𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, May 21, 2023
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Generated Mon 22 May 02:44:35 BST 2023
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2023/05/21/


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

⦿ British Police Refuses to Tackle Fraud That Took Place 100% Inside Britain (Sirius ’Open Source’) | Techrights

⦿ IRC Proceedings: Saturday, May 20, 2023 | Techrights

⦿ [Meme] The Sirius ’Open Source’ Revolutionary Tax: Quietly Stealing Money From People’s Salaries Under the Guise of ‘Pension’ (That Doesn’t Exist) | Techrights

⦿ When It Comes to Financial Spin-Doctoring, Microsoft is Now Marketers Marketers Marketers Marketers | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2023/05/21/british-police-tolerates-business-crime/#comments
		http://techrights.org/2023/05/21/irc-log-200523/#comments
		http://techrights.org/2023/05/21/sirius-open-source-stealing-money/#comments
		http://techrights.org/2023/05/21/spin-doctoring-demise-msft/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2023/05/21/kde-plasma-6-plans/#comments
		http://techrights.org/2023/05/21/lagrange-1-16/#comments
		http://techrights.org/2023/05/21/wordpress-6-2-2/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 58

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/21/british-police-tolerates-business-crime/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/21/british-police-tolerates-business-crime/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.21.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ British_Police_Refuses_to_Tackle_Fraud_That_Took_Place_100%_Inside_Britain_
(Sirius_‘Open_Source’)⠀✐


Posted in Deception, Fraud, Free/Libre_Software at 3:17 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 48e9263394120bccc9b1a1adaaa76670
Action Fraud Bots
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/action-fraud-does-nothing.webm


Summary: Sirius ‘Open Source’ stole money from its own staff and British police
isn’t doing anything on the matter (despite all the evidence being complete and
unambiguous), so one is left with the impression that British businesses can
basically get away with serious crimes, even against their own workers


TODAY I opened my E-mail client and I was greeted by a message or presented
with a rather familiar message, which at first I thought was sent in error — or
perhaps wrongly dated — because it closely resembled something that I had
already received a month ago. As it turns out, Action Fraud operates a bit like
a “bot”; instead of treating crime reports like reports of a crime (fraud) they
seem to be treating them a bit like statistics and nothing suggests they’ve
even looked into the report. They just waited a month before issuing a template
response, basically telling something that cannot be true, as the video above
explains. The troubling thing is, this signals to anyone in the UK (employers
in particular) that pension fraud or embezzlement is OK because law enforcement
agencies won’t even bother looking into complaints, even when the multiple UK
victims and multiple UK perpetrator are all in the UK (no need to cooperate or
work with entities outside the country).


“This is quite likely a very common modus operandi, basically programmed and
wired into the system.”I was going to phone Monday (after the Friday_call_fell
on_deaf_ears*) but sent on the weekend — both outside working days and outside
working hours — was a seemingly automated message. Despite all evidence
provided, there’s nothing to suggest anyone even looked into it and the message
was almost identical to the first, hence akin to an automated reply, timed for
28 days after the report got filed. This is quite likely a very common modus
operandi, basically programmed and wired into the system. This sort of
gaslighting will shatter faith in the system of justice and accountability
nationwide.


“This sort of gaslighting will shatter faith in the system of justice and
accountability nationwide.”Reporting this or referring this to the ombudsman
might not be practical, but at least we have real proof (as actual victims of a
crime) that the police is failing taxpayers who pay cops’ salaries while
protecting the abusers, who are cheating on their taxes (there's_a_separate
complaint_already_with_HMRC).


This is the message sent to me a month ago, as not merely a complainant but one
victim among several:


     RE: [redacted]


     Dear Mr schestowitz,


     I am sorry to hear you have been a victim of crime. Thank you for
     taking the time to report to Action Fraud. Your report has been sent
     to the National Fraud Intelligence Bureau (NFIB) for review.


     Experts at the NFIB will examine the information you provide. Where
     possible, the information is also matched against other available
     data in order to enrich and corroborate the details of the fraud. An
     assessment will be made as to whether there are viable lines of
     enquiry that would enable a law enforcement body, such as the police
     service, to investigate. The NFIB aim to provide you with an update
     on your report within 28 days.


     Please be assured that by contacting us you are giving the police
     vital information they need to protect you and others. The
     information you have provided may be used to disrupt criminal
     activity and inform prevention advice and campaigns.


     You should keep safe any evidence which you feel may be important. We
     continuously assess the content of individual and linked crime
     reports, if you set up an online account, you can use this to add
     additional information.


     If you have any queries regarding this letter please visit
     www.actionfraud.police.uk/FAQ. If you would like more information on
     how to protect yourself from fraud and cyber crime, please see the
     guidance at www.actionfraud.police.uk/support_for_you.


     We value your feedback, please visit this link and complete the
     survey:
     www.surveymonkey.co.uk/r/CSATREP


     Yours sincerely,


     Head of Action Fraud


     For real-time alerts and prevention advice follow Action Fraud https:
     //www.facebook.com/actionfraud/”actionfraud” or https://twitter.com/
     actionfrauduk “actionfrauduk”


Compare this text to what they sent hours ago (weekend outside working hours;
probably 100% automated):


     RE: [redacted]


     Dear Mr schestowitz,


     I am sorry to hear you have been a victim of crime. Thank you for
     taking the time to report to Action Fraud. Your report has been sent
     to the National Fraud Intelligence Bureau (NFIB) for review.


     Experts at the NFIB examine the information you provide. Where
     possible, the information is also matched against other available
     data in order to enrich and corroborate the details of the fraud. The
     NFIB assess whether there are viable lines of enquiry that would
     enable a law enforcement body, such as the police service, to
     investigate.


     On this occasion, based on the information currently available, it
     has not been possible to identify a line of enquiry which a law
     enforcement organisation in the United Kingdom could pursue.


     Registered users of our service have the opportunity to update their
     report, so if you have additional information about your crime which
     you believe could change the assessment, please log in to your
     account and submit that information. We continuously assess the
     content of individual and linked crime reports; in the event that a
     line of enquiry is identified we will provide you with an update.


     Please be assured that by contacting us you are giving the police
     vital information that they need to protect you and others. The
     information you have provided may be used to disrupt criminal
     activity and inform prevention advice and campaigns.


     If you have any queries regarding this letter please visit
     www.actionfraud.police.uk/FAQ. If you would like more information on
     how to protect yourself from fraud and cyber crime, please see the
     guidance at www.actionfraud.police.uk/support_for_you.


     Thank you for taking the time to report and helping us to make the UK
     a safer place.


     We value your feedback, please visit this link and complete the
     survey:
     www.surveymonkey.co.uk/r/CSAT28D


     Yours sincerely,


     Head of NFIB


Notice how many of the paragraphs are identical (the first and second messages
are similar). Is this the best a “civilised” police force has to offer**? This
kind of failure by the police seems_to_have_become_common_knowledge_by_now and
even_the_police_chief_in_London_(the_Met)_became_outspoken_about_it_earlier
this_month.


Some people might (at this point, in light of such experience) just go like,
“what’s the point reporting it to the police? What’s even the point?? What are
they gonna do about it???”


“To sum up, in the above case Action Fraud does nothing, does not even indicate
it looked into the report. No phonecall, nothing in the post, not even any
follow-up questions in the interim.”This is the hallmark of failing systems,
including justice systems designed to selectively enforce the law for the few
who hoard lobbyists, lawyers, and even politicians. Cops serve and protect
them.


To sum up, in the above case Action Fraud does nothing, does not even indicate
it looked into the report. No phonecall, nothing in the post, not even any
follow-up questions in the interim. Kafka would have had a short novel about
this kind of scenario. █
_______
* When I say that the Friday call fell on deaf ears I mean to say that nobody
even heard me at all. I was on the line for about 12 minutes and paid for a
call. I never got through the menu system to ever reach an actual human.


** An anonymous friend agreed with this assessment and further commented: “The
two automated messages indicate that 1) they are not doing anything and 2) it
probably hasn’t even reached someone’s desk yet.”



                    ䷩ 𝚕𝚒𝚗𝚎 285

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/21/irc-log-200523/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/21/irc-log-200523/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.21.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Saturday,_May_20,_2023⠀✐


Posted in IRC_Logs at 2:02 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-200523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-200523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-200523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-200523.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


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                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmXJbVjMgJLV5E7dFhoZEBSRNCRpMoAYeiQ2x94WwVCAE3



                    ䷩ 𝚕𝚒𝚗𝚎 412

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/21/sirius-open-source-stealing-money/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/21/sirius-open-source-stealing-money/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.21.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Sirius_‘Open_Source’_Revolutionary_Tax:_Quietly_Stealing_Money
From_People’s_Salaries_Under_the_Guise_of_‘Pension’_(That_Doesn’t_Exist)⠀✐


Posted in Finance, Fraud, Free/Libre_Software at 4:09 am by Dr. Roy Schestowitz


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sirius:_Little_salary_you_got_there,_I'll_just_steal_a
                                portion_of_it⦈_


Summary: The crimes of Sirius_‘Open_Source’ remain without punishment, albeit
we have plans to escalate up to three more levels to ensure justice is done (or
to expose a system inherently tolerant of large-scale fraud)


⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠐⠚⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣥⣴⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣧⣼⣷⣴⣾⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⣿⠛⠛⠿⠟⠀⣾⣿⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠏⠉⠹⡃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⢀⣻⡿⣿⣿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠆⠙⠙⠻⢯⢆⠀⠀⠉⠁⠀⠀⠀⠀⠀⣰⣮⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣤⣌⡓⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣴⡆⠀⢀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢹⣿⡗⠈⠻⣿⣿⣿⠏⠀⠠⡄⠀⠀⠀⠀⢠⢋⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣆⠀⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣾⣿⣿⣿⠗⠛⠛⠻⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣶⣶⠶⣤⠤⢤⠴⠶⠶⠶⠶⢶⠾⣿⠿⠿⢿⣿⡿⠿⣤⡴⠶⢶⡾⢿⣿⠿⠶⣶⠦⠤⢴⠶⢴⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣿⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⡟⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⡿⢤⣿⣶⣶⣶⣾⡷⠶⠿⠷⣶⣿⡶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⡶⠷⠶⠶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣷⢾⠳⣶⢶⣶⣿⣿⠃⠀⠀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⡀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠐⠚⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡴⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣷⣼⣦⣾⣷⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡗⡾⠹⠡⠻⠛⠀⣾⣿⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠏⠉⠹⡃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⢀⣻⠿⣿⣿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠆⠙⠘⠻⢯⡆⠀⠀⠉⠃⠀⠀⠀⠀⠀⣠⣮⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣤⣌⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣴⡆⠀⢀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢹⣿⡗⠈⠻⣿⣿⣿⠏⠀⠠⡄⠀⠀⠀⠀⠠⢋⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣆⠀⣿⣿⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⢁⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣾⣿⣿⣿⠗⠛⠛⠻⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣶⣶⠷⣤⠤⢤⠴⠶⠶⠶⠶⢶⠾⣿⠿⠿⢿⣿⡿⠿⣤⡴⠶⢶⡾⢿⣿⠿⠾⣶⠦⠤⢴⠶⢼⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⠿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣿⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⡟⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⡿⢤⣿⣶⣶⣶⣾⡷⠶⠿⠷⣶⣿⡶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⡶⠷⠶⠶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣷⢾⠳⣶⢾⣶⣿⣿⠃⠀⠀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣽⣷⣄⡀⠚⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡯⣯⠈⠒⠙⠟⠀⣸⣿⣷⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⠙⢏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⣸⣿⣿⣿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠙⠎⠻⢿⡧⡌⠀⠈⠉⠀⠀⠀⠀⠀⣠⣴⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⣬⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣴⡗⠀⢀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣄⠀⠀⢹⣿⡟⠈⠹⢿⣿⡿⠟⠀⠀⡄⠀⠀⠀⠀⠀⠊⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⣾⣿⣿⠷⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠠⠁⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡗⠋⠙⠛⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣶⣶⠶⣦⠤⢤⠴⠶⠶⠶⠶⢶⠼⣿⠿⠿⢿⣿⡿⠿⣤⡴⠶⢶⡾⢿⣿⠿⠿⣶⠶⠤⢴⠶⢴⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⡟⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⣿⣀⣿⣶⣶⣶⣾⣷⡶⠿⢷⣶⣿⡶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⠷⠶⠶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⡱⢾⢿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠙⠛⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⠻⠟⠃⣸⣿⣷⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠏⠀⠈⢏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠞⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠀⠀⣸⣿⣿⣿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠙⡏⢹⢯⣧⡌⠀⠀⠉⠀⠀⠀⠀⢀⠀⣼⣸⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣥⣶⣤⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⣴⣟⠀⢀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣆⠀⠀⢸⣿⡟⠈⠘⠿⣿⠿⠟⠀⠀⡄⠀⠀⠀⠀⠀⠘⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⣸⣿⣿⠿⠀⠀⠀⠠⠁⠀⠀⠁⠀⠀⠠⠒⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⡟⠋⠙⠛⠗⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣿⣿⠶⣶⠶⢶⠶⠶⠶⠶⠶⢶⠶⣿⠿⠿⢿⣿⡿⠿⣦⡴⠶⢶⡿⢿⣿⠿⠿⣶⠶⠦⢤⠿⢦⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⡿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⣿⣓⣿⣶⣶⣶⣾⣷⣶⠿⢷⣶⣿⡶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⠷⠶⠶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣼⢾⡿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡉⠙⠙⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⡟⠛⠙⠛⠂⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠋⠀⠈⢫⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠖⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣨⣿⣿⣿⡿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠷⠉⡃⢙⢟⣿⡌⠀⠀⠈⠁⠀⠀⠀⠀⠀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣶⣶⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢰⣟⠀⢀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣦⠀⠀⢸⣿⡟⠈⠘⠿⠿⠿⠟⠀⠀⡄⠀⠀⠀⠀⠀⡰⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⢸⣿⣿⠿⠀⠀⠂⠠⠀⠀⠀⠁⠀⠀⠠⠒⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣶⣿⣿⣿⣿⡟⠉⠉⠛⠗⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣿⣿⠷⣶⠶⢶⠶⠶⠶⠶⠶⢶⠶⣿⠿⠿⢿⣿⡿⠿⣦⡴⠶⢶⡿⢿⣿⠿⠿⣶⠶⠦⢤⠿⢦⠾⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⣿⣓⣿⣶⣶⣶⣾⣷⣶⠿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⡷⠶⠶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣷⣾⢶⡿⣿⣿⣿⠇⠀⠀⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⣠⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣉⠙⠙⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⡿⠇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠛⠙⠛⠃⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠫⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⣨⣿⣿⣿⡿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠷⠈⠻⢛⣻⣿⡾⠅⠀⠈⠁⠀⠀⠀⠀⠀⣠⣇⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⣶⣶⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢰⣾⡀⢀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣦⡀⠀⢈⣿⡟⠙⠈⠻⠿⠿⢿⠀⢀⡄⠀⠀⠀⠀⠀⣰⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣄⢸⣿⣿⠿⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠰⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⡟⠉⠉⠛⠛⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⠿⣷⠶⢶⠶⠶⠶⠶⠶⢶⠶⣽⠿⠿⢿⣿⡿⠿⣧⡴⠶⢾⡿⢿⣿⠿⠿⣷⠶⠦⢤⠿⢦⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⠿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⡾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⡶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣷⡿⢿⣿⣿⠇⠀⠀⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣈⡉⠋⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣗⣄⣤⣠⣠⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠟⠛⠋⢠⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠹⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣿⣿⣿⣟⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠷⠈⢻⠙⣻⣿⡶⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⣾⣾⣶⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢰⣾⣁⢀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⡀⠀⢀⣿⣿⣁⠈⠻⠿⠿⢟⠀⢠⡄⠀⠀⠀⠀⠀⣠⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣆⢸⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⡟⠉⠉⠙⠛⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⢐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⠿⣿⠶⢶⠶⠶⠶⠶⠶⢶⠦⣽⠿⠿⢿⣿⡿⠧⣦⡴⠶⢾⡿⢿⣿⠿⠿⣷⠶⠦⢴⠿⢶⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⠿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⢷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⢓⠀⠀⠀⠀⢠⣤⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣉⠁⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣟⣦⣠⣤⣠⣸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠿⣿⣿⣿⠏⣾⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡻⣿⠿⠓⠛⠚⠋⢠⡿⢿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢠⣿⣿⣿⣿⠻⣿⠿⣿⣿⠇⠀⠀⠀⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⢻⠉⢝⣾⡶⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⣶⣾⣷⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢰⣾⣁⣀⠄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣄⠀⢀⣿⣿⣁⠀⠛⠿⠿⠿⠀⠰⠆⠀⠀⠀⡀⠀⣤⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣦⣸⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣾⣿⣿⣿⣿⡟⠁⠈⠙⢛⣐⣤⣄⣀⡀⠀⠀⠀⠀⠀⣂⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⠿⣿⠷⢶⠶⠶⠶⠶⠶⢶⠦⣤⠽⠿⢿⣿⡿⠥⣦⡴⠶⢾⡿⢿⣿⠿⠿⣿⠶⠦⢴⠿⢶⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⠿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣷⣿⢿⠿⣿⣿⠇⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⢉⠀⠀⠀⠀⠠⣤⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⣄⣉⣁⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⣶⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡿⠏⣾⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⠟⠓⠃⠙⠋⢠⡿⠿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⢠⣿⣿⣿⣿⢛⣿⠿⢿⡿⠃⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⢙⣀⠝⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⣷⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣿⣁⡀⠔⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣆⠀⠀⣿⣿⣁⡀⠙⠛⠛⠛⠀⠘⠂⠀⠀⢀⠄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣧⣸⣿⣿⣛⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢫⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⡟⠁⠀⠈⣋⣱⣤⣤⣄⡀⠀⠀⠀⠀⢀⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣾⣿⠿⣿⠿⢶⠶⠶⠶⠶⠶⢶⠦⣤⠭⠿⢭⣿⡿⠤⣦⡴⠶⢿⡿⢿⣿⠿⠿⣿⠷⠦⢴⠾⢾⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⠿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣷⢾⡿⠿⢿⣿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣯⣠⡄⠀⠀⠀⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠻⠟⠋⠉⠉⠁⢰⠟⠛⢿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠰⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠲⣼⣿⣿⣿⡉⠿⠻⠿⠏⠀⠀⠀⠀⠀⢨⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣨⠀⡎⡿⡟⠁⠠⠀⠀⠀⠀⠀⠀⠀⣴⣣⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠘⣿⣤⡤⠊⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⢰⢃⣄⣈⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡀⠀⣿⣿⣤⡀⠈⠙⠛⠩⠀⠈⠀⠀⠀⠔⠂⣰⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣷⣼⢿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣥⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⡿⠟⠀⠀⢈⣩⣬⣶⣦⣤⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⠿⣿⠿⢷⠴⠶⠶⠶⠶⢶⠦⣤⠤⠤⢤⣿⡯⠴⣧⡶⠿⢿⡿⢿⣿⠿⠿⣿⠷⠶⢶⠾⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⡾⡷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢶⢷⠿⢿⣿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣯⣴⡄⠀⠀⠀⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠛⠉⠁⠀⠁⢰⠟⠛⢿⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢰⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⠰⣽⣿⣿⣿⡉⠿⠟⠻⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡨⣄⣊⡻⠿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⠀⠀⠠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⣿⣤⡄⠊⣿⣿⣿⣿⠇⣤⠀⠀⠀⠀⠀⠀⡼⢁⣄⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣷⡄⠀⣿⣿⣤⡄⠈⠉⠉⠉⠀⠀⠀⠀⠀⠊⢀⣴⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡴⠿⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢵⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠛⠀⢀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⢰⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⠿⣿⠿⢷⠶⠶⠶⠶⠶⢶⠦⣤⠤⠤⢤⣹⡥⠴⣦⡾⠿⢿⡿⢿⣿⠿⠿⣿⠷⠶⢶⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⠰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⡾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠾⠻⣿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣇⣀⣀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠙⠁⠁⠀⠀⠀⠟⠉⠻⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡔⣻⡿⢿⣿⣇⡛⠉⠉⠀⠀⠀⠀⠀⠠⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣆⣯⣘⠻⠈⠀⠀⠀⠀⠀⠀⢄⣴⡧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⠄⠀⠀⣽⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⢻⣶⡶⠇⢻⣿⣿⣿⠿⡆⠀⠀⠀⣀⠀⢠⠇⢀⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⣿⣿⣶⡆⠀⠈⠁⠀⠀⠀⠀⠀⠐⢀⣴⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⣿⣿⣿⡷⠛⠻⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣒⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⣿⣿⠟⢻⠀⣀⣠⣴⣶⣶⣶⣶⣦⣄⠀⠤⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣾⣿⠷⣾⠿⢿⠶⠶⠶⠶⠶⢶⠦⣤⠤⠤⢤⣨⡥⠶⣷⡿⠿⢿⡿⢿⣿⠿⠿⣿⠿⠶⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⢷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠙⢿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣷⣀⡀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠛⠉⠀⠀⠀⢀⠟⠉⠹⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⡌⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⡔⢻⡿⢿⣿⣇⡟⠙⠁⠀⠀⠀⠀⠀⢡⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣢⣭⣽⡛⠀⠀⠀⠀⠀⠀⠀⣴⡾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣴⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⢻⣶⡶⠇⠻⣿⣿⣿⠿⠄⠀⠀⠀⠄⢀⣼⠁⢠⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⠀⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⡷⠛⠛⠻⠗⠀⠀⠀⠀⠀⠀⠀⠐⣪⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⠟⠻⠀⣠⣠⣴⣶⣿⣿⣶⣶⣄⠀⠤⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣾⣿⠷⣾⠿⢿⠷⠶⠶⠶⠶⢶⠦⣤⠤⠤⢤⣠⡥⠶⣷⡿⠿⢿⡿⢿⣽⠿⠿⣿⠿⠷⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠻⠃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⢿⡿⠿⠿⠿⠃⣼⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠋⠀⠀⠀⠀⢠⠏⠀⠙⢏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠼⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⢸⣿⣿⣿⠿⣿⣿⠃⠀⠀⠀⠀⠐⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠌⠻⡟⣻⣿⣧⡭⠀⠀⠀⠀⠀⠀⠈⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣥⣿⣮⡛⠈⠀⠀⠀⠀⠀⢴⡿⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢰⣟⠀⠀⡰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡼⠀⢀⣀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣄⠀⠀⣻⣿⠟⠂⠹⢿⣿⠿⠏⠀⠀⠀⡰⠀⣴⠃⠀⢰⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢻⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣶⣿⣿⣿⣿⠟⠉⠉⠉⠉⢀⡀⠀⠀⠀⠀⠀⣨⡴⢋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⡿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⡿⠛⠩⢀⣤⣤⣶⣿⣿⣿⣿⣷⣦⡠⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⠿⣿⠿⢿⠷⠶⠶⠶⠶⢶⠦⣤⠤⠤⢤⣤⡶⠾⣿⡿⠿⢿⡿⢧⣼⠽⠾⣿⠿⠿⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠈⠙⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⠿⠓⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠋⠀⠈⢫⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⠀⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠘⣿⣿⣿⡿⣿⣿⠁⠀⠀⠀⠀⠘⢶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⠙⡛⢛⣿⣷⡌⠁⠀⠀⠀⠀⠀⣡⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣶⣶⣍⠀⠀⠀⠀⠀⠈⢰⡿⠓⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣀⠀⡈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡾⠀⠀⣀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣦⠀⠀⣸⣿⡟⠃⠘⠿⠿⠿⢟⠀⠀⠀⡐⠂⣾⠁⣀⢰⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣷⡄⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⡟⠁⠀⠈⠉⣀⣀⡀⠀⠀⠁⠀⣨⡞⢋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢨⣿⣿⠛⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⡿⠛⢁⢀⣤⣶⣾⣿⣿⣿⢿⣿⣦⡀⣒⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣾⣿⠿⣿⠿⢿⠿⠶⠶⠶⠶⢶⠦⣤⠤⠤⢤⣤⡶⠾⣿⡿⠿⢿⡿⢧⣤⠵⠶⣾⠿⠿⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡄⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⠀⠉⠃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⠏⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠟⠛⠛⢰⡿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠞⠀⠀⠹⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠳⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢦⠰⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⢀⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⢉⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠉⠻⠉⣟⣿⡖⠀⠀⠀⠀⠀⠀⣠⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢻⣶⣶⣶⣮⡀⠀⠀⠀⠀⠀⣿⠟⠑⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣿⣀⣀⡄⢻⣻⣿⣿⣿⠀⠀⠀⠀⡀⢠⡏⠀⠀⢀⡄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣧⡀⠀⢸⣿⣏⣁⠈⠛⠿⠿⠳⠀⠀⠀⠘⢁⣾⠀⣀⣰⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣄⣸⣿⣿⣿⡄⠀⠀⠀⠀⠄⠀⢀⠤⣻⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⣭⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⡟⠁⠀⠀⢀⣀⣀⣀⡀⠘⠀⡀⢠⣾⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣿⣿⣟⣿⣿⣦⠀⠈⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠋⣀⢃⣴⣶⣾⣿⣿⣿⠿⣿⣷⣞⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣾⣿⠿⣿⠿⢿⠿⠷⠶⠶⠶⢶⠦⣤⠤⠤⢤⣤⡶⠾⣿⡿⠿⢿⡿⢷⣤⠵⠶⣦⠿⠿⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⡶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⠄⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠛⠙⠋⢡⡿⠿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠘⠀⠀⠙⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⠿⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢦⠸⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⢹⣿⣿⣿⢻⠟⠀⠀⠀⠀⠀⣉⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢈⢻⠩⡟⢿⠖⠀⠀⠀⠀⠀⢀⣨⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣛⣷⣶⣷⣦⡄⠀⠀⠀⠀⠀⣿⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⣤⣀⡄⠻⣻⣿⣿⣫⠀⠀⠀⠀⡀⢰⡏⠀⠀⢤⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣷⣄⠀⢸⣿⣏⣁⠀⠙⠻⠛⠛⠀⠀⠀⠐⢡⣿⠀⣤⣠⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣦⣸⠿⠿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠔⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠉⢹⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⣿⣿⣿⣿⡟⠁⠀⠀⣀⣠⣤⣄⣀⠘⠀⡂⠰⣞⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣏⣽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠋⣠⣃⣴⣶⣿⣿⠿⣿⠿⢿⣿⣾⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⠿⣾⠿⢿⠿⠷⠶⠶⠶⢶⠶⣤⠤⠤⢤⣶⡶⠮⣭⡭⠿⢿⡿⢧⣤⠶⠶⣤⠿⠿⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⢿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣈⣄⢰⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠿⠛⠋⠉⠁⡾⠿⢿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠐⠁⠀⠈⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢵⡰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⣸⣿⣿⣿⡟⠟⠀⠀⠀⠀⠀⢄⡷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⡩⡃⠹⣹⡏⠀⠀⠀⠀⠀⣀⣴⣇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣈⣷⣿⣿⣷⡆⠀⠀⠀⠀⠀⣾⠋⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠻⣧⣤⣔⠙⣿⣿⣿⣯⠀⠀⠀⠀⡤⢰⠏⠀⠀⠤⣤⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣤⠀⢰⣿⣯⣤⡀⠈⠛⠛⠋⠁⠀⠀⠀⢠⡿⢀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣷⡼⠟⠿⣿⠅⠀⠀⠀⠀⡐⠂⠀⢘⡽⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⢠⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡿⠟⠀⠀⢀⣠⣤⣤⣤⣤⣀⠁⣴⠀⣛⣢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢃⣴⣧⣶⣿⣿⡿⠿⢿⠟⠿⢿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⠿⣤⠿⢿⠾⠿⠶⠶⠶⢶⠶⣤⠤⠤⢴⣲⡾⠷⣤⡤⠾⢿⡿⢦⣤⠶⠶⣦⠾⠿⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⠿⠶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⠿⠛⠉⠉⠁⡾⠛⢻⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠈⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠛⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡱⣐⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣘⣿⣿⣿⡏⠟⠀⠀⠀⠀⠀⠄⣭⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⣄⠃⣸⢹⡟⠀⠀⠀⠀⠀⣀⣴⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⢬⣽⣿⣿⣿⠆⠀⠀⠀⠀⠀⣿⠋⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⣷⣤⣴⠈⢯⣿⣿⣿⡀⠀⠀⠀⡞⢰⠏⠀⠀⢀⣶⡈⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡀⢰⣿⣿⣤⣄⠈⠉⠉⠉⠀⠀⠀⠀⣰⣿⢀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⡼⠛⠻⣿⠁⠀⠀⠀⠀⡨⠁⠀⢈⠽⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⢐⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⣿⣿⠟⡛⠀⡀⢀⣠⣤⣶⣶⣤⣄⡀⡼⠄⣹⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⡿⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠡⣶⣶⢿⣿⣿⡿⠟⠻⠟⠛⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⠿⣤⠿⢿⠶⠿⠶⠶⠶⢶⠶⣦⠤⠤⢤⣹⡿⠿⣤⡤⠾⢿⡿⢦⣤⠴⠶⣤⠴⠿⢿⠿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣾⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⠿⠶⠶⢶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣞⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠛⠉⠉⠁⢸⠛⠙⢿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠉⠛⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠰⢯⢺⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣤⣿⣿⣿⣿⡙⠁⠀⠀⠀⠀⠐⢼⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣨⣠⣓⡿⠀⠀⠀⠀⠀⢠⣴⡿⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣴⠀⠀⢠⣼⣿⣿⣿⡟⠀⠀⠀⢀⡀⣸⡏⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⣿⣶⣶⠄⠸⣿⣿⣿⡓⠀⠀⠀⠘⣁⡟⠀⡀⢐⣲⣆⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣷⡄⠀⣿⣿⣶⣶⠀⠈⠉⠉⠁⣀⠀⢀⡴⣿⢇⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⡟⠛⢻⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡦⠛⠻⢷⠀⠀⠀⠀⠀⢰⠂⡀⢀⣼⡃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⣽⣿⡿⢿⣷⣆⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⠿⠟⠁⠀⢀⣤⣶⣶⣶⣶⣦⣄⡰⠇⣨⣮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣿⡿⢻⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣄⣀⠀⣴⣿⠿⠋⠙⠛⠉⠛⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⠿⣧⠾⢿⠿⠿⠷⠶⠶⢶⠶⣦⠤⠤⢤⣤⡾⠿⣿⡿⠾⢿⡿⢦⣤⠶⠶⣶⠶⠾⢿⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣼⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⠿⠶⠶⣶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢻⠟⠁⠀⠀⢠⠟⠉⠻⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢥⡌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢠⡼⠿⢿⣿⡟⠁⠀⠀⠀⠀⠀⣰⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⣔⣀⣭⣿⠅⠀⠀⠀⠀⠀⣴⡾⢦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠆⠀⢀⢶⣿⣿⣿⡿⠀⠀⠀⢀⡀⢨⡏⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⢹⣷⡶⠇⠈⢿⣿⣿⡟⠂⠀⠀⠘⢁⡞⠀⣀⠀⣰⣦⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⢾⣿⣿⣶⠆⠀⠀⠀⠀⠤⡀⢀⠴⣿⢧⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⡍⠙⢛⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⠚⠙⢷⠀⠀⠀⠀⠀⢠⠇⡄⢠⣼⡛⢨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⢰⣿⣿⣻⣿⣷⡐⠀⠂⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⡿⠃⠀⢀⣤⣶⣾⣿⣷⣶⣤⡠⠗⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⠛⣿⣿⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡄⠀⠀⣴⣿⡿⠟⠉⠛⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⠿⣧⠴⢿⠿⠾⠷⠶⠶⢶⠶⣦⠦⠤⢤⣠⡾⠿⣶⡶⠶⢿⡿⢦⣤⠴⠶⣦⠶⠾⢿⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⣰⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⠿⠶⠶⣶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⡾⠉⠉⢿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⢂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠩⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣪⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠶⣿⢿⣿⣷⠁⠀⠀⠀⠀⠀⠲⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣳⣯⣬⡛⠀⠀⠀⠀⠐⣴⣿⠷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⡆⣿⣿⣿⣿⠁⠀⠀⠀⡤⢀⡿⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⢹⣿⡟⠇⠀⠹⣿⣿⣯⠁⠀⠀⠠⢡⣾⠃⢀⡀⣨⣾⣄⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⠀⢸⣿⡿⢿⠷⠀⠀⠀⠀⠦⠄⠀⠼⣻⣿⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⡾⠈⠉⣥⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⠞⠻⣧⠀⠀⠀⠀⠀⠀⠁⠤⠠⣾⡿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⢠⣿⣿⣟⣿⣿⣎⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣤⣶⣿⣿⣿⣿⣶⣄⠀⢚⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⠏⣹⣿⡟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡹⠁⠀⢰⣿⡿⠛⠉⠙⠉⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣾⠿⣿⠶⢿⠿⠾⠿⠶⠶⢶⠶⣦⠤⠤⢤⣠⡶⠶⣶⡶⠶⢿⡿⢧⣤⠴⠶⣤⠶⠶⢿⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⢠⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⠿⠶⠶⢶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠻⠋⠀⠀⠀⡸⠁⠈⠻⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⢮⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠶⢿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡻⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣡⣾⣽⡛⠀⠀⠀⠀⠀⣶⣿⠷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠃⠀⡈⠆⣿⣿⣿⣿⠁⠀⠀⠀⡤⢀⡾⠃⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⣟⠗⠀⠸⢿⣿⣧⠁⠀⠀⠀⣡⣼⡇⢀⡀⢨⣿⣥⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⠀⢸⣿⡿⠿⠷⠀⠀⠀⠀⠒⠄⠠⠞⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⠾⠂⠀⢹⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣷⠞⠹⣧⠀⠀⠀⠀⠀⠀⠀⠦⠰⣶⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠗⠀⠀⢀⣿⣿⣯⣿⣿⣧⡀⠈⠀⠀⠀⠀⢾⣶⣿⣿⣿⣿⣿⠋⠀⢀⣴⣾⣿⣿⣿⣧⣶⣄⡀⢘⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⠏⢸⣿⡏⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠻⠁⠀⢰⣿⡿⠛⠁⠈⠉⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣾⠿⣿⠶⢿⠿⠾⠿⠶⠶⢶⠶⣦⠤⠤⢤⣠⡴⠶⣶⡶⠶⢾⡿⢧⣤⠴⠶⣦⠶⠶⢿⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⢠⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣿⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⡿⠶⠶⢶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠿⠿⠏⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠋⠀⠀⠀⠸⠃⠀⠙⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢰⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢘⢷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⣦⡚⢿⠿⣿⣿⠂⠀⠀⠀⠀⠀⡀⣻⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣴⣯⡽⠀⠀⠀⠀⠈⢳⣿⠿⢄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⢀⠘⠀⢿⢿⣿⡿⡇⠀⠀⠀⡾⠀⣾⠃⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣟⡃⠀⠈⠿⣿⢿⠀⠀⠀⢀⣰⣾⡇⠀⡀⢠⣽⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢷⣤⠀⢸⣿⡿⠿⠿⠀⠀⠀⠀⡍⠂⠐⢋⣩⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠃⠀⢰⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣶⠞⠻⣧⠀⢀⣀⣀⣀⣰⠇⠐⠐⣿⡿⢟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠀⠀⢀⣾⣿⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⣦⣤⣶⣿⣿⣿⣿⠏⠀⢀⣴⣾⣿⣿⡿⢉⣼⡦⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⡏⢰⣿⡿⣸⡇⠀⠀⠀⠀⠀⠈⠛⠛⢿⡿⠛⠋⠀⢠⣿⣿⠋⠁⠀⠁⠀⠈⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣾⠿⣿⠶⢿⠿⠿⠿⠶⠶⢶⠶⣦⠤⠤⢤⣠⡴⠶⣶⡶⠶⢾⡿⢷⣤⠴⠶⣦⠶⠶⢾⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⢠⣿⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣾⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⠶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠿⠿⠟⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠋⠁⠀⠀⢠⠋⠀⠘⢯⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠠⣘⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⢒⣝⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢦⣜⢻⠿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣻⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣿⣿⠁⠀⠀⠀⠈⢳⣿⠿⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⢀⠸⠁⢸⣿⣿⣿⠇⠀⠀⠀⠜⠀⣾⠇⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠻⠿⠿⢀⠀⠀⢀⣵⣿⡏⠀⣠⢀⣽⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣷⣄⠀⢸⣿⡟⠿⠿⠃⠀⠀⠀⡎⠁⠀⢉⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠋⠀⠀⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⡞⠻⣧⠀⢀⣀⣀⣀⣰⡇⠘⣈⣿⡿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠁⠀⠀⣼⣿⣿⣾⣿⣿⣦⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⡟⠀⢀⣴⣾⣿⣿⣿⠟⣽⡶⣴⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⣼⣿⡟⢀⣿⡿⢸⡟⠀⠀⠀⠀⠈⠙⠛⠟⢿⡿⠟⠏⠀⢀⣾⣿⠏⠁⠀⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⠿⣿⠷⢾⠿⠿⠿⠶⠶⢶⠶⣦⠤⠦⢤⣠⡴⠶⣶⡶⠶⢾⡿⢷⣤⠴⠶⣶⠶⠶⢾⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⢀⣾⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣾⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⡶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡿⠟⠿⢱⡿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠋⠁⠀⠀⠀⡞⠀⠀⠹⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⢿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⣎⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠐⢻⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣮⣙⡿⢻⣿⡇⠀⠀⠀⠀⠀⠈⣾⠗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣷⡷⠁⠀⠀⣠⠀⢳⣿⠿⠢⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⢀⠿⠇⠘⣿⣿⣯⠃⠀⠀⠀⠊⡀⣾⠃⠀⠀⠀⢉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣂⢀⡀⠙⠿⠿⡤⣀⠀⣠⢾⡿⡧⠀⣤⣄⣼⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣈⣻⡻⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣆⡀⠀⣿⣿⠛⠛⠛⠋⠂⠀⠀⢲⢀⠀⣤⣾⢇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠀⠀⣺⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄⠿⣿⡇⠀⢀⣀⣀⣀⣀⡎⣠⣤⡿⠣⢝⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠁⠀⠀⣰⣿⡿⢷⣿⣿⣷⡀⠀⠀⠀⢠⣀⣀⣴⣿⣿⣿⣿⠏⠀⠈⣥⣾⣿⠿⣿⡿⠛⣿⣿⣉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⣰⣿⣿⠁⣼⣿⢃⡿⠀⠀⠀⠀⠘⠿⠿⠿⣿⡿⠿⠋⠀⠀⣼⣿⠏⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣼⠿⣿⠷⢾⠿⠿⠿⠷⠶⢶⠶⣦⠤⠤⢤⣠⡯⠴⣶⡶⠶⢶⡿⢿⣤⠶⠶⣦⠴⠶⢶⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⣼⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣼⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⡶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡿⠟⠿⢣⣿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⠋⠀⠀⠀⡞⠀⠀⠙⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠳⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⡎⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⣻⡝⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡙⡿⢻⣿⡏⠀⠀⠀⠀⠀⢈⣾⠗⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⣿⣿⣿⡾⠁⠀⠀⣤⠀⢳⣷⠿⠢⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠐⢾⠇⠈⣿⣿⣏⠁⠀⠀⠀⢇⡀⣾⠃⠀⠀⠀⢉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣷⣀⢀⡀⠘⠿⠿⠦⠄⢀⠼⢿⡿⡇⠀⢤⣄⣼⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣹⡟⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⢀⣿⡟⠛⠛⠛⠋⠃⠀⠀⢰⢤⠠⣴⣿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠁⠀⣺⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⣸⢿⣿⠀⠀⢀⣀⣀⣀⣀⡼⣰⣶⡿⠣⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⢰⣿⣿⢷⣿⣿⣿⡄⠀⠀⠀⢀⠀⣀⣴⣾⣿⣿⣿⠃⠈⠛⣠⣾⣿⡿⢿⡿⠟⣻⣿⣋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⣠⣿⣿⠃⣼⣿⢇⡿⠁⠀⠀⠀⠛⢿⣿⣿⣿⡿⠿⠃⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣴⠿⣿⠿⢾⠿⠿⠿⠿⠶⢶⠶⣦⠤⠤⢤⣨⡯⠶⣶⡶⠶⢶⡿⢿⣤⠶⠶⣶⠶⠶⢶⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⡿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⣸⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣷⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⣰⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⡶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡿⠿⠛⠋⣾⠿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠀⠀⠀⠸⠁⠀⠈⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠻⠿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⢠⡹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠚⡪⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⣻⠻⣿⡯⠀⠀⠀⢀⡀⢈⣼⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣻⣿⣶⠖⠀⠐⢐⡆⠀⢩⣿⡿⠲⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣽⣿⡟⠀⢻⣿⡇⠀⠀⠀⢐⣤⣄⣾⠏⠀⠀⠀⣈⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣤⣴⣴⣬⣀⣀⠈⠻⠿⠖⠂⠐⠋⣹⡿⢿⣄⢠⣤⣠⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣀⣈⣛⠻⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠚⠀⠁⠰⠶⠰⣷⣿⠧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠁⠀⢸⣿⣿⢷⣶⣤⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⡄⠀⣿⣏⠀⠀⠀⢂⣀⣠⣤⣀⣀⠂⣼⡿⠹⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠋⠀⠀⢠⣿⣿⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⡞⠛⣿⡄⣠⣾⣿⡿⠿⡿⠛⢁⣾⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⢠⣿⣿⠇⣸⣿⣟⣼⠃⠀⠀⣶⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⣴⠿⣿⠿⢿⠿⠿⠿⠿⠷⢶⠶⣬⠽⠿⢿⣿⡥⠶⣶⡶⠿⢿⡾⢿⣧⠶⠶⣶⠶⠶⢤⡼⢿⠿⢿⡿⢿⠿⢿⡿⢿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⢸⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣷⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⢠⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⠶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⡿⠟⠛⠋⣾⠿⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⠁⠀⠀⠀⠸⠃⠀⠈⢣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⠿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣻⣿⣿⣿⠿⠃⠀⠀⠀⠀⠲⣪⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⢻⢛⣿⡿⠀⠀⠀⢀⡀⢀⣜⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⢀⣻⣿⣾⠖⠀⠀⢰⡇⠀⢹⣿⡿⠓⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡟⠀⢻⣿⣇⠀⠀⠀⢈⣴⣤⣿⠏⠀⠀⠀⣈⡉⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣀⣀⣦⣬⣭⣀⣄⢈⠛⠿⠕⠂⠐⠉⣹⡿⢿⠀⢠⣤⣠⣾⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣠⣈⣛⠛⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⣿⣿⠟⠛⠛⠉⠉⠚⠀⠀⠰⠖⢘⣷⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡋⠁⠀⢠⣿⣿⢿⣶⣤⠀⠀⠀⠀⠀⠀⠘⠛⣷⣄⠀⢸⣿⡏⠀⠀⠀⢂⣀⣤⣤⣀⣀⠆⣸⣿⢻⡌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⢀⣾⣿⠿⣿⣿⢿⣧⠀⠀⠀⠀⢀⣀⣤⣿⣿⣷⠼⢿⣧⡀⣠⣾⣿⡿⠿⠿⠛⢁⣴⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⢀⣾⣿⡏⢠⣿⣟⣼⠇⠀⢰⣦⣶⣿⣿⣿⣿⣿⠟⠀⠀⠉⢱⣿⡿⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⣴⠿⣿⠿⢿⠿⠿⠿⠿⠷⢶⠦⣭⠿⠿⢿⣿⡭⠾⣶⡶⠿⢿⡿⢿⣧⠶⠶⣶⠶⠶⢦⡴⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⢰⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⢠⣿⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⠃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⡿⠶⠶⢶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⡿⠟⠛⠛⣸⠿⠿⣿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠀⠀⠀⠀⠋⠀⠀⠱⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡰⠛⠛⢻⣿⣿⣿⣿⣿⠟⠁⠀⠀⡄⣌⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⣸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠄⢷⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⢩⣏⢽⡿⠂⠀⣀⠀⢀⢄⣌⣿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣦⡀⣩⣿⡷⠋⠀⠀⠠⠏⠀⢸⣾⣿⠗⠦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠘⣿⣷⡀⠀⠀⣠⣾⣦⣾⠏⠀⠀⠀⣀⣉⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⡩⢻⣏⣤⣤⢀⡙⠛⢏⡁⢈⡁⣬⣿⠿⣕⣀⣶⣤⣾⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣤⣽⠙⠛⣓⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠋⢈⠻⠘⠃⠀⠘⠫⠈⣻⣿⠇⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⡟⠉⠀⢀⣿⣿⠿⣿⣶⡀⠀⠀⠀⠀⠀⠚⢿⣦⡀⠀⢸⣿⡏⠀⠀⠀⢘⣃⣤⣤⣤⣤⠇⣸⣿⠯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠀⠀⣼⣿⡟⢿⣿⡿⣿⠀⠀⠀⠀⠀⣀⣼⣿⣿⣦⣼⣿⣧⡄⢠⣾⣿⡿⠿⠿⠛⠁⣾⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⢀⣼⣿⡿⢠⣿⣿⣱⡟⠀⢠⣤⣶⣿⣿⣿⣿⣿⡏⠀⠈⠉⢁⣿⡿⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⣠⠾⣿⠿⢿⠿⠿⠿⠶⠿⢶⠾⣿⠿⠿⢿⣿⡭⠿⣶⡶⠿⢿⡿⢿⣷⠶⠶⣶⠶⠶⢦⡴⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⢠⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⢀⣾⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⠸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣾⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⡿⠶⠶⢶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡿⠟⠛⠛⢱⠿⠿⣿⡟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠁⠀⠀⠀⠋⠀⠀⠘⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠛⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣍⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢄⣸⣿⣿⣿⡟⠋⠀⠀⠀⠀⠈⣵⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢩⣟⣽⡿⠃⠀⣠⠀⢤⣀⣴⣿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⣶⡆⣶⣿⣿⠀⠀⠀⠀⢋⡀⢀⣾⣿⠟⠢⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠃⠘⣿⣿⡤⡀⢀⡴⢾⣷⣾⡟⠁⠀⠀⣀⣈⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢀⣰⣤⣿⣿⣢⣄⣄⡌⠛⣓⣄⢀⣄⣰⣿⠟⣇⡀⣶⣆⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣤⣬⡏⠛⢻⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡁⠀⠀⢈⠙⠒⠓⠀⠀⢙⠀⣼⣿⠇⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⡟⠉⠀⠀⣼⣿⡿⣿⣷⣆⠀⠀⠀⠀⠠⠾⣿⣄⡀⠀⢿⣿⡟⠋⠀⠀⢋⣠⣤⣤⣤⣄⠎⢰⣿⠏⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⣼⣿⡟⢻⣿⡿⣿⡆⠀⠀⠀⠀⢀⣾⣿⣷⣦⠼⣿⣧⣄⢀⣾⣿⡿⠻⠿⠟⠁⢾⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⠀⠀⣼⣿⣿⢀⣾⣿⣡⡟⠀⢀⣀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠩⡁⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⣠⠾⣿⠿⢿⠿⠿⠿⠶⠿⢷⠾⣿⠿⠿⢿⣿⡿⠿⣿⡷⠿⢿⡷⢿⣿⠶⠶⣶⠶⠶⢦⡾⢿⠿⢿⡿⢿⠿⢿⡿⢿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⢠⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⣼⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣼⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⠶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⠟⠛⠛⢱⠿⠻⣿⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠎⠀⠀⠈⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣧⡹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⢀⣼⣿⣿⣿⡟⠋⠀⠀⠀⠀⢀⣹⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⣹⣏⣿⠿⠣⠄⣠⠀⠠⣀⣴⣽⠟⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⡖⢿⣿⣿⠀⠀⠀⠀⢏⡀⠀⣿⡿⠟⠢⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠃⠈⣿⣿⡦⠄⢀⠴⠾⣿⣾⡟⠀⠀⠀⢀⣈⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⣀⣴⣤⣿⣿⣦⣤⣄⡈⠛⣿⣦⠀⣴⣰⣿⠟⣇⣀⣶⣦⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣦⣬⡏⠛⢻⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠀⠀⢨⡝⠡⠃⠀⠀⢙⠀⣼⣿⠧⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⡿⠉⠀⠀⣼⣿⡟⣿⣷⣆⠀⠀⠀⠀⠠⠾⣷⣄⡀⠀⣿⣿⠷⠀⠀⠀⢉⣢⣤⣤⣤⣄⠎⢰⣿⢏⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⣼⣿⡿⢻⣿⡿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣷⣦⠾⣿⣷⣤⢀⣾⣿⡿⠻⠿⠟⠁⠼⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⣸⣿⣿⣁⣾⣿⣧⡟⠀⢀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⣩⣁⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⣠⠾⣿⠿⢷⠿⠿⠿⠶⠾⢷⠾⣿⠿⠿⢿⣿⡿⠿⣿⡿⠿⢿⡷⢿⣿⠶⠶⣶⠶⠶⢶⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠀⢠⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⣼⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣼⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⡶⠶⠶⣶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⠟⠋⠋⢡⡿⠛⢿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠃⠀⠀⠀⠈⠀⠀⠈⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠈⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣰⢼⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⢢⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢰⣳⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣫⣽⣿⡿⠟⠃⠒⢠⡆⠐⡶⣴⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣟⢿⣿⣿⡅⠀⠀⠀⡘⣤⠀⣿⣿⠟⠛⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏⠈⢻⣿⣷⠂⠀⠔⠛⣻⣿⡟⠁⠀⠀⢀⣀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣀⣤⣦⣮⣿⣿⣷⣤⣆⣌⠛⡿⣷⡄⠶⣼⣿⠿⢧⣂⣰⣶⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣤⣤⡍⠙⢛⣧⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠍⠁⠀⠀⢠⡍⠋⠋⠀⠀⢘⡄⣴⣿⠧⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢯⣿⣿⠁⠀⠀⣸⣿⣿⣻⣿⣶⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⣿⣿⡀⠀⠀⠀⢉⣡⣤⣤⣤⣤⠼⢠⣿⠿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠁⠀⠀⣰⣿⡿⢛⣿⣿⢿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣶⠿⠿⣷⣤⢀⣴⣿⡿⠟⠻⠟⠃⠐⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠀⣰⣿⣿⣃⣼⣿⣯⡾⠁⠀⠀⢀⣠⣾⣿⣿⣿⡇⠀⠀⣈⣁⣼⣿⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠁⣠⠾⣿⠿⢿⠿⠿⠿⠷⠾⢷⠶⣷⠿⠿⢿⣿⡿⠿⣿⡿⠿⢿⡿⢾⣿⠶⠶⣦⠶⠶⢮⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠁⢀⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣷⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⣸⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣰⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠋⠉⢣⡿⠛⢿⡿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠈⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠈⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣰⣼⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣢⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢤⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣋⣽⣿⡽⠟⠋⠒⢢⡆⠐⢦⣴⣷⡟⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣏⢿⣿⣿⡇⠀⠀⠀⢘⣤⡀⣸⣿⠟⠋⠳⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⠏⠈⢻⣿⣿⡒⠀⠐⠋⢻⣿⣟⠁⠀⠀⢀⣀⡀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢴⣇⣀⣤⣦⣬⣿⣿⣷⣤⣀⣌⠛⡟⣿⡆⠸⣷⣿⠿⢯⣂⣰⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣤⣤⡭⠙⢛⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠉⠀⠀⠀⢠⡍⠋⠉⠀⠀⠂⡇⣰⣿⡷⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢯⣿⣿⠉⠀⠀⣰⣿⣿⢻⣿⣶⠀⠀⠀⠀⢀⣶⣧⣀⠀⠘⣿⣿⡀⠀⠀⠀⢘⣱⣤⣤⣤⣤⠼⢡⣿⠛⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠃⠀⠀⢠⣿⣿⠛⣿⣿⢿⡇⠀⠀⠀⠀⠀⣿⣿⣷⡶⠿⠿⣷⣤⢀⣴⣿⣿⠟⠻⠟⠋⠀⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠀⣰⣿⣿⣃⣼⣿⣯⣾⠁⠀⠀⠀⣠⣶⣿⣿⣿⡇⠀⠀⣈⣁⣼⣿⠏⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠃⣠⠾⣿⠿⢿⠿⠿⠿⠷⠾⢷⠶⣶⠾⠿⢿⣿⡿⠿⣿⡿⠿⢿⡿⢾⣿⠶⠶⣶⠶⠶⢶⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠁⠀⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣷⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⣸⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⣰⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⢶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠛⠛⠃⡿⠛⢿⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠋⠀⠀⠀⠘⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢹⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢠⣫⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣮⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠐⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣽⣿⡿⡛⠋⠈⠀⡾⠀⠙⣲⣯⣾⠇⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢽⣿⣿⣷⡀⠀⠀⢀⣵⣦⣰⣿⠟⠛⠓⠒⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⠟⠀⢻⣿⣿⣯⡁⠀⠉⢉⣿⣟⠉⠀⠀⢀⣳⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣇⣀⣠⣈⣊⣿⣿⣷⣤⣔⣀⡙⡿⣻⣿⠀⢻⣿⡿⠻⣂⣰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣴⣤⡽⠙⠛⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠁⠀⠀⠈⢀⡍⠋⠋⠀⠀⠀⣼⢠⣿⡿⢒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠏⠁⠀⢠⣿⣿⢻⣿⣶⡀⠀⠀⠀⢀⣴⣦⣀⠀⠸⣿⣇⠀⠀⠀⠀⠘⣙⣤⣤⣤⣤⡐⢃⣾⠯⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⢠⣿⣿⠛⣿⣿⢿⣷⠀⠀⠀⠈⠈⢹⣿⣷⣶⡿⢿⣧⡄⠀⣴⣿⣿⠟⠿⠟⠋⠀⢸⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⢠⣿⣿⣏⣰⣿⣯⣼⠃⠀⠀⠀⢀⣴⣾⣿⣿⡇⠀⢀⣉⣀⢸⣿⡟⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⣠⠶⣿⠿⢿⠾⠿⠿⠷⠶⢷⠶⣶⠶⠿⢿⣿⡿⠿⣿⡿⠿⢿⡿⢾⣿⠷⠶⣶⠶⠶⢶⡾⢿⠿⢿⡿⢿⠿⢿⡿⢿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠃⠀⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣷⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⢰⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⢠⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⠶⠶⠶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠛⠛⠋⡾⠛⢿⣿⠿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠀⠀⠀⠘⠁⠀⠀⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣽⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⢠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠐⣺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣬⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣽⣿⣿⠟⠋⠈⠉⠸⠃⠘⣖⣮⣿⡏⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣥⣶⣠⣿⡿⠋⠙⠒⠚⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣿⣿⣿⡟⠀⢻⣿⣿⣿⡍⠀⢈⢁⣽⣟⠉⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡇⠀⣀⣘⣌⣿⣿⣿⣤⣤⣀⡛⣿⢿⣿⠃⢙⣿⡿⢻⣖⣰⣶⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣰⣤⣽⠉⠛⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠏⠀⠀⠈⢀⣍⠋⠛⠁⠁⠐⣸⠂⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣽⣿⡏⠁⠀⢠⣿⣿⢿⣿⣶⡀⠀⠀⠀⢀⣴⣦⣀⠀⢹⣿⡁⠀⠀⠀⠀⠈⣙⣤⣤⣤⣤⡀⠋⣼⠟⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠀⠀⢀⣾⣿⠟⣿⣿⢿⣿⠀⠀⠀⠈⠈⢹⣿⣷⣾⣿⣿⣄⠀⠀⣴⣿⣿⠟⠿⠟⠛⠀⢰⣵⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⢀⣾⣿⣏⣰⣿⣿⣼⠃⠀⠀⠀⠀⣤⣾⣿⣿⡏⠀⢈⣉⣄⢸⣿⡟⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⣠⠶⣿⠿⢿⠿⠿⠿⠿⠶⢷⠶⣦⠶⠾⢿⣿⡿⠿⣿⡿⠿⢿⡿⢾⣿⠷⠶⣶⠶⠶⢶⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠃⠀⣿⠀⣿⠀⢸⡆⠀⣶⡆⠀⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣷⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⢰⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⢠⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⡶⠶⠶⣾⣿⣶⣶⣾⣶⣿⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠛⠛⠛⡾⠟⢿⣿⠿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠁⠀⠀⠰⠁⠀⠀⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⢹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢰⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⢢⣼⣿⣿⣿⣿⣿⣇⣀⢀⠄⡀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣽⣿⣿⡟⠏⠁⠀⠀⡞⠀⠈⣽⣷⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⣠⢾⣷⣼⣿⠛⠉⠀⡐⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⡟⠀⢻⣿⣿⣿⣷⣄⡀⣠⣠⣿⠏⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⡆⠀⢀⢘⣍⣿⣿⣿⣤⣤⣀⡛⣿⢿⣟⢿⠁⣹⣿⢿⣃⣰⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣄⣰⣤⣽⠙⠛⣃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠇⠁⠀⠈⢉⣭⠛⠟⠃⠑⠐⠄⣾⢠⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣽⣿⡏⠁⠀⢀⣿⣿⠿⣿⣶⡀⠀⠀⠀⠀⣴⣦⡀⠀⢿⡿⠀⠀⠀⠀⠀⠈⣛⣥⣤⣤⣄⡀⠂⢀⡟⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠀⠀⢀⣾⣿⠟⣿⣿⢿⣷⠀⠀⠀⠈⠉⢹⣿⣶⣼⣿⡆⠀⠀⠀⣠⣾⣿⡿⠿⠿⠿⠇⢀⣬⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠁⠀⢀⣾⣿⡟⣠⣿⣿⣼⠃⠀⠀⠀⠀⣠⣾⣿⣿⡏⠻⠷⣠⢄⢰⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⣠⠴⣿⠿⢿⠿⠿⠿⠿⠶⢷⠶⣦⠴⠾⢿⣿⡿⠿⣿⡿⠿⢿⡿⢾⣿⠷⠶⣶⠶⠶⢶⡿⢿⠿⢿⡿⢿⠿⢿⡿⠿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⣿⠿⠿⠿⡿⢿⠿⢿⠿⠿⡿⠿⠿⣿⠿⠿⣿⣿⣿
⠃⠀⣿⠀⣿⠀⢸⡆⠀⣶⡆⠠⣾⠀⣿⠀⠰⢾⣿⠀⠦⣼⡇⠀⢸⡇⢸⣿⠀⡀⢸⠀⠰⠀⣇⠘⢀⣿⣧⠘⢀⡏⠀⡆⢸⠀⠀⠀⣿⡇⠀⣀⣸⠀⠀⠀⣶⠀⢰⣿⣶⠀⢰⡇⠸⠀⢸⠀⠶⡇⠰⠀⣹⠀⠶⣿⣿⣿
⠀⢰⣿⠀⠿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠿⠀⠰⢾⣿⠓⡆⢘⠀⠀⠀⡇⠸⠿⠀⡃⢸⠀⢰⠀⣿⠀⢸⣿⣿⠀⢸⡇⠀⠇⢸⠀⠀⠀⣿⡇⠀⠆⢸⠀⠀⠀⣿⠀⢸⣿⣿⠀⢸⡇⢰⠀⢸⠀⠶⡇⢰⠀⢹⠀⠶⣿⣿⣿
⢀⣿⣿⣶⣶⣶⣾⣷⣶⣿⣷⣶⣿⣶⡶⠶⠶⣾⣿⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣿⣶⣶⣾⣷⣶⣾⣿⣶⣾⣿⣿⣶⣾⣷⣾⣶⣾⣶⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠁⠀⠀⠀⢁⠠⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢿⣿⠿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠲⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢠⡌⠉⠉⠛⠛⠛⠏⠀⠀⡀⠀⠀⠀⢀⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠈⠑⠀⠀⠀⠀⢃⠀⢀⢄⣼⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⠀⡀⠀⠰⠾⢇⡾⠃⠀⠀⠀⠚⠛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⣉⣁⣀⣨⡅⣀⠀⡄⣠⡏⠀⠀⠀⣀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⡆⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠁⠀⣰⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣠⣤⣭⠉⠛⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠟⠀⠀⢰⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣽⣿⠏⠁⠀⢀⣷⣿⠛⣿⣶⡀⠀⠀⠀⠀⣰⣆⡀⠀⢿⡏⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠰⠁⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⡇⠀⠀⠀⣾⣿⠏⣻⣿⢿⣷⠀⠀⠀⠈⠉⢹⣿⣦⣼⣷⠀⠀⠀⠀⣠⣾⣿⠿⠿⠟⠻⠟⢆⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢻⠀⠀⠀⣼⣿⡏⢠⣿⣟⡰⠃⠀⠀⠀⠀⣠⣾⣿⣿⡏⠻⠆⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠇⠀⠀⣼⣿⡟⢀⣿⣿⡷⠄⡠⡀⢠⣤⣾⣿⣿⡿⠛⣷⣶⣾⣿⣿⣜⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⣿⢕⣾⣿⣿⣿⣥⠀⠀⠈⠉⠉⠉⠛⣡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠀⠀⠀⠀⣂⠣⠅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢿⣿⡿⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⢹⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡌⠉⠋⡻⠿⠛⡿⠇⠀⠀⠀⡖⠀⠀⣼⠘⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⣴⡞⠋⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠤⠀⠐⢫⠟⠁⠀⠀⠚⠛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⣉⣹⣋⣨⡇⠀⢀⠀⠄⠰⡿⠀⠀⣀⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⢰⠀⣰⡿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣠⣤⣭⠉⠛⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣽⣿⠏⠁⠀⢀⣿⣿⠛⣿⣶⡀⠀⠀⠀⠀⣴⣄⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⡇⠀⠀⠀⣼⣿⠏⣻⣿⠿⣷⠀⠀⠀⠈⠉⢹⣿⣦⣼⣷⠀⠀⠀⠀⣠⣾⣿⠟⠿⠟⠻⠿⢷⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢻⠀⠀⠀⣼⣿⡏⢠⣿⡟⡰⠃⠀⠀⠀⠀⣠⣾⣿⣿⡟⠿⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠆⠀⠀⣼⣿⡟⢠⣿⣿⡷⠄⡠⡀⢠⣤⣾⣿⣿⡿⠛⣷⣶⣾⣿⣿⣜⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⣿⣧⣿⣿⣿⣿⣥⠀⠀⠀⠉⠉⠉⠋⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣧⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⢿⣿⡿⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠳⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠎⠉⠛⣛⠛⠛⠿⠇⠀⠀⠀⠀⠻⡠⣴⠊⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⣮⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣴⣶⣶⣤⠀⠀⠀⠀⠀⠤⠀⢪⠃⠀⠀⠚⠛⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⢩⣉⣹⣌⣨⠁⠀⠀⡀⠀⠐⣄⡛⠀⣀⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣴⠂⠀⠀⠃⠀⠀⠑⠁⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠘⠄⣼⠟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣠⣤⡭⠉⠓⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⣽⣿⠋⠁⠀⢀⣷⣿⠻⣿⣦⡀⠀⠀⠀⠀⣴⣄⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⠇⠀⠀⢀⣾⣿⠋⣾⣿⢿⡷⠀⠀⠀⠈⠉⢹⣿⣦⣼⡇⠀⠀⠀⠀⣠⣾⣿⠿⠿⠟⠿⠿⣷⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡻⠀⠀⢀⣾⣿⠏⢠⣿⣏⡼⠃⠀⠀⠀⠀⣠⣾⣿⣿⡟⠷⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠃⠀⠀⣼⣿⡟⢠⣿⣿⡷⠀⡂⡀⢤⣤⣾⣿⣿⡿⠛⣷⣶⣾⣿⣿⣜⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⡿⢡⣿⣿⣿⣧⡤⠀⠀⠈⠉⠉⠉⠋⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠟⠛⠋⡿⠿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⠁⠀⠀⠘⠁⠀⠈⢃⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡀⠀⠀⠀⠀⢀⣄⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢈⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⣵⢿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣜⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣃⣿⣾⣿⣿⣿⣿⣿⣯⠉⢠⠀⠀⠀⠊⠑⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠈⠀⢺⠀⠀⠀⠀⢀⡚⢂⡸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⠁⠀⠀⠈⠘⢿⣤⡀⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣶⠀⠀⡈⣫⣻⣿⣿⣿⣿⣶⣜⣿⣿⣿⣿⣠⡀⠀⠴⣧⡆⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣬⡿⠛⠛⣆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠿⠉⠉⠉⠛⢛⡽⡿⣿⢿⣿⣿⣿⠿⣷⣤⣤⣼⣿⣇⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⠋⠁⠀⢨⣿⣿⢿⣷⣦⠀⠀⠀⠀⢀⣤⡀⠀⠸⣿⠃⠀⠁⠂⠀⠀⠻⣿⣴⣧⣵⣯⣽⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⠏⠀⠀⢠⣿⣿⠿⣿⣿⢿⡇⠀⠀⠀⠋⠙⣿⣷⣤⣿⡇⠀⠀⠀⠐⣴⣾⣿⡿⢿⡿⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠀⠀⢠⣿⣿⠇⣸⣿⣏⣾⠃⠀⠀⠀⠀⣤⣿⣿⣿⠟⢷⣀⣠⠆⣸⣿⠟⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢃⡤⢶⠿⠿⢿⡿⠿⣿⣿⠾⢶⠶⡤⠤⣾⠿⣿⠿⠿⠷⣾⣿⠿⢿⠿⠿⠶⠶⠶⢶⠶⠶⡾⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⠁⢸⡇⢸⣴⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⢰⡀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣿⠀⠀⣇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⡇⠀⠆⢰⡆⢠⣾⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠠⢾⣿⠀⣷⡄⢰⣿⣿⣿
⠀⣼⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢠⠛⠢⠈⣿⠀⣿⣿⠛⠢⠈⣿⠀⣿⠀⠰⠇⠀⠀⢹⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⢸⠀⡇⠀⡆⢹⡇⢸⣿⠀⡇⠸⠀⢸⠀⡀⢸⣿⠀⠸⠀⡇⢰⣾⣿⠀⣿⠃⢸⣿⣿⣿
⢠⣿⣷⣾⣿⣶⣶⣷⣶⣾⣷⣶⣾⣶⡶⠞⠳⢶⣾⣿⣶⣿⣿⣷⣶⣾⣿⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠟⠛⠛⢇⡿⠿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠀⠀⠀⠘⠁⠀⠈⢃⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⢀⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢤⡼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣓⣿⣿⣿⣿⣿⣿⣿⣟⠙⢁⠃⠀⠀⠀⠀⠀⠋⠁⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠉⠙⢺⠀⢠⡀⠀⠀⢀⡤⠬⢥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠁⠿⢷⣦⣺⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣶⠀⠀⡘⣯⣻⣿⣿⣿⣿⣴⣜⣿⣿⣿⣿⣶⡆⠀⠼⣧⣖⣰⡌⣩⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣨⡟⠛⢻⣂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⣿⣿⢟⡙⠉⠉⠛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣿⣿⠋⠁⠀⢸⣿⡿⢿⣶⣄⠀⠀⠀⠀⢀⣦⡀⠀⠸⣿⠃⠀⠁⠂⠀⠀⠻⣿⣰⣧⣷⣯⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⠃⠀⠀⢠⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠋⠙⣿⣷⣤⣿⡇⠀⠀⠀⢐⣴⣾⣿⠿⢿⡿⠿⣿⣮⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠀⢠⣿⣿⠃⣼⣿⣇⡾⠁⠀⠀⠀⢀⣤⣿⣿⣿⠛⢷⣀⣰⠀⣾⣿⠟⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢁⡤⢶⠿⠿⢿⡿⠿⣿⣿⠷⢶⠶⡤⠴⡾⠿⣿⠿⠿⠷⣿⣿⠿⣿⠿⠿⠶⠶⠶⢶⠶⠶⡾⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⠁⢸⡇⢸⣴⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⢰⡀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣿⠀⠀⣧⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⡇⠀⠆⢰⡆⢠⣾⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠠⢾⣿⠀⣷⡄⢰⣿⣿⣿
⠀⣼⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢸⠛⠢⠈⣿⠀⣿⣿⠛⠢⠈⣿⠀⣿⠀⠰⠇⠀⠀⠹⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⢸⠀⡇⠀⡆⢹⡇⢸⣿⠀⡇⠸⠀⢸⠀⡀⢸⣿⠀⠸⠀⡇⢰⣾⣿⠀⣿⠇⢸⣿⣿⣿
⣰⣿⣷⣾⣿⣶⣶⣷⣶⣾⣷⣶⣾⣶⡶⠞⠳⢶⣾⣿⣶⣿⣿⣷⣶⣾⣿⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠛⠛⠿⠿⣸⡿⢿⣿⣿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⠓⠀⠀⠀⠀⠋⠀⠀⠫⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠑⠙⠛⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣋⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⢻⠀⠀⠒⠀⠀⠀⠀⠀⢀⣀⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠑⠘⣿⣤⠀⠈⠠⣀⠀⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢉⢿⣿⣿⣿⣿⡏⠀⠀⠀⠸⠋⠀⠀⠀⠺⣿⣿⣿⣾⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⠈⢿⣻⣿⣿⣿⣿⣶⣜⣿⣿⣿⣿⣷⣷⡖⢴⣿⣶⣴⣦⢨⣽⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣄⣘⣟⠻⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣷⠋⠛⠛⠻⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠃⠀⢰⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⣄⠀⠀⢸⣿⠟⠂⠀⠂⠀⠀⠺⠿⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠏⠀⠀⢀⣿⣿⢷⣾⣿⣿⡆⠀⠀⠀⠞⠛⣿⣦⣄⣿⡆⠀⠀⠀⠀⣢⣶⣿⣿⣿⡿⢿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⢀⣾⣿⠇⣸⣿⣏⣼⠃⠀⠀⠀⠀⣀⣿⣿⣿⡟⠷⠀⢀⡀⣸⣿⡿⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⢀⡴⢾⠿⠿⢶⡿⠿⣯⣵⠶⢶⠤⡤⠾⣿⠿⣿⠿⠶⠾⣿⣿⠶⣿⠿⠶⠶⠶⠶⢶⠶⠾⡿⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⠀⣼⡇⢸⣴⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⢰⡀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⣇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⡇⠀⠆⢰⡆⢠⣾⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠠⢾⣿⠀⣷⡄⢰⣿⣿⣿
⣰⣿⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢠⠛⠢⠈⣿⠀⣿⣿⠛⠢⠈⣿⠀⣿⠀⠰⠇⠀⠀⠹⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⢸⠀⡇⠀⡆⢹⡇⢸⣿⠀⡇⠸⠀⢸⠀⡀⢸⣿⠀⠸⠀⡇⢰⣾⣿⠀⣿⠃⢸⣿⣿⣿
⣿⣿⣷⣾⣿⣶⣶⣷⣶⣾⣷⣶⣾⡶⠶⠞⢷⣶⣾⣿⣶⣿⣿⣷⣶⣾⣿⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠛⠛⠻⠿⢣⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠀⠀⠀⠀⠀⠜⠁⠀⠙⢅⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠨⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣸⣿⣿⣿⣿⣿⣿⣽⡋⠉⠙⡻⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠊⠂⢠⣷⣤⠄⠉⠀⠀⢦⣠⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⠉⠀⠀⠀⠟⠁⠀⠀⠰⢾⣶⣾⣿⣿⣿⣦⣄⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⢶⡙⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣾⡦⢠⣿⣵⣶⣶⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢈⡻⠿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣾⠎⠛⠛⠹⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠋⠀⢀⣿⣷⣾⣤⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠸⠿⣖⣾⣥⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⣼⣿⣿⣶⣿⣿⣦⠀⠀⠀⠴⠻⢿⣦⣀⣹⣧⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⡟⢠⣿⡿⣸⡏⠀⠀⠀⠀⢀⣼⣿⣿⡿⢿⡄⠀⡀⢠⣿⣿⠛⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⡾⢿⠿⠷⢿⡿⠿⣿⣤⠴⢤⠤⡴⠿⡿⠿⣿⠷⠶⠿⣾⣷⠾⣿⠷⠶⠶⠶⠶⢶⠶⠿⡿⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⢀⣿⡇⢸⣴⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠠⡀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⡇⠀⠆⢰⡆⢠⣾⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠠⢾⣿⠀⣷⡄⢰⣿⣿⣿
⣿⣿⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢀⠛⠢⠈⣿⠀⣿⣿⠛⠢⠈⣿⠀⣿⠀⠰⠇⠀⠀⠱⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⢸⠀⡇⠀⡆⢹⡇⢸⣿⠀⡇⠸⠀⢸⠀⡀⢸⣿⠀⠸⠀⡇⢰⣾⣿⠀⣿⠃⢸⣿⣿⣿
⣿⣿⣷⣾⣿⣶⣶⣷⣶⣾⣷⣶⡞⠲⠶⠾⣷⣶⣾⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣴⣤⣥⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠛⠛⠙⠛⠃⣾⣿⣷⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠋⠀⠘⠍⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠱⠛⠛⠛⠋⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⣿⣿⣿⣿⣿⣼⡋⠉⠙⠛⣷⠀⠀⠀⠀⠀⠀⣰⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⠛⠓⠴⠐⡀⠀⣰⡴⠆⠀⠰⠿⠷⣩⣿⣿⣿⣿⣷⣤⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡗⠹⣿⣿⣿⣿⣿⠉⠁⠀⠈⠀⠴⠋⠀⠠⢴⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢲⠐⢿⣿⣿⣟⢄⣀⢻⣿⣿⣿⣿⣴⣤⠄⣰⣯⣤⣤⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢿⣧⣤⣴⠄⠡⠚⠛⠿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠈⢩⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠈⠀⠀⠀⠀⠀⣾⣯⠬⣋⣭⣿⣿⣯⣼⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣹⣿⣷⡀⠀⠀⠀⣠⣾⣦⣄⠀⢻⣇⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣯⣝⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⡟⢩⣿⡿⢻⡇⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⣼⣿⡟⠋⠉⠉⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⡿⢶⠾⠿⢷⡿⠤⡄⢀⠤⢤⠶⡿⠿⡿⠷⣾⠷⠶⠶⣼⣿⠿⢶⠶⠶⠶⠶⠶⢾⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⣿⣿⡇⢸⣰⠀⢸⡇⠀⣷⣾⠀⢸⠀⡇⠀⡀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⡇⠀⠆⢰⡆⢠⣶⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠠⢾⣿⠀⣷⠀⢰⣿⣿⣿
⣿⣿⡇⢸⣿⠀⠸⡇⠀⢷⣿⠀⢸⠀⠇⢀⠛⠢⠈⣿⠀⣿⣿⠛⠢⠀⣿⠀⣿⠀⠰⠇⠀⠀⠁⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⢸⠀⡇⠀⡆⢹⡇⢸⡯⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠸⠀⡇⠠⣾⣿⠀⣿⠀⢸⣿⣿⣿
⣿⣿⣷⣾⣿⣶⣶⣷⣶⣾⠷⠶⠚⢶⣶⣾⣷⣶⣾⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠛⠃⠙⠟⠀⣾⣿⣶⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⡛⢉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⠉⠉⠉⠁⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣿⣿⣿⣿⣿⣽⠟⠟⠛⠿⣷⣧⠀⠀⠀⠀⠀⢀⣼⣦⣄⣠⣾⣿⣟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⡿⠟⠧⢦⣔⠀⠈⠙⠀⣠⡤⢤⡲⠫⣉⣤⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⠚⠀⠄⠈⠀⠀⡠⠞⠁⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠⣿⣿⣿⠟⠀⠀⢿⣿⣿⣿⣿⣤⣄⣀⡤⠄⣼⣅⡀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⣾⣏⣀⣤⡄⠀⠠⠛⠿⠷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢻⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠉⠀⠀⠀⠀⠀⣴⡎⣙⠉⣝⡟⣿⣭⣼⡻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⡟⣻⣿⣆⠀⠀⠀⠀⢠⣶⣄⡀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣾⣿⡙⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⡟⢹⣿⡿⣿⡇⠀⠀⠀⠋⠉⣿⣿⣶⣿⣿⡀⠀⠀⠀⣴⣿⡿⠟⠉⠛⠉⠉⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡤⢾⠿⠷⢾⡤⠤⡀⢀⠤⢴⠿⡿⠿⡷⠿⣷⠶⠶⠶⣿⣿⠶⢦⠶⠶⠶⠶⠾⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⣿⣿⡇⢸⣠⠀⢸⡇⠀⣧⣼⠀⢸⠀⡇⠀⡀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⡇⠀⠆⢰⡆⢠⡶⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠠⢾⣿⠀⣷⠀⢰⣿⣿⣿
⣿⣿⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢀⠛⠂⠈⣿⠀⣿⣿⠛⠢⠀⣿⠀⣿⠀⠰⠇⠀⠀⠁⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⠸⠀⡇⠀⡆⢸⡇⢸⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠸⠀⡇⠀⣾⣿⠀⣿⠀⢸⣿⣿⣿
⣿⣿⣷⣾⣿⣶⣶⣷⣶⠞⠳⠶⢾⣶⣶⣾⣷⣶⣾⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣷⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠂⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠎⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⢻⠿⠛⠋⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⠻⠛⠛⠛⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⢠⣿⣟⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣕⣾⢹⣿⣿⣿⣯⠻⡿⠿⣿⣿⣿⣧⡀⠀⣠⡀⠀⠀⠀⢀⣼⣏⣩⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣿⣾⣿⢩⢿⣿⡿⣆⣄⣤⠄⠙⠻⢷⡀⠀⢉⠉⠀⢠⣿⢽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡊⠘⣿⣿⣿⣿⣾⠠⠀⠀⠹⠅⠀⠀⠀⣋⣀⣀⠁⠀⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⡯⠁⠀⣿⣿⣿⣿⣿⠀⠀⠄⣄⣀⣀⣀⠀⠴⣼⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠈⠀⠈⠻⠏⠀⢀⡀⣌⣻⣟⣿⡿⢥⢓⣗⣿⣿⣧⣼⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢿⣿⣿⠚⠀⠀⠀⠀⠀⢀⠙⠚⠋⠏⡷⠹⠒⠈⠿⠻⢛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠙⣁⣤⣤⣤⣅⣀⢖⠂⠅⣶⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣨⣿⣿⣦⠀⠀⠀⢀⡼⠿⣶⣄⣀⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠿⠿⢿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⣿⡿⢿⠿⠤⢤⡤⠤⡀⢀⠿⢿⠿⡿⠿⡶⠶⣶⠶⠿⠿⣯⡤⠶⢤⠤⠶⠾⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⡿⠿⠿⣿⣿⣿
⣼⣿⡇⢸⣠⠀⢸⡇⠀⣷⣿⠀⢸⠀⡇⠀⠀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⠃⠀⠆⢰⡆⢠⡆⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠀⢾⣿⠀⣷⠀⢰⣿⣿⣿
⣿⣿⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢀⠛⠂⠈⣿⠀⣿⣿⠛⠢⠀⣿⠀⣿⠀⠰⠇⠀⠀⠁⠀⠿⣿⠀⠂⠈⣿⡇⢰⣶⡇⠸⠀⡄⠀⡆⢸⡇⢸⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠸⠀⡇⠀⣾⣿⠀⣿⠀⢸⣿⣿⣿
⣿⣿⣷⣾⠿⠶⠶⠶⠶⠞⠳⠶⣾⣶⣶⣾⣷⣶⣾⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣾⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠆⠀⠠⠐⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⠿⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠈⠈⠉⠉⠉⠉⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣴⣿⣯⡍⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⢢⡟⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⢃⣼⡟⢻⣿⣿⣦⡀⠀⣉⠉⠻⣿⣿⣆⠀⠀⠉⠉⠛⠂⠀⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠈⠉⣯⣿⣷⣾⣝⣁⠉⠛⣻⡲⢄⠀⢼⣟⣆⡘⠂⢀⡀⢀⠀⣀⣻⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡛⠀⠸⣿⣿⣿⣿⣿⠀⠀⡀⡀⠀⠀⠀⠈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠇⠀⠘⢻⡟⠀⠀⠀⠻⢿⡿⣿⡯⢂⠄⠤⣻⡿⡋⣙⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣾⣧⣤⠲⠀⠀⠀⠀⠀⠀⠄⠴⠜⡺⢡⠯⠁⠙⢸⠿⠿⢽⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠄⠈⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣷⣆⠀⠀⠀⠀⠀⣴⣦⣀⠀⠸⣿⡁⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢷⠤⠤⢤⡼⠭⣹⣿⠷⢶⠿⡷⠶⡴⠶⢶⠾⠿⠿⣯⡤⠯⢤⠴⠾⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⣿⣿⡇⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣤⣶⠀⣶⣿⡀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⢰⠀⡇⢰⠀⠃⠀⠆⢰⡆⢠⡆⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢰⠀⡇⠀⢾⣿⠀⣷⠀⢰⣿⣿⣿
⣿⣿⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢀⠛⠂⠈⣿⠀⣿⣿⠛⠢⠀⣿⠀⣿⠀⠰⠇⠀⠀⠁⠀⠿⣿⠀⠀⠈⣿⡇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠰⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠸⠀⡇⠀⣾⣿⠀⣿⠀⢸⣿⣿⣿
⣟⣿⣷⡾⠛⠲⠶⠶⠶⠾⢳⣶⣾⣶⣶⣾⣷⣶⣾⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⣿⡷⣶⠅⠄⠀⠀⠠⠖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣿⢯⣭⣽⣿⣿⣴⠤⢤⡤⢤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣎⣿⣿⣿⣿⣿⣿⣏⣿⣯⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣾⣿⣿⣿⣿⣷⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠋⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠛⠉⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠒⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠠⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢱⡇⠀⠀⠸⡏⠈⠉⠛⠛⠿⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠹⢯⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⣀⠐⠢⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⠇⠰⠀⢀⣀⣠⣤⣶⣿⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠷⢿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⠇⠀⠀⠀⠀⠀⠀⢰⡀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⣿⣷⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠤⢤⠤⠤⢴⡦⠤⡀⢸⠿⢦⠤⡤⠤⡤⠶⢶⠿⠿⠿⣿⡿⠿⢿⠷⠶⠾⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⢻⣿⡇⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣤⣶⠀⣶⣿⠀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⠰⠀⡇⢰⠀⠃⠀⠆⢰⡆⠀⡆⠀⡇⢰⠀⢹⠀⠃⢸⣿⠁⢠⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠘⢹⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢀⠛⠂⠀⣿⠀⣿⢸⠉⠢⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⡇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠸⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⠷⢞⣙⣶⣶⣶⣶⠞⢳⣶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣏⣈⣳⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣾⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠖⠲⠸⠟⠻⠟⠻⢣⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣖⡒⢻⣟⢠⣀⡀⠀⡀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⣿⣌⣭⣼⠟⢹⣃⣰⣶⣶⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣹⣿⢻⣿⣿⣇⣀⡢⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡽⠿⠛⠉⣉⣽⣿⣿⣿⣿⣿⣫⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄⣰⣯⣍⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢠⡝⠉⠉⠙⠛⠛⠛⠻⠻⢿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠘⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⠀⠀⢀⡀⣀⣄⣤⣶⣶⣶⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢛⣽⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠯⠀⠀⠀⠀⠀⠁⠀⡀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠠⣾⣯⣠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠤⢤⠤⠤⢄⡠⠤⡸⣿⠧⢤⠤⡤⠤⡤⠶⢴⠶⠿⠿⣿⡿⠿⢶⠴⠶⠶⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⡄⢸⡇⢸⣠⠀⢸⡇⠀⣧⣿⠀⢸⠀⡇⠀⠀⠠⣤⣶⠀⣶⣿⠀⠠⣤⣶⠀⣶⠀⠰⣾⠀⠀⡇⠀⣿⣿⠇⠀⢸⣿⡇⠰⠀⡇⢰⠀⠃⠀⠆⢰⡆⠀⡆⠀⡇⢠⠀⢹⠀⠃⢸⣿⠁⢠⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠇⢸⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⢀⠓⠂⠀⣿⠀⣿⢼⠉⠢⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⡇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠸⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠈⠓⠚⢉⣶⣶⣶⣶⠾⣷⣶⣾⣶⣶⣾⣷⣶⣖⠛⠶⠋⠈⢳⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣷⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⢀⠆⠰⣶⣾⣿⣿⡿⠁⣴⣾⣿⣿⣿⣿⣿⣿⣾⣽⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠛⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣁⠀⠀⠀⠀⠀⠀⠦⠀⡄⣤⣄⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⢈⣠⡄⡀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢤⠤⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠋⠁⣠⣴⣿⣿⣿⣿⣿⣻⣽⣷⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠆⠃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢠⡆⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣿⣿⣿⣷⣧⣄⣤⠆⠀⣠⣤⣤⣀⣠⣄⣀⣀⣓⣊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⢿⣿⣿⢟⣠⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣁⣐⣦⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣥⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢤⠤⠤⢌⡿⠿⡏⢠⠴⢤⠤⡤⠤⡶⠶⢴⠦⠶⠶⣤⡴⠶⢶⠶⠶⠶⠶⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢸⡇⢸⣠⠀⢸⡇⠀⡇⢸⠀⢸⠀⡇⠀⠀⠠⣤⣶⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡆⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⢠⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⡇⢸⣿⠀⠸⡇⠀⢷⣿⠀⢸⠀⠇⠀⠃⠂⠀⣿⠀⣿⢸⠉⠂⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⡇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠈⠒⠚⢹⣶⣶⣶⠶⢾⠷⠶⠞⠶⣶⣾⠳⠶⠖⠛⠶⠋⠈⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⢀⣶⣿⣿⣿⢿⠶⣶⣶⣶⣷⡀⠻⣿⣄⠀⠀⠀⠀⣀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⡿⢄⣰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣽⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣀⣤⣤⢶⣱⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠿⠛⠉⣸⣿⣿⣿⣿⣿⣟⣻⣿⣯⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⡀⣠⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣈⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠚⠉⠉⠙⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣧⣄⠀⣀⡄⠀⢀⣄⣀⡀⢀⣀⠀⠀⠰⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡧⢀⡴⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⢋⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⡶⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠴⢤⠤⠿⢿⡾⠧⡄⢠⠤⢤⠤⡤⠤⡤⠴⢤⠴⠶⠦⣤⡤⠶⢤⠶⠶⠶⠶⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢸⡆⢸⣠⠀⢸⡇⠀⡇⢸⠀⢸⠀⡇⠀⠀⠠⣤⣦⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡆⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⡇⢸⣿⠀⠸⠇⠀⢷⣾⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠂⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⡇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠋⠓⢾⣿⣶⣶⣶⣶⣾⠳⠶⠺⣶⡶⠞⠓⠶⠖⠛⠶⠋⣽⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⢠⣾⣿⣿⣿⠀⠻⢷⣦⣀⠀⣿⣏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⠁⠀⡀⠀⣁⣿⣿⣿⣿⣾⣧⣤⣯⣼⣷⣂⡀⢀⠀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⡀⢾⡿⢷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢤⢛⣙⢉⣉⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣖⣄⣠⣴⣭⣭⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⢟⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣀⣌⣿⣿⣿⣿⣿⣏⣮⣞⣷⣶⣿⣿⣿⣿⣿⣿⠻⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠻⣟⣿⣿⣿⣻⣿⣿⣿⡿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣏⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠢⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠉⠉⠠⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⠙⠀⠉⠉⠈⠉⠉⠛⠙⠋⠻⢿⣿⣿⣿⣷⣧⣀⡴⠇⠀⣠⣵⣷⣤⣶⣦⣶⣤⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢿⠿⣿⠂⢠⢈⣰⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢟⣛⣮⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢤⠤⠤⢄⡬⠤⡀⢠⠴⢶⠶⡶⠦⡴⠶⢦⠶⠶⠦⣤⡴⠶⢦⠶⠶⠶⠾⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢸⡆⢸⣠⠀⢸⡇⠀⡇⢸⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣄⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠇⢸⣿⠀⠸⠇⠀⢷⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⣄⡀⠒⠚⢿⣶⠶⠶⠶⠞⠳⢶⣾⣶⡶⠚⠓⠶⠒⠛⣶⣿⣻⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠛⣿⣷⣶⣾⣿⣆⠀⠠⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠘⠹⣿⣿⣶⣅⣭⠀⣀⠄⣴⡦⠀⠀⠀⠀⠀⠀⣀⣤⡤⣼⣿⣶⣶⣶⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⣿⠇⠀⣴⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣷⣶⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⣀⣼⠒⠛⠋⣁⣬⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⣀⠀⢤⣾⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣾⣿⣿⣿⣯⣷⣾⣿⣿⣯⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠏⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠿⠋⠉⢻⡿⣿⣿⣿⢿⢫⣫⢿⣉⣽⣿⣾⣿⣿⣿⣿⢿⠿⠋⠃⠈⠁⠀⠀⠀⠀⠀⠀⠰⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣾⢿⣿⣿⡿⢿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣯⣿⣿⣭⣚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠒⠂⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠟⠛⡻⣃⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠟⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣠⠀⠀⣉⣠⣄⣀⣤⣴⣴⣄⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠄⡀⠘⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠶⠧⢀⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠛⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢤⠤⠴⢦⡤⠦⡄⢠⠤⢤⠴⡤⠬⡭⠽⢶⠶⠶⠶⣤⡤⠶⢶⠶⠶⠾⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣸⡆⢸⣠⠀⢸⡇⠀⡇⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢻⡇⢸⣿⠀⠸⠇⠀⢷⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠈⢶⣾⠟⠲⠶⠶⠶⠞⢳⣶⣾⣶⣶⣾⠷⠶⢶⣿⣶⡿⢿⢷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣄⠀⠸⣿⡇⠀⠀⠀⠀⢰⣿⡿⠛⠁⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣶⣿⣶⣶⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⠏⠀⠀⠀⠀⠀⢁⣡⣤⣤⣄⣀⢀⣀⣀⡀⠀⠀⡀⢀⡀⢀⣤⣮⢬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠟⢂⠀⠀⠀⠐⠲⠛⠙⠛⠷⠿⠿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣿⠟⠁⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣯⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⣀⢀⣠⡼⢷⡿⣿⡾⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣿⣿⣾⣿⣿⣾⣐⣿⣾⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⡿⣿⣿⣷⣿⣿⣷⣾⣧⣿⠿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⡿⠏⠉⢝⣻⡽⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⢉⡟⣻⣿⡿⠻⣓⣦⣽⣥⣴⣾⣿⣿⣿⢏⣸⠈⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣰⣿⣿⣿⣿⣽⡻⢌⠛⣿⣿⣿⣛⣿⣿⣿⡿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⣾⣛⣿⣿⣿⣷⣿⣿⣷⣮⣧⣠⣄⣀⡬⡴⠖⠀⠀⠀⠀⠀⠀⠐⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠖⠖⠂⠀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠉⠉⠉⠉⣫⡀⠀⠀⠀⠀⣸⣿⣶⣵⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠜⠛⠛⠋⠛⠛⠛⠿⠿⠛⢿⣿⣿⣿⣿⣧⣀⠀⡀⠄⠀⠀⢀⣶⣤⣾⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢟⣿⠿⢸⠂⠀⠀⠀⣷⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡑⣀⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢤⠤⠤⢤⡤⠤⡀⢀⠷⠶⠶⡶⠶⡷⠴⢤⠴⠶⠶⣄⡤⠶⢤⠶⠶⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢰⡀⢸⣠⠀⢸⡇⠀⡇⣼⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⣶⡿⠲⠞⠙⠲⠶⠶⠶⠾⠳⢶⣞⣶⣶⣞⠳⠶⠖⠻⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⣿⣦⣤⡼⡿⠿⣟⣋⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⡴⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⣾⣶⣶⣿⣿⣿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢿⡧⠀⠀⠀⠀⠄⣀⠀⠸⠯⡀⠀⠒⠔⠶⠢⣂⣀⣤⣦⣤⣤⣾⠟⠋⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⣠⣦⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣀⠂⣶⣿⣿⣬⣽⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢤⣖⣤⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣽⣏⣩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⣤⣶⢀⡄⢹⣀⣷⣾⣿⣀⣉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢱⣾⡟⣡⣤⣎⣋⣾⣩⡿⣿⣿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⠛⠛⠻⢝⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠉⠛⠛⡿⣿⣿⣿⡿⠚⢀⡂⠉⣩⣥⣶⣿⡿⠋⠛⠁⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣰⣴⣟⡿⡂⠠⠪⢷⣶⡿⠽⢿⣿⣙⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣻⣿⣿⣿⣿⣧⢀⣤⠴⣿⣿⣶⣀⠼⡏⣉⠐⠀⠀⠀⠀⣴⣶⡶⢤⣄⠀⢀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⣠⣾⣿⣿⣯⣝⣿⣻⣿⣖⣶⣬⣿⣿⣿⡟⠍⠛⠟⠛⠙⠃⠉⠉⠁⠀⠀⠴⣷⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡏⠈⠀⠀⠘⢿⣽⣿⠯⣭⣾⡛⣯⣽⠟⣟⣿⣿⣿⣧⡀⠀⠀⢀⠀⠀⢈⠂⡄⣀⣤⣠⣽⣟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠽⠿⢿⡽⡖⠀⠀⠀⠐⠀⣎⢈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠤⢤⠤⠤⢤⡤⠤⡠⣻⠷⠶⠶⠶⠦⡤⠤⢤⠴⠶⠦⣄⡤⠤⢶⠶⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢸⠀⢸⣠⠀⢸⡇⠀⡇⢻⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠀⢸⣿⠀⠸⠇⠀⢷⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣾⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠙⠲⠞⠙⠲⠶⠶⠶⠞⠳⠶⠞⠲⠶⠞⠷⠶⠖⣻⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⡦⣄⠀⠀⢠⣿⣽⣿⡿⠿⢿⣟⣟⣻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣤⣾⣿⣿⣋⣺⣿⣗⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣖⣶⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢜⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣸⣷⣄⢺⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠠⠀⠤⡤⢉⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠠⠀⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⢀⣤⡀⣩⣴⢀⠘⠻⣿⡿⣏⠿⢻⡶⢾⣿⠿⠻⠋⠁⠉⠠⠡⣼⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠟⡿⠟⠟⠉⣀⠌⢈⣠⡴⠾⣢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡀⠤⣊⡙⠀⠀⠀⠙⡋⠌⠑⠈⠣⣤⠖⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⢀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠑⠀⠀⠀⢈⣔⣿⣿⣿⣦⢀⡠⠐⠘⢿⣿⠤⠐⣚⠀⢀⣀⣀⣀⠀⠘⠿⠟⠋⠙⢀⡀⢤⣔⣆⠧⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⠀⢠⣴⣛⣻⠦⠘⢿⣀⡼⣤⣴⣦⣴⣝⡷⠆⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠈⣄⡷⢾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡏⠉⠁⠀⠀⠡⣤⣿⠯⠤⣤⠈⣱⣤⠞⢉⡉⢾⣶⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣺⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠑⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠽⡛⡕⠪⠀⠀⠀⠀⠀⠀⣄⣠⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠤⢤⠤⠤⢤⡤⠤⣤⣤⠶⠤⠤⠤⠤⡤⠤⢤⠤⠦⠤⣤⡴⠶⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠾⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⢸⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⠲⠞⠙⠶⠶⠶⠶⠾⠓⠶⠞⠶⠶⠞⠳⠶⠖⠳⢶⣿⢿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⣠⠴⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠈⢿⡯⢭⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤⣤⣤⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢰⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣤⣿⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣿⣤⣌⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣠⣠⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠐⠘⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣽⡶⢿⢿⣏⡉⣽⣿⡿⠿⡟⠛⠂⠐⢌⣻⣿⠯⠛⠁⠀⠀⠀⠀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⢀⠬⠄⠀⠀⠀⠈⠁⣀⡐⠉⠁⠛⠛⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠦⠄⠰⠚⠉⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣰⡶⠶⠠⠀⠀⠀⠈⠉⠩⡉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠀⠐⢫⡀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢂⢸⣦⣦⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡤⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⢉⢣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢃⡂⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠂⠀⠁⠂⠀⠐⢈⢙⢻⠪⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣾⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠤⢤⠿⠤⢤⡤⠤⡀⢀⠤⠤⠤⠤⠤⡤⠤⢤⠤⠶⠦⣤⡤⠶⢶⠾⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢸⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠨⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⠲⠞⠛⠲⠶⠶⠶⠞⠳⠶⠞⠲⠶⠞⠳⠶⠖⠳⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣘⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⠈⠉⠁⠼⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣣⣤⣬⣯⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣼⣷⣶⣠⡀⠀⠀⠀⠀⠀⢠⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡀⢀⢾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣶⣶⣾⣿⣿⣾⣧⣴⣾⣶⣴⣴⣿⡿⣷⣾⠁⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⢤⣤⣩⣿⣯⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣯⣿⣿⣿⣿⣿⣿⠿⠿⢛⣿⣿⣿⡿⠋⠁⠀⠀⠀⡀⣒⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠣⠉⢀⣨⣿⠿⠻⠿⠉⠉⠁⠐⣼⣿⠿⢿⠗⠛⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⡰⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢠⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠤⢤⠤⠤⢤⡤⠤⡀⢀⠤⠤⠤⠤⠤⡤⠶⢶⠶⠶⠶⣤⡴⠶⢶⠶⠷⠷⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢿⠀⢸⣠⠀⢸⡇⠀⡇⢸⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣰⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⠡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠀⢸⣿⠀⠸⠇⠀⢷⡼⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠐⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠈⠲⠾⠛⠶⠶⣶⡶⠞⠳⠶⠚⠲⠶⠚⠳⠶⠖⢳⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⠀⠰⠆⠶⠄⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠁⠀⠉⠛⠚⣸⢛⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣀⠀⠉⠀⠌⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠉⣿⡯⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣟⣿⣿⣿⢿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣀⠀⢈⣤⠐⢭⡻⣿⣿⣮⣿⡇⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣽⣿⡿⠃⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣯⣽⣿⣿⠿⣿⣿⣯⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⠏⠉⠀⠀⠀⡀⠤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠺⠏⢫⣿⣿⣿⣿⠿⠯⠉⣍⣼⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⢐⠰⠞⠽⠻⠉⠉⠉⠀⠀⠐⠒⠛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣏⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠋⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢯⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣤⣶⣆⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⠶⢶⠶⠶⢤⡤⠶⡀⢀⠶⠶⠶⠶⠶⡶⠶⢶⠶⠶⠶⣤⡤⠶⢶⠶⠶⠶⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⠿⣿⠿⠿⠿⠿⣿⣿⣿
⡆⢸⠀⢸⣠⠀⢸⡇⠀⡇⣼⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣰⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢰⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠉⢸⠀⢸⣿⠀⠸⠇⠀⢷⡾⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⣶⠾⠛⠶⠶⡶⠶⠞⠳⠶⠚⠲⠶⠞⠳⠶⠶⢷⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠐⠐⣴⠀⢠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣺⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈⠀⠀⡂⠊⡿⡟⣿⢟⣿⣯⣿⢯⣯⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠈⠙⠝⠰⢷⣾⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠹⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣙⣓⣲⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣖⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣪⠼⢻⢶⢿⣿⡖⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣰⣇⣰⣛⠽⡿⣿⣟⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣤⣤⣄⣀⠀⣱⡖⠊⣍⣿⣿⣅⣸⣽⣽⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣿⣿⣷⣾⣏⣿⣿⣿⣿⠿⣷⣷⣿⣿⣿⡿⠛⠁⡀⠀⢀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣾⡿⢿⣿⣿⣽⣭⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⠱⠟⠡⢿⣿⣿⣿⡿⠿⠯⠫⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢂⠤⠄⠟⠏⠉⠉⠁⠀⠀⠒⠚⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠘⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⢄⡀⢀⣠⣤⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡶⠶⣆⣴⠷⠶⠶⠶⠦⡤⠤⢤⠶⠶⠦⣤⡴⠶⢶⠶⠶⠶⠷⠶⢶⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⠿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⢿⠀⢸⣠⠀⢸⡇⠀⡿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⠁⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢸⠀⢸⣿⠀⠸⠇⠀⢷⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠘⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠈⠲⠞⠛⠲⠶⠶⠶⠞⠳⠶⠚⠲⠶⠚⠳⠶⠶⢷⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⠰⣶⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠉⠗⠃⣉⢛⣺⣾⣿⣿⣿⡭⣿⢟⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢙⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠀⠉⠙⡚⢰⠚⣿⣝⣻⣾⣾⡿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠈⠀⠈⠉⠃⠘⣋⣽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⠯⣫⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡒⠀⢀⠈⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡍⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡞⣻⣿⣤⣦⣤⣤⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡉⠄⠤⠀⠎⢻⡟⡛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⢢⡀⠰⠿⣿⣶⡄⠀⢠⣤⠂⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⣻⣿⣶⣶⣶⣾⣷⣮⣶⣿⣟⣿⣿⠟⠉⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣄⣐⣿⣿⣿⡟⢿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠯⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠂⡈⡁⢡⣿⡿⠿⠿⠏⠉⠁⠬⣽⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⢿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠿⠙⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢦⠼⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡶⠶⣤⣴⠶⠶⠶⠶⠦⡤⠤⢤⠶⠶⠶⣤⡤⠶⢶⠶⠶⠶⠶⠶⢷⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢹⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠐⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⠶⠞⠛⠶⠶⠶⠶⠞⠓⠶⠞⠶⠶⠾⠷⢶⣶⣷⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠈⠠⠪⠛⢻⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠈⠊⢁⡈⠛⣛⣾⢾⡿⣿⣟⣿⡿⢓⣛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡈⠀⠈⠈⠚⢶⠋⣯⣽⡾⣿⣿⣻⢌⡭⣿⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠂⠉⠈⠚⣾⣯⢽⣧⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡯⢝⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠁⠊⢡⣔⡛⣭
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈⠁⠀
⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⡒⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠢⠀⠠⠄⣀⣀⣤⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠙⠙⠐⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⣷⣦⠀⢀⡠⡠⠒⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠰⣶⣶⣶⣤⣴⣿⣤⣰⣠⣿⣗⣾⣿⣿⣷⣶⣤⣤⣾⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣜⣿⠿⣿⣾⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣴⣿⣟⣻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠋⠀⢸⣿⣿⣿⣿⠛⠙⢉⣓⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⢿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠴⢶⠶⠶⢶⡶⠶⣄⣤⠶⠶⠶⠶⠶⡶⠶⢶⠶⠾⠧⣤⡴⠶⢶⠶⠾⠶⠶⠶⢾⠷⠶⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣿⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⢴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⠶⠾⠟⠶⠶⣶⣶⠾⠷⣶⠾⠶⠶⠾⠳⠶⠶⢷⣶⣿⣹⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠀⠀⠠⠀⠀⠀⠠⠠⠐⠦⠀⠀⠀⠀⠀⠀⠀⡠⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣶⣦⣄⣀⠀⠈⠉⠨⠏⢐⠯⣯⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣬⣧⣿⣿⢿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠁⠁⠐⢞⠿⠟⠼⢿⣛⣟⣿⣿⣟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠤⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠅⠁⠛⠏⣟⡭⢿⣞⢾⣥⣯⣷⡿⢚⣿⢏⣷⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠈⠋⠈⠛⠏⠉⡝⣷⣕⣮⣜⡌⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠈⠛⠓⠛⡟⣽⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣭⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠁⠛⠘⠋⠛
⠀⠀⠀⠀⢠⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠂
⠀⠀⠀⠀⡘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠆⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢲⠲⠫⠛⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠐⣶⣆⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⣑⣤⠀⣌⣽⣿⣯⣤⣶⣾⣿⣇⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡿⣿⣿⣭⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣥⣶⣾⣿⢹⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⡝⠂⢺⣿⣿⣾⣿⣿⣿⠛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠋⠙⠛⠀⠀⠐⠒⠿⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠴⢶⠶⠶⢶⡶⠦⣄⣤⠶⠶⠶⠶⠶⡶⠶⢶⠶⠾⠿⣥⡶⠶⢶⠶⠶⠶⠶⠶⢶⠾⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⠿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣾⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢠⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠙⠶⠾⠻⠶⣶⣶⣶⡾⢷⠶⠾⠶⠶⠞⠳⠶⠶⠳⡶⠟⠻⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠂⠒⢲⠀⠲⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣙⡓⠲⠶⠿⠿⠒⣿⣷⣹⢿⣾⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠂⠀⡘⡽⡯⡿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠻⠛⠁⢻⠯⣭⣿⣿⣾⡧⢯⡿⠿⣿⢿⡿⣿⣿⣿⢿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠶⢮⠈⠘⠛⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠋⠂⠈⠙⠻⠯⡚⣻⣽⣿⣾⣾⡿⠏⡿⠿⠼⣿⠝⢉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠈⠁⠀⠙⠃⠐⡏⣽⢽⣷⣥⡴⡠⠏⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠯⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠊⠉⣕⡋⢥⡶⣂⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠈⠅⠀⢈⠹⢖⢱
⠀⠀⢠⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠁
⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⢸⣿⣿⣿⣏⣩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠌⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠈⠐⠛⡄⠀⠈⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣴⣦⣀⠀⢀⣤⣄⣤⣴⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⢀⣦⣖⣢⣡⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣶⣾⣺⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣼⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠓⠋⡿⠟⢰⣿⣿⣾⣿⣿⣿⡟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢈⠀⣤⡿⠟⠻⠛⠁⠀⠐⢶⠿⠿⠛⠹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠤⢦⠶⠶⢶⡶⠾⣄⣰⠶⠶⠶⠶⠦⡴⠶⢶⠶⠶⠶⣤⡴⠶⢶⠿⠿⠷⠶⠶⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣸⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣸⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠹⠶⠾⠿⠶⣶⡶⠶⠾⠷⠶⠞⠶⠶⠾⠷⠶⠶⠷⣶⠿⠛⣷⣶⡶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⠲⣶⠏⢶⠄⠰⠤⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣿⣷⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣻⣯⣭⣭⣿⣿⣷⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢤⣤⣈⣁⣴⣶⣁⣟⣝⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣶⣶⣶⣶⣤⣭⠉⠁⠀⠛⠻⠓⡗⢽⣣⣟⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠋⠩⡫⣷⠏⣿⣿⣻⢿⣿⣿⠿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⡆⠳⠛⠛⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈⠀⠐⠚⠹⢿⣻⣟⣻⣯⢯⣛⣷⣲⣾⠻⢿⡿⡳⣺⠿⠿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠐⠃⠙⠿⠋⢻⣟⣾⣵⣇⡳⠉⠒⠂⠉⠽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠙⠛⠟⣛⣫⣗⣄⢄⣁⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⣀⠈⠰⠓⡙⠙⢛⠛⣦⣖
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠘⠀⠈⢉⡏
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠂⢠⢀⡀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠴⠴⠐⣤⢄⣈⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⡸⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⣠⡰⣶⣶⣶⣦⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣻⣙⣿⢿⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢐⣄⣨⣿⣿⢛⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣿⣿⠟⠛⠓⣙⣺⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠠⠀⠸⠻⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠙⠿⡿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠴⢶⠶⠶⢦⡶⠶⣆⣴⠶⠶⠶⠶⠦⡴⠶⢦⠶⠶⠶⣤⡶⠶⢾⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣹⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⢻⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⠶⠾⠿⢶⣶⡶⣶⠾⠷⠶⠾⠶⠶⠞⠳⠶⠶⠷⠶⠿⠛⢷⣶⣶⢿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⠲⣶⠯⢶⠄⠠⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⢀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣯⣭⣽⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⣤⣤⣠⣷⣨⢵⢡⣵⣾⡿⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢢⣲⣶⣶⣦⣤⣀⡀⠀⢉⠋⠩⠉⠻⣟⣾⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣭⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠊⠁⠉⠞⡿⠃⢾⣿⣟⢟⣿⣽⣛⣿⣿⡯⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⢄⠒⠚⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠅⠀⠚⠭⠟⡽⢷⣻⢠⣿⣽⢿⡙⡛⡟⣝⢽⠻⣛⣿⣽⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠁⠉⠛⠋⠩⢏⣿⣲⣧⢽⡀⠉⠁⠄⢘⣺⣛⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⡉⢚⡭⡽⣫⣷⣀⣤⠤⠤⣈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡁⠈⠉⠌⢈⠹⢛⣳⣿⣟⣖
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡁⠀⠠⠅⠵⢟
⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡁
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠕⠤⠀⢀⣤⣤⣴⣦⣀⡀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣯⣳⣬⣤⣼⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⣐⢺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠠⢰⣶⣦⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣤⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠾⢿⡾⠅⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⡽⠻⠓⢂⠲⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡶⠶⣦⣼⠷⠾⠷⠷⠶⡶⠶⢷⠿⠿⠶⣾⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣻⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢡⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣾⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣻⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠙⠶⠾⠻⠶⣶⠶⠶⠾⠷⠶⠾⠶⣶⠾⠷⠶⠶⠷⠶⠿⠙⢷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠖⠲⣶⠧⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣤⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢳⣛⣿⣿⡿⢿⣿⣿⣟⣿⣿⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⢀⡠⠩⡭⠭⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣌⣉⣛⠓⠒⠛⠓⠫⣾⡷⠿⡷⣿⣻⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⢿⣿⣿⣿⣷⣶⣤⣀⠂⠈⠒⠨⠱⠻⢞⢿⣿⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣞⣿⠋⠙⠛⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠈⠊⢁⠨⠟⣷⡷⣿⠿⣷⣲⡻⢷⣽⣽⠿⣯⣿⢿⡭⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠷⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣈⠀⢀⠉⠁⠼⠱⢷⡿⠻⡿⢯⡓⣔⠰⡋⠫⠤⠐⢛⢾⢻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢀⠀⠑⠿⣿⠿⡿⡻⣄⣀⢁⡀⣉⠻⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠚⠶⠙⠫⠷⡛⣧⣍⣾⣣⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠁⠪⢞⢻⢿⣿
⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠚⠙
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⠀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣥⡧⣍⣈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣤⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠦⠥⢛⠿⢩⣿⣿⣿⣿⣿⣿⣿⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠴⢶⠶⠶⢾⡷⠶⣮⣿⠿⠿⠿⠿⠷⡶⠶⢷⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⢀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡃⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣾⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠸⠶⠾⠿⠶⣶⣶⡶⠾⠷⠶⠾⠶⢶⣾⢷⠶⠶⠿⣶⠿⠻⢷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠖⠲⣶⠛⢶⠆⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣘⠼⢿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠙⠻⠿⣟⣛⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢄⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⣿⣟⣻⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣂⣴⣆⣐⣼⣺⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠤⣤⣶⣶⣤⣉⡉⠉⠉⠀⠛⠛⡛⠻⢾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣻⠿⠿⠿⣿⣿⣷⣦⣤⣀⠀⠰⠉⠋⠭⢿⣿⡿⣿⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⡿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣈⠿⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡁⠀⠒⠁⠾⠻⣻⣫⠷⣞⠾⣧⣯⡷⣏⢛⣿⣝⡯⠻⢛⣿⣽⡷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠾⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⡀⠀⠙⠀⠙⠛⠉⠿⣿⣗⣿⡴⣒⠈⠉⠄⠰⣹⣼⣛⡠⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠉⠙⣫⢭⢮⣵⣖⣔⡄⠶⢐⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠉⠁⠀⡉⠶⡚⣻⣽⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡁⠈⠀⠘⠿⢿⣛
⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠈
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣷⣦⣠⣤⣤⣤⣤⣶⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣬⣿⣽⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠴⢶⠶⠿⢿⡿⠶⣿⣿⠿⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣾⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⠸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠀⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠘⢶⡾⠿⢶⣶⣶⣶⠾⠷⠶⠞⠶⠶⠞⣷⣶⠶⠿⠶⠿⠛⠷⢶⠶⠿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⠲⣶⠿⢶⠦⠰⠶⠶⠆⠀⠀⠀⠀⢷⠟⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⣿⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢢⣤⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⣄⡬⣭⡯⢾⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⣉⣙⡛⠒⠺⠛⠚⠿⣾⠿⢿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣹⡿⣿⠿⢿⣿⣷⣦⣌⣐⠀⠉⠒⡡⠽⣻⣺⣾⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣺⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣤⣈⡀⠁⠊⠁⡭⠟⣿⡷⡿⢿⣶⢾⣯⣬⣯⣿⢿⣿⣟⢏⡿⡿⣿⣟⣿⣿⣿⣿⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⢧⣴⠃⠀⠀⠀⢸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡄⡀⠈⠁⠇⠸⢾⡟⢻⣿⢿⠴⣋⠏⠽⢏⢄⡉⢟⣿⢿⢯⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠈⠀⠀⠒⡛⠽⢛⣿⢗⣄⢌⣄⢩⡍⢋⠡⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠈⠱⠒⡙⠙⢛⠿⡵⣾⣿⣦⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡘⠐⠈⠊⡉⠿⣿⡿⢿
⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣄⣈⠀⠉⠃
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⢀⣀⣀⣀⣠⣤⣤⣴⣦⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⠶⢾⠶⠾⢿⡿⠿⣿⣿⠿⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣼⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣾⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠛⢶⣾⡿⣶⣶⣶⣶⡾⠷⠶⠾⠶⠶⠾⠷⠶⠶⠿⣶⠿⠻⠷⣶⡶⢿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠖⠲⣶⠿⢶⠦⠰⠶⠖⠆⠀⠀⠀⢀⢴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⡈⠙⢿⣛⣻⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⠾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣟⣻⣿⣯⣭⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣉⣀⣽⣮⣽⣫⣽⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢶⣾⣷⣶⣶⣤⣄⣀⠀⠈⠉⠭⠉⠉⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣺⣯⣿⠋⠀⠀⣺⣿⣿⣶⣦⣤⣀⠈⠈⢐⠊⡿⠟⠻⡿⢿⣻⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣤⡷⢺⣛⠃⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡐⠉⢁⠋⠫⢯⣞⣻⣽⣻⣾⣾⣻⢌⡝⣷⠵⣊⡉⠽⢽⡷⣿⡿⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⠻⠿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠁⠀⠉⠁⠐⢫⣿⣿⣷⡾⣇⠐⡒⠀⠳⠓⡟⠥⠊⢋⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠄⠉⠾⣝⠲⢟⡱⠿⣊⣫⣷⣀⣀⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠠⠈⠈⠫⡿⢯⣿⣿⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣄⡘⠁⠁⠕⠕⠭⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣐⣲⣦⣴⣤⣤⣶⣾⣿⣿⣟⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣴⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⢾⡿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠾⢿⡿⠿⣿⣽⠿⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⢹⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣾⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠻⠶⠾⠿⣶⣶⡶⣶⠾⠷⠶⠾⠶⠶⠾⠷⣶⠶⠿⠶⠿⣿⣷⣶⡶⢿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⠶⣶⠿⢶⠆⠰⠶⠶⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⡿⠿⢟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣻⣿⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣐⠂⢀⣤⢒⣾⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣤⣬⣍⣉⠉⠉⠉⠺⢟⡛⡟⢺⣯⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣾⠟⠉⠉⣽⣷⣦⣤⣀⡀⠀⠎⠋⠫⡿⣿⡯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠤⠽⣟⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣤⣄⣈⠀⠐⠎⠸⠻⣻⣋⠿⣟⡻⣦⣯⡷⣏⢛⢿⣽⡫⠛⢛⣟⣿⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡳⢾⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠉⠉⠙⠛⠉⡽⣹⣷⣿⣬⣦⠈⡬⠄⠰⠽⣬⢟⣡⠐⠻⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⢩⠙⢩⣝⠭⣵⢞⣴⣦⠲⣸⡄⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠘⠁⠀⣍⠂⢼⢿⢿⢿⣿⣿⡦⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠖⠓⢛⠽⢷⡛⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣶⣮⣤⣤⣤⣤⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣷⣖⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣆⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣴⣶⣶⣞⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢿⡾⠿⣿⣿⠿⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣿⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠀⠻⠶⠾⢿⢶⣶⡶⣶⠾⠷⠶⠾⠶⠶⠾⠷⣶⣶⠿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⢶⣶⠿⢶⠆⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡋⠁⠁⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿
⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢄⣀⣯⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠄⣀⣨⡚⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣿⣿⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠓⠲⠶⠬⠿⠗⢺⣷⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣻⣿⣿⣿⠟⠁⠀⢠⣀⡁⠀⠐⠑⡨⢷⠷⢿⣿⡗⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣷⣿⠇⠀⠀⠀⢾⣿⣿⣷⣶⣤⣄⣀⠈⠉⠿⢊⠙⠗⣿⠾⣿⢿⣶⣞⠟⣭⣯⡿⢽⣿⣟⣉⢟⡷⢿⣻⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠶⢯⣭⣭⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠄⡀⠉⠑⡏⠻⣾⡟⢟⢿⣝⣸⡩⠚⠹⠃⠈⠩⡿⡿⠿⢫⣻⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠙⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠚⡛⠽⣛⣿⢕⣄⢅⢄⢩⡍⠃⠅⠈⠑⢎⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠊⠱⠒⡛⠛⢛⠟⡴⣾⣯⣴⣠⣆⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣔⡘⠀⠈⠛⠍⠿⣟⡿⠯⣷⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣈⠀⠉⠁⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⡀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣤⢶⣶⣾⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠿⠿⢿⡿⠿⣾⣿⠾⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣿⠀⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣾⣿⣿
⠀⣿⠀⢸⣿⠀⠸⠇⠀⢿⡿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⡀⠿⣶⣾⠿⣶⣶⣶⣶⡾⠷⡶⠾⠶⠶⠾⢷⣶⠶⢿⣶⣿⡿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠆⠰⣶⠿⢾⠆⠱⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⠟⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣤⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⢙⣛⣯⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⡘⣿⡯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣻⣿⣯⣽⣿⣷⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠰⠦⠤⣭⣴⣿⠤⣷⣦⡾⣿⣵⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢶⣿⣿⣿⠗⠀⠀⢀⡐⠨⠙⠫⠝⡛⡿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣿⣽⣿⡏⠀⠀⠀⢸⣿⣷⣶⣤⣌⣁⠀⠁⠛⠛⢑⣻⣿⣿⣽⣷⣿⣭⣿⡟⡻⣻⣿⣿⣿⢿⠽⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿
⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⣼⣟⣻⣿⣿⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣁⠂⠈⠙⠚⢞⠏⢳⣯⠿⢿⣿⣇⡵⢻⣗⠻⠬⠒⢳⢻⣹⡿⠛⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠙⠾⢷⡽⠷⡲⢄⣡⢁⡐⣛⠹⠐⠋⡊⠉⠙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠘⢂⠘⠿⠝⠻⠵⡓⣫⣭⣾⣣⣄⣤⠑⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣐⡀⠢⠀⠊⣺⢻⣾⣷⢟⣿⡬⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣶⣾⣿⠛⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣁⡀⠐⠁⠑⠊⢹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣦⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠿⢿⡿⠷⣾⣿⠿⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣿⡄⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠄⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠨⣿⠇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⣀⠻⣶⡾⠿⣶⣶⣶⣶⡾⠷⡶⠾⢶⣶⡾⢷⣶⠶⢿⣶⣿⡿⢷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠀⠖⠲⣶⠿⢿⠟⠲⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣯⣼⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠐⣿⣷
⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠙⠛⡿⠿⣟⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣟⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣐⣪⣶⣞⣰⣧⣪⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⡉⠉⠉⠁⠘⡛⡓⣚⠢⢟⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⠁⠀⠀⢰⣦⣤⣀⡀⠀⠘⠙⠝⡿⡟⠼⣿⣗⣟⣿⢽⣛⣻⣿⠽⡿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣶⠿⢿⣿⣿⠆⠀⠀⠀⣘⣿⣿⣿⣿⣿⣶⣤⣄⣁⠀⠃⠁⡚⠯⠏⡼⢿⣻⣝⣿⣿⢿⢹⢿⡷⢷⡕⠫⠿⣿⣟⣿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠿⢟⠿⠯⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠁⠈⠹⠃⠘⣙⣷⢿⣢⡥⣦⠘⠰⠘⠽⠿⠭⠴⠸⣟⡻⡯⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠂⠩⢆⣟⠿⣿⡵⢵⣸⣫⣦⣄⢀⡐⢐⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣥⣀⡀⠀⠠⠘⠨⣫⡿⣿⣿⣽⢗⣞⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⣠⣤⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡄⠁⠁⡓⠯⠯⠛⡭⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣹⣾⣿⣿⣿⣷⣖⣶⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣦⣶⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣰⣄⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡾⠿⣿⣿⠿⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣿⡄⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣟
⣶⣿⠇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠁⢻⣶⡾⠿⣶⣶⣶⣶⣾⣷⡶⠾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠻⠷⢶⣶⢿⣿⡿⠻⠿⠶⠶⠀⠈⠀⠉⠉⠃⠨⠉⢻⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠛⠛⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢸⣿⣯
⣿⣟⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣟⣛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⢀⣀⡀⠚⢁⣦⢒⣾⢒⣺⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣦⣤⣭⣍⡉⠉⠉⠉⡚⠿⣛⡛⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣿⣿⣿⡿⠁⠀⠀⢰⣬⣀⡀⠀⠜⠋⠩⡯⣿⣯⣿⡿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⠾⢿⣿⣟⠇⠀⠀⠀⣸⣿⣿⣿⣿⣶⣦⣄⣀⠀⠐⠎⠰⠻⣻⣫⠿⣟⡻⣦⣯⣿⣏⢛⡟⡽⣿⠛⢙⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠖⢊⢽⠿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣂⠄⠈⠁⠉⠛⠙⠽⣹⣧⣷⣬⣤⡈⠭⠄⠸⠿⢭⠋⡰⠻⣫⢿⢿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠂⠀⠉⠉⢩⢚⡩⡴⣮⣴⡦⢓⣤⡅⡀⢀⠄⠊⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣀⡀⠀⡀⣅⠊⢼⠿⢾⢽⣷⣿⣾⣹⡇⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣠⣴⣶⣾⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠐⠀⠿⠻⡭⠽⢧⢨⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣹⣶⣿⣿⣿⣶⡤⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠙⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡾⠿⣿⣿⠿⢷⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿
⠀⣿⡆⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣦⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣛
⡀⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠀⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⠐⠻⣶⣾⢿⣶⣶⣶⣶⣾⠷⠶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⠲⡶⠶⣶⣿⣿⡿⠽⠷⠷⠖⠀⠈⠉⠉⠉⢂⠀⠉⠿⣿⠫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠻⠿⠏⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⣶⣦⣐
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣬⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠐⢀⣀⡽⣿⠥⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣀⣀⣙⣓⠒⠲⠉⠁⠛⢷⡿⠿⢷⣷⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢉⣿⣿⣿⣿⡿⠀⠀⠀⢀⡀⠈⠑⠊⡼⠟⣗⣿⣿⣟⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣻⣾⣿⣟⠿⠀⠀⠀⣸⣿⣿⣶⣦⣤⣀⠈⠘⠙⢬⠿⣿⣿⣿⢿⣿⡽⣿⣻⣻⣿⠻⢿⣿⣷⡻⢿⢿⢿⣏⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠤⠏⣹⡟⡧⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠉⠿⠘⠻⠟⠛⡟⣿⣵⣧⣫⡉⢃⢂⠉⣿⣏⣻⢻⡉⡿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠈⠛⠗⣛⠟⣓⣭⣀⣤⡴⡄⣇⠘⠄⠀⠙⠚⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠛⠨⠁⠩⢍⣳⣿⣿⣶⣶⣦⡔⢷⣘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠐⣦⣶⣤⣶⣶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣁⠀⠀⠔⠵⡿⣟⡻⢿⡍⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⣾⣾⣿⣿⣿⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠁⠀⠁⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡶⠶⣶⣶⠶⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⡆⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣀⣶⠀⣴⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡄⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢱⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⡿⢿
⢠⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠁⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠃⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⡿⢿⣶⣾⣿⣶⣶⣶⣶⣾⣷⣶⠾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⢶⠾⠷⣶⢿⣿⠿⠿⠿⠷⠶⠀⠟⠿⠟⢋⠉⠛⢿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣾⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠿⠿⡿⠿⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣧⣥⣠
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣧⣸⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣈⣻⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⣀⢛⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣚⠒⠶⠶⠉⠁⠺⣿⣞⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠘⢛⣿⣿⣿⣿⡷⠀⠀⠀⢘⠂⠈⠚⣉⠭⡿⢾⢿⣿⢻⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⣾⣿⣻⡷⠀⠀⠀⢺⣿⣷⣦⣤⣄⡀⠉⠙⢇⡩⠟⣿⡷⡿⢿⣷⣾⢿⣨⣯⣿⢿⣿⣟⢟⢿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⠤⠨⢽⣿⡢⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣶⣤⣘⡀⠀⠉⠉⠽⢙⠾⡟⢻⣿⣟⢾⣋⠏⡽⢓⣈⢉⢿⣿⡿⢉⢭⣿⣿⡿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠙⡛⠽⣛⣯⣷⣤⢥⣤⢡⡭⡙⠉⠂⢃⢈⠣⠹⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣀⣀⣲⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣅⣉⡄⠑⠓⠉⠚⢫⠩⣾⣼⣿⣶⣴⣦⠰⡃⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣴⣦⣤⣤⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣥⣈⠠⠈⢸⠏⠟⢿⣟⡷⣷⠺⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⣦⣾⣿⣿⣟⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡁⠀⠉⠀⠉⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣄⢀⠀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣥⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠶⢶⠶⠶⢶⡶⠶⣾⣶⠾⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⡆⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣀⣦⠀⣴⣿⠀⠠⣄⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⡿⣿
⣀⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠀⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⣮⢿⣶⣾⣿⣶⣶⣶⣶⣾⣷⣶⢾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣷⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⡰⠿⠷⣶⢿⣿⡿⢿⠿⠷⠖⠀⠲⠾⠟⠟⠛⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣶⡄⠀⠀⠀⠀⠀⡄⠀⠉⢭⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣟⣉⢉⡥
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣿⣿⣿⣶
⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢹⣛⣻⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡢⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣽⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣬⡜⠉⠀⣿⣮⠾⣿⡿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⢶⣶⣿⣿⣦⡄⠀⠀⠀⠩⠉⠻⠏⡚⡿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣻⣭⣿⣿⣿⣿⠀⠀⠀⢱⣶⣤⣄⣁⠀⠑⠻⠻⢑⣛⣿⣿⣿⣿⣯⣯⣿⠗⢿⣻⣝⣿⡿⣯⢿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢤⠍⢉⡉⡹⣿⣇⠈⠀⠀⠀⡸⣿⣿⣿⣿⣿⣶⣤⣤⣁⠁⠈⠙⠚⢾⠫⢷⣯⠿⣿⣟⣃⡞⢿⠓⠥⠄⠚⡚⡝⠿⠿⢛⣻⢿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠐⠉⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠙⠿⢯⡿⡿⡢⣘⡙⣀⣉⡉⡟⠐⠁⢁⠛⠝⠉⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡦⠒⢲⣲⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠘⠶⢙⠫⠗⡛⢧⣷⣿⣤⣤⣄⡨⡦⡰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣶⣀⣠⣤⣤⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣄⣀⠂⡁⠉⣫⠻⣿⡿⢿⣵⡞⠌⠔⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣤⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠉⠋⠨⠃⠲⠲⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠰⣷⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣔⣶⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡶⠷⣦⣴⠾⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⡇⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣠⣦⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡀⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠃⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣶⣿
⣿⣿⣶⣾⣿⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣹⠿⠷⣿⣿⣿⣿⣿⣿⠿⠟⢠⢽⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠘⠀⠈⠉⣹⣿⣿⣿⣿⣿⡿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣛⣋⣉⡉
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⢸⣿⣿⣷⣶
⣽⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⢉⠉⠻⣟⣛⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡢⢿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣬⣁⡒⠀⠉⣿⣬⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠉⠉⠍⠝⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣽⣻⣿⣿⣷⠀⠀⠀⢰⣦⣄⣀⠀⠁⠐⢻⡯⢙⢿⣿⣿⣿⣿⣯⣽⡟⢗⣛⣿⣿⣿⡿⡟⡿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿
⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊⠉⠫⡛⠏⠐⠀⠀⠂⣸⣿⣿⣿⣿⣷⣦⣤⣀⡙⢀⠈⠑⠛⣱⠻⣯⣷⢿⣿⣿⣩⡞⣛⡺⠷⠑⠛⣟⣯⣿⠟⢟⣿⢿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠄⠐⠢⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣄⡈⠀⠀⠉⠈⢫⠿⣮⠿⢴⣦⣀⡌⣀⢘⣛⠃⢚⠑⠋⠈⢏⢛⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡲⠾⢶⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠩⠀⠋⡿⠹⠫⢞⢚⣭⣵⣿⣤⣠⣌⠢⣦⡐⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣦⣀⣀⣨⣭⡽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣀⠐⠀⠁⢉⡋⣳⣿⡿⣿⣦⢱⡀⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣤⣿⣿⣿⠿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣀⡀⠊⠉⠓⠍⠓⠂⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⠶⢶⠶⠶⢶⡾⠶⣦⣴⠿⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⡆⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣠⣦⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠂⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠠⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠀⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣷⣾⣿
⣺⣿⣶⣾⣿⣶⣶⣶⣶⣾⣷⣶⡾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣿⠶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⢹⠿⠿⣿⣿⣿⣿⣷⠿⠿⠿⣈⡛⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠸⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡭⠿⠒⠒⠁
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢻⣿⣿⣯⣄
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣩
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⡿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣟⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢀⣀⣀⡒⠋⡠⠐⠒⢳⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣦⣤⣭⣉⢉⠁⠀⠀⠘⢛⡻⠻⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣀⠀⠰⠙⠫⠽⢽⣟⠽⣿⣟⣟⣿⣿⣛⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠝⠛⣟⠿⠙⠛⠀⠀⠈⢸⣿⣿⣷⣶⣤⣄⡁⠐⠢⠁⠛⠯⡟⠽⢿⣻⣯⣿⣿⢿⢹⠿⡷⢷⣝⠯⠿⣾⢿⣿⠿⣿⣿⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⢖⣀⡠⣖⡀⠀⠀⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣔⣀⠀⠉⠘⠹⠓⠛⢟⣵⢭⣮⡥⣏⠘⠐⠘⠜⢾⠭⠔⠙⠟⡿⠿⢿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠈⠀⠩⢖⣟⠿⣿⡽⢵⣸⣫⣆⣀⣁⠕⢐⡁⡌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⣇⣰⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣧⣀⡀⠄⠠⢘⠪⣻⡿⣿⣿⣿⢗⣜⣲⠂⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣆⢘⣿⣿⣶⣾⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡐⠁⠁⠛⠓⠯⠛⠩⡤⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢤⣟⣿⣿⣿⣿⣿⣭⢽⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠠⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣦⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠶⢶⠶⠶⢶⡶⠶⣤⣴⠿⢿⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⡇⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣠⣦⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⠁⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠠⠀⢹⠀⠁⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠠⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠂⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⡃⢰⣶⡇⠸⠀⡀⠀⡄⢸⡇⠀⡇⠀⡇⠐⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣻⣿
⣤⣿⣷⣾⣿⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣷⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⠿⠿⣿⣿⣿⣿⣿⣿⡿⡿⢹⣭⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣡⢤⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⠭⠅⠐
⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⠠⠛⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⣷⣶⣶⣒⡀
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⢛
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣂⣤⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠠⠹⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⣈⣙⣓⠒⠒⠃⠀⠀⠸⠿⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣷⠂⠀⠀⡈⠉⠈⢠⠫⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠟⠿⡛⠟⠓⠀⠀⠀⣿⣿⣶⣦⣤⣀⠔⠊⢉⢌⠋⡿⣟⡿⣻⣿⢯⣫⣾⣷⣿⢿⣿⣝⣽⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠶⣤⣤⣀⣿⣄⣀⠀⠀⣀⣤⣻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣂⡄⠀⠁⠇⠛⢻⠏⢻⢿⣾⣿⣜⣓⠉⠉⡤⢸⣼⣿⢋⡤⡿⠯⣿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠋⡍⢋⣭⡿⣿⢞⣴⣶⠲⡪⡄⠈⠀⠆⠌⠃⡊⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⡎⣫⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣅⣁⠘⠍⠁⠉⠳⢊⢷⢿⣿⣿⣿⣶⠹⠇⠘⡈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠲⣾⣷⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣀⠀⡏⠓⠛⠽⢽⡛⢯⣓⡘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢉⢿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⢀⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣀⡀⠀⡀⢫⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠶⢶⠶⠶⢶⡶⠶⣤⣴⠶⢾⠿⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣿⡇⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣤⣦⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡇⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⠀⠀⢹⠀⠃⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⢀⣿⡇⢸⣿⠀⠸⠇⠀⢿⣿⠀⢸⠀⠇⠀⠃⠀⠀⣿⠀⣿⣿⠁⠂⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⡇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠘⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⢿⣿
⣀⣻⣷⣾⣿⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡶⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠘⠛⢛⣛⡒⠧⠬⠭⠭⢾⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡦⠄⠀⠀
⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡆⠀⢛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣚⣛⣉⡉⠀
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⢸⣿⣿⣷⣶⣠
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⡉⠻⢿⣟⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⢰⢶⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣤⣄⣃⣠⡖⠁⠈⢨⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⡤⣷⣶⣶⣦⣌⣈⠀⠀⠀⠈⠭⠙⢟⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⣿⢿⣿⡿⠆⠀⠀⣦⣄⣀⠉⠉⠐⢗⠿⠵⢻⢿⣝⣿⣿⣿⣽⣿⣿⣻⣻⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠁⠐⠉⠀⣤⠈⠀⠀⠀⠀⣀⣿⣿⣿⣿⣷⣶⣤⣀⡉⠂⠈⠙⠺⢑⡛⣯⣷⠾⣿⣟⣧⡿⢿⠛⠗⠝⠚⡻⡏⣿⡿⢻⣿⢿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢿⣯⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣥⣄⡀⠀⠁⠉⠀⠙⡿⢗⡿⢷⣺⣄⡁⣀⡑⣙⡇⠚⡁⠁⠙⢿⠛⠟⠿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠿⢿⣿⣿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠘⢀⠚⠽⠝⠻⢷⡛⣣⣷⡿⣴⣤⣴⡠⡤⠰⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣔⢀⣈⣛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠢⡁⢨⣫⢻⢿⣿⢿⣵⡌⠍⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣶⣺⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣅⣀⠘⠉⠛⠈⠁⠲⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣖⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⣶⣤⣴⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠴⢶⠶⠶⢶⡶⠶⣤⣴⠶⢶⠶⡿⠿⡿⠿⢿⠿⠿⠿⣿⡿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⣿⠿⢿⡿⠿⡿⢿⣿⣿⠿⢿⡿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿
⠀⣾⡇⢸⣠⠀⢸⡇⠀⣿⣿⠀⢸⠀⡇⠀⠀⠠⣤⣶⠀⣴⣿⠀⠠⣤⣶⠀⣶⠀⠰⡾⠀⠀⡇⠀⣿⣿⠃⠀⢸⣿⡆⠰⠀⡇⢰⠀⠁⠀⠆⢰⡆⠀⡆⠀⡇⢠⠀⢹⠀⠃⢸⣿⠁⠀⠀⡇⠀⢾⣿⠀⢰⠀⢰⣿⣿⣿
⠀⣿⡇⢸⣿⠀⠸⡇⠀⢿⣿⠀⢸⠀⠇⠀⠃⠂⠀⣿⠀⣿⣿⠉⠂⠀⣿⠀⣿⠀⠰⠇⠀⠀⠀⠀⠿⣿⠀⠀⠈⣿⠇⢰⣶⡇⠸⠀⡀⠀⡆⢸⡇⠀⡇⠀⡇⠸⠀⢸⠀⠀⢸⣿⠀⠀⠀⡇⠀⣾⣿⠀⢸⠀⢸⣿⣿⣿
⢠⣿⣷⣾⣿⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣿⣶⣾⣿⣷⣶⣶⣷⣶⣶⣾⣷⣶⣷⣶⣿⣶⣶⣿⣶⣷⣾⣿⣷⣶⣶⣷⣶⣿⣿⣶⣾⣶⣾⣷⣿⣿
⣼⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2268

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✐ When_It_Comes_to_Financial_Spin-Doctoring,_Microsoft_is_Now_Marketers
Marketers_Marketers_Marketers⠀✐


Posted in Deception, Finance, Microsoft at 12:05 am by Dr. Roy Schestowitz


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


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Stock_price_'most_important_lever'_to_get_pay_raise,
                        Microsoft_CMO_tells_employees⦈_


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_CMO_tells_employees_the_stock_price_is_the_‘most
important_lever’_to_get_a_pay_raise_after_cashing_out_on_$4.4_million_worth_of
                              stock_this_month⦈_


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_CMO_tells_employees_the_stock_price_is_the_‘most
important_lever’_to_get_a_pay_raise_after_cashing_out_on_$4.4_million_worth_of
                              stock_this_month⦈_


Summary: Marketers from Microsoft — and former Chief Marketing Officers or HR
VPs_too — are trying to spin Microsoft’s collapsing_business_units (and mass
layoffs that are under-reported and grossly under-counted in the media); how
much of Microsoft’s remaining financial activity is just financialization and
debt-loading (e.g. buying companies to offload debt onto them)?


Microsoft is 80_billion_dollars_in_debt (a lot higher than its cash reserves or
bank balance) and the layoffs carry on and on this year (example_from_this_past
Friday). The bleeding does not stop.


“The bleeding does not stop.”As an associate put it this morning, “it is
telling that Microsoft is [as per news_sites] linking the possibility of salary
raises to stock price because it suggest that Microsoft makes most of its money
through financialization and that the Office format monopoly rents are weak or
gone and that the OEM monopoly rents are weak or probably gone, since they are
now basically giving away Windows.” (Almost no cost, as the competition with
GNU/Linux is fierce)


“Notice how the media now quotes as financial expert a marketing person.”We’re
going to see some interesting things ahead because government bailouts will be
harder for Microsoft to secure (Trump_and_Biden_bailed_Microsoft_out_with
"defence"_contracts_worth_tens_of_billions_of_dollars). Now that the US
government grapples with the possibility of default (aside from almost_$32
trillion_in_national_debt there is also close to $18 trillion in US household
debt), not to mention many failing banks (hundreds more are said to be on the
verge of collapse right now) there are not many chips left on the table. Will
people’s pensions be thrown at the stock market, tied to stocks where the
valuation is massively inflated and unrealistic?


Notice how the media now quotes as financial expert a marketing person*. To
quote: “Microsoft’s Chief Marketing Officer Chris Capossela has reportedly told
employees that “the most important lever for almost all our employees’
compensation upside is the stock price.”” █


______
* That Microsoft “report” and similar ones (same ‘script’) has helped distract
from the layoffs (we saw numerous of the same spiel, an identical ‘script’).
Last week Microsoft spread a bunch of fluff about salaries and salary increases
while many layoffs were quietly signed off.


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣆⣁⣷⣁⣀⣥⡖⢈⣂⣿⣯⣿⣷⣈⣙⣹⣹⣟⣼⣿⣠⣉⣩⣉⣍⣉⣹⣿⣼⣿⣀⣙⣈⣹⣙⣉⣽⣟⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣷⣤⣤⣥⣬⣴⣾⣽⣧⣷⣤⣼⣽⣧⣤⣼⣤⣧⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠉⡿⠉⡏⡿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠏⠹⠹⢿⣿⠿⢿⠿⠿⠿⠿⡿⠿⢿⡿⠉⠿⠿⢿⢹⢹⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⡏⡿⠿⠿⢿⠿⠿⠿⡿⠿⠿⠿⢿⣿⠉⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⢠⠀⡆⡇⣄⠒⡀⢰⡀⠃⣀⠀⢠⡘⢂⡇⣿⠘⢻⣇⠀⠀⢀⡘⡀⠀⣄⠒⣸⣿⡀⢃⠀⢠⢸⢸⠀⢀⣿⡀⠀⡀⣴⢸⠀⠀⠃⡀⣄⠒⣰⠈⣰⡀⢀⡄⠀⣀⠀⢸⣿⡀⢃⠘⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠹⠿⠿⠿⠿⠿⡿⠿⡿⠿⠿⣿⢿⠿⢿⣿⠉⠟⢿⠿⢿⣿⡿⠿⠟⠻⡿⠿⡿⠿⢿⢹⠿⣿⠿⠿⢿⠿⢿⠿⠿⠉⡿⠿⡿⠾⠿⠿⠿⢿⠷⢶⠿⠿⡿⠿⢿⠿⢿⣿⡏⡿⠿⢿⣿⠙⠙⠿⠿⡿⡿⢿⣿⠿⠿⠏
⣿⡇⠀⢰⢰⠀⠀⠂⡀⢰⡀⠂⣀⠀⣄⠈⢀⣿⠀⡆⢚⠈⢀⣿⡀⠅⡆⠐⡐⠂⡀⠒⢒⢀⠸⣿⠀⠒⢀⠀⢀⠀⣶⢰⡀⠂⡀⢰⠀⡆⡆⠀⠈⠀⠀⡆⠀⠒⢒⠀⢀⣿⡇⡇⣶⢸⣿⠀⠀⠀⠀⡄⠃⢸⣯⠐⠂⡆
⣿⡿⠿⡿⠿⡟⢲⠿⣿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⢰⠂⠄⠀⠀⠀⢀⠠⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠧⠥⠤⠯⠼⠦⠬⠤⠿⠿⠿⠧⠤⠼⠤⠤⠤⠦⠤⠧⠤⠤⠤⠭⠽⠿⠤⠭⠼⠽⠂⠀⠀⠀⠀⠿⠷⠿⠓⠓⠒⠒⠚⠒⠒⠒⠒⠒⠒⠛⠒⠒⠓⠒⠒⠚⠓⠒⠚⠒⠒⠒⠚⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠆⠉⡍⠹⠇⠵⠩⠉⠉⡉⠍⠙⠩⠩⢽⡇⡇⡍⠉⠉⢉⣿⣿⠈⠉⡉⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⠿⢿⣿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠛⢛⡟⠛⠛⢻⣻⣿⠛⠛⠛⢻⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣾⣶⣶⣶⣾⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⡿⢿⣿⡿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⢿⡿⢿⣿⣿⣿⡿⠿⣿⠿⡿⣿⣿⢿⣿⣿⣿⢿⡿⣿⠿⣿⣿⣿⡿⢿⣿⢿⣿⡿⠿⢿⠿⣿⣿⡿⣿⡿⠿⠿⠿⣿⡿⢿⡿⠿⡿⢿⡿⣿
⣷⣷⣶⣶⣷⣤⣶⣶⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣶⣾⣶⣶⣶⣦⣾⣶⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣿⣶⣶⣶⣾⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣷⣦⣶⣶⣶⣷⣶⣾⣶⣶⣶⣶⣶⣷⣷⣶⣶⣶⣷⣶⣶⣦⣴⣾⣧⣿
⣛⣛⣛⣛⣏⣛⣿⣉⣻⣏⣻⣿⣹⣛⣛⣛⣻⣿⣙⣛⣙⡛⣿⣙⣻⣻⣛⣿⣝⣛⣋⣙⣛⣻⣟⣛⣛⣙⣟⣛⣟⣿⣉⡛⣻⣹⣝⣛⣛⣛⣿⣹⣛⣛⣛⣛⣋⣿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣴⣤⣴⣤⣤⣶⣤⣾⣧⣤⣦⣧⣤⣤⣼⣧⣤⣬⣤⣤⣷⣤⣤⣤⣤⣦⣦⣤⣤⣧⣧⣤⣤⣽⣤⣬⣤⣤⣤⣼⣤⣤⣦⣤⣴⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⢽⢙⢛⠻⡛⡽⣻⡛⡻⢛⡋⢟⠻⡛⣿⡟⡛⣻⢟⠻⠛⣛⣿⢙⢛⣛⣟⡛⢟⡻⢛⢛⣟⢻⢛⢟⣻⡏⣟⣛⠛⣛⢛⢛⣹⡋⣟⡻⡿⡛⢟⢛⣻⡟⡛⢟⢛⠛⣟⢛⢛⣏⡟⢻⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣽⣬⣬⣤⣭⣭⣼⣇⣵⣬⣥⣮⣥⣭⣿⣧⣥⣭⣮⣤⣥⣯⣿⣬⣬⣭⣝⣡⣮⣵⣬⣮⣧⣬⣬⣼⣽⣧⣯⣽⣶⣧⣽⣼⣿⣧⣯⣵⣏⣈⣬⣽⣽⣇⣥⣤⣜⣸⣿⣼⣬⣭⣥⣴⣬⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡁⡇⢫⣹⣻⣩⠋⢹⣉⠃⡌⣽⢫⡦⣆⠛⢰⢱⡎⣿⢩⠫⠃⡇⡏⢹⡏⢹⢩⢋⡏⡍⡆⢫⣉⠉⡍⢹⠉⡯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣷⣶⣾⣶⣶⣾⣶⣷⣷⣾⣷⣶⣶⣾⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣷⣾⣶⣶⣦⣴⣶⣶⣾⣵⣷⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢩⣍⣭⠍⠉⢍⠉⠉⠉⢩⡉⢉⠉⠭⠉⠉⡍⠉⢩⡉⢩⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣻⠛⡟⢻⡛⡟⡟⡟⢻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛
⣇⣾⣀⣇⣸⣇⣇⣣⣧⣸⣐⣿⣾⣾⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣾⣿⣿⣿⣿⣷⣷⣿⣷⣾⣿⣷⣿⣿⣷⣾⣿⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣷⣷⣿⣇⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣶⣷⣧⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡟⢻⢻⠿⠿⡿⡿⣿⠿⡿⢿⠫⠿⣿⢟⣿⣿⠻⡟⢻⢟⣟⢿⡿⢿⠿⡏⡏⡿⢿⡿⢿⠿⢿⢿⠿⢿⢹⠿⡿⢿⠿⢿⡿⡿⢿⡿⠻⠹⢿⠿⣿⡿⠿⢻⠿⣿⠿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣣⣜⣸⣘⣘⣃⣳⣘⣐⣈⣜⣸⣘⣘⣿⣌⣛⣟⣣⣜⣸⣜⣛⣼⣧⣸⣐⣇⣃⣂⣹⣇⣒⣘⣘⣘⢘⣸⣸⣘⡼⢨⣇⣒⣘⣒⣩⣿⣘⣸⣸⣐⣾⣗⣹⣘⣘⣤⣛⣃⣜⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⢛⡿⢿⢿⣿⢻⡿⣿⡿⡟⡿⣿⢿⣿⢻⢿⢿⢿⡿⣿⢿⠿⣿⢛⢿⢿⢿⢿⢿⡿⣿⢿⡿⡿⢿⣿⢿⡿⣿⡟⡿⡿⢿⢿⢿⢿⢿⢻⣿⢿⡿⣿⣿⠿⡿⢿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣓⣜⣲⣛⣘⣣⣓⣿⣘⣊⣿⣇⣃⣇⣇⣻⣿⣿⣸⣸⣸⣘⣐⣉⣘⣿⣀⣘⣘⣘⢘⣸⣘⣸⣸⣇⣋⣃⣇⣇⣇⣿⣃⣜⣺⣬⣇⣓⣐⣾⣿⣿⣘⣘⣸⡇⡁⣇⣺⣘⣿⣙⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣻⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣛⣿⠛⣿⡿⢻⣿⣿⣿⣟⡛⡞⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣓⣌⣇⣧⣱⣿⣰⣎⣇⣇⣪⣀⣳⣿⣹⣸⣸⣸⣘⣾⣰⣿⣘⣎⣅⣧⣹⣸⣸⣸⣸⡐⣁⢿⣇⣢⣘⣸⣘⣿⣸⣸⣸⣸⣟⣂⣥⣅⣛⣬⣸⣟⣰⣀⣀⣀⣇⣇⣇⣇⣇⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⡿⣟⢻⣿⣿⣿⡟⣻⣿⣿⢿⣿⣿⣿⠛⣿⣿⢿⠛⣿⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣡⣱⣐⣸⣰⣆⣿⣰⣸⣇⣇⣇⣿⣪⣀⣸⣐⣀⣷⣀⣸⣿⣸⣀⣾⣸⣬⣿⣇⣆⣆⣑⣨⣸⣸⣸⣰⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣮⣤⣷⣼⣤⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⢹⣿⡛⣿⣿⣯⣽⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⢹⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣿⡟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⠀⠀⠀⠀⠀⣠⣤⠘⠛⠉⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣧⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞⠳⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⢀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣛⡯⢹⡍⡫⣋⢝⢷⣥⢸⡉⡯⢹⡉⡯⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣯⣝⣟⣿⣿⣿⣿⣝⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⡟⡟⣿⡿⡿⡿⢿⢿⢿⣻⣻⢟⣿⢻⢻⢻⢻⡟⡿⢿⡟⢿⣿⡿⢿⢿⡿⣿⠻⡿⢿⣿⠿⡿⢿⣿⢻⠻⣿⢿⢿⡟⡿⣿⢿⠻⣿⢿⠿⡿⡿⡿⣿⡟⢿⣿⢻⠻⣿⢿⣿⠿⡿⢿⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣶⣿⣷⣷⣷⣷⣾⣾⣿⣿⣷⣿⣷⣿⣾⣾⣷⣷⣿⣷⣷⣿⣿⣾⣾⣧⣿⣶⣷⣧⣷⣿⣿⣷⣿⣾⣶⣷⣿⣿⣷⣷⣿⣾⣶⣿⣼⣶⣷⣷⣷⣿⣷⣷⣿⣾⣶⣿⣿⣿⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣹⣏⣿⣉⣏⣹⣇⣿⣹⣏⣇⣿⣏⣿⣉⣹⣍⣿⣿⣸⣹⣿⢩⣿⣽⣺⣿⣹⢹⣙⣏⣝⣿⣹⣋⣏⣝⣹⣽⣻⣇⣇⣏⣿⣹⣏⣿⣏⣝⣿⣹⣏⣿⢩⣿⣹⣏⣻⣸⣏⣿⣹⣿⣄⣏⣸⣏⣘⣏⣏⣹⣇⣸⣉⣏⣹⣿
⣿⠿⢿⠿⣿⢻⠿⣿⠿⡟⣿⢿⢻⢿⠿⣿⢿⣿⢻⡿⣿⢿⡿⡿⢿⠿⡿⢿⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣷⣾⣶⣿⣾⣷⣿⣶⣷⣿⣷⣾⣾⣶⣿⣶⣿⣾⣷⣿⣷⣷⣷⣾⣶⣷⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2437

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.21.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_21/05/2023:_Unifont_15.0.02_and_KDE_Plasma_6_Plans⠀✐


Posted in News_Roundup at 9:58 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Benchmarks
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o GNU_Projects
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Copyrights
    * § GNU/Linux⠀➾


          o ⚓ Linux Made Simple ☛ 2023-05-14_[Older]_Linux_Weekly_Roundup
            #235⠀⇛


          o § Audiocasts/Shows⠀➾


                # ⚓ 2023-05-17_[Older]_FLOSS_Weekly_732:_Update_Your_Kernels!_–
                  Greg_Kroah-Hartman,_Linux_Kernel,_Cyber_Resilience_Act⠀⇛


                # ⚓ 2023-05-20_The_Death_and_Life_of_Elementary_OS_and_How_to
                  Revive_It!⠀⇛


                # ⚓ 2023-05-20_Ubuntu_Linux_Ruined_It’s_Reputation_Before_It
                  Began⠀⇛


                # ⚓ 2023-05-20_This_19″_3U_Raspberry_Pi_Rack_Mount_is_Good_
                  (Enough)⠀⇛


                # ⚓ 2023-05-19_How_to_install_Ubuntu_Cinnamon_23.04⠀⇛


                # ⚓ 2023-05-19_Is_It_Safe_To_Use_Software_That_Isn’t_Actively
                  Maintained?⠀⇛


                # ⚓ 2023-05-19_Valve_in_Hot_Water:_Shocking_Lawsuit_Calls_Steam
                  Deck’s_Tech_into_Question!_|_Deck_News_84⠀⇛


                # ⚓ 2023-05-19_Ubuntu_23.04_Quick_Overview_#shorts⠀⇛


                # ⚓ 2023-05-18_[Older]_Ubuntu_Cinnamon_23.04_overview|_Ubuntu,
                  traditionally_modern.⠀⇛


                # ⚓ 2023-05-18_[Older]_Meet_Rhino_Linux_:_Ubuntu_based_+
                  Rolling_release_+_AUR⠀⇛


                # ⚓ 2023-05-18_[Older]_How_to_install_Notepadqq_on_MX_Linux
                  21.3⠀⇛


                # ⚓ 2023-05-18_[Older]_Google_Should_Retract_These_New_Top
                  Level_Domains⠀⇛


                # ⚓ 2023-05-17_[Older]_Fedora_38_Quick_Overview_#shorts⠀⇛


                # ⚓ 2023-05-17_[Older]_How_to_install_Zoom_on_MX_Linux_21.3⠀⇛


                # ⚓ 2023-05-17_[Older]_Why_is_Linux_So_Secure?_|_File
                  Permissions_and_Groups⠀⇛


                # ⚓ 2023-05-17_[Older]_Arch_Linux_Repos_Finally_Join_The_21st
                  Century⠀⇛


                # ⚓ 2023-05-17_[Older]_Installation_and_First_Look_at_WattOS⠀⇛


                # ⚓ 2023-05-17_[Older]_How_to_install_Red_Hat_Enterprise_Linux
                  9.2⠀⇛


                # ⚓ 2023-05-16_[Older]_Wayland_Is_Here:_Let_Xorg_Finally
                  Retire!⠀⇛


                # ⚓ 2023-05-16_[Older]_Why_the_BAD_design_of_WINDOWS_hurts
                  LINUX_desktops⠀⇛


                # ⚓ 2023-05-16_[Older]_How_to_install_Blender_on_MX_Linux
                  21.3⠀⇛


                # ⚓ 2023-05-15_[Older]_Fediverse_And_Mastodon_Aren’t_Doomed
                  But…⠀⇛


                # ⚓ 2023-05-15_[Older]_How_to_install_LeoCAD_on_MX_Linux_21.3⠀⇛


                # ⚓ 2023-05-15_[Older]_How_the_ROG_Ally_lends_the_Steam_Deck_a
                  helping_hand.⠀⇛


                # ⚓ 2023-05-15_[Older]_Google_will_FORCE_Ads_on_You⠀⇛


                # ⚓ 2023-05-15_[Older]_VirtualBox_Revisited_|_Creating_a
                  Virtual_Machine⠀⇛


                # ⚓ 2023-05-15_[Older]_VirtualBox_Revisited_}_Creating_a
                  Virtual_Machine⠀⇛


                # ⚓ 2023-05-15_[Older]_Ubuntu_Budgie_23.04_Quick_Overview
                  #shorts⠀⇛


                # ⚓ 2023-05-14_[Older]_Top_5_Best_Linux_Distros_Every_Software
                  Developer_MUST_Use_for_Ultimate_Productivity_in_2023!_(NEW)⠀⇛


                # ⚓ 2023-05-14_[Older]_How_to_install_Krita_on_MX_Linux_21.3⠀⇛


                # ⚓ 2023-05-14_[Older]_Have_You_Tried_These_Popular_Haskell
                  Programs?_(You_Should!)⠀⇛


                # ⚓ 2023-05-14_[Older]_One_Open_Source_Project_Runs_So_Many_Web
                  Forums⠀⇛


                # ⚓ 2023-05-13_[Older]_How_One_Linux_MAN_Easter_Egg_Caused
                  Chaos⠀⇛


                # ⚓ 2023-05-13_[Older]_COSMIC_will_be_customizable,_AMD’s_FOSS
                  firmware_&_Plasma_6_changes:_Linux_&_Open_Source_News⠀⇛


                # ⚓ 2023-05-20_More_HDR_work_for_Linux,_Ubuntu_revamps_PPAs,
                  KeePass_security_flaw:_Linux_&_Open_Source_News⠀⇛


                # ⚓ 2023-05-16_[Older]_Red_Hat_Enterprise_Linux_9.2_overview_|
                  security_functionality_and_performance_for_IT_environments⠀⇛


          o § Benchmarks⠀➾


                # ⚓ Tom’s Hardware ☛ Ampere_Unveils_192-Core_CPU,_Controversial
                  Benchmarks⠀⇛


                       Ampere’s AmpereOne CPU features 192 cores at 200W –
                       350W.


                # ⚓ Tom’s Hardware ☛ Intel_Meteor_Lake_16-Core,_14-Core_CPUs
                  Surface_In_New_Benchmarks⠀⇛


                       Hardware detective momomo_us finds two alleged
                       Intel 14th Generation Meteor Lake processors for
                       mobile devices in the SiSoftware benchmark
                       database.


          o § Applications⠀➾


                # ⚓ OMG! Linux ☛ More_Features_Added_to_Tuba,_a_GTK_Mastodon
                  App_for_Linux⠀⇛


                       A myriad of new features have been added to Tuba,
                       the terrific open source Mastodon client for Linux
                       I took a look at a few months ago.


                # ⚓ Ubuntu Handbook ☛ Pandora_App_‘Pithos’_1.6.1_Adds_Plugin
                  Support_for_Python_3.11⠀⇛


                       For Ubuntu 23.04, Fedora 38 and other Linux with
                       Python 3.11 as default, Pithos 1.6.1 was released
                       today to fix the plugin support! Pithos is a simple
                       free open-source GTK client for Pandora music &
                       podcasts, writing in Python programming language.


                # ⚓ tao-dialog⠀⇛


                       Tao-dialog is part of tao-utils commands group. It
                       assembles only tao-manager (simple file manager)
                       and tao-dialog currently. Tao-dialog aims to work
                       as zephyr/kdialog replacement, but it is currently
                       not done. Maybe in future, I will add xmessage
                       compatibility mode. Dialog compact mode rather
                       never been supported, due dialog have options
                       rather hard to implement using libgreattao.


                       Libgreattao have GUI and shell mode. Network mode
                       must be re-implemented. Many feature, working in V2
                       version must be rewriten to V3 (3.0 version). But
                       V2 is rather complicated and error-prone.
                       LibgreattaoV3 uses libexslt internally.


                       Zephyr and KDialog modes of tao-dialog are
                       partially implemented. You can do basic stuff like
                       displaying yes/no dialog, info dialog and file
                       dialogs. File dialogs are currently error-prone in
                       libgreattaoV3 (sometimes causes crash, when dialog
                       is destroyed), but I will work on this.


          o § Instructionals/Technical⠀➾


                # ⚓ TecAdmin ☛ Resolving_‘laravel.log_could_not_be_opened’:
                  Step_by_Step_Solutions⠀⇛


                       Laravel, an expressive and elegant PHP framework,
                       is widely employed for web application development
                       due to its syntax and robust functionalities.
                       However, like all technologies, it is not without
                       its share of challenges.


                # ⚓ TecAdmin ☛ A_Step-by-Step_Guide_to_Sending_Emails_using
                  cURL⠀⇛


                       cURL, short for “Client for URLs”, is an open-
                       source software project that provides a library
                       (libcurl) and a command-line tool (curl) for
                       transferring data using various network protocols.
                       While it’s commonly used to interact with HTTP and
                       HTTPS, it can also handle SMTP, which is the
                       standard protocol for sending emails on the
                       internet.


                # ⚓ Trend Oceans ☛ Nala:_A_Beautiful_and_Structured_Frontend
                  for_the_APT_Package_Manager⠀⇛


                       I bet once you start using the Nala package
                       manager, there’s no way going back to the apt
                       command. When you try to install any application or
                       utility using the apt command, what do you see?


                # ⚓ Linux Made Simple ☛ 2023-05-18_[Older]_How_to_install
                  Notepadqq_on_MX_Linux_21.3⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-05-17_[Older]_How_to_install_Zoom
                  on_MX_Linux_21.3⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-05-16_[Older]_How_to_install
                  Blender_on_MX_Linux_21.3⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-05-15_[Older]_How_to_install
                  LeoCAD_on_MX_Linux_21.3⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-05-14_[Older]_How_to_install_Krita
                  on_MX_Linux_21.3⠀⇛


          o § Games⠀➾


                # ⚓ New York Times ☛ The_E-Sports_World’s_Future_Is_Uncertain
                  as_Growth_Stalls⠀⇛


                       At least two organizations in America’s most
                       prominent league for professional video game
                       players are selling their teams, underscoring the
                       industry’s uncertain future.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ 9to5Linux ☛ KDE_Plasma_6_Desktop_Environment_Promises
                        Basic_HDR_Support⠀⇛


                             HDR support on the Linux desktop is probably
                             one of the most requested features these days
                             due to the fact that 4K displays are becoming
                             the norm while we slowly but shortly say
                             goodbye to Full HD screens.


                             KDE Plasma is one of the first GNU/Linux
                             desktop environments to receive HDR (High
                             Dynamic Range) support and initial support
                             was already merged for the upcoming KDE
                             Plasma 6.0 series during the recent HDR
                             hackfest organized by Red Hat in early May
                             2023 and last week’s Plasma 6 sprint in
                             Augsburg.


    * § Distributions and Operating Systems⠀➾


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Control_a_thermal_printer_with_your_Arduino⠀⇛


                       You would probably recognize a thermal printer as
                       the thing that spits out receipts at a cash
                       register. They offer a two key advantages: they do
                       not require ink cartridges and they are compact.
                       But because they print by applying heat to special
                       paper that darkens when hot, they have low
                       resolution and fidelity.


                # ⚓ Arduino ☛ DIY_air_hockey_table_uses_an_Arduino_to_keep
                  score⠀⇛


                       Inspired by game nights with her family, Lorraine
                       Underwood from element14 Presents wanted to build a
                       project that would be both fun and playable many
                       times over. Based on these parameters, she opted to
                       design and construct her own take on an air hockey
                       table that would be capable of keeping score
                       automatically.


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


          o § GNU Projects⠀➾


                # ⚓ Barry Kauler ☛ gcc_now_works_with_older_CPUs⠀⇛


                       Three people reported that when they tried to
                       compile with gcc, they got “illegal instruction”.
                       So, have to do something about it.
                       No problem for me; I compile on computers with
                       Intel i3 and Ryzen 5 CPU. Today booted up Easy on a
                       much older computer, with an earlier-gen i5 CPU,
                       with the devx SFS loaded, when ran “gcc –help” got
                       that “illegal instruction”. Hmmm.


                # ⚓ Andy_Wingo:_approaching_cps_soup⠀⇛


                       Good evening, hackers. Today’s missive is more of a
                       massive, in the sense that it’s another
                       presentation transcript-alike; these things always
                       translate to many vertical pixels.


                       In my defense, I hardly ever give a presentation
                       twice, so not only do I miss out on the usual per-
                       presentation cost amortization and on the
                       incremental improvements of repetition, the more
                       dire error is that whatever message I might have
                       can only ever reach a subset of those that it might
                       interest; here at least I can be more or less sure
                       that if the presentation would interest someone,
                       that they will find it.


                       So for the time being I will try to share
                       presentations here, in the spirit of, well, why the
                       hell not.


⚓ GNU ☛ unifont_@_Savannah:_Unifont_15.0.02_Released⠀⇛


     20 May 2023 Unifont 15.0.02 is now available. This is a minor
     release, but its the last expected version to build TrueType fonts by
     default. Future releases will only build their OpenType equivalents.
     This version also adds Doxygen HTML and LaTeX-generated PDF
     documentation, in the “doxygen” top-level directory.
     Also, by request, the CJK double-width characters in the
     U+FF00..U+FFEF range have been revised to non-boldface variants.
     Download this release from GNU server mirrors at:
     https://ftpmirror.gnu.org/unifont/unifont-15.0.02/
     or if that fails,
     https://ftp.gnu.org/gnu/unifont/unifont-15.0.02/
     or, as a last resort,
     ftp://ftp.gnu.org/gnu/unifont/unifont-15.0.02/
     These files are also available on the unifoundry.com website:
     https://unifoundry.com/pub/unifont/unifont-15.0.02/
     Font files are in the subdirectory
     https://unifoundry.com/pub/unifont/unifont-15.0.02/font-builds/
     A more detailed description of font changes is available at
     https://unifoundry.com/unifont/index.html
     and of utility program changes at
     http://unifoundry.com/unifont/unifont-utilities.html


§ Programming/Development⠀➾


    * ⚓ Junichi_Uekawa:_Shared_library_loading.⠀⇛


           Shared library loading. ld.so seems to load shared libraries
           serially, looking through the load paths, looking through
           DT_LOADED sections, and looking up library paths or what’s in
           ld.so.cache.
           I thought I could scan DT_LOADED with just reading approx first
           2kB of shared library, and get the full list of shared
           libraries first, and then readahead(2) the list of shared
           libraries available.


    * § Perl / Raku⠀➾


          o ⚓ Perl ☛ 2023-05-19_[Older]_Response_header_name_‘_Content-_type’
            contains_invalid_characters,_after_running_a_Perl_CGI_script.⠀⇛


          o ⚓ Perl ☛ 2023-05-16_[Older]_Perl_Weekly_Challenge_217:_Sorted
            Matrix_and_Max_Number⠀⇛


          o ⚓ Perl ☛ 2023-05-16_[Older]_TPRC_Hackathon_2023⠀⇛


          o ⚓ Perl ☛ 2023-05-14_[Older]_Perl_Weekly_Challenge_#216_–_Choosing_a
            Nickname_for_Your_Car⠀⇛


§ Leftovers⠀➾


    * ⚓ New York Times ☛ The_Tyranny_of_‘the_Best’⠀⇛


           In toasters and in life, the top-rated anything will never be
           good enough.


    * ⚓ New York Times ☛ 2_Bodies_Found_in_NYC_Rivers_Are_Identified_as_Missing
      Boys⠀⇛


           Alfa Barrie, 11, and Garrett Warren, 13, had been missing for
           several days. The police said their investigation into the
           boys’ deaths was continuing.


    * ⚓ CoryDoctorow ☛ Pluralistic:_Dumping_links_like_Galileo_dumped_the
      orange_(20_May_2023)⠀⇛


    * ⚓ Tedium ☛ Consider_the_Jackalope⠀⇛


           How a happy taxidermy accident created the jackalope legend.
           But it’s a legend that might have some real-world grounding.
           Jackalopes may have even helped us solve cancer.


    * § Science⠀➾


          o ⚓ Science Alert ☛ Strange_Crystal_Melts_And_Changes_Color_When
            Exposed_to_Light⠀⇛


                 A most unusual material.


          o ⚓ Science Alert ☛ Building_a_Satellite_Out_Of_Wood?_You_Have_to_Use
            This_Wood,_According_to_a_New_Study⠀⇛


                 There’s no rule saying a satellite can’t be made of wood.


          o ⚓ Science Alert ☛ The_Strange_Mystery_of_Champagne_Bubbles_Can
            Finally_Be_Explained⠀⇛


                 There’s something different about these bubbles.


    * § Hardware⠀➾


          o ⚓ Tom’s Hardware ☛ SanDisk_Extreme_Portable_SSD_Suffer_Sudden
            Failures:_WD_Responds⠀⇛


                 WD says that it is readying a firmware fix for a
                 frightening SanDisk Extreme Portable SSD sudden failure
                 issue, but it only mentions updates for 4TB users.


    * § Health/Nutrition/Agriculture⠀➾


          o ⚓ TwinCities Pioneer Press ☛ Pandemic-era_rise_in_road_crashes_in
            Minnesota_declining,_officials_say⠀⇛


                 The encouraging news is that at this point, the fatality
                 rate appears on a trend for a 20% decline this year,
                 according to information presented.


          o ⚓ Science Alert ☛ New_Research_May_Explain_How_This_Virus_Can_Cause
            Multiple_Sclerosis_in_Some_People⠀⇛


                 Confused antibodies.


          o ⚓ US News And World Report ☛ Why_Taking_Your_Kids_to_the_Park_Is
            Always_a_Healthy_Idea⠀⇛


          o ⚓ Federal News Network ☛ Shark_in_Florida_Keys_bites_angler_who
            reeled_it_in,_sending_man_to_hospital⠀⇛


                 Authorities in the Florida Keys say a shark bit the foot
                 of a fisherman who had reeled it in, sending the man to
                 the hospital. The Monroe County Sheriff’s Office said
                 Saturday in a statement that the 35-year-old man was
                 fishing off a dock in Summerland Key when he caught the
                 shark Friday night. While it was on the dock, it bit him
                 in the foot. The angler was flown by a trauma helicopter
                 to a hospital in Miami. The sheriff’s office said his
                 condition was not known on Saturday.


          o ⚓ Mexico News Daily ☛ A_rose_by_any_other_name?_How_do_alternative
            milks_measure_up?⠀⇛


                 Janet Blaser takes a look at the most popular kinds of
                 non-dairy milks out there to see how they compare to old-
                 fashioned leche de vaca.


          o ⚓ 2023-05-16_[Older]_In_Summertime_We_Now_Have_Wintertime-Like
            Death_(Mortality)_Levels_in_the_UK⠀⇛


    * § Security⠀➾


          o ⚓ SANS ☛ Phishing_Kit_Collecting_Victim’s_IP_Address,_(Sat,_May
            20th)⠀⇛


                 While reviewing my last findings today, I found a
                 phishing email that delivered a classic .shtml file
                 called “PROFORMA INVOICE.shtml”. Right now, nothing
                 special, emails like this one are widespread. When you
                 open the file in a sandbox, it reveals a classic form:


          o ⚓ Nyxt:_Hacker’s_Dream_Browser⠀⇛


                 In the ever-evolving digital landscape, the demand for
                 specialized tools and platforms has grown exponentially.
                 For hackers and technology enthusiasts, having a browser
                 that caters to their unique needs and empowers their
                 capabilities is crucial. Enter Nyxt, an innovative and
                 versatile web browser designed specifically with hackers
                 in mind.


    * § Defence/Aggression⠀➾


          o ⚓ RFERL ☛ Tens_Of_Thousands_In_Serbia_Again_Protest_Government
            Response_To_Violence;_Vucic_Holds_Own_Rally⠀⇛


                 Tens of thousands of people took to the streets of the
                 Serbian capital, Belgrade, on May 19 to join the third
                 opposition-led protest against the government’s response
                 to two mass shootings earlier in the month


          o ⚓ JURIST ☛ UNODC_reports_reveal_complex_smuggling_web_across_Sahel
            region_of_Africa⠀⇛


                 The United Nations Office on Drugs and Crime (UNODC) West
                 and Central Africa released a series of reports Saturday
                 revealing a complex trafficking web across the Sahel
                 region of Africa as part of its Transnational Organized
                 Crime Threat Assessment (TOCTA) Sahel project.


          o ⚓ Atlantic Council ☛ The_US_can_help_Central_Asia_avoid_China’s
            awkward_embrace⠀⇛


                 China just wrapped up a summit with Central Asian
                 countries, but the US should not cede the territory.
                 Washington should energize economic and security
                 cooperation.


          o ⚓ France24 ☛ Air_strikes_hit_Khartoum_as_Sudan_fighting_enters
            sixth_week⠀⇛


                 Air strikes hit outer areas of the Sudanese capital
                 Khartoum overnight and on Saturday morning, as fighting
                 that has trapped civilians in a humanitarian crisis and
                 displaced more than a million entered its sixth week.


          o ⚓ Federal News Network ☛ F-18_fighter_jet_accident_at_Zaragoza
            airbase_as_pilot_ejects_successfully⠀⇛


                 The Spanish defense ministry says an F-18 fighter jet has
                 crashed at an airbase in the Spanish city of Zaragoza but
                 the pilot ejected successfully. The aircraft landed
                 within the perimeter of the base, the defense ministry
                 said on Twitter. The air force says the pilot was already
                 in hospital and his life was not in danger. The Guardia
                 Civil says that its officers rescued the pilot after he
                 parachuted down outside the base. The Guardia Civil says
                 that the pilot suffered injuries to his legs.


          o ⚓ Helsinki Times ☛ Samí_people’s_future,_Finland_participation_in
            NATO_nuclear_weapons_exercise_and_frost_quakes:_Finland_in_the
            world_press⠀⇛


                 Here is a selection of what the international press has
                 published about Finland in the last week:


                 With the triumph of the right, Finland’s Sámi people face
                 bleak future


                 This article highlighting the concerns of Finland’s Sámi
                 people following the victory of conservative and far-
                 right parties in the 2023 Finnish elections was published
                 in El País on May 17.


          o ⚓ US News And World Report ☛ East_Timor_Heads_to_the_Polls_in
            Parliamentary_Election⠀⇛


          o ⚓ Axios ☛ School_gun_violence_torments_America’s_youngest
            generation⠀⇛


                 Data: Center_for_Homeland_Defense_and_Security; Note:
                 Includes any incident when a gun is “brandished, is
                 fired, or a bullet hits school property for any reason.”
                 Chart: Tory Lysik/Axios Visuals


More than 1,000 incidents involving firearms have shaken America’s schools
since 2018 — a dramatic increase over any similar period since at least 1970,
according to the K-12_School_Shooting_Database.


⚓ US News And World Report ☛ Congo_Security_Forces_Fire_Tear_Gas_at_Anti-
Government_Protesters⠀⇛


⚓ US News And World Report ☛ Oklahoma_Prisons_Locked_Down_Following_Inmate
Stabbing_in_Northeastern_Oklahoma⠀⇛


     The Oklahoma Department of Corrections has locked down all prisons
     statewide and canceled all visitations following a stabbing at a
     medium security prison in northeastern Oklahoma


⚓ JURIST ☛ Accused_Balkan_war_criminal_arrested_in_Boston_area⠀⇛


     The former supervisor of an infamous Bosnian prison camp during the
     Balkan Wars of the 1990s was arrested in the Boston area this week on
     charges of fraudulently obtaining U.S. citizenship by making false
     claims of persecution.


⚓ RFERL ☛ Three_Pakistani_Soldiers_Killed_In_Attack_On_Security_Post⠀⇛


     At least three soldiers were killed on May 20 in southwestern
     Pakistan as the threat of terrorism and violence flared in the
     country amid political turmoil.


⚓ Michael West Media ☛ G7,_rescheduled_Quad_in_Japan_to_focus_on_security⠀⇛


     Prime Minister Anthony Albanese has met US President Joe Biden on the
     sidelines of the G7 summit in Japan and signed an agreement to
     advance climate and clean energy action between the two nations.


⚓ France24 ☛ DR_Congo_security_forces_clash_with_anti-govt_protesters_in
Kinshasa⠀⇛


     Democratic Republic of Congo security forces fired tear gas and
     fought running battles in the streets of the capital Kinshasa with
     anti-government protesters demonstrating on Saturday over alleged
     irregularities in voter registration.


§ Environment⠀➾


    * ⚓ New York Times ☛ In_Flood-Stricken_Area_of_Italy,_Residents_Fear_This
      Won’t_Be_the_Last_of_It⠀⇛


           Flooding upended tens of thousands of lives this week in
           Emilia-Romagna, a region that has also experienced drought in
           recent years.


    * ⚓ France24 ☛ More_than_36,000_people_displaced_in_northern_Italy_floods⠀⇛


           More than 36,000 people have now been forced from their homes
           by deadly floods in northeast Italy, regional officials said
           Saturday, as rising waters swallowed more houses and fresh
           landslides isolated hamlets.


    * ⚓ New York Times ☛ Tropical_Storm_Mawar_Expected_to_Strengthen_as_It
      Moves_Toward_Guam⠀⇛


           The storm could bring damaging winds and flooding to the
           Mariana Islands in the Pacific, meteorologists said.


    * § Energy/Transportation⠀➾


          o ⚓ H2 View ☛ G7_Hiroshima_Summit:_Where_North_America_stands_on
            hydrogen⠀⇛


                 With the G7 Summit currently being held in Hiroshima,
                 Japan (May 19-21), H2 View has been diving deeper into
                 the hydrogen-related activities of each country.


    * § Wildlife/Nature⠀➾


          o ⚓ TwinCities Pioneer Press ☛ Baffert_back_from_ban,_wins_Preakness
            with_National_Treasure_after_another_horse_euthanized⠀⇛


                 Bob Baffert choked back tears and his voice cracked while
                 he tried to juggle the conflicting feelings of seeing one
                 of his horses win the Preakness Stakes hours after
                 another was euthanized on the same track.


          o ⚓ The Straits Times ☛ Black_panther_dies_after_road_accident_in
            Malaysia⠀⇛


                 The panther made its way to a nearby drain and eventually
                 died.


          o ⚓ US News And World Report ☛ Smoke_From_Canada_Wildfires_Prompts
            Air_Quality_Alerts_in_Colorado,_Montana⠀⇛


                 Officials in Colorado and Montana have issued air quality
                 alerts due to smoke from dozens of wildfires in Canada
                 that has drifted south into the United States


§ Finance⠀➾


    * ⚓ TwinCities Pioneer Press ☛ Debt_limit_standoff_brings_tough_talk,
      little_action_as_Biden,_world_leaders_watch_for_progress⠀⇛


           Debt limit talks between the White House and House Speaker
           Kevin McCarthy hung over the weekend with tough talk but little
           action.


    * ⚓ Michael West Media ☛ US_capital_quiet_as_debt_ceiling_deadline
      approaches⠀⇛


           White House and Republican congressional negotiators on raising
           the federal debt ceiling are not expected to meet in upcoming
           hours as the country inches closer to the debt ceiling deadline
           on June 1. US Representative Patrick McHenry, a Republican
           negotiator, said no meetings were scheduled for Saturday.


    * ⚓ Michael West Media ☛ Biden_to_call_McCarthy_from_Japan_on_debt_crisis⠀⇛


           US President Joe Biden is seeking a direct conversation with
           Republican House of Representatives speaker Kevin McCarthy as
           the country’s debt ceiling crisis nears a critical point.


    * ⚓ France24 ☛ Biden_meets_with_Indo-Pacific_leaders_at_G7_amid_US_debt
      limit_crisis⠀⇛


           President Joe Biden was seeking to rally regional cooperation
           against China on the margins of the Group of Seven summit
           Saturday, while confronting a stalemate in Washington over how
           to ensure the US avoids default.


    * ⚓ New York Times ☛ Biden_and_G7_Summit_Partners_Struggle_for_Support_Back
      Home⠀⇛


           The relatively weak approval ratings for President Biden and
           his Group of 7 partners highlight the fragility of free
           societies facing deep political divides.


    * ⚓ New York Times ☛ U.S._Default_Prospect_Hurts_Economy_in_the_Meantime⠀⇛


           Financial markets are still betting that Congress and the White
           House will strike a deal. But the uncertainty alone is having
           consequences.


    * ⚓ France24 ☛ Biden_says_he_still_believes_US_will_be_able_to_avoid_debt
      default⠀⇛


           Talks to avoid a US debt default were on a knife edge Saturday
           as President Joe Biden warned he would not accept “extreme”
           Republican demands but said he remained optimistic.


    * ⚓ 2023-05-20_[Older]_Getting_Sirius_Managers_Arrested_Before_They
      Dismantle_the_Company_and_Vanish⠀⇛


    * ⚓ 2023-05-19_[Older]_Action_Fraud:_Anybody_Home_or_Just_Bots?⠀⇛


    * ⚓ 2023-05-19_[Older]_Protecting_the_Rich_From_Poor_People’s_Crimes,_Not
      Poor_People_From_Rich_People’s_Crimes⠀⇛


    * ⚓ 2023-05-18_[Older]_‘Action_Fraud’_Reinforces_the_Narrative_That_Says
      Cops_Are_Apathetic_Towards_White-Collar_Crimes⠀⇛


    * ⚓ 2023-05-16_[Older]_Less_Than_a_Handful_Left_at_Sirius_‘Open_Source’⠀⇛


    * ⚓ 2023-05-14_[Older]_Over_Three_Weeks_and_Action_Fraud_is_Missing_in
      Action_(MIA)⠀⇛


    * ⚓ 2023-05-12_[Older]_Almost_3_Weeks_Since_Report_Filed_WithUK_‘Action
      Fraud’_and_Still_No_Sign_of_Action⠀⇛


    * ⚓ 2023-05-12_[Older]_Will_Anyone_Be_Left_at_Sirius_to_Turn_the_Lights
      Off?_Sirius_‘Open_Source’_Manager_(Who_Doesn’t_Use_Open_Source)_Has_Left
      the_Building.⠀⇛


    * ⚓ Federal News Network ☛ Debt_limit_talks_seem_to_make_little_headway_as
      Biden,_world_leaders_watch_from_afar_for_progress⠀⇛


           Debt limit talks between the White House and House Republicans
           stopped, started and stopped again heading into a weekend where
           President Joe Biden and world leaders watched from afar, hoping
           high-stakes negotiations would make progress on avoiding a
           potentially catastrophic federal default. In a sign of a
           renewed bargaining session, food was brought to the negotiating
           room at the Capitol on Saturday morning, only to be carted away
           hours later. No meeting was likely Saturday, according to a
           person familiar with the state of the talks. Biden is attending
           a meeting of global leaders in Japan and on Saturday he tried
           to reassure them that the United States would not default.


    * ⚓ New York Times ☛ On_‘Succession,’_Striving_Is_the_Worst_Insult_of_All⠀⇛


           It’s fine to have money and power, as long as you don’t admit
           how much you want them.


    * ⚓ New York Times ☛ Building_Boom_on_Mykonos_Reveals_‘Wretched’_Side_of
      Greece’s_Recovery⠀⇛


           Investors are eager to cash in on soaring demand for luxury
           properties, but an attack on an archaeologist investigating
           building violations brought a darker underbelly to light.


    * ⚓ Michael West Media ☛ PM_calls_out_China_coercion_after_trade_ban
      movement⠀⇛


           Anthony Albanese has thrown his support behind a statement
           calling out Chinese economic coercion just days after Beijing
           unwound trade restrictions for Australian timber. The prime
           minister said he had been consistent in saying China’s activity
           had provided cause for concern.


    * ⚓ New York Times ☛ Inflation_Persists_and_Car_Prices_Are_a_Big_Reason⠀⇛


           Prices of new and used vehicles were supposed to recede quickly
           as supply chain problems dissipated. The market had other
           ideas.


    * ⚓ Axios ☛ GOP_turned_down_White_House_offer_to_freeze_spending⠀⇛


           House Republican negotiators declined an offer from the White
           House to freeze government spending in the 2024 budget as part
           of a deal to raise the debt_ceiling, Axios has learned.


           Why it matters:The development underscores how far apart the
           two sides are on the fundamentals of a deal.


    * ⚓ New York Times ☛ Disney’s_‘Star_Wars’_Hotel,_Galactic_Starcruiser,_to
      Close⠀⇛


           The planned closure of Galactic Starcruiser, an immersive role-
           playing attraction, comes as Disney seeks to cut overall costs
           by more than $5 billion.


    * ⚓ Michael West Media ☛ New_retail_figures_to_pinpoint_Aussie_spending
      patterns⠀⇛


           The shopping habits of Australian households will be on display
           as the national statistics bureau releases fresh retail trade
           data.  Consumers have proved fairly resilient to the sky-high
           cost of living and financial pressures from higher interest
           rates.  But spending has started to slow, and become more
           concentrated on necessities like food rather than nice-to-
           haves.


    * ⚓ LRT ☛ Clothes_swaps_and_mending_socks:_Lithuanians_embrace_sustainable
      fashion⠀⇛


           Clothing swaps are becoming more popular in Lithuania, inviting
           people to exchange garments they no longer wear. Organisers say
           such events encourage sustainable living and awareness of the
           environmental impact of fast fashion.


    * ⚓ Hong Kong Free Press ☛ Combatting_‘job-hopping’_isn’t_the_solution,
      solidarity_with_Hong_Kong’s_migrant_domestic_workers_is⠀⇛


           I had a baby in Hong Kong in 2021, which highlighted for me how
           important caregiving support is – especially in a pandemic.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ US News And World Report ☛ Greeks_Head_to_Polls,_No_Outright_Winner
      Seen⠀⇛


    * ⚓ New York Times ☛ In_Sierra_Leone,_50_Cents_Can_Change_a_Life⠀⇛


           On my win-a-trip journey, a reminder that a fifth of the
           world’s people have worms.


    * ⚓ New York Times ☛ Timothy_Parlatore,_Former_Trump_Lawyer,_Describes
      Conflict_Inside_Legal_Team⠀⇛


           Timothy Parlatore, who withdrew this past week from
           representing the former president in the special counsel
           investigations, said he stepped aside over differences with a
           Trump adviser, Boris Epshteyn.


    * ⚓ US News And World Report ☛ Italy’s_Meloni_to_Leave_Japan_G7_a_Day_Early
      to_Tackle_Floods_Crisis_at_Home⠀⇛


    * ⚓ Marcy Wheeler ☛ Rudy’s_Very_Bad_Week⠀⇛


           The key point of Noelle Dunphy’s lawsuit against Rudy is to
           alert a lot of corrupt people that she has damning emails
           unprotected by a non-disclosure agreement.


    * ⚓ LRT ☛ Washing_powder_in_exchange_for_votes_–_Lithuania’s_referendum_on
      joining_EU⠀⇛


           This month 20 years ago, Lithuania held one of its most
           consequential referendums, one on joining the European Union.
           While the public’s support for membership was secure enough,
           there were reasons why the country’s leaders feared the vote
           could fail.


    * ⚓ US News And World Report ☛ India_to_Host_Quad_Summit_Next_Year,_PM_Modi
      Says⠀⇛


    * ⚓ US News And World Report ☛ At_G7,_Japan_and_Germany_Want_a_Rethink_on
      the_‘Global_South’⠀⇛


    * ⚓ US News And World Report ☛ At_G7,_Macron,_Meloni_Meet_to_Bury_Hatchet
      After_Migration_Spat⠀⇛


    * ⚓ Michael West Media ☛ Australia_leads_Quad_partners_meet_on_sidelines_of
      G7⠀⇛


           Prime Minister Anthony Albanese has convened a rescheduled Quad
           leaders’ meeting on the sidelines of the G7 summit in Japan.


    * ⚓ Michael West Media ☛ Quad_spruiks_‘force_for_good’_after_G7_sidelines
      summit⠀⇛


           Prime Minister Anthony Albanese and his counterparts from
           Japan, India and the United States have capped off a
           rescheduled Quad leaders’ meeting with a vow to co-operate for
           the benefit of the region.


    * ⚓ Federal News Network ☛ Biden_aims_to_reassure_world_on_US_debt_standoff
      as_he_consults_with_Indo-Pacific_leaders⠀⇛


           President Joe Biden tried to reassure world leaders meeting in
           Japan on Saturday that the U.S. would not default. Biden
           consulted with the leaders of Australia, Japan and India in a
           meeting of the so-called Quad partnership that had been hastily
           rescheduled because of the debt limit standoff back in
           Washington. Biden hopes to avert an outcome that would rattle
           the global economy and prove to be a boon to Beijing, The
           president opened his third day in Japan at the annual Group of
           Seven meeting with a briefing from his staff on the latest fits
           and starts in talks over how to raise the federal debt limit.


    * ⚓ US News And World Report ☛ South_Korea’s_Yoon_Thanks_Japan’s_Kishida
      for_His_Efforts_to_Mend_Ties⠀⇛


    * ⚓ European Commission ☛ World_Day_for_Cultural_Diversity_for_Dialogue_and
      Development:_Joint_Statement_by_High_Representative/Vice-President
      Borrell,_Vice-President_Schinas_and_Commissioner_Urpilainen⠀⇛


           European Commission Statement Brussels, 20 May 2023 The
           European Union’s motto of “united in diversity” shows how
           cultural diversity is at the very heart of the Union’s
           foundations.


    * ⚓ NYPost ☛ China_goes_for_‘broker’:_Digging_into_the_possible_concern
      over_stock-trading_apps⠀⇛


           The worry in DC and beyond, of course, is China’s vast
           surveillance state that has the final word on the operations of
           every Chinese company.


    * ⚓ Atlantic Council ☛ How_dependent_is_too_dependent_on_China?_Central
      Asia_may_soon_find_out.⠀⇛


           A region that even within the last few years championed “multi-
           vector diplomacy” today risks becoming dangerously dependent on
           Beijing.


    * ⚓ France24 ☛ G7_wants_‘stable,_constructive’_relations_with_China_but
      warns_against_‘militarisation’⠀⇛


           G7 leaders on Saturday warned China over its “militarisation
           activities” in the Asia-Pacific region but said the bloc also
           wanted “constructive and stable relations” with Beijing.


    * ⚓ France24 ☛ ‘War_is_not_an_option’:_Taiwan_president_vows_to_maintain
      status_quo_with_China⠀⇛


           Taiwanese President Tsai Ing-wen vowed Saturday to maintain
           peace and stability across the Taiwan Strait in the face of
           increased military pressure from China, saying that “war is not
           an option”.


    * ⚓ New York Times ☛ What’s_De-risking_and_How_Does_It_Compare_to
      Decoupling⠀⇛


           The newly fashionable term, reflecting an evolution in the
           discussion over dealing with a rising, assertive China, has a
           vexing history in financial policy.


    * ⚓ US News And World Report ☛ China_Complains_to_G7_Host_Japan_Over_Joint
      Statement⠀⇛


    * ⚓ The Straits Times ☛ G-7_summit:_While_giving_harshest_rebuke_to_China
      yet,_leaders_deny_wanting_to_thwart_its_progress⠀⇛


           >


           The G-7 also stressed that its intent was “de-risking and
           diversifying (and) not decoupling or turning inwards”.


    * ⚓ JURIST ☛ HRW:_Pakistan_police_carried_out_mass_arrests_of_political
      opposition⠀⇛


           Human Rights Watch (HRW) released a statement Saturday claiming
           that Pakistani police have carried out mass arrests of over
           4,000 people, including opposition party members of Pakistan
           Tehreek-e-Insaf (PTI)…


    * ⚓ RFERL ☛ Khan_Says_Pakistani_Government_Crackdown_Designed_To_Weaken_PTI
      For_Elections⠀⇛


           Former Pakistani Prime Minister Imran Khan said the
           government’s crackdown against him and his Pakistan Tehrik-
           e Insaf (PTI) party is designed to weaken the group “so we
           can’t compete in the elections.”


    * ⚓ Hong Kong Free Press ☛ ‘No_room_for_us’:_Hong_Kong_District_Councillors
      say_overhaul_of_local_bodies_serves_gov’t_interests,_not_residents⠀⇛


           When Paul Zimmerman through Pok Fu Lam on his motorbike, he
           knows he has left his mark. The trees that line a main road in
           the southern Hong Kong Island neighbourhood are courtesy of a
           planting project, one of his first initiatives after being
           elected as the area’s District Councillor in 2010.


    * ⚓ Hong Kong Free Press ☛ District_Council_overhaul:_Remembering_the
      failures_of_Hong_Kong’s_democratic_experiments⠀⇛


           The UK, often lauded as having the “mother of parliaments,” has
           exported its parliamentary system to many parts of the world –
           but not Hong Kong, until the British rulers were about to
           depart. London did seriously consider introducing some form of
           representative government in Hong Kong on two occasions.


    * ⚓ Hong Kong Free Press ☛ District_Council_overhaul:_Hong_Kong_never_had
      democracy,_but_that_is_no_reason_to_deny_it⠀⇛


           It is axiomatic that election winners do not rush to change the
           election system. Losers are quite another matter, losers who
           have lost really badly are even more desperate for change. That
           is why it is advisable to ignore all the nonsense being aired
           in justification of scrapping the District Council election
           system.


    * ⚓ Federal News Network ☛ Sinn_Fein_on_course_to_be_largest_party_in
      Northern_Ireland_local_elections⠀⇛


           Irish nationalist party Sinn Fein is set to take the most seats
           in Northern Ireland’s local elections. That would be a repeat
           of its success from last year’s assembly elections, when it
           became the region’s largest party for the first time. With
           about 400 of 462 local government seats counted Saturday, Sinn
           Fein took 128 seats and made breakthroughs in some areas. It
           was ahead of its main rival. The Democratic Unionist Party
           secured 111 seats so far. Sinn Fein’s vice president Michelle
           O’Neill said it was “on course to have a very momentous
           election result.” Sinn Fein seeks unification of Northern
           Ireland with the Republic of Ireland.


    * ⚓ Latvia ☛ President’s_office_responds_to_auditor’s_criticism_of_costs⠀⇛


           The State Audit Office, after evaluating the expenditures of
           the state’s central administrative institutions last year,
           recently criticised excessive expenditure by the president’s
           office during the Three Seas Initiaitive Summit meeting held in
           Rīga last year.


    * ⚓ Mexico News Daily ☛ Teachers,_taxes_and_‘transformation’:_the_week_at
      the_mañaneras⠀⇛


           President López Obrador covered everything from economic
           stability to “banishing” corruption to armored vehicles at the
           week’s pressers.


§ Censorship/Free Speech⠀➾


    * ⚓ New Yorker ☛ Salman_Rushdie_Remembers_the_British_Novelist_Martin
      Amis⠀⇛


           To read the late writer’s work was to behold his singular
           style.


    * ⚓ RFA ☛ INTERVIEW:_‘They_threatened_to_arrest_us_both_together’⠀⇛


           Son of veteran Wuhan dissident Zhang Yi flees to the
           Netherlands as authorities target his father


    * ⚓ Off Guardian ☛ A_Closed_System⠀⇛


           There is so much going on we don’t know about. Like I’ve said
           before, we definitely have reached that critical point of being
           a “closed system.” The mainstream media are all in on it, so
           they control the flow of information. No one knows what is
           happening unless they literally see it or …


§ Freedom of Information / Freedom of the Press⠀➾


    * ⚓ RFERL ☛ Afghan-American_Journalist_Freed_After_Detention_In_Kabul⠀⇛


           Afghan-American journalist Ali Latifi said on May 19 that he
           has been released from detention one day after being held in
           Kabul, calling it a “misunderstanding.”


§ Civil Rights/Policing⠀➾


    * ⚓ RFERL ☛ Iran_Executes_Man_Convicted_Of_Being_Leader_Of_Sex-Trafficking
      Gang⠀⇛


           Iran’s judicial authority announced it has executed the
           purported head of a gang that trafficked Iranian girls and
           women to neighboring countries.


    * ⚓ New Yorker ☛ Title_42_Is_Gone,_But_What_Are_Asylum_Seekers_Supposed_to
      Do_Now?⠀⇛


           It’s hard to imagine an area of federal policymaking more vexed
           than immigration, generally, and asylum, specifically.


    * ⚓ US News And World Report ☛ Prosecutors_Refile_Charges_Against_Officer
      in_2020_Protest_Arrest_After_Judge_Dismisses_Case⠀⇛


           A Philadelphia judge dismissed all charges against a former
           police officer accused of assaulting a woman who accidentally
           drove a sport utility vehicle into a 2020 protest with her
           young son in the vehicle — but prosecutors quickly refiled the
           case


    * ⚓ JURIST ☛ Investigation_launched_after_Australia_police_taser_elderly
      woman_with_dementia⠀⇛


           An Australian police force is launching an internal
           investigation after police officers tasered a 95-year-old woman
           at an elderly care facility.


    * ⚓ JURIST ☛ Australia_to_become_first_OECD_nation_on_UN_human_rights_non-
      compliance_list⠀⇛


           The UN is set to sanction Australia for failing to meet its
           international human rights obligations. On Saturday, in an
           exclusive interview with The Saturday Paper, vice-chair of the
           Subcommittee on the Prevention of Torture (SPT), Aisha Shujune
           Muhammad, said that Australia has failed to implement the
           Optional Protocol to the Convention Against Torture…


    * ⚓ Mexico News Daily ☛ Mexican_migration:_not_just_about_leaving_Mexico⠀⇛


           While famous for its citizens leaving Mexico, throughout
           history, the nation’s also welcomed many foreign groups looking
           for a better life.


§ Internet Policy/Net Neutrality⠀➾


    * ⚓ Federal News Network ☛ Television’s_biggest_mystery:_how_long_will
      pipeline_for_new_programming_be_closed?⠀⇛


           The week in May when ABC, CBS, NBC and Fox traditionally
           unveiled programming plans in glitzy presentations to
           advertisers has always spoken to the networks’ power over
           popular culture. It was decidedly muted this year, both to the
           continued growth of streaming and uncertainties caused by the
           Hollywood writers strike. Picketers marched this week in front
           of the Manhattan venues where the annual presentations took
           place, and stars stayed away. More importantly, the strike
           lends mystery to whether TV will have much of a fall season at
           all. Some of the broadcast networks took strikingly different
           tacks in how they approach a future that is in shadows.


§ Monopolies⠀➾


    * § Patents⠀➾


          o ⚓ IP Kat ☛ 2023-05-19Unified_Patent_Court:_Milan_will_be_the_third
            seat_of_the_Central_Division [Ed: This is patently illegal, so
            it'll explode after start and destroy the EU's reputation in the
            process; whose money are the lobbyists passing to politicians?
            Disaster in the making.]⠀⇛


    * § Copyrights⠀➾


          o ⚓ Digital Music News ☛ What’s_the_Deal_With_Sped-Up_Songs?⠀⇛


                 Sped-up songs are a trend right now. People love fast
                 songs so much that Spotify has a playlist devoted solely
                 to “150%” fast songs. Why though? Who knows – trends come
                 and go because something in the zeitgeist bubbles up.


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



                    ䷩ 𝚕𝚒𝚗𝚎 3913

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.21.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Gemini_Links_21/05/2023:_ScummVM_and_Lagrange_1.16⠀✐


Posted in News_Roundup at 6:45 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Announcements
                # Programming
    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Angel_Rocks_Hike_2023-05-20_(east_of_Fairbanks,_AK,_USA)⠀⇛


                       Emily and I went on a hike today to Angel Rocks, a
                       trail east of Fairbanks, which goes along the Yukon
                       River and then passes several “tors”, or rocky
                       outcroppings. I have many pictures to share, so
                       I’ll just list them each with a brief description.


                # ⚓ 🔤SpellBinding:_DGIZNRL_Wordo:_ROBES⠀⇛


                # ⚓ it’s_you_and_me,_phone_–_entertain_me⠀⇛


                       The ego-driven, hyped privilege of the mental/
                       emotional DEMAND that a device I own *entertain*
                       me. And also, why? Entertainment is good and needed
                       in the world, especially that rendering
                       physiological stimulation, feedback of positive
                       consequence, et al., but why the effort/stress of
                       picking up my phone and thinking: “ok, let’s find
                       some digital amusement”


          o § Technical⠀➾


                # ⚓ To_remember_that_ScummVM_is_great⠀⇛


                       I had a knowledge of ScummVM existence for a long
                       time but I’ve been playing only occasionally in
                       several games for a short while that way. /Pierre
                       Gilhodes/ created this month Gobliiins 5 as the
                       classical 2D original [Gobliiins] style game, so
                       I’ve been made to run also the first Gobliiins
                       again. I’ve tried the playable Gobliiins 5 demo,
                       and then I’ve returned to the original Gobliiins
                       series.


                # ⚓ Will_code_you_a_chatbot_for_free,_Anyone_interested?⠀⇛


                       My chatbots can be tailored to your needs for
                       Personal use (just not NSFW/Sex Bots, Please!).
                       They can run in a terminal or cmd or with GUI and
                       text-to-speech (see the link below in the demos
                       section). My chatbots can, if needed, run on a
                       Linux web server for online usage.


                # § Internet/Gemini⠀➾


                      # ⚓ How_to_Download_Konpeito_Using_Diohsc⠀⇛


                             Well, it has been ages since I wrote to my
                             gemlog, something that I should do more
                             often, but needless to say it has been a very
                             busy year, and a lot of my attention has also
                             gone to my GoToSocial instance, which is
                             doing fairly well.


                             Even though I don’t browse Gemini much these
                             days, I still hold a lot of appreciation for
                             the content that is available on the network
                             thanks to the great user community. This is a
                             sentiment that has been echoed recently in
                             our chat room.


                      # ⚓ Re_Hello_others⠀⇛


                             Your client must present a certificate and
                             then Bubble will present a registration link.
                             I can see how that might not be entirely
                             clear from just those instructions. If you
                             are using Lagrange on desktop, navigate to
                             the Bubble instance, look for the “Identity”
                             menu in the menu bar at the top and select
                             the option “New Identity for Domain”. Create
                             your certificate and refresh the page. If
                             you’re using Lagrange on Mobile you won’t
                             have a menu bar, but you’ll have a toolbar.
                             Look for the person icon and click on it to
                             get the same menu as above. Other clients
                             will have other ways of adding client
                             certificates. Some clients might not have
                             support for them, although it is in the
                             Gemini spec.


                # § Announcements⠀➾


                      # ⚓ Lagrange_v1.16:_Zoomable_Input_Prompt,_Better_Tab
                        Creation⠀⇛


                             It has been a few months since the previous
                             release, and work on Lagrange has been
                             focusing on bug fixing. v1.16 continues this
                             trend as it mostly contains quality of life
                             improvements.


                # § Programming⠀➾


                      # ⚓ When_Test_Driven_Development_Shines⠀⇛


                             TDD is often explained as a flow chart to
                             follow, along an example of the “don’t code
                             it until you test it” rule; in Ainent’s post
                             the example given is that if “2 + 2” is a
                             test case then the answer should be hard-
                             coded as 4; it’s the next test case that will
                             force you to “implement” addition.


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



                    ䷩ 𝚕𝚒𝚗𝚎 4080

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.21.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_21/05/2023:_WordPress_6.2.2_and_ESPClicker⠀✐


Posted in News_Roundup at 6:50 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o SaaS/Back_End/Databases
          o Licensing_/_Legal
          o Programming/Development
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Monopolies
                # Patents
                # Copyrights
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Linux Links ☛ 7_Best_Free_and_Open_Source_Replacements_for
                  ls⠀⇛


                       ls is a command to list computer files. ls is
                       specified by POSIX and the Single UNIX
                       Specification. When invoked without any arguments,
                       ls lists the files in the current working
                       directory.


                       The GNU Core Utilities or coreutils is a package of
                       GNU software containing implementations for many of
                       the basic tools, such as cat, ls, and rm, which are
                       used on Unix-like operating systems.


                       There are many enterprising developers that look to
                       update and enhance many of the commands available
                       in coreutils. ls is no exception.


                       Here’s our recommended replacements for ls. They
                       are all command-line programs published under an
                       open source license.


          o § Instructionals/Technical⠀➾


                # ⚓ Ryan Mulligan ☛ Full-bleed_Table_Scrolling_on_Narrow
                  Viewports⠀⇛


                       I found the following to be a rather decent
                       solution for having HTML tables overflow the inline
                       edges of smaller/tighter/narrow viewports. Try
                       resizing the width of the browser window if viewing
                       this page on a larger screen.


                # ⚓ Adam_Young:_System_Tap_on_Fedora_38⠀⇛


                       Getting System Tap up and running on F38 has
                       involved chasing down a few modules.


                # ⚓ Djalel Oukid ☛ How_to_optimize_your_laptop_battery_life_on
                  Linux?⠀⇛


                       Commonly, you get shorter battery life (run time on
                       a full charge) on GNU Linux compared to other
                       operating systems, as your favorite distribution is
                       probably not optimized for laptops, and your
                       laptops are not Linux-optimized. However, as a
                       Linux user, you still can get a better laptop
                       battery life thanks to TLP.


                # ⚓ ID Root ☛ How_To_Install_Kubernetes_on_Rocky_Linux_9⠀⇛


                       In this tutorial, we will show you how to install
                       Kubernetes on Rocky Linux 9. For those of you who
                       didn’t know, Kubernetes is an open-source container
                       orchestration platform that automates the
                       deployment, scaling, and management of
                       containerized applications.


                # ⚓ Trend Oceans ☛ Easy_Way_to_Fix:_Sudo_Unable_to_Resolve_Host
                  Name_or_Service_Not_Known⠀⇛


                       Getting error sudo unable to resolve host name or
                       service not known after executing the sudo command,
                       then read these steps to fix it up. As you know,
                       while installing a new operating system like
                       Debian, Ubuntu, or any other Linux distribution,
                       installers ask you to set the hostname.


                # ⚓ Adam_Young:_Testing_an_MCTP_Driver_via_Echo_request⠀⇛


                       MCTP stands for Management Component Transport
                       Protocol. While it is designed around a server, it
                       is also designed as a network protocol. As such,
                       the Linux implementation makes use of the Socket
                       interface and the Kernel plumbing for dealing with
                       network protocols. To support a new transport
                       mechanism, you implement a new device driver
                       specific to that transport mechanism that
                       implements the struct net_device contract, which
                       includes implementing the functions for struct
                       net_device_ops.


                       Before I write a full implementation, I want to
                       write something that only echos a packet back to
                       the receiver. This mimics the behavior of themctp-
                       echo server in the user tools, and can make use of
                       the mctp-req echo client.


                # ⚓ 2_Ways_to_Remove_Ubuntu_Software_Center_Packages⠀⇛


                       The Ubuntu Software Center provides a graphical
                       user interface to easily install and manage various
                       software packages.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Get_some_quality_deck-building_in_this_game
                  bundle⠀⇛


                       Love your deck-building roguelikes? Well there’s a
                       Luck of the Draw Humble Bundle just for that so
                       here’s what’s included and the compatibility on
                       Steam Deck and desktop Linux.


                # ⚓ GamingOnLinux ☛ Fanatical’s_Prestige_Collection_build_your
                  own_bundle_has_some_good_picks⠀⇛


                       Build your own little bundle with a discount on
                       Fanatical, as their Bundle Fest once again comes to
                       a close and the latest bundle worth a look is the
                       Prestige Collection.


                # ⚓ Hackaday ☛ It’s_DOOM,_But_In_Teletext⠀⇛


                       We’ve seen the 1993 id Software classic DOOM
                       running on so many pieces of unexpected hardware,
                       as “Will it run DOOM?” has become something of a
                       test for any new device. But will it run in the
                       circuitry of a 1970s or 1980s TV set? Not quite,
                       but as [lukneu] has demonstrated, it is possible to
                       render the game using the set’s inbuilt Teletext
                       decoder.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Nate Graham ☛ This_week_in_KDE:_Preliminary_HDR
                        support⠀⇛


                             KWin developer Xaver Hugl put a lot of work
                             into HDR support in KWin during the recent
                             HDR hackfest and Plasma sprint, and as a
                             result, the first parts have now been merged
                             for the Plasma 6.0 Wayland session! This also
                             lays the groundwork for color management on
                             Wayland. It’s an interesting and complex
                             subject, so if you’d like to know more, check
                             out Xaver’s excellent blog post on the
                             subject.


                             While you’re here, let me also do a bit of
                             self-promotion. Fellow KDE contributor
                             Neofytos Kolokotronis and I will be giving a
                             virtual pre-Akademy talk at the University of
                             Macedonia in a few days, on May 23rd. Learn
                             more and register here!


    * § Distributions and Operating Systems⠀➾


          o ⚓ OMG Ubuntu ☛ Bodhi_Linux_7.0_Beta_is_Now_Available_for_Testing⠀⇛


                 For those unfamiliar with it, Bodhi Linux is a
                 lightweight Linux distro based on Ubuntu long-term
                 support releases. It uses an Enlightenment-based desktop
                 and Moksha window manager by default. The distro is
                 notable for its resource efficiency and modularity, both
                 enable it to run well on low-end hardware.


                 Bodhi Linux 7.0 is based on Ubuntu 22.04 LTS. This
                 foundation means users get access to better hardware
                 support, security and performance improvements, and a
                 repo stocked to the rafters with newer versions of apps,
                 tools, and software.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Using_BTT_Pad_7_touchscreen_display_with
                  Raspberry_Pi_CM4⠀⇛


                       The BTT Pad 7, or BIGTREETECH Pad 7 in full, is a
                       7-inch touchscreen display that ships with the CB1
                       Allwinner H616 system-on-module compatible with
                       Raspberry Pi CM4. The display is mostly designed
                       for 3D printers with its SPI and CAN Bus
                       interfaces, but it can also be used as a standard
                       tablet PC. So today, I’ll switch the CB1 with a
                       Raspberry Pi CM4 Lite module and report my
                       experience doing the conversion and using it as a
                       Raspberry Pi CM4 tablet PC running Raspberry Pi OS,
                       and test it with a 3D printer with Klipper in
                       another post later on.


          o § Open Hardware/Modding⠀➾


                # ⚓ Hackaday ☛ ESPClicker_–_An_Elegant_Solution_For_Integrating
                  Dumb_Devices_Into_Home_Assistant⠀⇛


                       Integrating non-smart devices into your home
                       automation system can be a cumbersome process,
                       involving the wiring of multiple modules. However,
                       [Pricelesstoolkit] has created the ESPClicker – a
                       compact, ESP8266-based module that can remotely
                       “press buttons” and simplify this process.


                # ⚓ DroidGazzette ☛ The_Free_Way_To_Speed_Up_An_Old_Apple_Mac⠀⇛


                       I promised I’d install Linux Mint alongside macOS
                       to see if that could bring back some of the iMac’s
                       old spark, and it’s done just that. A machine that
                       would struggle to even watch a YouTube video
                       without stuttering has been transformed into a
                       spritely, responsive system.


                       Here’s how the owners of ageing Macs can bring
                       their old hardware roaring back to life.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Pico_Piano_Helper_Lights_Up
                  Keys_to_Teach_Songs⠀⇛


                       The Pico controls a series of LEDs that line up
                       with the keys on a keyboard (or piano). The LEDs
                       illuminate on specific keys so the player knows
                       which key to press next in the song. When not in
                       use, it can also demonstrate a nice gradient
                       effect. The Pico charts out songs by interpreting
                       MIDI files to determine the note and length of time
                       the note is played for.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Nokia Power User ☛ Nokia_T10_officially_confirmed_as
                  Android_13_compatible_now_–_Nokiapoweruser⠀⇛


                # ⚓ GSM Arena ☛ Android_14_will_make_the_screen_recording
                  feature_more_privacy-friendly_–_comments⠀⇛


                # ⚓ The Sun ☛ People_are_just_realizing_hidden_Android_button
                  gives_you_huge_free_perk_–_it’s_too_useful_to_ignore_|_The_US
                  Sun⠀⇛


                # ⚓ XDA ☛ Pixel_Tablet_vs_Samsung_Galaxy_Tab_S8:_Which_Android
                  slate_ticks_all_the_boxes?⠀⇛


                # ⚓ SlashGear ☛ 5_Of_The_Best_AI_Art_Generator_Apps_For
                  Android⠀⇛


                # ⚓ SlashGear ☛ Changing_These_5_Android_Settings_Will_Make
                  Your_Phone_Less_Frustrating⠀⇛


                # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this
                  week_–_Android_Apps_Weekly⠀⇛


                # ⚓ Tom’s Guide ☛ How_to_use_Nearby_Share_on_Android_|_Tom’s
                  Guide⠀⇛


                # ⚓ Android Police ☛ How_to_make_a_video_call_on_Android⠀⇛


                # ⚓ XDA ☛ How_to_download_the_Android_14_beta_to_the_Nothing
                  Phone_1⠀⇛


                # ⚓ Pocket Lint ☛ How_to_get_Google_Search_on_Android_to_open
                  in_Chrome_by_default⠀⇛


                # ⚓ Forbes ☛ Many_Android_Phones_Can_Be_Unlocked_With_A_Photo⠀⇛


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


          o ⚓ Jussi Pakkanen ☛ Annotated_PDF,_HTML,_exporters⠀⇛


                 The way A4PDF aims to solve the issue is to stay low
                 level enough. It merely exposes PDF primitives directly
                 and ensures that the syntax of the generated PDF is
                 correct. It is up to the caller to ensure that the output
                 is semantically correct. This should afford every
                 application to easily and directly map their document
                 output to PDF in just they way they want it (color
                 managed or not, annotated or not and so on).


          o § SaaS/Back End/Databases⠀➾


                # ⚓ [Old] uni Michigan ☛ A_Relational_Model_for_Large_Shared
                  Data_Banks [PDF]⠀⇛


                       Future users of large data banks must be protected
                       from having to know how the data is organized in
                       the machine (the internal representation). A
                       prompting service which supplies such information
                       is not a satisfactory solution. Activities of users
                       at terminals and most application programs should
                       remain unaffected when the internal representation
                       of data is changed and even when some aspects of
                       the external representation are changed. Changes in
                       data representation will often be needed as a
                       result of changes in query, update, and report
                       traffic and natural growth in the types of stored
                       information. Existing noninferential, formatted
                       data systems provide users with tree-structured
                       files or slightly more general network models of
                       the data. In Section 1, inadequacies of these
                       models are discussed. A model based on n-ary
                       relations, a normal form for data base relations,
                       and the concept of a universal data sublanguage are
                       introduced. In Section 2, certain operations on
                       relations (other than logical inference) are
                       discussed and applied to the problems of redundancy
                       and consistency in the user’s model.


          o § Licensing / Legal⠀➾


                # ⚓ Hackaday ☛ How_Far_Can_An_EULA_Go?⠀⇛


                       We read this news with mixed glee and horror: a
                       company called Telly is giving TVs away, for the
                       low price of having to live with an always-on
                       advertisement bar and some pretty stringent terms
                       and conditions. Break the terms, and they’ll
                       repossess your TV. If you don’t give them the TV,
                       they have your credit card on record and they think
                       the set is worth $1,000.


          o § Programming/Development⠀➾


                # ⚓ University of Toronto ☛ Some_notes_on_the_cost_of_Go
                  finalizers_(in_Go_1.20)⠀⇛


                       I recently read Daniel Lemire’s The absurd cost of
                       finalizers in Go (via), which reports on a
                       remarkably high cost of using a finalizer to insure
                       that C memory is freed. Lemire’s numbers aren’t
                       atypical; in my own testing in a different
                       environment I found a rough factor of ten
                       difference between directly calling C malloc() and
                       free() and using a finalizer to call free().


                # ⚓ Adriaan Roselli ☛ Be_Careful_Using_‘Menu’⠀⇛


                       TL;DR: Be careful when using the word menu. Be
                       certain you have chosen the term that accurately
                       describes the control you want.


    * § Leftovers⠀➾


          o ⚓ Scheerpost ☛ Patrick_Lawrence:_The_Origin_of_the_Specious⠀⇛


                 “Why is our collective mood so sour? We are awash with
                 material wealth, and technology provides us with
                 unprecedented powers. But this veneer of well-being masks
                 a deeper crisis. …  Our institutions are crumbling,
                 leaving us vulnerable and aimless.


          o § Science⠀➾


                # ⚓ Michael West Media ☛ Scientist_defects_as_CSIRO_is_co-opted
                  in_controversial_deep_sea_mining_venture⠀⇛


                       A defecting CSIRO scientist has labelled the agency
                       an “extravagant consulting company” due to its
                       involvement in a controversial deep sea mining
                       project. Suzanne Arnold reports.


                       CSIRO has become an “extravagant consulting
                       company,” according to Professor David Karoly who
                       cut ties with the agency in May last year.


          o § Education⠀➾


                # ⚓ Pro Publica ☛ An_Arrest_With_Dropped_Charges_at_Winston-
                  Salem_School_Board_Meeting⠀⇛


                       An image of a shooting target — with two bullet
                       holes to the head and five scattered around the
                       chest — serves as a warning to visitors who climb
                       the brick steps and pass the American flag to reach
                       Eric Jensen’s front door.


                       “If you can read this you’re in range,” the sign
                       says. Another warning, posted near the doorbell,
                       states: “No Solicitation. … This property charges
                       $50 per minute to listen to any vaccine/medical
                       advice.” He ordered that one in 2021, after mobile
                       units offering COVID-19 vaccines began riding
                       through his community outside Winston-Salem, North
                       Carolina.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Easy_Graphene_Production_With_A_Laser_Engraver⠀⇛


                       Graphene isn’t easy to produce at scale. But making
                       small batches of graphene is doable in a few ways.
                       [Robert Murray-Smith] decided to try producing
                       “flash graphene.” This requires a big capacitor
                       bank that is moderately expensive, so he decided to
                       explain a different technique he read about using
                       an ordinary laser cutter. Check it out in the video
                       below.


                # ⚓ Hackaday ☛ Hexed_Home_Assistant_Monitors_3D_Printers⠀⇛


                       You can babysit your 3D printer 100% of the time,
                       or you can cross your fingers and hope it all
                       works. Some monitor their printers using webcams,
                       but [Simit] has a more stylish method of keeping
                       tabs on six 3D printers.


                # ⚓ Hackaday ☛ THOR_Microwaves_Drone_Swarms⠀⇛


                       In recent years small drones have gone from being
                       toys and photography tools to a deadly threat on
                       the battlefield. Kamikaze drones have become
                       especially prominent in the news due to their use
                       in the war in Ukraine by both sides. While we
                       haven’t seen coordinated swarms being actively
                       employed on the modern battlefield, it’s likely
                       only a matter of time, making drone swarm defense
                       an active field of development in the industry.


                # ⚓ Hackaday ☛ Op-Amp_Challenge:_MOSFETs_Make_This_Discrete_Op
                  Amp_Tick⠀⇛


                       When it comes to our analog designs, op-amps tend
                       to be just another jellybean part. We tend to spec
                       whatever does the job, and don’t give much of a
                       thought as to the internals. And while it doesn’t
                       make much sense to roll your own op-amp out of
                       discrete components, that doesn’t mean there isn’t
                       plenty to be learned from doing just that.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Science Alert ☛ Long_COVID_Seems_to_Make_Distinct_Changes
                  to_The_Immune_System⠀⇛


                       It leaves a mark.


                # ⚓ Off Guardian ☛ Don’t_let_them_rewrite_history:_Ventilators
                  KILLED_people…and_it_was_no_accident⠀⇛


                       Kit Knightly A new study from Northwestern
                       University has concluded that the majority of
                       “Covid19” patients put on ventilators were actually
                       killed by bacterial pneumonia, not the alleged
                       virus. You can read that paper here.


                # ⚓ YLE ☛ STT:_Government_negotiations_consider_smartphones_in
                  schools⠀⇛


                       Schools can require pupils to keep their phones
                       silent and out of sight during class time. However,
                       without tightening current laws, it is not possible
                       for them to completely ban the use of mobile phones
                       throughout the entire school day.


          o § Proprietary⠀➾


                # ⚓ Arjen Wiersma ☛ Using_AI_in_academics⠀⇛


                       Using AI, in particular generative models such as
                       GPT, are in contention within academics. The purity
                       of academics resides in students writing on their
                       research and having their work peer-reviewed. But
                       how can you now be sure that the student wrote the
                       paper and how can you trust its content? Many
                       universities, including the OU have written about
                       it. The OU published an article in Modulair about
                       it. Generally, the consensus seems to be that it is
                       ok to use AI as an assistant, but you must write
                       your texts.


                       For me AI has proven to be a valuable assistant.
                       Here are some ways in which I found AI to be
                       extremely useful: [...]


                # ⚓ Terence Eden ☛ Does_AI_mean_we_don’t_need_the_Semantic
                  Web?⠀⇛


                       If you hang around with computerists long enough,
                       they start talking about the Semantic Web. If you
                       can represent human knowledge in a way that’s easy
                       for computers to understand it will be
                       transformative for information processing.


                       But computers, traditionally, haven’t been very
                       good at parsing ambiguous human text.


                # § Windows TCO⠀➾


                      # ⚓ [Repeat] Data Breaches ☛ Peachtree_Orthopedics_alerts
                        patients_to_cyberattack;_third_patient_data_breach_in
                        seven_years⠀⇛


                             Their description of potentially involved
                             data is consistent with Karakurt’s claim that
                             the information they obtained includes “many
                             lines with SSNs, almost 1000 of credit cards,
                             other detailed personal information, medical
                             records and tons of corporate data.”


          o § Security⠀➾


                # ⚓ Linux_Kernel_DoS,_Info_Disclosure_Bugs_Fixed⠀⇛


                       Several important security issues have been found
                       in the Linux kernel, including a slab-out-of-bound
                       read problem (CVE-2023-1380), a heap out-of-bounds
                       read/write vulnerability in the traffic control
                       (QoS) subsystem (CVE-2023-2248), and an out-of-
                       bounds write issue in the kernel before 6.2.13
                       (CVE-2023-31436). The vulnerabilities have received
                       a National Vulnerability Database (NVD) rating of
                       “high-severity” due to their high confidentiality,
                       integrity and availability impact.


                # ⚓ Important_runC_Privilege_Escalation_Flaws_Fixed⠀⇛


                       Several important security issues were identified
                       in the runC Open Container Project. It was
                       discovered that runC incorrectly performed access
                       control when mounting /proc to non-directories
                       (CVE-2023-27561), and incorrectly handled /proc and
                       /sys mounts inside a container (CVE-2023-28642).


                       These bugs could possibly allow an attacker to
                       escalate privileges or bypass AppArmor, and
                       potentially SELinux.


                       A runC security update that fixes these flaws has
                       been released. We strongly recommend that all
                       impacted users apply the runC updates issued by
                       their distro(s) as soon as possible to protect the
                       confidentiality, integrity and availability of
                       their systems.


                # ⚓ The New Stack ☛ Scan_Container_Images_for_Vulnerabilities
                  with_Docker_Scout⠀⇛


                       The security of your containers builds on a
                       foundation formed from the images you use.


                # ⚓ WordPress ☛ WordPress_6.2.2_Security_Release⠀⇛


                       WordPress 6.2.2 is now available!


          o § Defence/Aggression⠀➾


                # ⚓ NDTV ☛ Pak_Drone_Carrying_Narcotics_Shot_Down_Near_Punjab
                  Border⠀⇛


                       The BSF said that four luminous strips were also
                       found attached to the consignment for easy
                       detection of smugglers.


                # ⚓ Craig Murray ☛ Lawyers_For_Israel_Oppose_Conscience⠀⇛


                       Two months ago I wrote an article entitled “Fascist
                       judges” about the concerted move by judges in
                       England to outlaw jury nullification.


                # ⚓ Scheerpost ☛ Netanyahu’s_Tactical_Mistake:_A_Fragmented
                  Israel_Faces_Palestinian_Unity⠀⇛


                       With Israel divided after Netanyahu’s victory, the
                       country faces an unexpected enemy: Palestinian
                       unity.


                # ⚓ Meduza ☛ Has_Bakhmut_been_captured?_Meduza’s_updated_battle
                  map_and_a_discussion_of_the_bloodiest_battle_of_the_Russia-
                  Ukraine_war_—_Meduza⠀⇛


                       Since the start of the full-scale invasion of
                       Ukraine, Meduza has adopted a consistent antiwar
                       position, holding Russia responsible for its
                       military aggression and atrocities. As part of this
                       commitment, we regularly update an interactive map
                       that documents combat operations in Ukraine and the
                       damage inflicted by Russia’s invasion forces. Our
                       map is based exclusively on previously published
                       open-source photos and videos, most of them posted
                       by eyewitnesses on social media. We collect reports
                       already available publicly and determine their
                       geolocation markers, adding only the photos and
                       videos that clear this process.


                # ⚓ Meduza ☛ ‘She_didn’t_kill_Milady’:_Dramatist_Mikhail
                  Durnenkov_talks_about_his_fellow_playwright_Svetlana
                  Petriychuk_and_the_real_reason_she’s_now_on_trial_—_Meduza⠀⇛


                       On May 5, the playwright Svetlana Petriychuk was
                       arrested by the Russian authorities just before
                       boarding a flight from Moscow’s Vnukovo Airport.
                       Shortly afterwards, she and director Zhenya
                       Berkovich, who produced her play Finist the Bright
                       Falcon in 2021, were both charged with “justifying”
                       terrorist propaganda. In her play, Petriychuk told
                       the story of hundreds of Russian women who had been
                       recruited by the Islamic State, married members of
                       the extremist group via Skype, and moved to Syria
                       to join them in the jihad. When they ultimately
                       returned to Russia, many of them were convicted of
                       terrorism and sentenced to years in prison, in
                       spite of the trauma they’d endured. In 2022, Zhenya
                       Berkovich’s production of Finist the Bright Falcon
                       won two prestigious Golden Mask theatrical awards
                       in Russia. One of them was for best costume design;
                       the other honored Svetlana Petriychuk and her play.
                       Petriychuk’s longtime colleague, the dramatist
                       Mikhail Durnenkov, told Meduza about Svetlana, her
                       swift rise as one of Russia’s most promising new
                       playwrights, and what her plays are really all
                       about.


                # ⚓ Meduza ☛ Weighing_symbolic_and_strategic_significance_The
                  threat_of_a_Ukrainian_counteroffensive_is_affecting_the
                  situation_at_the_front,_but_it_remains_unclear_whether
                  liberating_Bakhmut_is_worth_the_AFU’s_manpower._Meduza’s
                  updated_combat_map_shows_the_latest_developments_in_the_war.
                  —_Meduza⠀⇛


                # ⚓ European Commission ☛ President_von_der_Leyen_at_Session
                  VIII_of_G7,_‘Toward_a_Peaceful,_Stable_and_Prosperous
                  World’⠀⇛


                       European Commission Statement Hiroshima, 21 May
                       2023 Nobody wants peace more than the Ukrainians
                       themselves.


                # ⚓ Federal News Network ☛ Russian_private_army_head_claims
                  control_of_Bakhmut_but_Ukraine_says_fighting_continues⠀⇛


                       The head of the Russian private army Wagner claims
                       his forces have taken control of the city of
                       Bakhmut after the longest and most grinding battle
                       of the Russia-Ukraine war, but Ukrainian defense
                       officials have denied it. In a video posted on
                       Telegram, Wagner head Yevgeny Prigozhin said the
                       city came under complete Russian control at about
                       midday Saturday. He spoke flanked by about half a
                       dozen fighters, with ruined buildings in the
                       background and explosions heard in the distance.
                       However, after the video appeared Ukrainian deputy
                       defense minister Hanna Maliar said heavy fighting
                       was continuing. Fighting has raged around Bakhmut
                       for more than 200 days.


                # ⚓ Federal News Network ☛ Ukraine’s_Zelenskyy_arrives_in
                  Hiroshima_for_G7_summit_as_world_leaders_sanction_Russia⠀⇛


                       Ukrainian President Volodymyr Zelenskyy is in Japan
                       for diplomatic talks with the leaders of the
                       world’s most powerful democracies as they tighten
                       sanctions meant to punish Moscow over its 15-month
                       invasion of Ukraine. Japan says Zelenskyy’s
                       decision to visit Hiroshima stems from his “strong
                       wish” to participate in talks with G7 and other
                       countries that will influence his nation’s defense
                       against Russia. Bolstering international support is
                       a key priority for Ukraine as it prepares for what
                       is seen as a major push intended to take back
                       territory seized by Russia. Among other leaders,
                       Zelenskyy met with Indian Prime Minister Narendra
                       Modi to brief him on Ukraine’s peace plan, which
                       calls for the withdrawal of Russian troops from the
                       country before any negotiations.


                # ⚓ France24 ☛ Russia’s_Prigozhin_claims_capture_of_Bakhmut;
                  Ukraine_says_fighting_continues⠀⇛


                       Russian mercenary chief Yevgeny Prigozhin said on
                       Saturday his Wagner fighters had completed the
                       capture of Bakhmut – the eastern Ukrainian town of
                       little strategic importance but great symbolic
                       significance. Ukraine, however, rejected the claim,
                       saying fighting was still going on. Read our live
                       blog below to see how the day’s events unfolded.
                       All times are Paris time (GMT+2).


                # ⚓ France24 ☛ Ukraine_NGO_provides_searchlights_to_detect
                  Russian_missile_attacks⠀⇛


                       The Ukrainian army says it has intercepted over a
                       thousand Russian missiles and nearly 2800 drones
                       since the beginning of the year – but keeping
                       Ukraine’s civilians safe from air strikes is still
                       an immense challenge. FRANCE 24′s Emmanuelle Chaze
                       met the volunteers who provide the searchlights
                       supporting Ukraine’s air defence.


                # ⚓ Meduza ☛ Russian_Telegram_channels_report_armed_incursion
                  from_Ukraine_into_Belgorod_region_—_Meduza⠀⇛


                       An armed group tried to enter Russia’s Belgorod
                       region from Ukraine, report Telegram channels Baza,
                       Mash, and Shot.


                # ⚓ Meduza ☛ Wagner_founder_Prigozhin_says_his_troops_have
                  taken_Bakhmut;_Kyiv_denies_it_—_Meduza⠀⇛


                       Wagner Group founder Evgeny Prigozhin says that his
                       troops have taken full control of Bakhmut.


                # ⚓ RFERL ☛ Pope_Asks_Italian_Cardinal_To_Carry_Out_Peace
                  ‘Mission’_On_Ukraine_War,_Vatican_Says⠀⇛


                       Pope Francis has asked Cardinal Matteo Zuppi, head
                       of the Italian bishops conference, to carry out a
                       peace mission to try to help bring an end to the
                       war in Ukraine, the Vatican said on May 20.


                # ⚓ RFERL ☛ ICC_Slams_Russian_Arrest_Warrant_For_Hague-Based
                  Prosecutor_Who_Issued_Warrant_Against_Putin⠀⇛


                       The International Criminal Court (ICC) said it is
                       “profoundly concerned” about Russia’s move to issue
                       a warrant for the arrest of an ICC prosecutor and
                       judges who earlier had issued a war-crimes arrest
                       warrant for President Vladimir Putin, accusing him
                       of illegally deporting children from Ukraine.


                # ⚓ US News And World Report ☛ France’s_Macron_Says_G7_Is
                  Opportunity_to_Convince_India,_Brazil_Over_Ukraine⠀⇛


                # ⚓ RFERL ☛ Zelenskiy_Set_To_Meet_With_Biden_In_G7_Diplomatic
                  Push_As_Bakhmut_Situation_Called_‘Critical’⠀⇛


                       Ukrainian President Volodymyr Zelenskiy is set to
                       continue his diplomatic push in Japan on May 21 as
                       he bids to bolster support for his country’s
                       defense against the Russian invasion following vows
                       by Western allies to supply Kyiv with F-16 fighter
                       jets.


                # ⚓ US News And World Report ☛ Russia_Says_Supplying_F-16_Jets
                  to_Ukraine_Would_Carry_‘Colossal’_Risks_for_West_–_TASS⠀⇛


                # ⚓ RFERL ☛ U.S._Lifts_Sanctions_Against_Russian_Tech_Tycoon⠀⇛


                       For the first time since Russia’s February 2022
                       invasion of Ukraine, the United States has lifted
                       sanctions imposed against a Russian individual.


                # ⚓ RFERL ☛ G7_Leaders_Urge_China_To_‘Press_Russia’_To_Withdraw
                  From_Ukraine⠀⇛


                       The leaders of the Group of Seven (G7) leading
                       economies have urged China to “press Russia” to end
                       its invasion of Ukraine and withdraw its forces
                       from Ukrainian territory.


                # ⚓ US News And World Report ☛ Biden_Meeting_Ukraine’s
                  Zelenskiy,_South_Korea_and_Japan_on_Sunday⠀⇛


                # ⚓ US News And World Report ☛ Hiroshima_G7_Marks_Costs_of_War
                  and_Welcomes_Ukraine’s_Zelenskiy⠀⇛


                # ⚓ US News And World Report ☛ Vatican:_Pope_Francis_Tasks
                  Cardinal_With_Mission_Aimed_at_Paving_‘Paths_to_Peace’_in
                  Ukraine⠀⇛


                       The Vatican says Pope Francis has tasked a leading
                       Italian cardinal with a mission it hopes it can
                       “ease tensions” in the Ukraine war and lead to path
                       of peace


                # ⚓ US News And World Report ☛ Pope_Asks_Italian_Cardinal_to
                  Carry_Out_Ukraine_Peace_Mission⠀⇛


                # ⚓ US News And World Report ☛ Explainer-How_Important_Is_the
                  Claimed_Capture_by_Russia’s_Wagner_Group_of_Ukraine’s
                  Bakhmut?⠀⇛


                # ⚓ US News And World Report ☛ Jeddah,_Sleep,_and_a_French
                  Plane,_How_Zelenskiy_Reached_Japan’s_G7⠀⇛


                # ⚓ US News And World Report ☛ Key_Moments_in_the_Battle_of
                  Bakhmut_in_Ukraine’s_East⠀⇛


                # ⚓ US News And World Report ☛ Russia_Says_Ukrainian_City_of
                  Bakhmut_Captured⠀⇛


                # ⚓ US News And World Report ☛ Russia_Says_Wagner_Private_Army,
                  With_Help_From_Russian_Troops,_Seized_Bakhmut⠀⇛


                       Russia’s defense ministry says forces of the Wagner
                       private army, with the support of Russian troops,
                       have seized the Ukrainian city of Bakhmut


                # ⚓ US News And World Report ☛ Ukraine_Denies_Russia’s_Wagner
                  Has_Captured_Bakhmut⠀⇛


                # ⚓ US News And World Report ☛ Russia’s_Prigozhin_Claims
                  Capture_of_Bakhmut,_Ukraine_Says_Fighting_Goes_On⠀⇛


                # ⚓ US News And World Report ☛ France’s_Macron:_Zelenskiy’s
                  Japan_Visit_a_‘Game_Changer’⠀⇛


                # ⚓ US News And World Report ☛ Trump_or_DeSantis?_Neither,_Say
                  Ukrainian-American_Voters_Angry_at_War_Stance⠀⇛


                # ⚓ US News And World Report ☛ Zelenskiy_Invites_India_PM_Modi
                  to_Join_Ukraine’s_Peace_Formula⠀⇛


                # ⚓ US News And World Report ☛ Ukraine’s_Zelenskiy_Meets_World
                  Leaders_on_Sidelines_of_G7_Summit⠀⇛


                # ⚓ New York Times ☛ Zelensky_Asks_G7_Leaders_for_More_Ukraine
                  Aid⠀⇛


                       He urged his supporters to stay the course and
                       tried to convince fence sitters like India and
                       Brazil that there is no middle ground.


                # ⚓ New York Times ☛ Wagner_Chief_Says_Bakhmut_Is_Taken;
                  Ukraine_Rejects_Claim⠀⇛


                       The head of the Russian paramilitary group said his
                       forces had captured the eastern city, a claim
                       Ukrainian officials were quick to deny even as they
                       called the situation “critical.”


                # ⚓ Scheerpost ☛ China,_India,_and_the_Emerging_New_World
                  Order⠀⇛


                       What was once the American century is now
                       potentially the century of the G-3: China, India,
                       and the US.


                # ⚓ New York Times ☛ Live_Updates:_Wagner_Group_Says_It_Took
                  Control_of_Bakhmut⠀⇛


                       There was no response from Ukraine, which earlier
                       had insisted that fighting continued. President
                       Volodymyr Zelensky is in Japan, meeting with
                       leaders from the Group of 7.


                # ⚓ New York Times ☛ Battle_for_Bakhmut:_Key_Events_in_Russia-
                  Ukraine_War’s_Longest_Fight⠀⇛


                       The city has for months been the center of the
                       fighting in the Donbas region of eastern Ukraine.
                       Here’s a look at the critical moments.


                # ⚓ New York Times ☛ Bakhmut_Exposes_Feud_Between_Russian
                  Officials_and_Wagner’s_Prigozhin⠀⇛


                       Yevgeny V. Prigozhin, once a caterer for the
                       Kremlin, has made capturing the city a personal
                       obsession.


                # ⚓ Atlantic Council ☛ Experts_react:_A_‘game_changer’_G7
                  summit_in_Japan⠀⇛


                       As leaders of the Group of Seven countries gather
                       in Hiroshima, Atlantic Council experts share their
                       insights on what is coming out of the summit about
                       Russia, China, the global economy, and more.


                # ⚓ New York Times ☛ How_Ukraine_Changed_Russia’s_Battle_for
                  Bakhmut⠀⇛


                       Ukraine, this month, pressed ahead with three days
                       of maneuvers that gained ground on the flanks of
                       Bakhmut. But Russian forces still appear to hold
                       the center of the strategic city.


                # ⚓ US News And World Report ☛ ICC_Members_‘Deeply_Concerned’
                  by_Russia’s_Decision_to_Put_Prosecutor_on_Wanted_List⠀⇛


                # ⚓ US News And World Report ☛ Russia’s_Lavrov_Says_G7_Is_Bent
                  on_‘Double_Containment’_of_Russia_and_China⠀⇛


                # ⚓ YLE ☛ Volunteers_call_off_summer_search_for_WWII-period
                  Finnish_soldiers⠀⇛


                       Security concerns are preventing searches from
                       being carried out on the Russian side of the border
                       this summer, reports the Finnish news agency (STT).


                # ⚓ US News And World Report ☛ UN_Official_Criticised_After
                  Meeting_Russian_Sought_by_ICC⠀⇛


                # ⚓ Atlantic Council ☛ Don’t_call_it_a_Quint,_but_South_Korea
                  does_have_a_future_with_the_Quad⠀⇛


                       There is space for South Korea to participate in
                       aspects of the Quadrilateral Security Dialogue and
                       other minilateral structures aimed at maintaining
                       international order and security in the Pacific.


                # ⚓ US News And World Report ☛ Warring_Factions_in_Sudan_Agree
                  to_Temporary_Ceasefire,_Say_US-Saudi_Mediators⠀⇛


                       Sudan’s warring factions have agreed to a new
                       short-term ceasefire after several previous
                       attempts to broker a truce that holds have failed


          o § Environment⠀➾


                # ⚓ Vox ☛ Catalytic_converters_are_being_stolen_in_record
                  numbers._Here’s_why.⠀⇛


                       Although thefts slowly began creeping up in 2019,
                       they grew in 2020 and boomed in 2021 mostly because
                       of the pandemic, the experts I spoke with told me.
                       Like everywhere else in the world, workers couldn’t
                       mine, process, and ship these metals due to
                       restrictions. And if they did, it’s likely there
                       were other hurdles and disruptions along the supply
                       chain.


                       The fact that people weren’t driving their cars as
                       often during the beginning of the pandemic combined
                       with higher valuations for these metals created a
                       perfect storm to incentivize catalytic converter
                       theft.


                # ⚓ US News And World Report ☛ G7_‘Outreach’_an_Effort_to_Build
                  Consensus_on_Global_Issues_Like_Ukraine,_China,_Climate
                  Change⠀⇛


                       Leaders of the Group of Seven wealthy democracies
                       are sitting down with a carefully chosen set of
                       counterparts from other countries during their
                       summit in Japan in an effort to expand the G7’s
                       sway and to include voices from the so-called
                       Global South


                # ⚓ The Straits Times ☛ Behind_the_scenes,_G-7_nations_wrangle
                  over_ambitious_climate_commitments⠀⇛


                       G-7 leaders are struggling to reconcile climate
                       goals with the need for stable and affordable
                       energy supplies.


                # ⚓ New York Times ☛ At_G7_Summit,_Leaders_Wrangle_on_Coal,
                  Natural_Gas_and_Climate⠀⇛


                       The U.S. finds itself caught between defending
                       President Biden’s climate change agenda and aiding
                       allies intent on increasing their access to fossil
                       fuels.


                # ⚓ New York Times ☛ Alberta_Fires_Rage_While_Election_Ignores
                  Global_Warming⠀⇛


                       For politicians, discussing climate change in a
                       province enriched by oil money is fraught.


                # § Energy/Transportation⠀➾


                      # ⚓ US News And World Report ☛ Will_Biden’s_Hard-Hat
                        Environmentalism_Bridge_the_Divide_on_Clean_Energy
                        Future?⠀⇛


                             Perhaps the most unlikely feature of high-
                             stakes budget negotiations going on in
                             Washington is a debate over permitting


                # § Overpopulation⠀➾


                      # ⚓ NPR ☛ More_than_half_of_the_world’s_largest_lakes_are
                        shrinking._Here’s_why_that_matters⠀⇛


                             People overusing water for agriculture and
                             development, and human-caused climate change
                             are the primary drivers of the decline,
                             particularly in natural lakes, said Fangfang
                             Yao, the study’s lead author. In reservoirs,
                             dirt and sand piled up behind dams also
                             played a major role in declining water
                             levels.


                             The findings were staggering, the authors
                             said.


          o § Finance⠀➾


                # ⚓ Axios ☛ Biden_and_McCarthy’s_shared_debt_ceiling_math
                  problem⠀⇛


                       Behind the deep philosophical differences between
                       President Biden and House Speaker Kevin McCarthy
                       lies a more mundane issue — how to get any deal
                       through the House.


                       Zoom in:The White House seized on Friday’s
                       breakdown in debt_ceiling_talks to argue for its
                       preferred approach to a deal — a bipartisan bill
                       that will rely on a big chunk of Democratic votes.
                       Talks restarted Friday night after Republicans
                       announced a “pause” earlier in the day.


                # ⚓ YLE ☛ Court_orders_YouTuber_pay_€37k_in_back_taxes⠀⇛


                       The individual did not file 160,000 euros in
                       earnings.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ US News And World Report ☛ Ukraine’s_Zelenskiy_Meets_UK’s
                  Sunak_on_Sidelines_of_G7_Summit⠀⇛


                # ⚓ US News And World Report ☛ G7_Urges_China_to_Press_Russia
                  to_End_War_in_Ukraine,_Respect_Taiwan’s_Status,_Fair_Trade
                  Rules⠀⇛


                       The Group of Seven wealthy democracies have urged
                       China to push Russia to end its war on Ukraine


                # ⚓ Scheerpost ☛ Ralph_Nader:_A_Response_to_NY_Times’_Gail
                  Collins⠀⇛


                # ⚓ Vice Media Group ☛ How_Space_Companies_Plan_to_Build_Roads
                  and_Bases_on_the_Moon⠀⇛


                       Science fiction is filled with dazzling cities
                       constructed on the Moon and Mars, but it will be a
                       huge challenge to bring these extraterrestrial
                       bases into reality. Nonetheless, the dream of
                       establishing a long-term human presence on the Moon
                       has been gaining momentum, especially as NASA and
                       its partners prepare to return astronauts to the
                       lunar surface this decade as part of the Artemis
                       program.


          o § Censorship/Free Speech⠀➾


                # ⚓ Turkey ☛ Sweden_arrests_far-right_politician_Rasmus_Paludan
                  in_absentia:_Report⠀⇛


                       Far-right Danish-Swedish politician Rasmus Paludan,
                       who burned a copy of the Quran earlier this year,
                       has been reportedly arrested in absentia in Sweden.


                # ⚓ France24 ☛ Chinese_stand-up_comedy_warned_to_toe_the_line
                  following_viral_joke_about_army⠀⇛


                       A Chinese comedian was severely punished on
                       Wednesday for making a joke about the People’s
                       Liberation Army and his production company fined
                       roughly two million dollars. This incident
                       demonstrates that Chinese censors are now turning
                       their attention to the small but growing world of
                       stand-up comedy in China, which until now has
                       enjoyed a certain measure of freedom.


                # ⚓ Techdirt ☛ Twenty_Years_Ago_Today:_Barbra_Streisand_Sued_A
                  Photographer_And_The_Streisand_Effect_Was_Born⠀⇛


                       Normally on Saturday we have our “this week in
                       history” posts, highlighting Techdirt stories from
                       many years ago. But this week I wanted to highlight
                       a story that didn’t happen on Techdirt, but turned
                       into a Techdirt thing. Twenty years ago today,
                       actress/singer Barbra Streisand sued photographer
                       Kenneth Adelman for daring to photograph her
                       coastal mansion as part of his (fascinating)
                       project to photograph the entire west coast of the
                       US from a helicopter to track erosion over time.


          o § Civil Rights/Policing⠀➾


                # ⚓ Scheerpost ☛ ‘We_Do_Not_Need_a_School_for_Assassins’:_Hours
                  of_Public_Comment_Unanimously_Against_‘Cop_City’⠀⇛


                       Hundreds of Atlantans spoke out against the
                       proposed authorization of $33.5 million taxpayer
                       dollars for the Atlanta Police Foundation to fund
                       the construction of ‘Cop City’ during the public
                       comment section at city council on Monday.


                # ⚓ [Repeat] Quartz ☛ Elon_Musk_told_Twitter_employees_to_sleep
                  in_the_office,_and_now_San_Francisco_is_investigating_if_he
                  broke_the_law⠀⇛


                       The complaint—filed by six erstwhile Twitter
                       workers—accuses Musk of transforming the company’s
                       headquarters into a so-called “Twitter Hotel”
                       without the proper permitting.


                # ⚓ [Old] Public Interest Network ☛ Stranded:_Repair
                  Restrictions_Immobilize_Wheelchair_Users [PDF]⠀⇛


                       When you rely on your powered wheelchair to get
                       around, any delay in repair is not only a quality-
                       of-life issue, but a matter of life and death. Yet
                       a constrained market for wheelchair service and
                       repair makes delays for repair of weeks or even
                       months common.


                       This is Monopolies 101: when there is only one
                       option for getting something done, quality and
                       customer service go down while prices go up. One of
                       the main goals of the Right to Repair campaign is
                       to foster an open market for repair and service
                       that offers real choice and price competition to
                       consumers.1


                       But today, a skewed market for wheelchair repairs
                       often results in even simple, mechanical repairs
                       taking weeks or months to complete. In this report,
                       we’ll assess the reasons that repair choice is
                       constrained and investigate policy options for
                       state and federal leaders such as so-called “right
                       to repair” laws that provide wheelchair owners with
                       access to the information, software and parts to
                       repair their own equipment. We’ll also review the
                       results of a survey we conducted of 141 American
                       wheelchair users that provides insights into the
                       state of wheelchair repair, and whether wheelchair
                       users believe that right to repair reforms would
                       improve conditions.


                # ⚓ uni Michigan ☛ GEO_Strikes_Again⠀⇛


                       This final episode of The Daily Weekly season 14.
                       The team is capturing the ongoing Graduate Student
                       instructor strike and the widespread impact on
                       student’s academic experience during the winter
                       semester.


                # ⚓ RFA ☛ New_details_about_Uyghur_law_school_student’s_suicide
                  come_to_light⠀⇛


                       Meryem Ismayil was distraught over father’s
                       detention and mother’s interrogation by police.


                # ⚓ RFERL ☛ U.S._Condemns_Lukashenka_Regime,_Urges_Release_Of
                  1,500_Political_Prisoners_In_Belarus⠀⇛


                       The United States condemned the regime of
                       authoritarian ruler Alyaksandr Lukashenka of
                       Belarus, saying it was “unjustly holding over 1,500
                       political prisoners.”


          o § Monopolies⠀➾


                # ⚓ Axios ☛ Why_you_can’t_find_cheap_Taylor_Swift_concert
                  tickets⠀⇛


                       What Swift didn’t also use, however, was a separate
                       Ticketmaster program called Face Value Ticket
                       Exchange. This would have prevented brokers and
                       others from reselling tickets for more than face
                       value (plus fees).


                # § Patents⠀➾


                      # ⚓ Kluwer Patent Blog ☛ The_UPC_Takes_Shape_and_Color
                        [Ed: UPC is illegal. They're trying to tam down
                        everyone's throat something that will inevitably
                        explode.]⠀⇛


                             With less than 2 weeks to go before 1 June
                             2023, it was about time for the UPC to tie
                             several loose ends and to clarify various
                             questions before becoming (more or less)
                             fully operative.


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Popular_Pirate_Bay_Proxy_Site
                        Disappears_From_GitHub⠀⇛


                             With more than a million monthly visits, The
                             Proxy Bay was one of the most popular Pirate
                             Bay proxy information portals. Hosted on
                             GitHub, the site also was a thorn in the side
                             of rightsholders, which attracted the
                             attention of UK police. While initial
                             takedown efforts failed, The Proxy Bay
                             eventually disappeared a short while ago,
                             along with several dedicated proxy sites.


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