical_Implementation_Guide_for
                  TOSS_4_Operating_System_–_ExecutiveBiz⠀⇛


                       The Defense Information Systems Agency has released
                       a security technical implementation guide to ensure
                       the secure installation of the Tri-Lab Operating
                       System Stack 4.


                       The TOSS 4 STIG outlines requirements to guide the
                       installation of the production simulation
                       environment in compliance with the Defense
                       Department’s security requirements, the DoD Cyber
                       Exchange said Thursday.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Adafruit ☛ John_Deere_&_Co._will_allow_farmers_to_repair
                  their_own_equipment⠀⇛


                       As the agriculture sector accelerates its adoption
                       of technology, the reliance on high-tech machinery
                       such as GPS-guided combines and tractors has become
                       more common-place.


                       But equipment makers such as Deere have generally
                       required customers to use their parts and service
                       divisions for repairs and until recently, only
                       allowed authorized dealers the means and tools to
                       access the complex computerized systems of their
                       tractors and other machinery.


                       The “right-to-repair” movement has gained steam as
                       input costs have surged in recent years – as has
                       the price of repairs.


                # ⚓ Reuters ☛ Deere_&_Co._will_allow_farmers_to_repair_their
                  own_equipment
                  ⠀⇛


                       The American Farm Bureau Federation and machinery
                       manufacturer Deere & Co (DE.N) signed a memorandum
                       of understanding on Sunday that ensures farmers
                       have the right to repair their own farm equipment
                       or go to an independent technician.


                       As the agriculture sector accelerates its adoption
                       of technology, the reliance on high-tech machinery
                       such as GPS-guided combines and tractors has become
                       more common-place.


                       But equipment makers such as Deere have generally
                       required customers to use their parts and service
                       divisions for repairs and until recently, only
                       allowed authorized dealers the means and tools to
                       access the complex computerized systems of their
                       tractors and other machinery.


                # ⚓ The Register UK ☛ John_Deere_signs_right_to_repair
                  agreement⠀⇛


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Michael Geist ☛ Listen_Up:_My_Recent_Podcast
                        Appearances_on_Bills_C-11,_C-18_and_Canadian_Copyright
                        Law_–_Michael_Geist⠀⇛


                             Parliament remains on break for most of the
                             month of January, but that hasn’t cooled
                             interest in Bills C-11 and C-18. I’ve
                             appeared on several podcasts in recent weeks
                             on these bills that may interest. Last week,
                             I was pleased to appear on CBC’s Front Burner
                             for an episode titled “Will Canada Make Web
                             Giants Pay For News?”. The discussion with
                             host Jayme Poisson focused on the
                             implications of paying for links, the
                             inclusion of the CBC in the system, and
                             potential alternatives that would mitigate
                             against the harms created by the bill.


                      # ⚓ Public Domain Review ☛ Eating_and_Reading_with
                        Katherine_Mansfield_–_The_Public_Domain_Review⠀⇛


                             Like fast food and snacks, the short story
                             has been derided as minor cuisine, ephemeral
                             and insubstantial, light fare compared to the
                             novel’s sustenance. For Katherine Mansfield,
                             a great master of the form, eating offered a
                             model for the sensuous consumption of her
                             fiction — stories, in turn, that are filled
                             with scenes of alimentary pleasure. On the
                             centenary of the New Zealand writer’s death,
                             Aimée Gasston samples her appetites.


                             When in 1920 Katherine Mansfield quoted
                             Coleridge in her notebook — “I, for one, do
                             not call the sod under my feet my country.
                             But language, religion, laws, government,
                             blood — identity in these makes men of one
                             country”— she replied beneath resolutely with
                             the words: “The sod under my feet makes
                             mine”.1 For Mansfield, the messy materiality
                             of the external world was more keenly
                             significant than any secondary intellectual
                             ordering of it, as the redolent sensuousness
                             of her prose still attests. Reviewing the
                             version of Mansfield’s journal published by
                             her lover/husband John Middleton Murry in
                             1927, Virginia Woolf concluded: “She is a
                             writer, a born writer. Everything she feels
                             and hears and sees is not fragmentary and
                             separate; it belongs together as writing”.2
                             Writing for Mansfield was a holistic
                             expression of every one of her heightened
                             senses. But Woolf omitted one faculty that
                             was crucial to Mansfield — taste.
                             Mansfield wrote poems about food in her
                             notebooks, as well as recipes and grocery
                             lists, and would interrupt her prose with
                             famished declarations such as: “Im so hungry,
                             simply empty, and seeing in my minds eye just
                             now a surloin of beef, well browned and with
                             plenty of gravy and horseradish sauce and
                             baked potatoes I nearly sobbed”.3 More recent
                             additions to New Zealand’s Alexander Turnbull
                             Library’s manuscripts collection add to its
                             store of food-related Mansfieldian matter,
                             comprising shopping lists, receipts, and
                             recipes for orange soufflé and cold-water
                             scones. This expanding wealth of material,
                             both fictional and biographical, is not
                             circumstantial evidence of everyday life and
                             art intermingling — it is far more often
                             proof that, to Mansfield, the two could never
                             be separated.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Do_not_overthink_treasure_placement⠀⇛


                       If you’re not sure about the amount of treasure to
                       add to your treasure, I’m here to tell you: don’t
                       fret. Instead, make sure you have a solid
                       restocking rule and you’re golden. There will
                       always be enough treasure if restocking adds
                       treasure. And if you’re running a Megadungeon, it
                       never gets cleared out so there’s always restocking
                       to do.


                # ⚓ Epsom_Salt_Crystals⠀⇛


                       I grew one crystal for a week or so, using a slow
                       evaporation process. You can see in the images that
                       several additional crystals_20230109_ were growing
                       off of it, and several on the sewing thread.


                # ⚓ All_is_fucked⠀⇛


                       I should be studying for this shit exam of this
                       shit class I have tomorrow. “Requirements and
                       Software Architecture” is the class, if you must
                       know. Can you think of anything that’s more boring
                       than this? I’m going through past exams to prepare
                       (because we rarely did any such exercises during
                       classes; grading is mostly based on a PA) and I’m
                       wondering if it makes any difference. The (theory)
                       lectures were so damn boring and uninteresting I
                       couldn’t bear to be there, I couldn’t concentrate
                       on what the professor said, I couldn’t not think to
                       myself “what a bunch of bull!” So instead I stopped
                       attending, naturally.


                # ⚓ So_you_do_like_beer_after_all⠀⇛


                       I had a dream that continued the timeline of
                       another dream I had some days ago, like consecutive
                       episodes of a series. This is the first time it
                       happened to me I think.


                       I was in an open space, at night, palm trees around
                       and many lights, some kind of event, many people
                       were around, almost like a festival or something of
                       the sort. The place was somewhere in Asia (not
                       because there were specific features I can point
                       out to, but because it was a dream, I just know
                       alright?). A guy crossed paths with me and asked if
                       I didn’t like beer, or why I wasn’t drinking beer,
                       or something like that. I replied that I don’t much
                       appreciate beer. He gave me a dark, almost black,
                       beer bottle, the label was black, and it was in
                       Thai or similar (so I assume I was in Thailand). I
                       gave it a sip and indeed not that bad, nothing like
                       the crap I tasted in real life…


          o § Technical⠀➾


                # ⚓ An_epiphany_about_bloated_web_pages_might_be_the_result_of
                  a_dumb_network⠀⇛


                       I was scared by an epiphany I had the other day
                       when I read a quote by John Carmack [1]. But before
                       I get to the quote and the ephiphany, I need to
                       give some background to understand where I was, and
                       where I am.


                       First, for the years I was working for The
                       Corporation (and later, The Enterprise), I was in
                       essense, working in telephony networking, and I was
                       never a fan of telephony networking (the Protocol
                       Stack From Hell [2] notwithstanding).


                # ⚓ My_first_game.⠀⇛


                       I have long tried many different ways of making
                       games. I’ve used large engines such as Godot,
                       Unity, and Unreal. I’ve used purpose-built
                       frameworks like MonoGame, XNA, LOVE, and PyGame.
                       I’ve even tried close to the metal low-level
                       libraries like Raylib and Bevy.


                       It wasn’t until I was browsing my Itch.io purchases
                       and stumbled across a license to DragonRuby in the
                       Palestinian Aid Bundle that I finally found a way
                       to make games that is fun for me. Everything just
                       clicked, and effortlessly, I was rendering text and
                       blinking it on screen within an hour. For
                       reference, I had 0 Ruby knowledge up until this
                       point, it’s just that easy to learn. The Discord
                       community was essential in getting me hooked, and
                       helping me through some of the thinking involved in
                       my first game.


                # ⚓ Invidious:_Make_Youtube_cool_again⠀⇛


                       I have a complicated relationship with Youtube
                       like, I imagine, a lot of people.


                       While I really dislike everything that Google is
                       doing with the platform and
                       their idiotic algorithm, there are tons of
                       exceptionnaly good content on the
                       platform.


                       You can find everything regarding computer science,
                       3d printing, physics talks,
                       video games, history and so much more. It’s full of
                       dedicated people
                       talking about their passion. I used to only use the
                       “Subscriptions” page of
                       Youtube. The default home page has always been
                       irrelevant, and the Popular tab
                       is just plain cancer.


                # ⚓ Collect_traffic_data_for_your_Capsule⠀⇛


                       As everyone else around here, I love a good
                       tracking of visitors.


                       Kidding… screw that.


                       However, I feel it’s pretty good to know if your
                       capsule gets any traffic at all
                       and which part of it people find it more
                       interesting. Some may not care, some may.


                # ⚓ Running_molly-brown_in_a_container⠀⇛


                       In order to do that, I just need a gemini server (I
                       choose molly-brown), docker and my content (that’s
                       my *.gmi files).


                # ⚓ Creating_slim_container_images_for_rust⠀⇛


                       This is the Dockerfile that I’m currently using
                       when I need to create some proof of concepts with
                       rust.


                       In this case, I’m building a simple rust
                       application using the rocket framework as
                       dependency.


                # § Internet/Gemini⠀➾


                      # ⚓ On_Gemini_mentions⠀⇛


                             I didn’t take too much time reading
                             everything in detail, but “Why though?” is
                             also my thought.


                             I certainly won’t be using it. For one, my
                             capsule is hosted on SourceHut, so I couldn’t
                             use it even if I wanted. But most of all, I
                             don’t see the point. I know that if I had
                             something like that, something others could
                             use to let me know they’d linked to a post of
                             mine, I would get FOMO and that’s not cool. I
                             understand this is very individual, maybe you
                             get peace of mind by having this system
                             giving you the latest mentions and whatnot,
                             that’s alright. For me, “what if someone
                             replied but didn’t let me know?” would be at
                             the back of my mind too frequently, I can
                             smell it. And that’s another reason to ask
                             “why though?” If your RFC, that you wrote for
                             yourself, requires others to adopt it to be
                             useful to you, then it’s not much use, I
                             don’t think.


                      # ⚓ Why_did_I_work_on_gemini_mention⠀⇛


                             After publishing yesterday an idea of gemini
                             mention kind of “standard” and a couple of
                             implementations, I realized I haven’t
                             explained why I decided to “work” on this
                             proposal.


                      # ⚓ Have_one’s_cake_and_eat_it_–_likes,_comments,
                        backlinks_and_so_on⠀⇛


                             Inspired by [My take on gemlog responses] by
                             Bacardi55. On the one side is so convenient
                             and tempting to have the whole achievements
                             of the modern web. It’s not that I oppose it,
                             or I don’t want it at all, and I renounce it.
                             On the other hand, are we not creating
                             mechanisms for small-net whose distorted
                             operation drives the big-net in the opposite
                             direction to what is expected?


                      # ⚓ Re:_Gemlog_responses⠀⇛


                             To me these proposals feel like Web
                             technology. They are (relatively) complex
                             technical solutions that are difficult to
                             apply universally to everyone, and require
                             (relatively) costly commitment from both
                             gemlog authors and readers.


                             Gemlogs are not meant for interaction, per
                             se. It’s a bit like having a discussion with
                             someone by publishing open letters in a
                             newspaper. It’s a many-to-many, open ended
                             forum.


                      # ⚓ My_take_on_gemlog_responses⠀⇛


                             The Gemini community is globally very nice
                             and I’ve really been enjoying the different
                             interaction I had with fellow geminauts over
                             station¹, tinylogs², gemlog entries or via
                             email (keep emails coming!).
                             I really like those interactions, but I feel
                             like interacting with each other over gemlog
                             entries remains difficult. At least to ensure
                             the author see all the responses to their
                             posts.
                             It’s very common to see a gemlog entry being
                             a response to another author entry, but we
                             don’t have yet a simple way to notify each
                             other.


                      # ⚓ My_RE:log_experiment_(RE:_“Introducing_the_Re:log
                        concept”_by_Freezr)⠀⇛


                             Freezr made an interesting proposal about
                             having a “Re:log” for replies in the
                             geminispace, separate from the gemlog…


                      # ⚓ Gemlog_responses_–_1st_update_(after_response_from
                        Sean_Conner)⠀⇛


                             As I wrote in the initial post, I am not an
                             expert in programming and have a non-IT
                             engineering background. Nevertheless I have
                             some coding experience (I do some Python
                             coding every now and then), so I understand
                             the argument, that log-parsing is in the more
                             complex than a CGI script. I also have to say
                             that I wrote this post from my perspective,
                             self-hosting my gemini capsule on a virtual
                             Rootserver, which gives me access to all
                             Logs. I see the point, that not every user
                             has access to this.


                      # ⚓ Introducing_the_Re:log_concept⠀⇛


                             The Gemini-space is really versatile and
                             offers countless ways to interact with, one
                             aspect I love so much on Gemini is this
                             direct thread that links a capsule to another
                             one! On dynamic aggregators, like Antenna,
                             you can often find entries that directly
                             address other Gemlogs by simply adding a “Re:
                             ” before the title’s Gemlog they are
                             referring to, exactly as you would reply to
                             an email from your favorite client!


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



                    ䷩ 𝚕𝚒𝚗𝚎 4441

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/01/2023:_Lots_on_Gaming_and_More_Twitter_Departures⠀✐


Posted in News_Roundup at 12:19 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
          o Devuan_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Education
          o Programming/Development
    * Leftovers
          o Security
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Patents
                # Copyrights
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ HTOP_–_Terminal_Task_Manager_–_Invidious⠀⇛


                # ⚓ Video ☛ Manjaro_21.3.7_KDE_Plasma_Edition_Quick_overview
                  #shorts_–_Invidious⠀⇛


                       A Quick Overview of Manjaro 21.3.7 KDE Plasma
                       Edition


                # ⚓ Video ☛ Linux_Is_Free_So_Should_I_Expect_FREE_Support?_–
                  Invidious⠀⇛


                       New Linux users often ask “who do I turn to for
                       support?” And even as a long-time Linux user, this
                       is a tough question to answer in just a single
                       sentence.


          o § Instructionals/Technical⠀➾


                # ⚓ It’s Ubuntu ☛ How_To_Install_Linux_Kernel_6.1_On_Ubuntu_|
                  Itsubuntu.com⠀⇛


                       There are multiple ways to install Linux Kernel 6.1
                       on Ubuntu.


                       [...]


                       Once the app is installed, You can easily install
                       the latest available Linux 6.1 kernel packages from
                       the mainline tool. You will see Linux Kernel 6.1 at
                       the top of the app.


                # ⚓ Beginners_Guide_for_Who_Command_in_Linux⠀⇛


                       The who command is a built-in Linux utility that
                       shows a list of users who are currently logged on
                       to the Linux system.


                       In this article, you will learn how to use this
                       command and what options it has to offer (with
                       practical examples).


                # ⚓ H2S Media ☛ 3_ways_to_Install_Emacs_text_editor_on_Linux
                  Mint_–_Linux_Shout⠀⇛


                       Find the steps given in this tutorial to use the
                       command terminal on Linux Mint for installing Emacs
                       Editor – a highly customizable text editor.


                       Emacs is a well-known text editor among the
                       developer community because of its powerful
                       features and ability to get highly customized.
                       Developers and programmers prefer to use Emacs, as
                       it provides a wide range of plugins and extensions
                       for enhancing the functionality of the editor.


                # ⚓ Video ☛ How_to_Easily_Write_SD_cards_for_use_with_the
                  Raspberry_Pi_–_Invidious⠀⇛


                       Every computer needs an operating system – and the
                       Raspberry Pi is no different. Primarily, the
                       Raspberry Pi boots from an SD card. But how do you
                       write an operating system to that SD card? Well, if
                       you’re just starting out – then this is the video
                       for you!


          o § Games⠀➾


                # ⚓ Hackaday ☛ Tetris_Joins_Minecraft_And_DOOM_In_Running_A
                  Computer⠀⇛


                       There is a select group of computer games whose in-
                       game logic is enough for them to simulate computers
                       in themselves. We’ve seen it in Minecraft and DOOM,
                       and now there’s a new player in town from a
                       surprising quarter: Tetris.


                # ⚓ GamingOnLinux ☛ DOSBox_Staging_adds_dual-mouse_gaming_and
                  ReelMagic_support⠀⇛


                       DOSBox Staging is a favourite of mine to follow
                       that expands on the original DOSBox but with a
                       focus on implementing new features and fixes. A new
                       major update went out in December 2022 with some
                       big additions. It’s supposed to be a drop-in
                       replacement for the old original DOSBox.


                # ⚓ LinuxTechLab ☛ How_To_Play_Nintendo_GameCube_Games_on_Linux
                  –_LinuxTechLab⠀⇛


                       How to play Nintendo GameCube Games on Linux.
                       Emulators have managed to build a bridge between
                       different gaming platforms.


                # ⚓ GamingOnLinux ☛ 20_years_later_the_open_source_Colonization
                  game_FreeCol_hits_1.0⠀⇛


                       Took a while huh? It’s not quite as well-known or
                       as loved as some other free and open source games,
                       but worth pointing out: FreeCol 1.0 is out now. 20
                       years in the making for this Sid Meier’s
                       Colonization remake!


                # ⚓ GamingOnLinux ☛ GameCube_and_Wii_emulator_Dolphin_got_a_big
                  speed_boost_for_Steam_Deck⠀⇛


                       GameCube and the Wii emulator Dolphin had a
                       progress report posted up in late December, and
                       it’s looking really good, especially so with their
                       performance optimization work.


                # ⚓ GamingOnLinux ☛ Decky_Loader_makes_Steam_Deck_plugins_even
                  EASIER_with_new_installer⠀⇛


                       Decky Loader is a project I’ve covered before
                       multiple times now because it can add a lot to the
                       Steam Deck with plugins, and now it’s even easier
                       to use.


                # ⚓ GamingOnLinux ☛ Valve_adding_a_Steam_feature_for_game
                  transfers_between_PCs_and_Steam_Decks⠀⇛


                       Something it seems Valve has been working on for a
                       while now, is an easy way to transfer game installs
                       between PCs and Steam Deck.


                # ⚓ GamingOnLinux ☛ Building_a_Retro_Linux_Gaming_Computer_–
                  Part_20:_The_Antediluvian_World⠀⇛


                       Return to Part 1: Dumpster Diving


                # ⚓ GamingOnLinux ☛ Multiplayer_voxel_RPG_‘Veloren’_v0.14_out
                  with_musical_instruments,_more_graphics_work⠀⇛


                       Version 0.14 of the Multiplayer voxel RPG Veloren
                       is out now, adding in some fun sounding additions
                       while they work towards giving you more to do. It’s
                       still very much a sandbox right now, as a lot of
                       the work going into Veloren is still building up
                       the tech behind the game.


    * § Distributions and Operating Systems⠀➾


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


                # ⚓ Unicorn Media ☛ OpenMandriva’s_Rolling_Release,_ROME:
                  Mostly_Ready_for_Prime_Time⠀⇛


                       On Friday, OpenMandriva announced that ROME 23.01,
                       the Linux distribution’s rolling release version,
                       has been released and is ready to stand beside its
                       conventionally released Rock edition. Being a
                       rolling release, as long as users keep up with
                       updates they will have the most up-to-date version
                       of the operating system available. Users of Rock,
                       on the other hand, will need to wait for the next
                       point release to have all of the features added
                       since the last release.


          o § Devuan Family⠀➾


                # ⚓ PeppermintOS ☛ Twitter_Account_Deactivated⠀⇛


                       Our Twitter account has been deactivated. As of Dec
                       27, if you update your Peppermint tools you will
                       notice the Welcome Screen has removed twitter as
                       well.


          o § Open Hardware/Modding⠀➾


                # ⚓ Linux Gizmos ☛ Raspberry_Pi_launches_new_camera_modules⠀⇛


                       Raspberry Pi just launched four variants of camera
                       modules based on the Sony IMX708 12MP sensor with
                       HDR and autofocus. The new Camera Module 3 is also
                       available in Wide and NoIR variants to target
                       different applications.


                # ⚓ Adafruit ☛ Maker_Feather_AIoT_S3:_an_ESP32-S3_board
                  programmable…⠀⇛


                       Cytron Make Feather AIoT S3 is an ESP32-S3 board
                       compatible with the Adafruit Feather form factor
                       and suitable for makers and STEM education with
                       features like LEDs for GPIOs, a buzzer, expansion
                       headers and connectors, and support for
                       CircuitPython & Arduino.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ SamMobile ☛ Carrier_Galaxy_A42_5G_is_now_getting_Android_13
                  in_the_USA_–_SamMobile⠀⇛


                # ⚓ TechCrunch ☛ Google’s_Extension_SDK_aims_to_bring_latest
                  features_to_older_Android_versions_•_TechCrunch⠀⇛


                # ⚓ Samsung_Looks_Set_To_Announce_A_Budget_120Hz_Android_Phone
                  –_Droid_Gamers⠀⇛


                # ⚓ Giz China ☛ How_to_choose_a_good_Android_smartphone_in_2023
                  –_Gizchina.com⠀⇛


                # ⚓ Android Police ☛ Best_gardening_games_on_Android_in_2023⠀⇛


                # ⚓ 9to5Google ☛ Android_13_QPR2_is_changing_how_the_taskbar
                  works⠀⇛


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


          o ⚓ Jason Rose ☛ OpenZFS:_the_final_word_in_file_systems⠀⇛


                 OpenZFS, arguably the heart of TrueNAS, is the open-
                 source file system and volume manager based on Sun/
                 Oracle’s ZFS. ZFS development began at Sun Microsystems
                 in 2001 with the aim of completely reframing how systems
                 administrators manage their storage systems. Its original
                 development team outlined several guiding principles that
                 still shape the project today: storage should be
                 flexibly-pooled, always consistent, self-healing, and
                 simple to manage.


                 In ZFS, disks are grouped into virtual devices (or vdevs)
                 usually with some form of redundancy/protection against
                 disk failure. A ZFS pool may have one or more vdevs; if a
                 pool has more than one vdev, they’re striped together to
                 form one giant bucket of storage. A vdev’s redundancy
                 might be based on simple multi-disk mirrors or RAIDZ
                 where administrators can pick from single-, double- or
                 triple-disk parity protection.


          o ⚓ Torrent Freak ☛ Warner_Bros._Fights_‘Mortal_Kombat_II’_Source
            Code_Leak [Ed: Microsoft censoring/banning Free software again]⠀⇛


                 GitHub has removed a recent “Mortal Kombat II” source
                 code leak following a request from Warner Bros.
                 Discovery. The leak purportedly reveals unused artwork
                 and an alternative storyline for the iconic arcade game,
                 first released by Midway in 1993. Three decades later,
                 the current rightsholder seems keen to plug the leaks.


          o § Education⠀➾


                # ⚓ Felix Crux ☛ Feeds:_The_Only_Civilised_Way_to_Read_Online⠀⇛


                       There’s a better way — and there has been for
                       decades! Amazingly, it seems underused even within
                       tech circles, and almost completely unknown to the
                       general public. It’s super easy to use, actually
                       more convenient than social media apps, and leaves
                       you in complete control of what you see.


                       I’m talking, of course, about RSS/Atom web feeds,
                       and I contend that they are not only a better
                       alternative, but in fact I’d go so far as to say
                       that a feed reader is the only tolerable and
                       civilised way to read online! The system works
                       really well and more in line with what (I think)
                       most people actually want; it minimizes the use of
                       harmful social media platforms; and it helps foster
                       a more vibrant, independent, creative, and non-
                       commerical Web. So drop your non-chronological
                       algorithmically-obscured sponsored timeline, and
                       let’s have a whirlwind overview of what feeds are
                       and how to use them!


          o § Programming/Development⠀➾


                # ⚓ Daniel Stenberg ☛ My_weekly_report_on_email_|
                  daniel.haxx.se⠀⇛


                       Starting this week, you can subscribe to my weekly
                       report and receive it as an email. This is the
                       brief weekly summary of my past week that I have
                       been writing and making available for over a year
                       already. It sums up what I have been doing recently
                       and what I plan to do next.


                       Topics in the reports typically involve a lot of
                       curl, libcurl, HTTP, protocols, standards,
                       networking and related open source stuff.


                # ⚓ Exploratory_DataXray_Analysis_(EDXA)⠀⇛


                       Do you know how long EDA (exploratory data
                       analysis) used to take me? Not hours, not days… A
                       full week! Listen, you don’t know how good you have
                       it. With this new R package I’m about to show you
                       (plus one BONUS hack), you’ll cut your EDA time
                       into 5 minutes. Here’s how.


                # ⚓ Data Science Tutorials ☛ Lottery_Prediction-Comparison
                  between_Statistics_and_Luck⠀⇛


                       Lottery Prediction-Comparison between Statistics
                       and Luck, statistics and luck all go hand in hand.


                # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppTOML_0.2.0:_TOML
                  1.0.0_rewrite_with_toml++⠀⇛


                       A few years since the last release in late 2020,
                       the RcppTOML package is now back with a new and
                       shiny CRAN release 0.2.0. It is now based on the
                       wonderful toml++ C++17 library by Mark Gillard and
                       gets us (at long last!) full TOML v1.0.0 compliance
                       for use with R.


                       [...]


                       This package is a rewrite of the internals
                       interfacing the library, and updates the package to
                       using toml++ and C++17. The R interface is
                       unchanged, and a full run of reverse dependencies
                       passed. This involved finding one sole test failure
                       which turned to have been driven by a non-
                       conforming TOML input file which Jianfeng Li kindly
                       fixed at the source making his (extensive) set of
                       tests in package configr pass too. The actual
                       rewrite was mostly done in a one-off repo
                       RcppTomlPlusPlus which can now be considered
                       frozen.


                # ⚓ Dirk Eddelbuettel ☛ Thinking_inside_the_box⠀⇛


                       Another quick update to the still new-ish package
                       spdl is now om CRAN, and in Debian. The key focus
                       of spdl is a offering the same interface from both
                       R and C++ for logging by relying on spdlog via my
                       RcppSpdlog package.


                       This release add support for the stopwatch()
                       facility. One can now instantiate such an object,
                       and referencing it in a log message shows the
                       elapsed time. No more, no less, and it works the
                       same way in R and C++.


                # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RVowpalWabbit
                  0.0.18:_Maintenance⠀⇛


                       A new maintenance release, now at version 0.0.18,
                       of the RVowpalWabbit package arrived on CRAN. It
                       improves several sprintf() calls by changing them
                       to snprintf() (though there is a remaining one
                       creeping in from a linked-to library).


                       As noted before, there is a newer package rvw based
                       on the excellent GSoC 2018 and beyond work by Ivan
                       Pavlov (mentored by James and myself) so if you are
                       into VowpalWabbit from R go check it out.


                # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppSpdlog_0.0.12_on
                  CRAN:_Added_Stopwatch⠀⇛


                       Version 0.0.12 of RcppSpdlog is now on CRAN and in
                       Debian. RcppSpdlog bundles spdlog, a wonderful
                       header-only C++ logging library with all the bells
                       and whistles you would want that was written by
                       Gabi Melman, and also includes fmt by Victor
                       Zverovich.


                       This release adds support for the stopwatch object,
                       a simple container around a std::chrono object. It
                       makes (simple) time measurements of routines and
                       code segments trivially easy. Instantiate a
                       stopwatch object, and ‘formatting’ it in a logging
                       string displays elapsed time. And given that the
                       whole mojo of RcppSpdlog (and its sibbling package
                       spdl) is to make use easy in both R and C++ we can
                       do this nicely and consistently in both languages.
                       The vignette has an added section with a concrete
                       example.


                # ⚓ Henrik Warne ☛ There_Is_No_Software_Maintenance⠀⇛


                       Every time I hear about software maintenance as a
                       distinct activity, I cringe. That’s because it is
                       based on the outdated notion that first software is
                       developed, then it is maintained. But that is not
                       how software development works today. Software
                       development does not have the two phases
                       development and maintenance – it is a continuous
                       process. Software maintenance is simply software
                       development.


                       It is fairly common to come across the concept of
                       software maintenance. Recently I have seen it in
                       posts on LinkedIn (how developers leave if they
                       have to do maintenance), in books (“it is well
                       known that the majority of the cost of software is
                       not in its initial development, but in its ongoing
                       maintenance”), and in surveys (do you develop new
                       features, or do you maintain existing features).
                       But this is based on the false premise of the
                       software project.


                # ⚓ OpenSource.com ☛ How_to_use_methods_in_Java⠀⇛


                       A method in Java (called a “function” in many other
                       programming languages) is a portion of code that’s
                       been grouped together and labeled for reuse.
                       Methods are useful because they allow you to
                       perform the same action or series of actions
                       without rewriting the same code, which not only
                       means less work for you, it means less code to
                       maintain and debug when something goes wrong.


                       A method exists within a class, so the standard
                       Java boilerplate code applies:


                       A package definition isn’t strictly necessary in a
                       simple one-file application like this, but it’s a
                       good habit to get into, and most IDEs enforce it.


                       By default, Java looks for a main method to run in
                       a class. Methods can be made public or private, and
                       static or non-static, but the main method must be
                       public and static for the Java compiler to
                       recognize and utilize it. When a method is public,
                       it’s able to be executed from outside the class. To
                       call the Example class upon start of the program,
                       its main method must be accessible, so set it to
                       public.


    * § Leftovers⠀➾


          o ⚓ The Nation ☛ A_Higher_Plane⠀⇛


                 Early on in “Sea Oak,” a short story from Pastoralia, the
                 second of five collections by George Saunders, the
                 characters watch a TV show called How My Child Died
                 Violently. The show is hosted by “a six-foot-five blond,”
                 Saunders writes, “who’s always giving the parents
                 shoulder rubs and telling them they’ve been sainted by
                 pain.” The episode they’re watching features a 10-year-
                 old who killed a 5-year-old for refusing to join his
                 gang.


          o ⚓ Telex (Hungary) ☛ The_world’s_oldest_living_olympian,_Ágnes
            Keleti_turns_102,_and_celebrates_with_a_documentary_about_her
            life⠀⇛


          o § Security⠀➾


                # ⚓ Techdirt ☛ It’s_2023_And_The_FCC_Only_Just_Proposed_Rules
                  Requiring_Telecoms_Immediately_Inform_Consumers_When_Their
                  Data_Is_Compromised⠀⇛


                       Back in 2015, the nation’s top telecom regulator
                       attempted to create some very basic (by
                       international standards) privacy guidelines for
                       telecom providers, demanding they do things like
                       (gasp) be transparent about the consumer data they
                       were collecting and selling, while also requiring
                       that consumers (gasp) opt in to the sale of any
                       particularly sensitive data.


                # ⚓ Krebs On Security ☛ Identity_Thieves_Bypassed_Experian
                  Security_to_View_Credit_Reports⠀⇛


                       Identity thieves have been exploiting a glaring
                       security weakness in the website of Experian, one
                       of the big three consumer credit reporting bureaus.
                       Normally, Experian requires that those seeking a
                       copy of their credit report successfully answer
                       several multiple choice questions about their
                       financial history. But until the end of 2022,
                       Experian’s website allowed anyone to bypass these
                       questions and go straight to the consumer’s report.
                       All that was needed was the person’s name, address,
                       birthday and Social Security number.


                # ⚓ EFF ☛ EFF_and_Partners_Call_Out_Threats_to_Free_Expression
                  in_Draft_Text_as_UN_Cybersecurity_Treaty_Negotiations
                  Resume⠀⇛


                # ⚓ FOSSLife ☛ FCC_Proposes_New_Data_Breach_Rules_for
                  Telecoms⠀⇛


                       The U.S. Federal Communications Commission (FCC)
                       has proposed updated rules for how telecoms notify
                       customers of data breaches.


                       Specifically, the organization proposes
                       “eliminating the current seven business day
                       mandatory waiting period for notifying customers of
                       a breach,” according to the press release.


                       Current FCC rules, which were adopted in 2007,
                       “require that carriers that have more than 5,000
                       customers notify the FCC of a data breach within
                       seven days of discovery, while breaches affecting
                       fewer than 5,000 customers must be reported no
                       later than 30 days,” notes CyberScoop.


                # ⚓ Bruce Schneier ☛ ChatGPT-Written_Malware_–_Schneier_on
                  Security⠀⇛


                       ChatGPT-generated code isn’t that good, but it’s a
                       start. And the technology will only get better.
                       Where it matters here is that it gives less skilled
                       hackers—script kiddies—new capabilities.


                # ⚓ Ars Technica ☛ ChatGPT_is_enabling_script_kiddies_to_write
                  functional_malware_|_Ars_Technica⠀⇛


                       Researchers at security firm Check Point Research
                       reported Friday that within a few weeks of ChatGPT
                       going live, participants in cybercrime forums—some
                       with little or no coding experience—were using it
                       to write software and emails that could be used for
                       espionage, ransomware, malicious spam, and other
                       malicious tasks.


                # ⚓ Ruben Schade ☛ Rubenerd:_Using_scp(1)_to_transfer_multiple
                  files⠀⇛


                       This came up during a customer call last year,
                       where the engineer was running it a few times. On
                       the backend it’s sftp(1) now anyway, as it probably
                       should be.


                # ⚓ LWN ☛ Security_updates_for_Tuesday_[LWN.net]⠀⇛


                       Security updates have been issued by Debian
                       (libtasn1-6), Fedora (nautilus), Oracle (kernel,
                       kernel-container, nodejs:14, tigervnc, and xorg-
                       x11-server), Red Hat (grub2, nodejs:14, tigervnc,
                       and xorg-x11-server), Scientific Linux (tigervnc
                       and xorg-x11-server), SUSE (systemd), and Ubuntu
                       (firefox, linux-aws, linux-aws-5.15, linux-azure,
                       linux-azure-5.15, linux-azure-fde, linux-azure,
                       w3m, and webkit2gtk).


          o § Defence/Aggression⠀➾


                # ⚓ Scheerpost ☛ Caitlin_Johnstone:_Unprovoked!⠀⇛


                       In the mass media you’re not allowed to talk about
                       the U.S.-NATO actions that diplomats, politicians,
                       academics — even the head of the C.I.A. — have long
                       warned would lead to war in Ukraine.


                # ⚓ Michael West Media ☛ The_war_powers_inquiry_–_Michael
                  West⠀⇛


                       The Parliamentary Inquiry into War Powers heard the
                       pros and cons of a parliamentary vote to go to war
                       versus the status quo, that is, the Prime Minister
                       alone can make the call.


                # ⚓ The Nation ☛ Why_the_New_Hampshire_Presidential_Primary_Is
                  Good_for_Democracy⠀⇛


                       Not all that long ago, America was at war. The
                       Vietnam conflict of the 1960s and ’70s meant the
                       deaths of our young people, then subjected to
                       mandatory drafts to fill quotas. Over 50,000
                       Americans and allies died, with many others
                       suffering lifelong injuries. An estimated 3
                       million-plus citizens of North and South Vietnam,
                       Laos, and Cambodia were killed. President after
                       president got our nation more deeply involved, with
                       no ending in sight—goaded in large part by the
                       military-industrial complex.


                # ⚓ The Nation ☛ Thoughts_and_Prayers…_but No_Action⠀⇛


                # ⚓ Scheerpost ☛ Pentagon_Doc_Reveals_US_Lied_About_Afghan
                  Civilians_Killed_in_2021_Drone_Strike⠀⇛


                       One Amnesty International campaigner called the new
                       report “more evidence that we need a huge change in
                       how the U.S. uses lethal force and assesses and
                       reveals its consequences.”


                # ⚓ Scheerpost ☛ On_MSNBC_and_‘Authoritarianism’⠀⇛


                # ⚓ Scheerpost ☛ Itamar_Ben_Gvir_Just_Banned_the_Palestinian
                  Flag⠀⇛


                       The new Israeli Minister of National Security
                       banned the display of the colors of the Palestinian
                       flag in public spaces. It is the latest Israeli
                       attempt to erase Palestinian identity.


                # ⚓ Techdirt ☛ Independent_Reporting_Shows_Cops_Are_Still
                  Killing_People_At_An_Alarming_Rate⠀⇛


                       Law enforcement agencies have no interest in
                       tracking how often officers kill people. Despite
                       all the talk about police reform, very few states
                       require accurate reporting on deadly force
                       deployments.


                # ⚓ Counter Punch ☛ An_Interview_With_Jefferson_Morley_on_the
                  CIA,_Nixon_and_the_Assassination_of_JFK⠀⇛


                       Jefferson Morley is a Washington intelligence
                       expert and investigative journalist. He is co-
                       founder and editor of JFK Facts and vice president
                       of the Mary Ferrell Foundation, which sponsors the
                       internet’s largest archive of records related to
                       JFK’s assassination.


                       His latest book is Scorpion’s Dance: The President,
                       The Spymaster, and Watergate. The book  reveals the
                       Watergate scandal in a completely new light: as the
                       culmination of a concealed, deadly power struggle
                       between President Richard Nixon and CIA Director
                       Richard Helms.


                # ⚓ Counter Punch ☛ Prince_Harry’s_Great_Afghan_Shooting
                  Party⠀⇛


                       What to make of it?  History is filled with the
                       deeds of blood-thirsty princes bold in ambition and
                       feeble of mind.  Massacres make the man, though
                       there is often little to merit the person behind
                       it.  The Duke of Sussex seemingly wishes to add his
                       name to that list.   In what can only be described
                       as one of his “Nazi uniform” moments, Prince Harry
                       has revealed in his memoir Spare that he killed a
                       number of Taliban fighters. (In the same memoir,
                       the weak-willed royal blames his brother for the
                       uniform idea, though not for organising the Afghan
                       shooting party.)


                       The prince, wishing to show that he was no toy
                       soldier or ceremonial ornament of the British Army,
                       puts the number of deaths at 25.  “It wasn’t a
                       statistic that filled me with pride but nor did it
                       make me ashamed.”  He recalls being “plunged into
                       the heat and confusion of battle”, and how he
                       “didn’t think about those 25 people.  You can’t
                       kill people if you see them as people.”  Doing so
                       from the security of a murderous Apache helicopter
                       certainly helps.


                # ⚓ The Nation ☛ The_United_States_Thinks_It’s_the_Exception_to
                  the_Rules_of_War⠀⇛


                       Let me start with a confession: I no longer read
                       all the way through newspaper stories about the war
                       in Ukraine. After years of writing about war and
                       torture, I’ve reached my limit. These days, I just
                       can’t pore through the details of the ongoing
                       nightmare there. It’s shameful, but I don’t want to
                       know the names of the dead or examine images caught
                       by brave photographers of half-exploded buildings,
                       exposing details—a shoe, a chair, a doll, some
                       half-destroyed possessions—of lives lost, while I
                       remain safe and warm in San Francisco.
                       Increasingly, I find that I just can’t bear it.


                # ⚓ The Nation ☛ Merchants_of_Death⠀⇛


                # ⚓ Common Dreams ☛ Militarized_Japan_and_the_Biden-Kishida
                  Summit_Signal_Moment_in_the_New_Cold_War⠀⇛


                       “Japan in December adopted a set of three security
                       and defense strategy documents that break from its
                       exclusively self-defense-only stance. Under the new
                       strategies, Japan vows to build up its
                       counterstrike capability with long-range cruise
                       missiles that can reach potential targets in China,
                       double its defense budget within five years and
                       bolster development of advanced weapons.” —Asahi
                       Shimbun


          o § Environment⠀➾


                # ⚓ The Nation ☛ Global_Warming_Is_the_Front-Page_Story_of_Our
                  Lifetime⠀⇛


                       Let me start 2023 with a glance back at a December
                       news moment that caught my eye. To do so, however,
                       I have to offer a bit of explanation.


                # ⚓ The Nation ☛ Letters_From_the_January_23/30,_2023,_Issue⠀⇛


                       A Bridge Too Far… or Too Late?


                       Kudos to The Nation for hosting a debate on whether
                       governments should reinvest in nuclear power to
                       fight climate change [“The Debate,” by Paul
                       Hockenos and Jessica Lovering, November 28/December
                       5, 2022]. A key question among others that need to
                       be addressed is whether there is a viable
                       compromise position on nuclear power. Can it be
                       used as a component of our energy system for only a
                       few decades as part of the transition to clean
                       renewables?Ferd Wulkan montague, mass.2


                # § Energy/Transportation⠀➾


                      # ⚓ Telex (Hungary) ☛ The_effect_of_increased_gas_prices
                        on_European_capitals_and_where_Budapest_stands_in
                        comparison⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Protect_This_Place:_Oregon’s_Twin
                        Lake⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Meduza ☛ Orthodox_activists_report_Little_Big_leader_Ilya
                  Prusikin_for_skateboarding_on_crucifix_—_Meduza⠀⇛


                       Orthodox Christian activists from the radical Sorok
                       Sorokov movement have reported Ilya Prusikin,
                       leader of the Little Big rave band, for a
                       “blasphemous” Instagram video, in which Prusikin,
                       dressed as a Catholic priest, skateboards on top of
                       a crucifix.


                # ⚓ Meduza ☛ Bisexual_Dagestani_teen_reports_4_months_in_brutal
                  ‘conversion_therapy’_paid_by_her_parents_—_Meduza⠀⇛


                       Elina Ukhmanova, a bisexual 18-year-old from
                       Dagestan, claims having spent four months in
                       captivity at the Alliance Recovery “rehab center”
                       in Makhachkala, undergoing a violent conversion
                       treatment at the behest of her parents.


                # ⚓ Telex (Hungary) ☛ Szijjártó:_Hungary_will_vote_against
                  Kosovo’s_admission_into_European_organizations⠀⇛


                # ⚓ Scheerpost ☛ Under_Musk,_Twitter_Continues_to_Promote_US
                  Propaganda_Networks⠀⇛


                       Dozens of accounts that are part of US overt
                       propaganda networks are given special treatment
                       from Twitter, violating Twitter’s own policies


                # ⚓ Scheerpost ☛ Patrick_Lawrence:_Europe_and_the
                  Legitimization_of_Deception⠀⇛


                       The U.S., having no need of or gift for statecraft,
                       has long practiced what I’ve taken to calling the
                       diplomacy of no diplomacy. You can’t expect much
                       from bimbos such as Antony Blinken or Wendy
                       Sherman, Blinken’s No. 2 at the State Department.
                       All they can do is […]


                # ⚓ Scheerpost ☛ McKinsey’s_Addiction_Corporations⠀⇛


                       Almost 30 years ago, tobacco CEOs were forced to
                       answer questions – under oath. For the first time,
                       corporate bosses had to admit that tobacco
                       companies were designing cigarettes to sustain
                       addiction – a dark day for corporate
                       profits, tobacco corporations, and the ever
                       supportive management consultancy firm: McKinsey.
                       Yet, it was a good day for everyone else. […]


                # ⚓ The Nation ☛ US_Democracy_Is_Under_Attack._These_Human
                  Rights_Defenders_Are_Not_Backing_Down.⠀⇛


                       If ever there was a year when progressives faced an
                       uphill climb, it was 2022. Democrats had control of
                       the White House and Congress, but corporate-aligned
                       centrists stalled progress on major pieces of
                       legislation. The Russian invasion of Ukraine in
                       February, rising gas prices and inflation, and
                       challenges posed by the lingering coronavirus
                       pandemic contributed to a sour mood on the part of
                       the electorate. Then, in June, the US Supreme Court
                       overturned its 1973 Roe v. Wade decision and put
                       abortion rights in jeopardy nationwide. It was easy
                       to feel overwhelmed, yet progressives persevered.
                       They played a pivotal role in preventing a
                       Republican takeover of the Senate in November—and
                       even flipped a GOP seat in Pennsylvania to John
                       Fetterman. They thwarted the ambitions of election
                       deniers and proponents of voter suppression in
                       states across the country. And in cities like Los
                       Angeles, they beat the big-money interests that now
                       seek to control every branch of government—with
                       grassroots progressives scoring victories against
                       all odds. Here are some of the campaigners,
                       activists, intellectuals, and artists who spoke
                       truth to power, defended democracy, and bent the
                       arc of history toward justice in 2022.1


                # ⚓ The Nation ☛ Hannah_Arendt_Was_Really_a_Prophet_Against
                  Conformity⠀⇛


                       Hannah Arendt did more than anyone else to give the
                       idea of totalitarianism the importance we accord it
                       today. But like her contemporary George Orwell, in
                       her subtlest trains of thought Arendt was seldom
                       writing about the “-ism,” the social and political
                       entity. She was more concerned with the
                       implications of the adjective “totalitarian.”1


                # ⚓ Democracy Now ☛ Biden_Visits_Border_But_Doesn’t_Meet_with
                  Asylum_Seekers_as_Administration_Cracks_Down_on_Immigration⠀⇛


                       Immigrant rights groups are denouncing President
                       Biden’s recent announcement that the United States
                       will start to block migrants from Haiti, Nicaragua
                       and Cuba from applying for asylum if they’re
                       apprehended crossing the U.S.-Mexico border. The
                       move is an expansion of the contested Trump-era
                       Title 42 pandemic policy set to be reviewed by the
                       Supreme Court. Over the weekend, Biden visited El
                       Paso, one of the country’s busiest border
                       crossings, in his first visit to the border as
                       president. He reportedly did not meet with or see
                       any migrants during his four-hour visit. For more,
                       we speak with two immigrant rights activists who
                       have been urging the Biden administration to drop
                       Title 42 and create the infrastructure to welcome
                       asylum seekers: Guerline Jozef, executive director
                       of Haitian Bridge Alliance, and Fernando García,
                       executive director of the El Paso, Texas-based
                       Border Network for Human Rights.


                # ⚓ The Nation ☛ In_the_Windy_City⠀⇛


                       Located in Chicago’s historic Pilsen neighborhood,
                       1831 South Racine Avenue is currently the site of a
                       luxury shared-living complex. Advertised as having
                       “eliminated things that make city living a
                       challenge,” Pilsen Coliving offers its tenants
                       private beds and bathrooms inside a completely
                       furnished suite that they share with others.
                       Outfitted with hardwood floors, stainless steel
                       appliances, washers and dryers, subway-tiled
                       bathrooms,


                # ⚓ Democracy Now ☛ Bolsonaro_Backers_Storm_Brazil’s_Key_Gov’t
                  Buildings_in_Jan._6-Style_Attempt_to_Oust_Lula_from_Power⠀⇛


                       Brazilian President Luiz Inácio Lula da Silva is
                       condemning thousands of supporters of far-right
                       former President Jair Bolsonaro who stormed the
                       Brazilian Congress, Supreme Court and presidential
                       palace Sunday in a scene reminiscent of the U.S.
                       Capitol insurrection. Rioters smashed windows,
                       ransacked offices and set fire to a carpet inside
                       the Congress building before authorities made over
                       400 arrests. Bolsonaro has never formally conceded
                       the race to third-term President Lula and fled to
                       Florida, where he has reportedly met with Donald
                       Trump at Mar-A-Lago, while his supporters have
                       blockaded highways and set up protest encampments
                       outside military bases and in the capital Brasília
                       to protest what they falsely claim was a rigged
                       election. We get an update from Brazilian newspaper
                       columnist and professor Thiago Amparo in São Paulo
                       and reporter Michael Fox, host of the “Brazil on
                       Fire” podcast.


                # ⚓ The Nation ☛ From_a_Clown_Coup_to_a_Clown_Speakership⠀⇛


                       Last Friday, as Kevin McCarthy was nearing the end
                       of his grueling, humiliating, multiday quest to
                       become the new House speaker, former Obama adviser
                       Dan Pfeiffer tweeted, “Kevin McCarthy becoming
                       Speaker by offering concessions to the pro-
                       insurrection caucus on the two year anniversary of
                       January 6th is just a perfect statement about the
                       GOP.” As it turns out, Pfeiffer’s tweet wasn’t
                       quite accurate, because McCarthy didn’t actually
                       have all the votes he needed on January 6. It was
                       only after one final round of begging Florida
                       Representative Matt Gaetz to just vote “present”
                       that McCarthy, in the 15th round of ballot
                       counting, finally won the bare majority he needed
                       to become speaker in the early hours of January 7.
                       But Pfeiffer’s tweet remains poetically true: Two
                       years and a day after the assault on the Capitol on
                       January 6, 2021, the Republican Party provided
                       fresh proof that it remains in thrall to its
                       insurrectionist caucus.1


                # ⚓ The Nation ☛ Kevin_McCarthy’s_Reign_Begins—for_Now⠀⇛


                       Our long national nightmare is just beginning.
                       After a week of futile posturing and trench warfare
                       on the House floor, the House GOP caucus somehow
                       managed to elect Kevin McCarthy speaker of the
                       House on the 15th ballot. In the early hours of
                       January 7, after the second anniversary of the 2021
                       insurrection at the US Capitol, McCarthy appeared
                       doomed for more purgatorial humiliation as the 14th
                       vote broke against expectations and failed to
                       produce a majority for him. But just as the House
                       was going to vote to adjourn, Florida
                       Representative Matt Gaetz, one of the hard-right
                       ringleaders of the “Never Kevin” insurgency,
                       buttonholed the speaker-in-waiting for an impromptu
                       conference. Moments later, McCarthy rushed to take
                       back his endorsement of the pending adjournment,
                       and finally claimed his battered, tarnished,
                       dubiously functional leadership prize.


                # ⚓ The Nation ☛ George_Santos⠀⇛


                       George Santos invented an alternate life, With
                       chutzpah we’ve seen only rarely. Mendacity in all
                       his statements was rife. He beat Trump in lying,
                       though barely.


                # ⚓ Techdirt ☛ Arizona_Government_Thinks_It_Should_Be_Able_To
                  Decide_What_You_Wear_And_When⠀⇛


                       Trying to legislate sexual identity is a fool’s
                       errand. Plenty of Arizona state fools are backing a
                       bill that attempts to do that, though. When you
                       can’t figure out how to stop people from outward
                       displays of their sexual identity, you start
                       getting unconstitutional in a hurry.


                # ⚓ Counter Punch ☛ Which_Government_Does_the_United_States
                  Recognize_in_Venezuela?⠀⇛


                       On January 3, 2023, Shaun Tandon of Agence France-
                       Presse asked U.S. State Department spokesperson Ned
                       Price about Venezuela. In late December, the
                       Venezuelan opposition after a fractious debate
                       decided to dissolve the “interim government” led by
                       Juan Guaidó. From 2019 onward, the U.S. government
                       recognized Guaidó as the “interim president of
                       Venezuela.” With the end of Guaidó’s
                       administration, Tandon asked if “the United States
                       still recognize[s] Juan Guaidó as legitimate
                       interim president.”


                       Price’s answer was that the U.S. government
                       recognizes the “only remaining democratically
                       elected institution in Venezuela today, and that’s
                       the 2015 National Assembly.” It is true that when
                       the U.S. government supported Guaidó as the
                       “interim president” of Venezuela, it did so because
                       of his role as the rotating president in that
                       National Assembly in 2019. Since the presidency of
                       the National Assembly rotates annually, Guaidó
                       should have left the position of “interim
                       president” by the end of 2020. But he did not,
                       going against Article 233 of the Venezuelan
                       Constitution of 1999, which he cited as the basis
                       for his ascension in 2019.


                # ⚓ Counter Punch ☛ Biden_Isn’t_Great_for_Latin_America,_But
                  Trump_Was_Far_Worse⠀⇛


                       Two major developments can be inferred from the
                       results of the November 8, 2022 mid-term elections
                       in the United States. First, the voters did not
                       punish Joe Biden after his first two years as
                       president as the pre-election polls had predicted
                       they would.  Consequently, Donald Trump’s political
                       standing has diminished along with the legitimacy
                       of his leadership role in the Republican Party.


                       All 435 seats in the House of Representatives were
                       up for election, and Republicans now have control
                       of the lower chamber, though by a narrow margin.
                       Since the end of World War II, the opposition party
                       has usually won at least one of the two legislative
                       bodies in the first mid-term election after a new
                       president takes over. Historically, however, the
                       opposition victory margin is much higher than what
                       the Republicans were able to obtain this time
                       around.


                # ⚓ Counter Punch ☛ How_Biden_Can_Resolve_America’s_Immigration
                  Crisis⠀⇛


                       No pundit can predict what heated issue will
                       dominate the presidential and congressional
                       elections in 2024. However, aside from the Supreme
                       Court making a historic decision to eradicate
                       another established freedom, like marrying who you
                       wish, regardless of gender or race, migration will
                       remain a national issue.


                       Public opinion polls have consistently ranked
                       controlling immigration as a significant concern
                       for Americans. For example, a Gallup opinion
                       poll taken in July 2022 showed that 38% of
                       Americans wanted a decrease in immigration, the
                       highest percentage since July 2016, when Donald
                       Trump was nominated as the Republican presidential
                       candidate.


                # ⚓ The Nation ☛ Protect_Democracy_by_Bolstering_Organized
                  Labor⠀⇛


                       Twenty twenty-two was a decent year for democracy.
                       Legislative districts remained gerrymandered, but
                       the maps were not as extreme as they were in the
                       2010s. State governments were still engaging in
                       voter suppression, but it was partly counteracted
                       by pro-voter policies and mobilization by voter
                       turnout groups. Perhaps most important, many
                       candidates who were promoting “Stop the Steal”
                       voter-fraud conspiracy theories lost in the 2022
                       midterms. Is American democracy out of the woods?
                       The answer, unfortunately, is no. The events of
                       2022 certainly moved us away from the brink. But
                       the threats remain. The situation is not hopeless,
                       however, particularly if Democrats can focus on
                       long-term strategies, such as rebuilding the labor
                       movement.


                # ⚓ The Nation ☛ Ben_Jealous:_Never_Forget_Our_People_Were
                  Always_Free⠀⇛


                       My great-grandmother wrote my grandmother’s birth
                       certificate herself, as she did for every Negro
                       child in her Virginia county at that time. Back
                       then, the county clerk would explain, “We don’t
                       write birth certificates for cows, so we don’t
                       write them for Negroes.” It was 1916, and my people
                       were far from human in the eyes of the
                       segregationist government that ran Dinwiddie
                       County, Va.


                # ⚓ Telex (Hungary) ☛ Orbán_promises_to_make_Hungary_a
                  ‘regional_middle_power’_–_and_keeps_us_guessing_about_the
                  hows⠀⇛


                # ⚓ Common Dreams ☛ ‘Disaster_for_Everyone_Except_Corrupt
                  Politicians’:_House_GOP_Votes_to_Gut_Ethics_Office⠀⇛


                       In one of their first acts in the majority, House
                       Republicans on Monday approved a rules package that
                       will dramatically hinder the Office of
                       Congressional Ethics, an independent body tasked
                       with investigating complaints about sitting
                       lawmakers.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Democracy for the Arab World Now ☛ Saudi_Arabia:
                        Government_Agents_Infiltrate_Wikipedia,_Sentence
                        Independent_Wikipedia_Administrators_to_Prison⠀⇛


                             The Saudi Arabian government infiltrated
                             Wikipedia by recruiting the organization’s
                             highest ranked administrators in the country
                             to serve as government agents to control
                             information about the country and prosecuting
                             those who contributed critical information
                             about political detainees, said SMEX and
                             Democracy for the Arab World Now (DAWN)
                             today.


                             Following an internal investigation in 2022,
                             Wikimedia terminated all of its Wikipedia
                             administrators in Saudi Arabia in December.
                             DAWN and SMEX documented Wikipedia’s
                             infiltration by the Saudi government based on
                             interviews with sources close to Wikipedia
                             and the imprisoned administrators.


          o § Censorship/Free Speech⠀➾


                # ⚓ Scheerpost ☛ Free_Speech_and_Academic_Freedom_in_the
                  American_Corporate_University⠀⇛


                       Free speech and academic freedom  are under attack
                       in American higher education. From the right the
                       allegation is that wokeness and political
                       correctness  have taken over, articulating  a
                       political agenda that is  anti-white, anti-
                       Christian, anti-capitalism, and pro LGBTQ.  From
                       the left  the indictment is that schools continue
                       to replicate stereotypes […]


                # ⚓ Meduza ☛ Alexey_Navalny_starts_2023_in_punishment_cell_—
                  Meduza⠀⇛


                       Alexey Navalny, who is serving his sentence in
                       Prison Colony No. 6 in the Vladimir region, has
                       been placed in the punishment cell for the tenth
                       time.


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


                # ⚓ The Nation ☛ Access_to_Journalism_Is_a_Human_Right⠀⇛


                       In 1974, when the Irish statesman and humanitarian
                       Seán MacBride was awarded the Nobel Peace Prize, he
                       delivered an acceptance speech emphasizing the
                       urgent need for nuclear disarmament. But at a key
                       moment, MacBride turned to the growing role of mass
                       media in world affairs. The media’s exploding reach
                       and speed, he asserted, could grant “a much greater
                       degree of influence to public opinion in the world
                       than it has ever had.” The US withdrawal from
                       Vietnam proved it. For the first time, MacBride
                       said, a country at war had been stopped in its
                       tracks by public opinion—shaped through the media.
                       But this shift in power was not yet fully
                       understood. “Greater vigilance than ever will have
                       to be exercised to ensure that the press and the
                       mass media do not become controlled by governments
                       or financial interests,” he warned.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Nation ☛ Pakistan’s_Transgender_Community_Rises_Up⠀⇛


                       Dr. Sarah Gill was just 14 when she ran away from
                       home in Karachi. For most of her childhood, she had
                       suffered the humiliation of feeling like a girl but
                       being told she was a boy. She used to quarrel with
                       her mother for making her dress like a boy and
                       would refuse to study unless she was allowed to
                       grow her hair long. “From my features, it was
                       always very obvious that I wasn’t a guy,” she says.
                       “People used to degrade me a lot because of my
                       looks. They would come to my house and tell my
                       parents all sorts of things about me.”


                # ⚓ Democracy Now ☛ Harvard_Faces_Outcry_for_Rescinding_Post_to
                  Ex-Head_of_Human_Rights_Watch_over_Criticism_of_Israel⠀⇛


                       We speak with the longtime former head of Human
                       Rights Watch, Kenneth Roth, about losing a
                       prestigious position at Harvard over his criticism
                       of Israeli human rights abuses. Roth was set to
                       begin as a senior fellow at the Harvard Kennedy
                       School’s Carr Center for Human Rights Policy after
                       he retired as director of the renowned human rights
                       organization in April. But the school’s dean,
                       Douglas Elmendorf, vetoed the move over Roth’s and
                       Human Rights Watch’s “anti-Israel bias,” The Nation
                       reports. “We hold Israel to the same standards as
                       everybody else,” Roth says of Human Rights Watch’s
                       work. He adds that while it’s unclear what pressure
                       the Kennedy School may have faced in its decision,
                       reporting truthfully on Israel’s rights record
                       often brings down the ire of pro-Israel groups who
                       want to shut down all criticism. “They want us to
                       exempt Israel from human rights scrutiny, and no
                       credible human rights group could possibly do
                       that.”


                # ⚓ The Nation ☛ Ye_Is_a_Right-Wing_Tool—and_Black_People_Know
                  It⠀⇛


                       Kanye “Ye” West has been spewing white nationalist
                       talking points for a decade. His current anti-
                       Semitic road show was preceded by years of evident
                       anti-Blackness, from hawking Confederate flag merch
                       in 2013, to declaring that Black enslavement was “a
                       choice” in 2018, to appearing repeatedly at the
                       White House during the Trump years, to attempting,
                       in 2021, to coerce Black election workers in
                       Georgia to falsely confess throwing the vote to
                       Biden. Unsurprisingly, wariness of Ye among Black
                       folks has been steadily growing for years,
                       particularly among disappointed former fans. In
                       2018, the writer Channing Hargrove wrote a
                       satirical obituary for West; Black Twitter declared
                       him stuck in Get Out’s “sunken place”; and
                       journalist and filmmaker dream hampton indicted him
                       for pushing “the same old white supremacy.”
                       Comedian Zachary Fox had the prescience to warn
                       that we should all disembark from “the Kanye train
                       before it inevitably reaches the ‘Hitler was a good
                       guy’ stop.” In October 2022, an Economist/YouGov
                       poll found that a greater share of Black Americans
                       (40 percent) viewed the rapper very negatively than
                       either Hispanic Americans (32 percent) or white
                       Americans (33 percent).


                # ⚓ Common Dreams ☛ Malignant_Idiots_Incoming⠀⇛


                       Lesson from the clusterfuck that was the “once-in-
                       a-century humiliation” of “Titan of Mediocrity”
                       Kevin McCarthy bumbling through 15 votes to become
                       Speaker of a shambolic House held hostage by a
                       rabid band of insurrectionist wingnuts: Elect
                       clowns, get a circus. The tragicomedy, years in the
                       gerrymandering, confirms there is no GOP normal;
                       this was MAGA eating its own. After days of
                       concessions – he’ll teach Boebert to read! – Kevin
                       is now the feckless “mayor of Crazytown.” Mazel
                       tov, dude.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Decades_Late,_The_FCC_Might_Start_Cracking_Down
                  On_Terrible_Telecom_Prison_Monopolies._Maybe.⠀⇛


                       However terrible telecom monopolies are in the free
                       world, they’re arguably worse in prisons. For
                       decades, journalists have outlined how a select
                       number of prison telecom giants like Securus have
                       enjoyed a cozy, government-kickback based monopoly
                       over prison phone and teleconferencing services,
                       resulting sky high rates (upwards of $14 per
                       minute) for inmate families.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ [Old] The Register UK ☛ Software_fees_to_make_up_10%_of
                  John_Deere’s_revenues_by_2030⠀⇛


                       US farm machinery giant John Deere has estimated
                       software fees will make up 10 percent of the
                       company’s revenues by the end of the decade.


                # ⚓ [Old] uni Tampere ☛ Parody_And_Copyright_In_The_European
                  Union_Law⠀⇛


                       Parody and copyright are both linked to fundamental
                       rights in the EU law; parody to the freedom of
                       expression and copyright essentially to the right
                       to property even though it can be seen to advance
                       the freedom of expression as well. The relationship
                       between parody and copyright in the EU law is
                       regulated essentially in the Information Society
                       Directive (The InfoSoc Directive). According to it
                       the Member States may set out a parody exception to
                       copyright holders’ rights found in Articles 2
                       (right of reproduction) and 3 (right of
                       communication to the public of works and right of
                       making available to the public other subject-
                       matter). The exception means that one can create
                       and publish a parody without violating these
                       rights. Setting out the parody exception is
                       voluntary for the Member States. However, the
                       InfoSoc Directive does not define parody. A change
                       to the lack of definition was provided in the
                       European Court of Justice’s (ECJ) preliminary
                       ruling Deckmyn and Vrijheidsfonds (Deckmyn) in
                       which parody was established as an autonomous
                       concept in the EU law and given a uniform
                       definition in the EU law. The ECJ based the
                       definition on its usual meaning. According to the
                       definition ‘the essential characteristics of
                       parody, are, first, to evoke an existing work,
                       while being noticeably different from it, and
                       secondly, to constitute an expression of humour or
                       mockery’. It is argued in the paper that ‘humour’
                       refers to a humorous intent as opposed to a
                       humorous effect because this is more in line with
                       the freedom of expression and because of practical
                       reasons.


                # ⚓ Techdirt ☛ John_Deere_Once_Again_Pinky_Swears_It_Will_Stop
                  Monopolizing_Repair⠀⇛


                       Once just the concern of pissed off farmers and
                       nerdy tinkerers, the last two years have seen a
                       groundswell of broader culture awareness about
                       “right to repair,” and the perils of letting
                       companies like Apple, John Deere, Microsoft, or
                       Sony monopolize repair options, making repairing
                       things you own both more difficult and way more
                       expensive.


                # ⚓ Hackaday ☛ You_Can_Now_Fix_Your_Deere⠀⇛


                       Over the last few years we have brought you many
                       stories about John Deere tractors, and how their
                       repair has been locked down such that only
                       manufacturer-authorised technicians can work on
                       them. They’ve become a poster child in the battle
                       for the right to repair, a symbol of the worst
                       practices. Finally now we can bring you some good
                       news of sorts, as the agricultural giant has signed
                       a memorandum of understanding with the American
                       Farm Bureau Federation to ensure that their
                       products will henceforth be repairable by people
                       without Deere approval.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Common Dreams ☛ ‘The_Sheer_Greed_Is_Obscene’:_Moderna
                        Plans_4,000%_Markup_for_Covid_Vaccine⠀⇛


                             The Massachusetts-based pharmaceutical giant
                             Moderna faced angry backlash on Tuesday
                             following the CEO’s announcement that the
                             firm is considering pricing its Covid-19
                             vaccine somewhere between $100 and $130 per
                             dose in the United States.


                # § Copyrights⠀➾


                      # ⚓ Creative Commons ☛ Celebrate_Public_Domain_Day_2023
                        with_Us:_The_Best_Things_in_Life_Are_Free⠀⇛


                             This year ushered in a wealth of creative
                             works published in 1927 into the Public
                             Domain, which now contribute to our cultural
                             heritage. Iconic authors like Sir Arthur
                             Conan Doyle, Marcel Proust, and Virginia
                             Woolf, silent film classics like the
                             controversial The Jazz Singer with Al Jolson
                             and Fritz Lang’s dystopian Metropolis, and
                             snappy musical compositions like “You Scream,
                             I Scream, We All Scream For Ice Cream”.


                      # ⚓ Torrent Freak ☛ Police_Pay_Home_Visits_to_Warn_Pirate
                        IPTV_Users⠀⇛


                             Anti-piracy group FACT is helping UK police
                             to deliver warning messages to alleged pirate
                             IPTV users. Instead of simply sending letters
                             in the mail, some cease-and-desist notices
                             will be delivered in person. A recent IPTV
                             crackdown resulted in the identification of
                             over 1,000 subscribers, who will be asked to
                             immediately stop any illegal activity, or
                             else.


                      # ⚓ Torrent Freak ☛ 370_Pirate_IPTV_Sellers_Faced_Legal
                        Action_After_CJEU_‘Filmspeler’_Ruling⠀⇛


                             When streaming became the preferred way for
                             millions of EU-based pirates to consume video
                             content, the name Jack Frederik Wullems
                             would’ve meant nothing. For 370 pirate IPTV
                             suppliers targeted in the Netherlands in
                             recent years, Wullems’ defeat in a landmark
                             case back in 2017 is the reason their wallets
                             are lighter today than they were before.


                      # ⚓ Public Domain Review ☛ Art_Brut:_The_Scare-Fox_(1910)
                        –_The_Public_Domain_Review⠀⇛


                             A mechanical device, designed to keep foxes
                             away from pheasants, which opens onto a story
                             about American gamekeeping in the early
                             twentieth century.


                             [...]


                             Lawyer, editor, and indefatigable leader of
                             the “More Game” movement in America, Dwight
                             W. Huntington published this photograph of
                             the scare-fox in Our Wild Fowl and Waders
                             (1910) as part of his campaign to raise
                             American awareness of the devastating
                             depredations caused by “vermin”: a word that
                             Americans used largely to refer to bed lice,
                             but which in British gamekeeping circles had
                             long been applied to any animal — from foxes,
                             weasels, snakes, and stoats to rats, moles,
                             and even shrews — that competed with hunters.
                             Enthusiastically introducing the term in his
                             March 1908 Independent “Game Bird Enemies”,
                             Huntington would routinely employ it for the
                             next three decades while cheerleading for
                             “MORE GAME AND FEWER GAME LAWS”. Two journals
                             he edited — Amateur Sportsman (1909–1912) and
                             The Game Breeder (1912 –1938) — are a unique
                             chronicle of the antagonistic reactions of
                             hunters and “shooters” (waterfowl and other
                             bird gunners) to the early twentieth century
                             growth of the wildlife conservation movement.
                             While Audubon Societies and kindred
                             organizations lobbied legislatures to protect
                             mammals and birds from destruction by both
                             hunters and habitat loss, the Game
                             Conservation Society (founded by Huntington
                             in 1912) marshaled a nationwide campaign to
                             stymie the “naturalists”: his generic and
                             largely derogatory label for all of those who
                             impinged on his dream of making America the
                             world’s leading producer of game animals.


                      # ⚓ CNBC ☛ ABBA_Voyage:_Avatar_show_in_London_offers
                        glimpse_of_future_for_live_music⠀⇛


                             Before the launch of “ABBA Voyage,” the
                             London concert performed by 3D digital
                             avatars of the iconic Swedish band, member
                             Björn Ulvaeus said they hoped audiences would
                             “feel that they’ve gone through something
                             that they’ve never seen before.”


                             Following its May 27 debut, much of the
                             reaction from domestic and international
                             critics, fans and industry professionals has
                             been rapturous.


                      # ⚓ Adafruit ☛ Cyberpunk_2077_Investors_and_Developers
                        Settle_Class_Action_Lawsuit⠀⇛


                      # ⚓ Walled Culture ☛ How_Minecraft’s_‘End_Poem’_ended_up
                        in_the_public_domain_–_Walled_Culture⠀⇛


                             Minecraft is the best-selling video game of
                             all time according to Wikipedia, with
                             hundreds of millions of copies sold. The game
                             concludes with the End Poem by the writer and
                             musician Julian Gough, created in 2011. In
                             December 2022, Gough wrote a post on his
                             Substack site “The Egg and the Rock” in which
                             he explains in detail how the poem came
                             about. It’s a well-written, fascinating tale
                             that touches on many aspects that are likely
                             to be of interest to Walled Culture readers.
                             It is, however, very long: some 10,000 words.


                             [...]


                             As that indicates, when he wrote the End
                             Poem, Gough did something that this blog has
                             recommended for all creators: to retain
                             copyright in their work, rather than
                             assigning it to a company, whatever the
                             pressure to do so. Admittedly, he did this
                             passively rather than actively, since he
                             never got around to signing or even reading
                             the contract that had been sent to him. When
                             he did read it, he found it full of the usual
                             – outrageous – demands to hand over just
                             about every right that a creator typically
                             has under copyright.


                             One amusing consequence of Gough’s oversight
                             is that after Minecraft was sold in 2014 to
                             Microsoft for $2.5 billion, the latter was
                             almost certainly infringing on Gough’s
                             copyright by selling the game without any
                             licence from him. But rather than taking the
                             obvious route of suing the company for a few
                             million dollars or more, Gough did something
                             remarkable.


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



                    ䷩ 𝚕𝚒𝚗𝚎 6190

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.10.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/01/2023:_Yet_More_Security_Issues_in_Rust⠀✐


Posted in News_Roundup at 9:11 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Debian_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o Funding
          o Programming/Development
                # Python
                # Rust
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Daniel Pocock ☛ Daniel_Pocock:_Cardinal_George_Pell:_a
                  brief_tribute⠀⇛


                       While Cardinal Pell was known for his skepticism
                       about climate change, I will always be grateful for
                       donations of surplus fileservers from the dioecese
                       for me to recycle with Debian GNU/Linux.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Linux_Mint_MATE_21.1_–_Invidious⠀⇛


                       This video looks at the new Linux Mint MATE
                       edition, kernel, RAM, software, and other
                       considerations.


                # ⚓ Video ☛ ChatGPT_|_The_Revolutionary_AI_Chatbot_That_Will
                  Transform_Your_Life!_–_Invidious [Ed: This is mostly
                  promoting Microsoft agenda of plagiarism]⠀⇛


                       What’s up, Linux Community! In this video, I’ll
                       introduce ChatGPT, the revolutionary AI chatbot
                       that uses advanced language processing to deliver
                       engaging, personalized conversations.


                # ⚓ Video ☛ Coding_Is_Easy_#programming_#coding_–_Invidious⠀⇛


                # ⚓ Video ☛ Vanilla_OS_–_The_Future_Of_Linux_Part_2_|_Immutable
                  –_Solid_–_Invidious⠀⇛


                       A video covering the newest release of Vanilla OS.
                       Like my previous video covering Nitrux OS, Vanilla
                       OS brings a lot of enhancements to the table to
                       make this Linux distro almost unbreakable. Take a
                       look and let me know what you think in the comments
                       below.


                # ⚓ Video ☛ OpenMandriva_Lx_ROME_23.01_overview_|_ROME,_the
                  OpenMandriva_rolling_edition_–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       OpenMandriva Lx ROME 23.01 and some of the
                       applications pre-installed.


                # ⚓ Video ☛ The_SMART_Home_is_a_DUMB_idea,_and_a_privacy_and
                  security_NIGHTMARE_–_Invidious⠀⇛


                # ⚓ Video ☛ HDR_Gaming_Is_Coming_To_Linux_Right_Now!!_–
                  Invidious⠀⇛


                       I made a video a short while ago about HDR coming
                       to Linux and I didn’t think we’d see much else
                       about it for at least a few months, oh how wrong I
                       was because Valve is on the case.


          o § Applications⠀➾


                # ⚓ Converseen_0.9.10.0_with_Improved_WebP_Support_–
                  Fasterland⠀⇛


                       Converseen, the cross-platform image converter, and
                       resizer, has now been updated to version 0.9.10.0,
                       by adding some improved WebP features, and now it’s
                       also possible to remove EXIF metadata after every
                       conversion or change of format process.


          o § Instructionals/Technical⠀➾


                # ⚓ APIban_MySQL_client_–_TelecomsXChange_(TCXC)_Blog⠀⇛


                       APIBAN helps prevent unwanted SIP traffic by
                       identifying addresses of known bad actors before
                       they attack your system. Bad actors are collected
                       through globally deployed honeypots and curated by
                       LOD/APIBAN.


                # ⚓ Kifarunix ☛ Deploy_Nagios_Core_as_a_Docker_Container_–
                  kifarunix.com⠀⇛


                       In this tutorial, you will learn how to deploy
                       Nagios Core as a Docker container.


                # ⚓ ZDNet ☛ How_to_easily_locate_your_mouse_pointer_in_Ubuntu
                  and_other_GNOME-based_Linux_distributions⠀⇛


                       If you have trouble locating your mouse pointer in
                       Linux, this little tip will give you some much-
                       needed relief.


                # ⚓ Network World ☛ Linux_filels:_creating,_listing,_updating,
                  and_more_|_Network_World⠀⇛


                       Linux provides a number of handy commands for
                       managing file permissions, understanding who has
                       access to the files and checking on file content.


                # ⚓ Make Use Of ☛ 4_Ways_to_Check_Whether_cron_Is_Working_on
                  Linux⠀⇛


                       cron is a job scheduler and process automation
                       utility for Linux. Here’s how you can check if cron
                       is working properly on your system.


                # ⚓ UNIX Cop ☛ How_to_deploy_MariaDB_and_PhpMyAdmin_using
                  Docker⠀⇛


                       In this short post, you will learn how to deploy
                       MariaDB and PhpMyAdmin using Docker. These are some
                       simple images without so many additives, so you can
                       by yourself edit it and improve it to your liking.


                # ⚓ Copy,_Cut_And_Paste_On_The_Command_Line_With_Clipboard_–
                  Linux_Uprising_Blog⠀⇛


                       Clipboard is a new command line tool to cut, copy
                       and paste text, files and folders. The software
                       works on Linux, Windows, macOS, Android and *BSD.


                       This tiny yet powerful command line utility can be
                       useful to both new and power users. Besides
                       allowing you to cut, copy and paste anything from a
                       terminal, it can show the clipboard contents, clear
                       the clipboard, and there’s also support for
                       multiple (infinite) clipboards.


                # ⚓ Video ☛ How_to_install_WPS_Office_2019_on_KDE_Neon_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install WPS
                       Office 2019 on KDE Neon.


                # ⚓ ID Root ☛ How_To_Install_AppImage_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       AppImage on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, AppImage is a package format for
                       distributing portable software on Linux. It is a
                       single executable file that contains all the
                       necessary dependencies and libraries required to
                       run the software, making it easy to run on any
                       Linux distribution.


                       AppImages are self-contained and do not need to be
                       installed in the traditional sense. Instead, they
                       can be run directly from the file manager or
                       terminal by making the file executable and then run
                       it. This makes it easy to use AppImages on systems
                       where you don’t have administrator privileges or
                       don’t want to modify the system libraries.


                       One of the main advantages of using AppImages is
                       that they allow you to run software that might not
                       be available in your distribution package manager.
                       This can be particularly useful for running newer
                       or specialized software on older or niche
                       distributions.


                       AppImages are also portable, meaning that you can
                       easily move them between different systems and run
                       them without any additional setup. This makes it
                       easy to use the same software on multiple systems,
                       even if they have different package managers or
                       libraries installed.


                       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 AppImage on Ubuntu 22.04 (Jammy
                       Jellyfish). You can follow the same instructions
                       for Ubuntu 22.04 and any other Debian-based
                       distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Linux Made Simple ☛ How_to_install_Blender_3.4.1_on_a
                  Chromebook⠀⇛


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


                # ⚓ Linux Made Simple ☛ How_to_install_Ghostery_Dawn_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Ghostery
                       Dawn on a Chromebook.


                # ⚓ ZDNet ☛ How_to_install_Kali_Linux_on_Apple_Silicon_Macs_|
                  ZDNET⠀⇛


                       I’ve had messages from a number of people asking me
                       for information on how to install Kali Linux on
                       Macs running the M1 and M2 Apple Silicon chips.


                # ⚓ Ubuntubuzz ☛ How_To_Write_Javanese_Script_Hanacaraka_on
                  Ubuntu_Computer⠀⇛


                       This tutorial will help you writing one of
                       Indonesian traditional scripts, Javanese, also
                       known as Aksara Jawa (ꦲꦏ꧀ꦱꦫꦗꦮ) or Hanacaraka
                       (ꦲꦤꦕꦫꦏ), on Ubuntu computer. This is the real
                       Javanese language spoken by Javanese people in Java
                       island and not a programming language with similar
                       name. We will show you that you can type Javanese
                       using Firefox browser, Text Editor, LibreOffice,
                       Gimp, Inkscape and Scribus. Now let’s exercise.


                # ⚓ Make Tech Easier ☛ How_to_Encrypt_Files_in_Linux_with_Tomb
                  –_Make_Tech_Easier⠀⇛


                       Tomb is a simple shell script that allows you to
                       encrypt files in Linux. Unlike full disk
                       encryption, Tomb enables you to only include the
                       files and folders that you want to encrypt. Here we
                       show you how to install and use Tomb on Ubuntu.


                # ⚓ Own HowTo ☛ How_to_Install_easypanel_on_Ubuntu_22.04⠀⇛


                       Easypanel is a server control panel software that
                       you can use to deploy many apps on your website.


                       In this tutorial you will learn how to install
                       easypanel on Ubuntu 22.04.


          o § Games⠀➾


                # ⚓ Godot Engine ☛ Godot_Engine_–_Dev_snapshot:_Godot_4.0_beta
                  11⠀⇛


                       With the end-of-the-year celebrations past us, we
                       are ready to get back to work and continue our
                       regular Godot 4.0 beta releases. Over the course of
                       the last four months the engine has seen many
                       changes, making it more stable and feature
                       complete, and it’s getting very close to the state
                       that we would be happy with.


                       We took a bit longer to prepare this beta as there
                       were a number of fairly big GDScript refactoring
                       PRs (needed to fix many bugs), which we wanted to
                       merge all at once. As such we expect that this beta
                       11 might introduce some new GDScript regressions,
                       which we’ll aim to fix for beta 12 next week. Be
                       sure to report anything that stops working as
                       expected in your scripts.


                # ⚓ Make Use Of ☛ 6_Linux_and_Open-Source_Technologies_That
                  Made_the_Steam_Deck_Possible⠀⇛


                       While Steam’s user interface isn’t open source, nor
                       are most of the games, the experience wouldn’t be
                       possible without an entire stack of free and open-
                       source technology underneath. Valve knows this, and
                       they’re paying numerous developers to improve the
                       technologies they depend on.


                       So what are the technologies that the Steam Deck
                       utilizes to deliver an experience that has
                       impressed much of the gaming world?


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ 9to5Linux ☛ GNOME_42.8_Enables_Atomic_Mode-Setting
                        for_NVIDIA/GBM,_Improves_Wayland_and_AMDGPU_Support⠀⇛


                             GNOME 42.8 is a pretty small update for those
                             still using the GNOME 42 desktop on their
                             GNU/Linux distribution. However, it brings an
                             updated Mutter window and composite manager
                             that disables client modifiers when the open-
                             source AMDGPU driver is in use and enables
                             atomic mode-setting for the NVIDIA graphics
                             driver with GBM support.


                             Previous GNOME 42 releases denied using the
                             atomic mode-setting with the proprietary
                             NVIDIA graphics driver because the mode-
                             setting device was initiated before
                             attempting to initialize the renderer because
                             EGLStream-based page flipping is not
                             compatible with atomic mode-setting.


    * § Distributions and Operating Systems⠀➾


          o ⚓ 9to5Linux ☛ Endless_OS_5.0_Beta_Is_Here_with_a_New_Desktop
            Interface_and_Wayland_Support⠀⇛


                 Endless OS 5.0 is finally here in a beta variant that you
                 can download and try on your personal computer if you
                 want to enjoy the new desktop interface built on top of
                 the GNOME 41 desktop environment, the revamped App Center
                 that no longer features hard-coded lists of apps, as well
                 as support for the next-generation Wayland display server
                 protocol.


                 Endless OS 5.0 also promises improved multi-GPU support
                 as the system UI and most apps now use the integrated
                 graphics card by default to save battery life on laptops.
                 GPU-demanding apps like video games or 3D graphics
                 software, such as Blender, are automatically started with
                 the discrete graphics card.


          o ⚓ ZDNet ☛ Mabox_Linux_is_a_throwback_to_old-school_Linux_with_a
            new-school_look_and_feel_|_ZDNET⠀⇛


                 I’ve run the gamut of Linux distributions, from the
                 incredibly simple to the overly complex, from modern
                 interfaces to old-school throwbacks.


                 I’ve used Fvwm95, CDE, KDE, Xfce, AfterStep, Blackbox,
                 Enlightenment, Cinnamon, Mate, GNOME, and nearly every
                 desktop that has ever been available to Linux. I’ve also
                 used Ubuntu-based, Fedora-based, Arch-based, and just
                 about any distribution based on nearly any other
                 distribution. The combinations have been staggering over
                 the years. Needless to say, I’ve experienced it all since
                 I started using Linux in 1997.


                 Because of using so many Linux distributions over the
                 years, very little surprises me these days. But when I
                 spun up a virtual instance of Mabox Linux, I couldn’t
                 help but smile. Why? Because it reminded me of my early
                 days using Linux, only with a bit of a modern, user-
                 centric twist.


                 You see, back in the early days, Linux wasn’t so user-
                 friendly. Quite the opposite in fact. Linux was hard in
                 its infancy. So, when I see a Linux distribution that
                 reminds me of those days but manages to make it easy on
                 users without years of experience under their belts, it
                 reminds me how far the open-source operating system has
                 come.


                 Such is the case with Mabox Linux.


          o § Fedora Family / IBM⠀➾


                # ⚓ Fedora ☛ Schedule_for_Tuesday’s_FESCo_Meeting_(2023-01-
                  10)⠀⇛


                # ⚓ CentOS ☛ CentOS_Board_Meeting_Recap,_December_2022⠀⇛


          o § Debian Family⠀➾


                # ⚓ Utkarsh Gupta ☛ Utkarsh_Gupta:_FOSS_Activites_in_December
                  2022⠀⇛


                       Here’s my (thirty-ninth) monthly but brief update
                       about the activities I’ve done in the F/L/OSS
                       world.


          o § Open Hardware/Modding⠀➾


                # ⚓ Linux_Format_298⠀⇛


                       Get your hot Pi projects here! Grab your Pis,
                       Picos, soldering iron and start building cool maker
                       projects from IoT smart home devices, tracking
                       planes, create a live currency converter, discover
                       NeoPixel control, choose a perfect case, get faster
                       SD cards and more!


                # ⚓ Raspberry Pi ☛ What_to_expect_from_the_Raspberry_Pi
                  Foundation_in_2023⠀⇛


                       Welcome to 2023.  I hope that you had a fantastic
                       2022 and that you’re looking forward to an even
                       better year ahead. To help get the year off to a
                       great start, I thought it might be fun to share a
                       few of the things that we’ve got planned for 2023.


                # ⚓ Arduino ☛ This_interactive_art_installation_is_a_study_in
                  magnetism_|_Arduino_Blog⠀⇛


                       Art is inherently subjective and its meaning varies
                       from one person to the next. But many pieces have
                       widespread appeal as they tap into some emotion we
                       all share. Interactive art pieces tend to stimulate
                       our senses of curiosity and wonder. Niklas Roy’s
                       “Visitors Magnet” installation harnesses the
                       mystique of magnetism to provide that wonder.


                # ⚓ Arduino ☛ Tracking_sleep_quality_with_embedded_ML_and_the
                  Arduino_Nano_33_BLE_Sense_|_Arduino_Blog⠀⇛


                       Ensuring adequate and restful sleep is vital for
                       maintaining good health, as decreases in sleep
                       quality have been proven to cause a whole host of
                       problems. University of Toronto students Zongyan
                       Yao and Xilin Liu recognized this vital aspect to
                       well-being and wanted to build an inexpensive
                       device that could classify the various stages of
                       sleep as well as report the resulting data
                       wirelessly.


                       Clinical sleep evaluation is performed by taking
                       polysomnograms, which are essentially measurements
                       of brain, heart, respiratory, and other
                       physiological features. Zongyan and Xilin decided
                       on using an Arduino Nano 33 BLE Sense to classify
                       single-channel EEG values with a lightweight
                       machine learning model due to its relatively fast
                       processor and available RAM. Training data for the
                       model was sourced from the Sleep-EDF Expanded
                       Database that contains several hours of sleep
                       telemetry, including EEG, EOG, airflow, and body
                       temperature, although only the EEG data was kept.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Police ☛ Android_13_QPR2_Beta_2_can_force-theme_all
                  icons_on_your_home_screen⠀⇛


                # ⚓ Phone Arena ☛ Android_13_arrives_on_the_Galaxy_A71_5G,
                  marking_its_final_major_update_–_PhoneArena⠀⇛


                # ⚓ Digital Trends ☛ 5_features_the_iPhone_needs_in_2023_for_me
                  to_ditch_Android_|_Digital_Trends⠀⇛


                # ⚓ Kim Kommando ☛ 5_Android_gestures_you_need_to_try_today⠀⇛


                # ⚓ Android Police ☛ How_we_test_and_review_products_at_Android
                  Police⠀⇛


                # ⚓ Make Use Of ☛ How_to_Use_the_Privacy_Dashboard_on_Android⠀⇛


                # ⚓ Reuters ☛ Exclusive:_Google_warns_Android_growth_in_India
                  will_stall_due_to_antitrust_order_|_Reuters⠀⇛


                # ⚓ TechCrunch ☛ India’s_antitrust_order_will_stall_Android’s
                  progress_in_the_country,_Google_warns_•_TechCrunch⠀⇛


                # ⚓ This_New_Android_Feature_Actually_Excites_Me⠀⇛


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


          o § Content Management Systems (CMS)⠀➾


                # ⚓ WordPress ☛ WordPress_is_Turning_20:_Let’s_Celebrate!_–
                  WordPress_News⠀⇛


                       2023 marks the 20th year of WordPress. Where would
                       we all be without WordPress? Just think of that!
                       While many technologies, software stacks, and
                       fashion trends have come and gone throughout the
                       past two decades, WordPress has thrived. This is
                       due to the fantastic work and contributions of the
                       WordPress community, comprised of thousands of
                       contributors; and millions of users who have
                       embraced the four freedoms of WordPress and the
                       mission to democratize publishing.


          o § Funding⠀➾


                # ⚓ Julia Evans ☛ Some_business_graphs_for_2022⠀⇛


                       Hello! I like looking at other independent authors’
                       business graphs, so I thought I’d share some
                       percentages and graphs of my own this year.
                       Hopefully some of this is useful to other writers
                       who run internet businesses.


                       All of the graphs are about Wizard Zines’ business
                       selling zines – I don’t do sponsorships or
                       consulting or commissions or anything.


          o § Programming/Development⠀➾


                # ⚓ Daniel Lange ☛ Daniel_Lange:_Happy_tenth_birthday,_dear
                  Thunar_bug⠀⇛


                       Thunar, the Xfce4 file manager, has a bug that is
                       underflows the time remaining for a file copy since
                       ten years now (bugzilla, gitlab). Happy birthday!


                # § Python⠀➾


                      # ⚓ LWN ☛ PEP_703:_Making_the_Python_global_interpreter
                        lock_optional_[LWN.net]⠀⇛


                             In late 2021, LWN covered a plan to eliminate
                             the Python global interpreter lock (GIL),
                             thus improving the language’s thread-level
                             concurrency. This plan has now been codified
                             as PEP 703, which includes an extensive
                             discussion of the changes that would be made.


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ The_Rust_Programming_Language_Blog:
                        Security_advisory_for_Cargo_(CVE-2022-46176)⠀⇛


                             The Rust Security Response WG was notified
                             that Cargo did not perform SSH host key
                             verification when cloning indexes and
                             dependencies via SSH. An attacker could
                             exploit this to perform man-in-the-middle
                             (MITM) attacks.


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ IoT_Archaeology_Leads_To_API_Resurrection⠀⇛


                 What happens when someone’s personal project is turned
                 into a startup which becomes something of a publicity
                 darling, then collapses with very little product shipped
                 and takes all its customers’ money with it?


          o ⚓ Hackaday ☛ Human-Powered_Strandbeest⠀⇛


                 Once you’ve seen a strandbeest, it’s hard to forget the
                 mesmerizing movement of its mechanical limbs. [Adam
                 Savage] built a pedal-powered strandbeest in (more than)
                 one day in full view of the public at the San Francisco
                 Exploratorium.


          o § Education⠀➾


                # ⚓ Telex (Hungary) ☛ “We’ll_have_to_see_what’s_going_to
                  happen”_–_Navracsics_on_the_exclusion_of_foundation-run
                  universities_from_Erasmus_programs⠀⇛


                # ⚓ Counter Punch ☛ Free_Speech_and_Academic_Freedom_in_the
                  American_Corporate_University⠀⇛


                       Free speech and academic freedom  are under attack
                       in American higher education.


                       From the right the allegation is that wokeness and
                       political correctness  have taken over,
                       articulating  a political agenda that is  anti-
                       white, anti-Christian, anti-capitalism, and pro
                       LGBTQ.  From the left  the indictment is that
                       schools continue to replicate stereotypes in their
                       curriculum that perpetuate discrimination against
                       marginalized groups.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Wipe_On,_Wipe_Off:_Make_Your_Own_Rain
                  Repellent⠀⇛


                       Once upon a time, we drove an old six-volt VW
                       Beetle. One sad day, the wiper motor went out, and
                       as this happened before the Internet heyday, there
                       were no readily-available parts around that we were
                       aware of. After briefly considering rubbing a
                       potato on the windshield as prescribed by the old
                       wives’ tale, we were quite grateful for the
                       invention of Rain-X — a water-repelling chemical
                       treatment for car windshields.


                # ⚓ Hackaday ☛ Clever_Mechanism_Makes_A_Linear_Control_From_A
                  Rotary_Hall_Sensor⠀⇛


                       Every once in a while we stumble across something
                       so simple yet so clever that we just have to call
                       it out. This custom linear Hall effect sensor is a
                       perfect example of this.


                # ⚓ Adafruit ☛ Vintage_aircraft_instrument_becomes_an_USB
                  peripheral⠀⇛


                       The completed and assembled board. The board
                       features a USB 2.0 Type C connector, a PIC16F1459,
                       four MCP41HV31 digital potentiometers, and a screw
                       terminal strip to connect to power and the
                       indicator.


                # ⚓ Adafruit ☛ Making_a_magnetic_cocoa_stirrer⠀⇛


                # ⚓ Adafruit ☛ Dracula_Sucks_Indoor_Light_to_Power_IoT
                  Devices⠀⇛


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Texas_Lawsuit_Against_Planned_Parenthood
                  Challenges_Medicaid_Reimbursements⠀⇛


                # ⚓ Project Censored ☛ The_Case_for_“U.S._Out_of_Africa,”_and
                  the_High_Childbirth_Mortality_Rate_of_African_American_Women
                  –_The_Project_Censored_Show⠀⇛


          o § Security⠀➾


                # ⚓ CISA ☛ Microsoft_Releases_January_2023_Security_Updates_|
                  CISA⠀⇛


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


                # ⚓ USCERT ☛ CISA_Adds_Two_Known_Exploited_Vulnerabilities_to
                  Catalog [Ed: This is 100% about Microsoft and Windows, but
                  the title does not say this]⠀⇛


                       CISA has added two new vulnerabilities to its Known
                       Exploited Vulnerabilities Catalog, based on
                       evidence of active exploitation. These types of
                       vulnerabilities are frequent attack vectors for
                       malicious cyber actors and pose significant risks
                       to the federal enterprise. Note: To view the newly
                       added vulnerabilities in the catalog, click on the
                       arrow in the “Date Added to Catalog” column, which
                       will sort by descending dates.


                # ⚓ Bleeping Computer ☛ Microsoft:_Kubernetes_clusters_hacked
                  in_malware_campaign_via_PostgreSQL [Ed: Microsoft and its
                  media "assets" are tying to change the subject and blame
                  "Linux" etc. for risk, never mind if Microsoft puts back
                  doors in things and isn't patching actively-exploited
                  flaws]⠀⇛


                # ⚓ CISA ☛ Adobe_Releases_Security_Updates_for_Multiple
                  Products_|_CISA⠀⇛


                       An attacker could exploit some of these
                       vulnerabilities to take control of an affected
                       system.


                # ⚓ CISA ☛ CISA_Releases_Two_Industrial_Control_Systems
                  Advisories_|_CISA⠀⇛


                       CISA released two Industrial Control Systems (ICS)
                       advisories on January 10, 2023. These advisories
                       provide timely information about current security
                       issues, vulnerabilities, and exploits surrounding
                       ICS.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Site36 ☛ „AI_Act“:_German_government_in_favour_of
                        facial_recognition,_but_against_lie_detectors⠀⇛


                             A proposed EU regulation provides for rules
                             against profiling that are worldwide unique.
                             Now it is up to the EU Parliament to save
                             essential points from deletion.


          o § Defence/Aggression⠀➾


                # ⚓ Common Dreams ☛ 1,500_Bolsonaro_Backers_Detained_After_Far-
                  Right_Coup_Attempt_in_Brazil⠀⇛


                       Brazilian Justice Minister Flávio Dino said Monday
                       that “about 1,500″ people have been arrested since
                       supporters of Brazil’s far-right former President
                       Jair Bolsonaro attacked government buildings in
                       Brasília the previous day.


                # ⚓ Common Dreams ☛ ‘Bolsonaro_Must_Not_Be_Given_Refuge_in
                  Florida,’_Say_US_Lawmakers⠀⇛


                       Prominent U.S. lawmakers said Sunday that Jair
                       Bolsonaro should not be given safe harbor in
                       Florida after his supporters—animated by the far-
                       right former president’s election lies—launched a
                       massive attack on Brazil’s main government
                       buildings, an assault that came a week after
                       leftist President Luiz Inácio Lula da Silva was
                       inaugurated.


                # ⚓ Common Dreams ☛ Watchdog_Says_Social_Media_Giants_‘Directly
                  Aided’_Fascist_Insurrection_in_Brazil⠀⇛


                       The fascist attack on Brazil’s main government
                       complex was “directly aided” by major social media
                       platforms such as Facebook, TikTok, and Telegram,
                       the global watchdog group SumOfUs said Monday as
                       the country’s authorities continued their cleanup
                       efforts, investigation, and arrests of suspects
                       involved in the anti-democratic assault.


                # ⚓ Common Dreams ☛ ‘Horrid’:_Steve_Bannon_Rebuked_for
                  Celebrating_Brazilian_Fascists_as_‘Freedom_Fighters’⠀⇛


                       “Freedom fighters” is what Steve Bannon, the far-
                       right propagandist and former top aide to Donald
                       Trump, called the supporters of Jair Bolsonaro in
                       Brazil who on Sunday launched a violent assault on
                       the nation’s government offices in the capital of
                       Brasilia.


                # ⚓ Common Dreams ☛ Brazil’s_Fascist_Right_Attack_Lula’s_Pro-
                  Worker,_Pro-Democracy_Agenda⠀⇛


                       Far-right election deniers cut short the
                       celebration of Brazilian President Luiz Inácio Lula
                       da Silva’s remarkable political comeback with
                       violent attacks in the country’s capital yesterday.
                       Echoing the assault on the U.S. Capitol two years
                       ago, supporters of defeated ex-President Jair
                       Bolsonaro stormed the Brazilian Congress, Supreme
                       Court, and presidential palace.


                # ⚓ TruthOut ☛ Bolsonaro_Backers_Storm_Government_Buildings_in
                  January_6-Style_Attempted_Coup⠀⇛


                # ⚓ TruthOut ☛ Cruel_and_Not_at_All_Unusual⠀⇛


                # ⚓ Meduza ☛ Armenia_refuses_to_hold_CSTO_exercises_on_its
                  territory_—_Meduza⠀⇛


                       Armenian authorities have notified the Collective
                       Security Treaty Organization (CSTO) that Yerevan
                       considers holding the organization’s exercises in
                       the country to be inappropriate. Interfax reported
                       this news, citing Armenian Prime Minister Nikol
                       Pashinyan.


                # ⚓ Meduza ☛ Officials_in_Samara_region_refuse_to_publish_list
                  of_killed_and_injured_in_Makiivka_attack_—_Meduza⠀⇛


                       Alexey Vdovin, military commissar of the Samara
                       region, announced that the government would not be
                       publishing the list of those who were killed and
                       injured in the New Year’s attack in Makiivka.


                # ⚓ Common Dreams ☛ We’re_Exceptional!_And_It’s_Horrible_to
                  Witness⠀⇛


                       Let me start with a confession: I no longer read
                       all the way through newspaper stories about the war
                       in Ukraine. After years of writing about war and
                       torture, I’ve reached my limit. These days, I just
                       can’t pore through the details of the ongoing
                       nightmare there. It’s shameful, but I don’t want to
                       know the names of the dead or examine images caught
                       by brave photographers of half-exploded buildings,
                       exposing details — a shoe, a chair, a doll, some
                       half-destroyed possessions — of lives lost, while I
                       remain safe and warm in San Francisco.
                       Increasingly, I find that I just can’t bear it.


                # ⚓ Meduza ☛ Plane_crash_in_Russia’s_Nenets_Autonomous_Okrug
                  reportedly_kills_two_—_Meduza⠀⇛


                       A plane carrying ten passengers and two crew
                       members crashed in Russia’s Nenets Autonomous Okrug
                       on Monday. First responders reported that the
                       incident was a result of icy conditions.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ UN_Report_Shows_Ozone_Layer_Recovery_Effort
                  ‘Sets_a_Precedent_for_Climate_Action’⠀⇛


                       An assessment released Monday by leading science
                       agencies highlights the effectiveness of an
                       international treaty intended to protect the
                       stratospheric ozone layer as well as the power of
                       taking action now to limit global heating driven by
                       human activity.


                # § Energy/Transportation⠀➾


                      # ⚓ Hackaday ☛ The_Intricacies_Of_Creating_Fuel_For
                        Nuclear_Reactors⠀⇛


                             All nuclear fission power reactors run on
                             fuel containing uranium and other isotopes,
                             but fueling a nuclear reactor is a lot more
                             complicated than driving up to them with a
                             dump truck filled with uranium ore and
                             filling ‘er up. Although nuclear fission is
                             simple enough that it can occur without human
                             intervention as happened for example at the
                             Oklo natural fission reactors, within a
                             commercial reactor the goal is to create a
                             nuclear chain reaction that targets a high
                             burn-up (fission rate), with an as constant
                             as possible release of energy.


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ Alliance_for_the_Wild_Rockies_and
                        Native_Ecosystem_Council_Sue_Forest_Service_to_Stop
                        Cabinet-Yaak_Grizzly_Bear_Habitat_Destruction⠀⇛


                             There’s no other way to put it, the Cabinet-
                             Yaak grizzly population is going downhill
                             fast – which is the opposite of the agency’s
                             legal mandate to recover, not extinguish,
                             endangered species.  In 2018 the U.S. Fish &
                             Wildlife Service counted 54 grizzlies in its
                             monitoring report.  In 2019 only 50, down to
                             45 in 2020 and the 2021 estimate is only 42
                             bears. That’s a stunning crash of nearly one-
                             quarter of the population in only four years!


                             Given the precipitous population loss – and
                             the increasing threat of irreversible
                             inbreeding – the Alliance and Native
                             Ecosystems Council felt we had no choice but
                             to file a lawsuit on January 6th to overturn
                             the Kootenai National Forest’s approval of
                             the massive Black Ram logging and road-
                             building project.


          o § Finance⠀➾


                # ⚓ TruthOut ☛ “The_Rent_Is_Too_High”:_Warren,_Bowman_Ask_Biden
                  to_Fight_Crushing_Housing_Costs⠀⇛


                # ⚓ Common Dreams ☛ Bowman,_Warren_Push_Biden_to_Protect
                  Renters_From_Corporate_Price_Gouging⠀⇛


                       A pair of progressives in Congress on Monday led
                       four dozen other lawmakers in calling on U.S.
                       President Joe Biden “to pursue all possible
                       strategies to end corporate price gouging in the
                       real estate sector and ensure that renters and
                       people experiencing homelessness across this
                       country are stably housed this winter.”


                # ⚓ Pro Publica ☛ How_Congress_Ended_“Syndicated_Conservation
                  Easement”_Tax_Scams⠀⇛


                       After six years of failed efforts by the IRS,
                       Justice Department and lawmakers, new legislation
                       is expected to prevent the worst abuses of a tax-
                       avoidance scheme that has cost the U.S. Treasury
                       billions of dollars. Tucked into the massive, $1.7
                       trillion government spending bill signed into law
                       by President Joe Biden on Dec. 29, a provision in
                       the law seems poised to accomplish what thousands
                       of audits, threats of hefty penalties and criminal
                       prosecutions could not: shutting down a booming
                       business in “syndicated conservation easements,”
                       which exploit a charitable tax break that Congress
                       established to preserve open land.


                       Under standard conservation easements, landowners
                       give up development rights for their acreage, often
                       an appealing, bucolic space. In return, they
                       receive a charitable deduction equal to the
                       property’s development value, and the public
                       benefits by the preservation of the land, which in
                       some cases is made available as a park.


                # ⚓ Common Dreams ☛ When_Big_Pharma_Spends_More_on_Stock
                  Buybacks_Than_R&D⠀⇛


                       The 14 largest publicly-traded pharmaceutical
                       companies spent $747 billion on stock buybacks and
                       dividends from 2012 through 2021 — substantially
                       more than the $660 billion they spent on research
                       and development. So argue economists William
                       Lazonick, professor emeritus of economics at the
                       University of Massachusetts, and Öner Tulum, a
                       researcher at Brown University, in a new paper.


                # ⚓ Counter Punch ☛ Contrary_to_the_NYT,_the_Problem_in_An
                  Aging_Society_is_Income_Distribution⠀⇛


                       The New York Times had a major article reporting on
                       how many people in South Korea, Hong Kong, and
                       Japan are being forced to work well into their
                       seventies because they lack sufficient income to
                       retire. The piece presents this as a problem of
                       aging societies, which will soon hit the United
                       States and other rich countries with declining
                       birth rates and limited immigration.


                       While the plight of the older workers discussed in
                       the article is a real problem, the cause is not the
                       aging of the population. The reason these people
                       don’t have adequate income to retire is a political
                       decision about the distribution of income.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Common Dreams ☛ Progressives_Call_Out_House_Republicans,
                  Whose_First_Bill_Adds_Over_$100_Billion_to_Deficit⠀⇛


                       Progressive U.S. lawmakers on Monday took House
                       Republicans to task after the Congressional Budget
                       Office said the erstwhile deficit hawks’ first bill
                       before the 118th Congress—a measure critics say is
                       meant to “protect wealthy and corporate tax
                       cheats”—will swell the federal deficit by more than
                       $100 billion.


                # ⚓ Common Dreams ☛ Congressional_Union_Vows_to_Fight_‘Anti-
                  Worker_Attack’_by_House_GOP⠀⇛


                       After House Republicans passed a rules package that
                       contains union-busting language aimed at preventing
                       Capitol Hill staff from exercising their right to
                       organize and collectively bargain for better wages
                       and conditions, the Congressional Workers Union
                       pledged Monday to keep fighting for more workplace
                       democracy.


                # ⚓ Telex (Hungary) ☛ 29_teachers_in_Szentgotthárd_school_begin
                  practicing_indefinite_civil_disobedience⠀⇛


                # ⚓ Techdirt ☛ Kevin_McCarthy’s_First_Order_Of_Business:_Waste
                  A_Ton_Of_Time_Misleading_The_Public_Over_The_Bogus_Twitter
                  Files⠀⇛


                       It took a week of nonsense, in which we got to see
                       just how dysfunctional this session of the House of
                       Representatives will be, but late last week, Kevin
                       McCarthy sold just enough of what was remaining of
                       his soul to get the Speaker of the House gavel.
                       And, apparently, part of the many favors he doled
                       out to convince the nonsense peddlers who were
                       demanding “concessions” was to create a panel to
                       investigate the incredibly misleading
                       nothingburgers of the Twitter Files.


                # ⚓ TruthOut ☛ What_Did_McCarthy_Promise_GOP_Extremists_in
                  Backroom_Deals?⠀⇛


                # ⚓ Common Dreams ☛ ‘What_Did_McCarthy_Promise?’_Concerns
                  Raised_Over_Backroom_Deals_With_GOP_Extremists⠀⇛


                       Rep. Kevin McCarthy finally seized the House
                       speaker’s gavel in the early hours of Saturday
                       morning, capping off a chaotic week of voting and
                       heated floor confrontations that were nationally
                       televised and closely documented by reporters
                       stationed at the U.S. Capitol.


                # ⚓ Democracy Now ☛ At_Summit_in_Mexico,_AMLO_Urges_Biden_to
                  End_U.S._“Disdain”_for_Latin_America⠀⇛


                       We go to Mexico City for an update on the North
                       American Leaders’ Summit, where the presidents of
                       Mexico, the United States and Canada are discussing
                       migration, the economy, trade and security. The
                       summit comes just days after Biden announced that
                       the United States will start to block migrants from
                       Haiti, Nicaragua, Venezuela and Cuba from applying
                       for asylum at the U.S.-Mexico border. We speak with
                       Elías Camhaji, Mexican journalist and reporter with
                       the Spanish newspaper El País, and Erika Guevara-
                       Rosas, human rights lawyer and Americas director
                       for Amnesty International.


                # ⚓ TruthOut ☛ George_Santos_Hit_With_Campaign_Finance
                  Complaint_2_Days_After_Being_Sworn_In⠀⇛


                # ⚓ Common Dreams ☛ GOP_Congressman_Santos_Hit_With_Four
                  Campaign_Finance_and_Ethics_Complaints⠀⇛


                       Serial liar and Republican U.S. Congressman George
                       Santos was the subject of four complaints filed
                       Monday by advocacy groups alleging campaign finance
                       and ethics violations, including an alleged scheme
                       to hide the true and unknown source of over
                       $700,000 in campaign funds.


                # ⚓ TruthOut ☛ Lauren_Boebert_Says_Republicans_Will_Push_for
                  Term_Limits_in_Congress⠀⇛


                # ⚓ TruthOut ☛ Biden’s_Expansion_of_Title_42_Takes_Us_Further
                  From_Humane_Border_Policy⠀⇛


                # ⚓ Counter Punch ☛ Title_42,_“Safe”_Third_Countries_and
                  Bipartisan_Hypocrisy⠀⇛


                       President Biden recently announced changes to US
                       immigration rules that will effectively embed two
                       Trump-era policies, one of which the Supreme
                       Court’s conservative majority has temporarily
                       refused to halt: Title 42. It is a measure
                       ostensibly intended to curtail the spread of COVID-
                       19 by expelling or refusing entry to migrants from
                       Central America. The other is the so-called “safe
                       third country” policy, which requires migrants to
                       apply for asylum in a country through which they
                       transit on their way to the southern border. They
                       must show that the request was denied before
                       attempting to make an asylum claim in the United
                       States.


                       Employing these measures displays the hypocrisy of
                       both major political parties when it comes to
                       asylum seekers and refugees. Also, defending these
                       indefensible rules is often done with the aid of
                       lies and misinformation.


                # ⚓ Meduza ☛ Putin_introduces_bill_on_denouncing_Criminal_Law
                  Convention_on_Corruption,_leaving_GRECO_—_Meduza⠀⇛


                       Russian President Vladimir Putin has introduced a
                       bill on denouncing the Criminal Law Convention on
                       Corruption and terminating Russia’s membership in
                       the Group of States Against Corruption (GRECO), the
                       Council of Europe’s anti-corruption body.


                # ⚓ Common Dreams ☛ In_‘Act_of_Fascism_and_Supremacy,’_Israel
                  Bans_Palestinian_Flags_in_Public_Spaces⠀⇛


                       After protests in which tens of thousands of
                       Israelis marched “together against fascism and
                       apartheid,” Israel’s far-right security minister on
                       Sunday ordered police to tear down Palestinian
                       flags wherever they are found in public.


                # ⚓ Common Dreams ☛ GOP,_Right-Wingers_Filed_Nearly_100_Anti-
                  Voter_Lawsuits_in_2022:_Report⠀⇛


                       The Republican Party, GOP candidates and voters,
                       and aligned groups filed 93 anti-voter lawsuits in
                       2022, and although most were unsuccessful, the
                       trend underscores how right-wing attacks on ballot
                       access and election administration are taking place
                       in courtrooms as well as state legislatures
                       nationwide.


                # ⚓ TruthOut ☛ Georgia_Grand_Jury_Completes_Final_Report_on
                  Trump’s_Efforts_to_Overturn_Election⠀⇛


                # ⚓ Meduza ☛ United_Russia_uses_‘AI_and_special_algorithms’_to
                  purge_war_critics_from_party_database_—_Meduza⠀⇛


                       Russia’s ruling political party, United Russia, has
                       conducted a “thorough purge” of its database of
                       supporters in advance of the upcoming election
                       cycle, removing anybody who doesn’t support the war
                       against Ukraine, Vedomosti reported on Monday.


                # ⚓ Meduza ☛ Journalist_Eva_Merkacheva:_Putin’s_secret_decree
                  pardoned_convicts_prior_to_their_joining_Wagner_Group_—
                  Meduza⠀⇛


                       Russian journalist and member of the Presidential
                       Human Rights Council Eva Merkacheva has told RIA
                       Novosti that convicts recruited by the Wagner Group
                       for the war in Ukraine had been pardoned prior to
                       leaving the penal colony — not six months later, as
                       stated by the military company’s founder Evgeny
                       Prigozhin. Citing Merkacheva, RIA Novosti reports
                       that their pardon was legalized by a classified
                       decree signed by President Vladimir Putin.


                # ⚓ Counter Punch ☛ Is_the_US_Headed_for_a_Breakdown⠀⇛


                       The governing structures of the United States seem
                       to be on the verge of some sort of national nervous
                       breakdown. The symptoms are in our face.


                       The inability of the House Republican majority to
                       elect a speaker, in its 13th round of voting as of
                       this writing, is the latest, most visible sign. A
                       group of hardcore, ideologically committed right-
                       wing representatives has frustrated the bid of
                       Kevin McCarthy to succeed Nancy Pelosi as House
                       speaker. Whatever the outcome, they will extract
                       concessions that will make it difficult to govern
                       the body, and run the federal government as a
                       whole.


                # ⚓ Counter Punch ☛ On_the_Chopping_Block⠀⇛


                       Those who value Montana’s Constitution are
                       concerned—terrified, actually—of what the
                       Legislature’s supermajority (and its new Freedom
                       Caucus) are going to try to do to it this session.


                       Here’s how it can happen:  Article XIV of our
                       Constitution sets forth how it can be revised…


                # ⚓ Meduza ☛ ‘No_one_here_tells_you_how_to_live’:_The_anti-war
                  Russians_who_have_made_Latin_America_their_new_home_—
                  Meduza⠀⇛


                # ⚓ Counter Punch ☛ The_Political_Hubris_of_Long-Term_Plans⠀⇛


                       Few sights are more absurd or unreal than political
                       leaders announcing their long-term plans for
                       radical changes benefitting millions or their
                       intention to reform giant institutions in a year or
                       two. Grandiose pledges to create a better world
                       trip off the tongue and they pretend to have a
                       degree of control over events that they must know
                       they do not possess.


                       I always liked the caustic remark of French Prime
                       Minister Georges Clemenceau when told in 1918 about
                       President Woodrow Wilson’s Fourteen Points for
                       ending the First World War and for establishing a
                       lasting peace. “Why does he need 14 points?” asked
                       Clemenceau derisively. “Even the Good God only had
                       10.”


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


                # ⚓ Meduza ☛ TV_Rain_receives_broadcast_license_in_the
                  Netherlands_—_Meduza⠀⇛


                       The Dutch authorities have issued a TV broadcast
                       license to the independent Russian news outlet TV
                       Rain, which had its Latvian license revoked in
                       December.


                # ⚓ Meduza ☛ ‘A_retaliatory_media_operation’_Not_even_Russian
                  pro-war_Telegram_channels_believe_Moscow’s_claims_about_its
                  attack_on_Kramatorsk_—_Meduza⠀⇛


                       Early on January 8, hours after Moscow’s Orthodox
                       Christmas “ceasefire” ended, the Russian military
                       launched seven missile strikes on the city of
                       Kramatorsk in Ukraine’s Donetsk region, damaging at
                       least two buildings. Russia’s Defense Ministry
                       announced afterwards that the attack had been a
                       “retaliatory operation” in response to Ukraine’s
                       deadly New Year’s Day strike on a Russian barracks
                       in Makiivka. Moscow says it killed more than 600
                       Ukrainian soldiers in the Kramatorsk strike, but
                       Ukrainian officials and international journalists
                       on the ground have been unable to find evidence of
                       even a single casualty. The evidence they’ve
                       provided to the contrary has led several of the
                       invasion’s loudest cheerleaders on Telegram to
                       criticize Russia’s own military leadership.


          o § Civil Rights/Policing⠀➾


                # ⚓ Techdirt ☛ Appeals_Court_Hands_Immunity_To_TSA_Agents_Who
                  Forced_Man_To_Delete_His_Recording_Of_Them⠀⇛


                       Yeah, this is not great. This is yet more case law
                       basically saying don’t bother suing federal agents
                       because, unless they’ve very specifically done the
                       same thing other federal agents have been held
                       accountable for, they’re just going to walk away
                       from lawsuits.


                # ⚓ Meduza ☛ Moscow_police_charge_publisher_with_violating
                  ‘LGBT_propaganda’_ban,_marking_first_case_under_new
                  legislation_—_Meduza⠀⇛


                       Moscow police have filed misdemeanor charges
                       against Popcorn Books, a publishing company whose
                       novels address “uncomfortable” topics such as
                       “self-identification, racism, and sexism,”
                       according to its own website. The company stands
                       accused of violating the authorities’ newest anti-
                       LGBT law, which bans materials that promote “non-
                       traditional” relationships among people of any age.


                # ⚓ Democracy Now ☛ “Never_Forget_Our_People_Were_Always_Free”:
                  Civil_Rights_Leader_Ben_Jealous_on_His_New_Memoir⠀⇛


                       We speak with civil rights leader Ben Jealous about
                       his new memoir, “Never Forget Our People Were
                       Always Free,” which examines his long career as an
                       activist and organizer, and growing up the son of a
                       white father and a Black mother. He discusses the
                       lessons he drew from his mother, Ann Todd Jealous,
                       and his grandmother, Mamie Todd, about the racism
                       they experienced in their lifetimes. Jealous has
                       led the NAACP and the progressive advocacy group
                       People for the American Way, and is set to be the
                       next executive director of the Sierra Club.


                # ⚓ Democracy Now ☛ Rosewood_Massacre:_Families_Mark_100_Years
                  Since_White_Mob_Razed_Black_Town_&_Killed_Black_Residents⠀⇛


                       As ceremonies mark the 100th anniversary of when a
                       white mob attacked and burned down the Black town
                       of Rosewood, Florida, we look at the largely untold
                       story of how a racist mob murdered at least six
                       Black residents and forced the rest of the town to
                       flee. Many eyewitnesses said the true death toll
                       was far higher. The bloodshed began after a white
                       woman accused a Black man of assault, resulting in
                       several days of violence by the white mob that
                       ultimately destroyed the once-thriving community.
                       We speak with Jonathan Barry-Blocker, whose late
                       grandfather, Reverend Ernest Blocker, was a
                       survivor of the 1923 massacre.


                # ⚓ TruthOut ☛ 7,000_New_York_Nurses_Go_on_Strike,_Decrying
                  “Unimaginable”_Working_Conditions⠀⇛


                # ⚓ Common Dreams ☛ As_7,000+_Nurses_Strike_in_NYC,_‘Greedy
                  Hospitals’_Told_to_Approve_Fair_Deal⠀⇛


                       More than 7,000 unionized nurses at two of New York
                       City’s largest hospitals began a strike on Monday
                       morning “for fair contracts that improve patient
                       care.”


                # ⚓ Techdirt ☛ AI_Lawyer_Will_Represent_Client_In_Traffic
                  Court,_Threatening_Nonexistent_Market_For_Traffic_Court
                  Lawyers⠀⇛


                       It’s the rise of the lawbots, something not even
                       foretold by Futurama, which allowed a “simple
                       hyper-chicken from a backwoods asteroid” to perform
                       much of the series’ criminal justice work.


                # ⚓ Common Dreams ☛ Italy_Must_Revoke_New_Decree_That
                  Facilitates_Death_of_Migrants_at_Sea⠀⇛


                       The latest migration decree by Italy’s government
                       represents a new low in its strategy of smearing
                       and criminalizing nongovernmental organizations
                       saving lives at sea. The government’s goal is to
                       further obstruct the life-saving work of
                       humanitarian groups, meaning that as few people as
                       possible will be rescued in the central
                       Mediterranean.


                # ⚓ Site36 ☛ Two_men_died_in_custody_in_Braunschweig_and
                  Berlin,_police_investigate_the_cause⠀⇛


                       Both were not found to have been subjected to
                       violence, the police said. For the 38-year-old man
                       who died in Lower Saxony, an anonymous posting on
                       Instagram states otherwise.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Amateur_Radio_Log_2023-01-10_Mid-day_(Fairbanks,_AK,_US)⠀⇛


                       During the lunch break (12:00 AKST) I was able to
                       spend some time at the beginning of Yak road on
                       Chena Ridge doing mobile radio. Radio was an ICOM
                       IC-746PRO with a 3-foot 20-meter mag-mount antenna
                       attached to the top of my SUV. I had tuned the
                       antenna for 14.250 Mhz.


          o § Technical⠀➾


                # ⚓ Wholesomedonut’s_Gemlog:_–_RISC-V_and_Toki_Pona⠀⇛


                       I’m taking a course on RISC-V.


                       It’s the LFD-110X course as offered by the Linux
                       Foundation, and hosted by edX.


                       You can get in on it too for free by taking the
                       Audit track of the course. You don’t get a
                       certification (though you do have an option to
                       upgrade to getting one later and paying for the
                       exam like everyone who did it originally); and you
                       still get access to all the non-graded course
                       content.


                # ⚓ 4:3_isn’t_bad⠀⇛


                       I’ve used 4:3 for about one week. It isn’t bad at
                       all, I can see why many people enjoy this aspect
                       ratio, in the future if I get a monitor I’ll
                       probably try to get a 4:3 one. It’s comfortable,
                       and cozy.


                       Although, on my laptop it looks good, on my desktop
                       monitor it looks blurry because of the sheer size
                       of the screen itself, which is not that pleasant. I
                       still find I enjoy it like that, although 16:9 is
                       better in some tasks, or just in having crisp text
                       in my case.


                # ⚓ New_Year,_New_Blog⠀⇛


                       I started blogging around this time two years ago
                       and one of the things I’ve found is that having
                       just a little pressure to have something
                       interesting to share can be a good motivator in
                       getting things done. With my final semester of
                       school just now starting and wanting to finish
                       strong, one of the things I’ve been thinking about
                       stepping up is my blogging efforts. This is just an
                       experiment and I’ll start to back off if it gets to
                       be too much, but I’m hopeful that setting goals to
                       share more will be a good motivator.


                # ⚓ Winamp_2023⠀⇛


                       I was browsing the snap store and came across
                       Foobar2000, a music player that quite closely
                       resembles the old, original Winamp. Being an old
                       nerd, I was curious and decided to install the
                       snap; however, the installer is currently stuck at
                       around 24%, which I attribute to the installation
                       of Wine. Regardless of that, I was reminded that
                       every (six months, year, two years?) I inevitably
                       look to the winamp.com website. For YEARS they
                       promised goodness and great things to come, that
                       the company was working hard on bringing it back…so
                       I stuck with it and went back to the website every
                       now and then. I didn’t sign up for the mailing list
                       simply because I just didn’t want to get more spam.


                # § Science⠀➾


                      # ⚓ Embracing_Degrowth⠀⇛


                             I’m utterly exhausted – I haven’t been
                             sleeping well, work has been kicking my butt,
                             and I’ve been preparing to go to a con in a
                             few days, but I wanted to write this as a
                             precis of a more detailed post to come.


                             I’ve historically viewed capitalism, while
                             flawed, as a basically reformable system.
                             That has increasingly become impossible for
                             me. In particular, the excesses of consumer
                             culture, both inside my industry and outside
                             of it, are horrifying. The incentive
                             structure of capitalism rewards mass
                             ecological destruction, labor exploitation,
                             and waste on an astounding scale. These
                             factors are intimately linked with racism,
                             sexism, and other forms of structural
                             oppression. I have increasingly realized that
                             while those problems are easiest for me to
                             see in my own industry, they are ubiquitous
                             to the capitalist system.


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


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