𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, February 18, 2022

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Generated Sat 19 Feb 02:41:17 GMT 2022

Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)

Full hyperlinks for navigation omitted but are fully available in the originals

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Gemini index for the day: gemini://gemini.techrights.org/2022/02/18/

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

⦿ António Campinos Wants to Undo His Father’s Legacy for Several More Years, Spreading Corruption Across Europe and the World | Techrights

⦿ BREAKING NEWS/EXCLUSIVE: António Campinos Confirms That He is Seeking Reappointment | Techrights

⦿ FFII: In PL Holdings, European Court of Justice Confirms EU Law Cannot be Outsourced to International Courts Like Unified Patent Court (UPC) | Techrights

⦿ List of Currently Active Gemini Capsules on the Internet | Techrights

⦿ IRC Proceedings: Thursday, February 17, 2022 | Techrights

⦿ Linux Foundation Board in 2022: 86% Corporate and 81% Proprietary Software Companies | Techrights

⦿ Rest Assured the Linux Foundation Does Not Really Speak for Linux (Not Anymore) | Techrights

⦿ LXer Not Reachable Since February 16th (Updated) | Techrights

⦿ [Meme] Megaphone of António Campinos | Techrights

⦿ [Meme] A ’Social Democracy’ Where Every Vote is for Sale | Techrights

⦿ When AMD Sends You a Crate of CPUs Worth (Market Value of) Roughly $500,000 | Techrights

䷼ Bulletin articles (as HTML) to comment on (requires login):

	http://techrights.org/2022/02/18/antonio-campinos-corruption/#comments

	http://techrights.org/2022/02/18/antonio-campinos-reappointment/#comments

	http://techrights.org/2022/02/18/ffii-on-pl-holdings-upc/#comments

	http://techrights.org/2022/02/18/gemini-capsules-on-the-internet/#comments

	http://techrights.org/2022/02/18/irc-log-170222/#comments

	http://techrights.org/2022/02/18/linux-foundation-board-2022/#comments

	http://techrights.org/2022/02/18/linux-hostile-foundation/#comments

	http://techrights.org/2022/02/18/lxer-not-reachable/#comments

	http://techrights.org/2022/02/18/megaphone-for-campinos/#comments

	http://techrights.org/2022/02/18/meme-a-social-democracy-where-every-vote-is-for-sale/#comments

	http://techrights.org/2022/02/18/phoronix86-amd/#comments

䷞ Followed by Daily Links (assorted news picks curated and categorised):

	http://techrights.org/2022/02/18/easy-3-4-1-soon/#comments

	http://techrights.org/2022/02/18/rednotebook-2-23/#comments

                ䷩ 𝚕𝚒𝚗𝚎 78

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/antonio-campinos-corruption/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/antonio-campinos-corruption/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ António_Campinos_Wants_to_Undo_His_Father’s_Legacy_for_Several_More_Years,

Spreading_Corruption_Across_Europe_and_the_World⠀✐

Posted in Europe, Patents at 3:10 pm by Dr. Roy Schestowitz

Video_download_link | md5sum ffb2a8b0327f8592a584f33af5a5edc5

EPO Covering Up After 13 Years

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/epo-mafia-buying-time.webm

Summary: The so-called ‘Mafia’ at the EPO (the staff of the EPO calls it “the

Mafia”) doesn’t want to let go; perhaps in an act of cover-up — basically

ensuring nobody outside the Mafia gets access to checks and balances — there’s

already an approach for the Government of Portugal to cement a second term for

the controversial Frenchman (whose father had come from Portugal and stayed in

France to dodge political persecution)

THE low blow to Alison Brimelow [1, 2] is the succession by the same sort of

Mafia she had warned about and had personally suffered from (she later stepped

down, almost understandably, leaving the EPO without leadership for quite some

time).

“The future of Europe is at stake because EPO corruption is like a cancer that

spreads far beyond the Office and has already infested the Commission.”That

Benoît_Battistelli ruined the EPO for 8 years is bad enough; what if António

Campinos is allowed to do the same? We might soon be in an agonising scenario

where in a period of 25 years more_than_85%_of_the_time_the_EPO's_President_was

in_effect_French. Is this “diversity”? But it’s not even about nationality but

about a cabal conspiring to break the law for personal gain, mostly for the

benefit of litigation (at the expense of science, which Team UPC doesn’t

exercise; it’s all about lawsuits or doing to the courts what they did to the

EPO, i.e. to examination guidelines — nowadays rendered a production line or

rubber-stampers, beholden to coup plotters instead of the EPC).

This coming weekend we plan to say a lot more about patents. The_state_of_news

about_patents_is_beyond_a_farce. The very same firms that hijacked — albeit by

proxy — the EPO (they also want to do the same to courts) have taken over more

than 90% of what one finds in the so-called ‘media’. This leads to a state of

“alternative realities”, imposed by an echo chamber wherein litigation

lobbyists preach to their choir, mentally masturbating to the tune of

intentional lies (such as UPC being beneficial to SMEs).

The future of Europe is at stake because EPO corruption is like a cancer that

spreads far beyond the Office and has_already_infested_the_Commission. █

                ䷩ 𝚕𝚒𝚗𝚎 147

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/antonio-campinos-reappointment/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/antonio-campinos-reappointment/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ BREAKING_NEWS/EXCLUSIVE:_António_Campinos_Confirms_That_He_is_Seeking

Reappointment⠀✐

Posted in Europe, Patents at 12:45 pm by Dr. Roy Schestowitz

           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇A hardcore António Campinos⦈

Summary: António_Campinos confirms that he is seeking a renewal of his mandate

and emphasises that he is seeking the endorsement of the Portuguese and not the

French government

Today it was unofficially revealed that EPO President António Campinos is

seeking reappointment as EPO President for a second term.

EPO insiders report that during an in-house video-conference Campinos responded

to questions from staff by confirming that he is actively seeking

reappointment.

However, his attempt to secure a second mandate is subject to him obtaining the

endorsement of “his” government. He was at pains to emphasise that this

referred to the Portuguese and not the French government!

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Battistelli and Kongstad⦈ The inauguration of the new

Portuguese government has been delayed_until_mid-March due to the need for a

partial rerun of voting after a court decision which declared that more than

157,000 expatriate votes from 139 voting stations across Europe were invalid.

So it could take some time before Campinos finally gets the green light from

“his” government to pursue his plans for an extension of his EPO appointment.

Campinos took over at the helm of the EPO in July 2018 after having been

appointed for a five-year term. Thus, his current term is due to expire next

year on 30 June 2023.

It is expected that the EPO’s Administrative Council will discuss the renewal

of his mandate at its 170th meeting scheduled to be held on 22_March_2022.

(warning: epo.org link)

If Campinos were to fail to secure the approval of the Portuguese government

together with the backing of three-quarters of the delegations on the Council,

then this would require the opening of a selection procedure to choose a

successor.

In the event of such a situation materialising, the Council could be expected

to open the selection procedure at its June 2022 meeting.

“The reason for this is that back in 2009/2010, the Council encountered great

difficulties in arriving at a consensus and the election process was widely

criticised for its lack of transparency.”However, the history of the EPO over

the last decade or so has made the Council cautious about conducting such a

procedure and it does its best to avoid it whenever it can.

The reason for this is that back in 2009/2010 [PDF], the Council encountered

great difficulties in arriving at a consensus and the election process was

widely criticised for its lack of transparency.

Leading the chorus of criticism about the lack of transparency was the outgoing

President herself, Alison Brimelow who began her rebuke to the Council with the

following words:

“As President and the guardian of the EPC, I have to bring a problem to your

attention.”

Brimelow deplored the fact that those outside the closed circle of delegates

participating in the confidential “C-point” discussions on the election of a

new President had no clear idea of what had been decided and that these

decisions were not made available to the wider public.

Even IAM which normally restricts its coverage of EPO affairs to churning out

uncritical puff-pieces had the following to say [PDF] after Benoît_Battistelli

had finally managed to secure election in March 2010:

 “One of the striking aspects of the election process was its complete

 lack of transparency. Although all four candidates did go on the

 record about why they were standing and what their priorities would

 be as EPO president, at no stage was there any news about which

 countries were voting for which person and why. Even when Battistelli

 was elected there was no statement from the Administrative Council

 that explained the reasons for giving him the job.”

In June_2014 (local_copy [PDF]), a year before Battistelli’s term of office was

due to expire, the Council – led by Battistelli’s “protector” the notoriously

corrupt Jesper_Kongstad – decided to extend the Corsican despot’s mandate by

another three years in order to save themselves the bother of having to conduct

a selection procedure to find a successor.

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Cuno Tarfusser⦈ When the time finally came to elect a

successor to Battistelli in_2017, the Council adopted a much more cautious

approach than it had done in 2009. This time there was, for all intents and

purposes, only one candidate, António Campinos.

The disgruntled_Italian_delegation which felt that it had been cheated of a

Vice-President position in 2012 due Battistelli’s sponsorship of Željko Topić

tried to field an opposing candidate in the person of Cuno_Tarfusser.

But Tarfusser’s “lack of an IP background” – compared to the self-styled

“trademark expert” Campinos – was used to undermine his candidacy and ensure

that Battistelli’s designated successor got the job.

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

EPO propaganda organ IAM joined in efforts to discredit Tarfusser by pointing

                  to his lack of an “IP background”.

Now that Campinos is gradually approaching the end of his first term of office,

the Council is probably keen to reappoint him in order to avoid the

“disruption” of having to organise a new selection procedure.

“Now that Campinos is gradually approaching the end of his first term of

office, the Council is probably keen to reappoint him in order to avoid the

“disruption” of having to organise a new selection procedure.”However, it

remains to be seen whether the growing unrest among EPO staff and the impending

threat of industrial_action by the staff union SUEPO will derail the Portuguese

Pretender's plans to secure a second term of office.

Watch this space… █

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⡿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣖⣴⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣆⣤⣄⣤⣴⣄⠀⠀

⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⠀⡠⢠⣿⠉⠨⠟⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠁⠀⠉⠀⣠⣶⡄⠀⠀⡈⣂⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⣿⠾⣷⠶⠆⠀⠁⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣤⣄⣀⠄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⡿⢁⣀⢶⣾⣿⣿⣿⣿⣧⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⡶⢶⡶⠶⠖⠀⠀

⠀⠀⠀⠀⠀⠀⠛⠿⣛⠿⣿⣯⣍⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠭⠂⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠋⠃⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣩⣻⣴⡶⢟⣂⣈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣻⣟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣣⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⢾⣿⠿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠭⢛⡟⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣟⠓⢾⡙⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣸⣿⣿⣿⠟⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠿⣿⢿⣿⣿⡿⠿⠯

⠀⠀⢠⡄⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠆⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠿⠶⢙⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣳⡚⡷⢶⠚⢛⣺

⠀⢀⣼⣧⡧⡧⣧⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢛⡠⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢨⡟⠡⠫⠷⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⠏⠈⠭⠝⡀⠈⠉

⠀⠀⢨⣤⠇⠴⢦⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣡⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠈⢵⡀⠶⠟⢀⣼⣿⢻⣿⣿⣿⣿⣿⣿⡧⠻⠿⠟⣉⣃⣉⡁⠁⠀

⠀⠀⢸⡀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣛⣛⠛⠛⠛⠿⠟⠛⢻⣿⣿⠿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⡠⠊⠀⠀⠀⠸⣿⣶⠔⣸⠟⠋⣼⣿⣿⣿⣿⣿⣿⡃⣤⣶⠾⠻⠟⠋⠁⠀⠈

⠀⠀⢸⡛⡂⢻⣿⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣿⣿⣿⣿⣷⣶⣶⣦⣄⡀⠘⠉⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⡀⠙⠛⠙⠋⡀⣾⣿⣿⣿⣿⣿⣿⣿⡇⡟⠛⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⡗⠁⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠙⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠙⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⠋⡉⣈⣤⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠐⢺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠠⠴⣯⣭⣽⣾⡿⠗⣾⠿⠛⠹⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢼⣿⠀⢠⣿⡏⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢰⣿⠇⢠⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢠⣿⡟⠀⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣼⡿⠁⣰⣿⠇⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣰⣿⠃⢠⣿⡟⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡏⠀⣼⡿⠁⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠀⢰⣿⠃⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⢀⣿⠇⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⡙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣾⡏⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣸⡟⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠁⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠃⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣽⣿⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣿⣿⣻⣿⣿⣏⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢘⠥⠀⠫⠩⣖⣞⣿⣿⣿⡏⠀⢀⠁⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⢠⣿⣿⡟⠀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣿⣤⣿⣯⣥⣾⣷⣸⡤⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⢠⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢉⣉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣉⡉⠉⠉⣉⣿⣿⣿⣿⣿⠿⠋⠀⠂⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⣴⣮⣯⣝⣖⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣿⣿⣿⣿⡿⠌⠻⣦⠙⢿⣿⣿⣿⢻⣿⣿⣗⠀⠀⠹⡀⠀⠀⢀⢠⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢯⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠆⠈⠻⣿⣿⠘⣿⠏⢸⠀⠀⠀⣷⣶⣶⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⠃⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⡎⠂⢀⢸⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⠏⠘⠀⣀⡴⠂⠡⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣰⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠀⠀⢻⣿⣿⣶⣶⣤⣀⡀⠀⢻⣿⠓⠀⣼⢸⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡏⠀⢰⡿⠋⡠⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣿⣿⢿⣻⣿⣯⣤⣤⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣦⢸⡟⠀⢤⡟⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⡟⠀⠀⣨⣾⣊⣴⣾⡆⠸⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⠃⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⡁⠀⠀⢰⣿⣿⣿⣿⣿⣄⠀⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⠀⠀⠀⠿⣛⣩⣥⣶⣶⣦⡀⠙⢇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⣸⣿⣿⡿⠛⠁⠀⠀⠀⠘⠟⠻⣿⣿⣿⣽⣃⠀⡈⡄⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⠋⠀⢰⣿⡿⠏⠁⠀⠀⠀⠀⠀⣀⣈⠙⢻⣟⡟⣛⢯⠀⠈⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⢀⣤⣶⣾⣿⣦⣀⣰⣤⣶⣶⣤⣿⢿⣶⣴⡶⡄⢸⣿⣷⣤⣻⡞⠦⠀⠀⠀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣺⡻⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣛⣋⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡹⣿⣮⠻⠍⠣⠈⠿⡟⠘⢿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠨⣿⣿⣿⣿⣿⣿⣯⣧⣿⣿⣿⠿⣡⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠃⢹⣿⣿⣿⢿⣿⣿⣿⠻⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣭⣿⣻⠿⠿⠟⠛⠋⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣭⣭⣥⣤⣶⣾⣿⣿⣿⠋⢰⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡆⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠟⣿⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⠿⢱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣸⡛⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣫⡵⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠈⠿⠿⠿⠻⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣀⠹⢿⣿⣿⣿⣿⣿⣿⡀⠀⠛⢻⣒⣺⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⡇⠀⠀⡛⠈⠉⠉⠉⠉⠉⢛⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠙⠿⣿⣿⣿⣿⣿⣳⢐⡓⠒⠛⠻⢣⠟⠣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⠀⠀⣿⡀⠀⠀⡀⣀⣤⣾⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠉⠩⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⠀⠀⣿⡄⠀⠀⠉⠉⣽⣿⣿⣿⡟⠉⠙⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠟⠋⠅⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⡇⠀⣿⡇⠀⠀⠒⠊⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⡇⠀⣿⣷⣦⣤⣀⣠⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠒⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣴⣴⣮⣿⣶⠒⢘⣿⣤⣽⡷⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣟⠏⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠊⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠂⠂⠀⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⢿⣛⠛⠀⠀⠀⠀⠀⣠⠔⣰⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⡆⢭⠟⠛⠁⠉⠀⠀⠀⠀⠀⠀⣾⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⠇⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠸⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⢲⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠉⠉⠹⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⢸⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣶⡀⠀⠀⢸⠀⢀⣶⢤⣤⣀⣀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣧⣦⠀⣿⣇⠤⠀⠀⣉⠉⠛⠓⠒⠒⠤⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠙⢛⡋⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣾⣿⣿⣿⢸⣿⣿⣿⡟⠁⣸⣿⣿⣄⣰⣇⠰⠀⠀⢀⣸⡦⠀⠤⡄⢸⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣦⣤⣤⣛⣿⣶⣦⡶⠊⢼⣿⣿⣿⣿⠁⠀⣀⣤⣀⠀⠀⠀⠀⠠⢭⡀⠳⢶⣲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⢠⡬⢿⣿⣿⣿⣇⠀⠈⢿⣿⡎⠃⣼⡄⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣰⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⡞⢐⣾⣿⡿⠉⣿⣶⣀⣬⣽⣗⣄⣈⣁⣒⣖⣾⠪⠀⠀⠀⠀⠂⢀⣀⣶⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣥⣿⣿⣟⠁⠀⢻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣛⣿⣀⣴⣶⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠸⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣶⣯⣸⣿⣿⣿⣿⣿⣿⣿⣷⠯⣬⣿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠙⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣧⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡀⢻⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⠀⣿⡟⡷⣿⣷⣿⣿⣿⣿⣿⣿⣿⠽⠿⢚⠚⠟⠿⢿⡿⠇⢉⠑⠀⠄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣼⣿⣿⣿⠀⣿⢿⣧⣿⣿⣿⣭⣽⣿⣿⠡⡠⠖⠂⠈⠀⠀⠀⠀⠀⠸⢿⠀⣀⣤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣇⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢹⣿⣿⣿⠀⠸⠶⠷⠸⣿⣿⣟⣹⣿⣇⠀⠈⠙⠗⠀⠠⠔⠟⠀⠀⠘⣤⢸⣛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⢿⣾⠷⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⠀⢀⠀⠀⠩⢿⣿⣿⡟⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠻⢶⣦⣭⡍⢾⠄⠘⠚⠿⢿⣿⣿⡿⠛⣿⣿⣿⣯⣁⢦⡿⡟⠀⠈⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⡀⠨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠚⠏⠭⠉⢀⣾⣿⣿⣥⠹⢯⣿⢫⡃⡁⠒⡤⢤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⡓⠁⢠⣖⡰⠆⢀⠀⡄⠀⠀⠀⠒⠂⠶⣖⡀⠀⠀⣴⠂⠄⣀⣼⣿⣿⣿⡿⣿⣿⡶⡹⡟⠢⠁⠈⢉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠘⠸⠉⡀⢠⡁⠀⠀⠀⠀⠀⠀⠠⣌⢠⡤⢀⠀⣾⣟⢠⣤⣿⡿⣿⣿⣿⣗⣺⣿⣧⢣⡃⢢⠃⠘⠀⡀⠁⠀⠀⠀⠀⣤⣶⣤⠘⣷⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣶⣂⣣⢟⠁⠟⣟⡀⠀⣂⣻⣷⣦⣦⣤⣾⣿⣿⣾⡛⣯⣧⡟⣛⠁⠯⡿⠿⡟⣿⢿⡼⣿⣿⠾⡦⡈⠤⠄⡀⠀⠀⠀⢰⡏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣆⢋⣞⣾⣿⢿⣧⣀⡿⣽⠿⣿⣿⣿⢿⣻⣿⣷⣽⡋⡻⠐⢶⡼⠇⡧⣶⣿⣿⣾⡿⣿⡞⠃⢅⣵⡶⠌⢀⡀⠀⠀⠸⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠖⣶⣶⢶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⡀⣻⣿⣿⣿⣿⡿⣿⡜⡝⢢⠘⡇⠈⠀⠑⡈⠦⡧⣈⣫⡓⣝⠙⠃⢀⡡⣝⠿⠩⠭⢠⡇⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⡟⣿⣿⣿⣏⣣⣿⣠⣿⡆⠡⢠⢀⠓⠀⠈⣠⣑⠯⡋⠻⣀⠰⠤⠞⡢⠩⣀⣶⣿⠃⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣭⢷⣦⢊⡤⣤⠠⣑⣜⡲⠵⠄⣚⠅⠀⠤⢴⣠⣾⣿⣿⡟⢠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣎⣶⣽⣿⣽⣲⣞⣛⣶⣴⣿⣿⣿⣿⡿⣰⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠙⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣽⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣯⣞⣿⣧⣄⠁⠀⠀⠀⠈⠂⠩⠛⠛⠿⡻⡻⠿⠿⡉⠛⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢀⠀⡀⢀⢀⠀⠄⠀⠀⠀⡂⠀⠀⠀⢈⣠⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠠⢀⢐⠀⠆⠂⠀⢀⠀⠁⠠⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠠⠀⠈⠨⠡⢁⠁⢐⢐⢀⠄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠅⠯⠨⠀⡾⣀⠂⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢀⢅⠁⠊⠨⢨⢤⠃⡂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠀⡃⡉⠠⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢀⢀⢀⠀⠀⠀⠀⠤⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⠏⠀⠀⠀⠐⠠⠨⠀⠌⠉⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⢿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⠸⡟⠀⠄⠀⠀⡍⡈⢀⠐⠀⠀⡀⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠟⠛⣋⣠⣤⠀⣠⣠⡄⠀⠀⠙⠛⠿⣿⣿⣿⡟⠂⠁⠀⠀⠀⠀⡂⡃⡂⠀⠀⠀⠀⠀⡄⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡻⡟⢿⣻⣿⣿⣿⣿⢿⢻⡿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣻⣿⣿⣿⢿⢿⣿⣿⣿⡿⣿⡿⡿⢿⡿⣿⢿⡿⣿⣿⣿⢻⣿⡟⣿⣿⢻⡿⣿⡿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣷⣿⣧⣯⣿⣿⣽⣿⣿⣯⣴⣽⣿⣯⣾⣽⣥⣿⣿⣽⣿⣽⣿⣽⣿⣯⣿⣾⣿⣭⣿⣽⣿⣿⣯⣾⣿⣿⣽⣧⣿⣷⣥⣯⣾⣽⣮⣧⣿⣯⣽⣼⣿⣷⣧⣽⣼⣽⣿⣿⣽⣿⣵⣿⣭⣿⣵⣿⣽⣿⣿⣿⣿⣿⣿

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✐ FFII:_In_PL_Holdings,_European_Court_of_Justice_Confirms_EU_Law_Cannot_be

Outsourced_to_International_Courts_Like_Unified_Patent_Court_(UPC)⠀✐

Posted in Europe, Law, Patents at 7:05 pm by Guest Editorial Team

By Benjamin HENRION, originally_posted_February_15,_2022

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇CJEU⦈_

Brussels, 17th Feb 2022 — The European Court of Justice has confirmed that EU

law cannot be outsourced to international courts in its “PL Holdings sarl Vs

Poland” decision. It is problematic for the architecture of the Unified Patent

Court (UPC), which is an international court outside of the judicial system of

the European Union, despite the claims of its supporters.

The European Court of Justice (CJEU) has recalled in PL Holdings that Member

States cannot remove disputes from the judicial system of the EU which deal

with EU law:

 Lastly, it follows both from the judgment in Achmea, and from the

 principles of the primacy of EU law and of sincere cooperation, not

 only that theMember States cannot undertake to remove from the

 judicial system of the European Union disputes which may concern the

 application and interpretation of EU law […].

 — Court of Justice of the European Union, Press Release No 190/21,

 Luxembourg, 26 October 2021, Judgment in Case C-109/20, PL Holdings,

 https://curia.europa.eu/jcms/upload/docs/application/pdf/2021-10/

 cp210190en.pdf

Since EU law covering patents is the Biotech directive and the Enforcement

directive (IPRED), the interpretation of EU law is removed from the judicial

system of the European Union, which is composed of the CJEU and the National

Courts.

The PL Holdings decision follow the same line of thought as the Achmea

decision, where the European Court of Justice dissolved intra-EU investment

courts (ISDS). In its Achmea decision (2018), the CJEU recalled the same

functional link principle with the National Courts, as in Miles (2011):

 However, the arbitral tribunal at issue in the main proceedings is

 not such a court common to a number of Member States, comparable to

 the Benelux Court of Justice. Whereas the Benelux Court has the task

 of ensuring that the legal rules common to the three Benelux States

 are applied uniformly, and the procedure before it is a step in the

 proceedings before the national courts leading to definitive

 interpretations of common Benelux legal rules, the arbitral tribunal

 at issue in the main proceedings does not have any such links with

 the judicial systems of the Member States (see, to that effect,

 judgment of 14 June 2011, Miles and Others, C‑196/09, EU:C:2011:388,

 paragraph 41).

 — CJEU’s Case Case C-284/16, Achmea, https://eur-lex.europa.eu/legal-

 content/EN/TXT/?uri=CELEX%3A62016CJ0284&qid=1639573183575

Supporters of the UPC keep claiming it will be a Court Common to the Member

States:

 The Unified Patent Court (UPC) will be a court common to the

 Contracting Member States and thus part of their judicial system.

 — Unified Patent Court website, About page, https://www.unified-

 patent-court.org/about

If the Unified Patent Court is really part of their judicial system, why does

the staff of the court need diplomatic immunity via the Protocol on Privileges

and Immunities (PPI) of the Unified Patent Court?

The European Court of Justice has allowed the Benelux Court of Justice to be

part of the judicial system of the European Union, because it has a dialogue

with National Courts, via a system of prejudicial questions. The UPC does not

have any dialogue with the National Courts, it simply replaces them.

The European Court of Justice is very much attached to the concept of Autonomy

of EU law, which is in danger each time an international court outside of the

judicial system of the European Union is allowed to interpret EU law.

Member States which are no signatory of the UPC (because it is a super too-

expensive court for SMEs) like Poland, Hungary, Spain or Czech Republic should

use Art259 TFEU to ask the question to the European Court of Justice whether

this construction is compatible with the architecture of the European Union:

 A Member State which considers that another Member State has failed

 to fulfil an obligation under the Treaties may bring the matter

 before the Court of Justice of the European Union.

 — Article 259 TFEU, EUR-Lex https://eur-lex.europa.eu/legal-content/

 EN/TXT/?uri=CELEX%3A12016E259

§ Links⠀➾

* Enforcement directive (IPRED): https://en.wikipedia.org/wiki/

  Enforcement_Directive

* Biotech directive: https://en.wikipedia.org/wiki/

  Directive_on_the_legal_protection_of_biotechnological_inventions

* CJEU judgment on ‘PL Holdings’, Press release No 190/21, 26 October 2021,

  Case C-109/20: https://curia.europa.eu/jcms/upload/docs/application/pdf/

  2021-10/cp210190en.pdf

* Protocol on Privileges and Immunities (PPI) of the Unified Patent Court:

  https://www.unified-patent-court.org/sites/default/files/

  ppi_final_ii_en_clean.pdf

* FFII: Unified Patent Court is a fake Common Court and violates CJEU’s

  jurisprudence of the last 10 years, will explode at launch, says Pr

  Jaeger https://ffii.org/unified-patent-court-wont-survive-a-legal-

  challenge-at-the-european-court-of-justice-says-dr-thomas-jaeger/

* Wikimedia Commons: Palais de la Cour de Justice CJEU, July 2021, Sign and

  Towers B and C https://commons.wikimedia.org/wiki/File:

  Palais_de_la_Cour_de_Justice_CJEU_July_2021_Sign_and_Towers_B_and_C.jpg

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⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠶⠂⢠⣦⢿⣌⣧⣿⡿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣇⣻⣫⣿⣶⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠖⠀⣸⡻⣯⣿⣞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣻⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢤⠀⢀⣟⣿⣝⣿⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣽⣿⡆⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⢸⢿⣮⠿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢇⣿⢻⣿⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢉⠁⠀⢻⣷⡻⢷⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣭⡏⣾⣿⣿⣿⢸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠚⠚⠀⠀⣷⡈⠣⣞⠻⢞⢻⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⢿⢿⣻⣼⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠶⠶⠆⠀⢰⡈⠻⢠⡙⠧⡛⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⡤⡤⠀⠀⡈⠻⡆⡘⢷⡄⠻⡞⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠘⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠁⠀⠀⢻⣦⠀⢿⣦⠙⣧⡁⢿⡻⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠀⠀⣴⣤⡙⢸⣦⡙⢴⣌⠻⣾⢻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠏⠔⠐⠒⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣠⢰⢶⠆⠀⢠⡀⠙⠇⣄⡙⢇⣦⡙⢷⡾⣵⡭⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⠀⠀⡼⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠉⠉⡈⡀⠀⠀⠘⠿⣶⢀⠙⢿⢠⡙⠇⣍⠋⣦⡑⣦⣸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠚⠰⣀⣀⣀⣀⡴⠁⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⠻⠻⠿⠇⠀⠠⣷⣄⡀⠘⢷⡄⡘⢿⢠⡙⢷⣌⡿⣾⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⠀⠠⡀⢆⠆⠢⠠⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣄⡄⡄⡤⠀⠀⣀⠈⠛⢁⣦⣄⠁⢿⡦⣈⡻⣮⡻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡂⢤⣀⠀⣰⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿

⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠻⢿⡆⢀⠉⠻⣰⣦⡁⠻⡗⣜⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⠀⠀⠀⠀⢠⣆⣆⡞⡾⠀⠀⣰⣤⣀⠁⠻⢿⡆⣄⠙⠸⣶⢄⠟⢷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⡠⢠⠀⠂⠀⣴⡀⡡⠉⠃⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠿⢰⣦⣄⠀⠻⠟⣦⣌⠘⢷⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠈⠈⠁⠀⠀⣀⠀⠤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿

⠀⠀⠀⠰⠧⠏⠟⠿⠀⠀⢸⣷⣦⡄⡈⠙⠋⢼⣶⢄⡉⠛⢿⣦⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠠⠀⠀⠘⠀⠘⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿

⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⡀⠉⠙⠠⢿⣷⢂⣄⡈⠘⠿⣧⣤⣊⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣴⡂⢢⠲⢰⠄⠄⡦⣼⢰⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⠀⠀⠸⠧⠏⠟⠿⠀⠀⠰⣿⣷⡆⣠⣀⡈⠘⠻⠏⣶⣦⣴⣫⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿

⠀⠀⡀⣀⣀⢀⠀⠀⠀⣀⡀⠉⠁⠛⠿⠇⣶⣶⢥⣅⣩⢟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

                ䷩ 𝚕𝚒𝚗𝚎 631

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/gemini-capsules-on-the-internet/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/gemini-capsules-on-the-internet/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ List_of_Currently_Active_Gemini_Capsules_on_the_Internet⠀✐

Posted in Site_News at 7:21 pm by Dr. Roy Schestowitz

Summary: The list of known (to Lupa) Gemini capsules continues_to_grow; it grew

from 519 in February 2021 to 1,724 in February 2022

* 000000.flounder.online

* 0gitnick.flounder.online

* 0×1.net

* 0×735.com

* 0×80.org

* 0xbad.flounder.online

* 100sexts.flounder.online

* 100words.flounder.online

* 108mhz.flounder.online

* 1436.ninja

* 158.nu

* 202x.moe

* 2mas.smol.pub

* 2pie.flounder.online

* 3baid.flounder.online

* 68k.myfirewall.org

* 7-ph.com

* 725.be

* 7irb.tk

* 80h.dev

* 85-harvest.flounder.online

* 9p.sdf.org

* 9til.de

* a.flounder.online

* a1000duck.flounder.online

* aaoth.xyz

* abildgaard.com

* acdtv.hopto.org

* acdw.net

* acesoren.cities.yesterweb.org

* acidic.website

* acompanionofowls.flounder.online

* adam.cities.yesterweb.org

* adam.flounder.online

* adare.flounder.online

* adele.pollux.casa

* adele.work

* admin.flounder.online

* adnano.co

* adny.flounder.online

* aelspire.info

* aetin.art

* agees.flounder.online

* ageinghacker.net

* aiex.flounder.online

* ailepet.pollux.casa

* ailpet.pollux.casa

* ailurocrat.flounder.online

* ainent.xyz

* airmack.de

* ait.place

* ajax.flounder.online

* ajdiaz.me

* ajith.flounder.online

* ajroach42.flounder.online

* ajtjp.com

* ake.crabdance.com

* ake.crabdance.com:1966

* akkartik.flounder.online

* akuxie.flounder.online

* alanxoc3.xyz

* alchemi.dev

* aldrik.flounder.online

* alephalpha0.flounder.online

* alex.corcoles.net

* alex.flounder.online

* alex2.flounder.online

* alexey.shpakovsky.ru

* alexschroeder.ch

* alexwennerberg.com

* alissa.earth

* alixandercourt.flounder.online

* alltext.umaneti.net

* almaember.com

* almanac.smol.pub

* alpha.lyk.so

* alsd.eu

* alsostarring.flounder.online

* alvawang.flounder.online

* alvin.flounder.online

* alvin.paiges.net

* amadeus.flounder.online

* amanharwara.flounder.online

* amdg.flounder.online

* amer.pollux.casa

* amethyst.cities.yesterweb.org

* amiga5000.flounder.online

* amigadu.de

* amok.flounder.online

* amomentzine.flounder.online

* amplifibeats.pollux.casa

* amvc.mx

* anachronauts.club

* and3rson.flounder.online

* andinesia.flounder.online

* andreafeletto.com

* andygrn.co.uk

* anime.flounder.online

* anjune.lol

* anniez1995.flounder.online

* anorlondo.net

* ansi.hrtk.in

* antimass.flounder.online

* antiphasis.flounder.online

* antonio.e-worm.club

* antonio.flounder.online

* aoalmeida.com

* aoeu.cities.yesterweb.org

* aosync.me

* aperalesf.flounder.online

* aphrack.org

* apintandaparma.club

* appl.garden

* aprates.dev

* archipielago.uno

* archiwistka.blog

* armen138.flounder.online

* armitage.flounder.online

* arok.xyz

* artur.gadziev.online

* arydev.flounder.online

* ascendinganthem.xyz

* ascii.mozz.us

* ascii.mozz.us:7070

* asciibene.flounder.online

* asciinema.hrtk.in

* ashaslan.flounder.online

* aslowcab.flounder.online

* asp.flounder.online

* astrobotany.mozz.us

* astroglitch.cities.yesterweb.org

* astrognome.smol.pub

* ataraxia.flounder.online

* atlantis.luxe

* atyh.cc

* augers.srht.site

* auken.flounder.online

* auragem.space

* autione.srht.site

* auzziejay.cities.yesterweb.org

* avalos.me

* avfig.com

* avocadosh.xyz

* ax.flounder.online

* axiomatika.flounder.online

* axionfield.space

* axolotl.flounder.online

* azq.geminet.org

* babiak.duckdns.org

* baconicsynergy.flounder.online

* bad-gateway.smol.pub

* bakertribe.co.uk

* bartender.midnight.pub

* bartf1969.flounder.online

* bbs.archaicbinary.net

* bbs.ec

* bcalderon.io

* bearforceone.net

* bebomuchocafe.flounder.online

* beer.smol.pub

* bel.flounder.online

* benaaron.dev

* benburwell.com

* bencollver.cities.yesterweb.org

* benj.smol.pub

* bentsai.smol.pub

* beta.lyk.so

* beucismis.flounder.online

* beyondneolithic.life

* bi-rabittoh.flounder.online

* billy.flounder.online

* binarycat.flounder.online

* binarythicket.xyz

* birabittoh.smol.pub

* bitdweller.flounder.online

* bitshift.tokeniser.uk

* bjornwestergard.com

* bjw.flounder.online

* bl4kers.flounder.online

* blekksprut.net

* blitter.com

* bloatedloaf.flounder.online

* blog.datapulp.de

* blog.dumpr.org

* blog.emisocks.com

* blog.locrian.zone

* blog.schmidhuberj.de

* blube.club

* bobignou.red

* bobpelle.cities.yesterweb.org

* bogart.flounder.online

* bogwonch.net

* bogwonch.smol.pub

* bonehead.flounder.online

* booksin.space

* bootes.me

* boss.flounder.online

* botond.online

* bouncepaw.flounder.online

* brandontaylor2021.flounder.online

* breadpunk.club

* brewed.midnight.pub

* brewed.smol.pub

* brightblue.midnight.pub

* brotfrau.flounder.online

* bucareli.online

* buetow.org

* bugrother.flounder.online

* bulletpr00f.host

* bvnf.space

* bwog-notes.chagratt.site

* byrontakeda.flounder.online

* byzoni.org

* c0d3sh4p3r.flounder.online

* c3po.aljadra.xyz

* c3po.flounder.online

* cabooshy.flounder.online

* cadence.moe

* cae.cities.yesterweb.org

* caffo.flounder.online

* cal.discordian.de

* calcuode.com

* calico.flounder.online

* calonaur.flounder.online

* campaignwiki.org

* caolan.uk

* caoom.smol.pub

* capsula.adrianperales.com

* capsula.rodolpho.onoeck.com.br

* capsula.rodolpho.onoeck.de

* capsule.adrianhesketh.com

* capsule.fdn.fr

* capsule.ghislainmary.fr

* capsule.ml

* capsule.theparanoidtimes.org

* capsule.town

* capsule.usebox.net

* capsule.wetterberg.nu

* caracolito.mooo.com

* carboncopy.xyz

* carcosa.net

* cark.flounder.online

* cassum.smol.pub

* casualtyhere.midnight.pub

* cat-girl.gay

* caterste.cities.yesterweb.org

* catherine.e-worm.club

* catpokemon.flounder.online

* cats-shadow.cats-home.net

* cats-shadow.flounder.online

* causa-arcana.com

* celehner.com

* cena.flounder.online

* cetacean.club

* cfdocs.wetterberg.nu

* chad.flounder.online

* chanc.ee

* chaosadmins.de

* charick.srht.site

* charlie.town

* chartjunk.flounder.online

* chat.mozz.us

* chefdeadpool.com

* chess.lanterne.chilliet.eu

* chris.bracken.jp

* chris.e-worm.club

* chrislloyd.flounder.online

* chronowerks.de

* chryste.pl

* chtabs.flounder.online

* cinni.cities.yesterweb.org

* cipay.ca

* circumlunar.space

* cities.yesterweb.org

* cjc.im

* clearleaf.flounder.online

* clemat.is

* clifton.kaznocha.net

* cobaltblue.flounder.online

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* officialdonut.smol.pub

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* ofmanytrades.com

* ogg.elwinar.com

* oh.mg

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* okoyono.de

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* olav.flounder.online

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* olicauli.cities.yesterweb.org

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* om.gay

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* openbsd.org.ru

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* oppen.digital

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* owise1.cities.yesterweb.org

* owocean.cities.yesterweb.org

* pachapunk.space

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* parsley.farm

* parsley.smol.pub

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* paxavis.dev

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* peguero.xyz

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* pgorl32jhgkgald7tcsp6k7zpujvd763kywenr72yr76fqjaomxf7kid.onion

* phreedom.club

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* plot47.space

* pluviam95.smol.pub

* pojntfx.flounder.online

* pollux.casa

* polluxnrko5evevpgom4cucif4rpgcde3kqs2ydnxzfcusvdqexp7xyd.onion

* porkbuns.smol.pub

* port1965.eu

* portal.mozz.us

* posixcafe.org

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* privacy.flounder.online

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* pub.heathens.club

* pulham.info

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* random-projects.net

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* rasputin.selfip.net

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* rawtext.club

* rdelaage.ovh

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* real-changeling.hispagatos.org

* red.flounder.online

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* repos.wetterberg.nu

* reptilic.us

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* retrocate.com

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* review.treeblue.space

* rfmpie.smol.pub

* rhino.flounder.online

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* rick.smol.space

* rina.cities.yesterweb.org

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* robertbrook.smol.pub

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* rochelimit.uk

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* rocketnine.space

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* roly.cities.yesterweb.org

* rooibos.cities.yesterweb.org

* rosenzweig.io

* rosie88.midnight.pub

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* royniang.com

* rpy.ink

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* ruario.flounder.online

* ruinous.space

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* russell19.flounder.online

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* s.tymo.name

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* sadness.cities.yesterweb.org

* sakjrn.smol.pub

* sakurina.flounder.online

* salejandro.me

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* sam.bossley.us

* samhsmith.net

* samsai.eu

* sanctum.geek.nz

* sandmage.de

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* scientology.srht.site

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* sdf.org

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* senders.io

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* she12.midnight.pub

* sherwood.at

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* six-dots.app

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* sotd.sysrq.in

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* source.community

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* space.fqserv.eu

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* spellbinding.tilde.cafe

* spicycilantro.cities.yesterweb.org

* spikydinosaur.com

* spline-online.ml

* splitcells-net.srht.site

* spool-five.com

* spxtr.net

* squaredance.flounder.online

* srht.site

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* stacksmith.flounder.online

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* status.shit.cx

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* striker.net.eu.org

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* sunshinegardens.org

* sunshinegardens.org:1968

* supergrizzlybear.smol.pub

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* synthe.ist

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* tdem.in

* tdmm.eu

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* tecnologiaensimple.cl

* teitoklien.smol.pub

* telescope.omarpolo.com

* ten2.one

* tenebre.cities.yesterweb.org

* tenebre.flounder.online

* tensor.work

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* test.samebchase.com

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* tetris.smol.pub

* text.adventuregameclub.com

* text.eapl.mx

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* thasmanie.fr

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* thegonz.net

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* tilde.cafe

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* tlf.smol.pub

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* tobik.me

* tofu-tester.random-projects.net:1966

* tokeniser.uk

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* toki.transjovian.org

* tom.flounder.online

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* twins.rocketnine.space

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* uirapuru.midnight.pub

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* vps01.rdelaage.ovh

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* κρόνοσ.transjovian.org

* ♊.thebackupbox.net

* 🦈🖥.ws

                ䷩ 𝚕𝚒𝚗𝚎 2379

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

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§ Bulletin for Yesterday⠀➾

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Gemini version at gemini://gemini.techrights.org/2022/02/18/linux-foundation-board-2022/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Linux_Foundation_Board_in_2022:_86%_Corporate_and_81%_Proprietary_Software

Companies⠀✐

Posted in Deception, Free/Libre_Software, GNU/Linux, Kernel at 7:21 am by Dr.

Roy Schestowitz

It has only been getting worse over time

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Linux_Foundation's_board_in_2022⦈_

Summary: The Linux_Foundation has become just another phony apparatus like the

Gates_Foundation and it cannot represent Linux, instead it_punishes_the_founder

of_Linux; Still no update_or_IRS_filing_disclosed_since_the_2018_report (4

years ago; screenshot below is minutes old)

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

⣿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⢿⡿⠿⠿⣿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣀⢀⣀⣸⣀⣀⣀⠀⠀⠀⠘⠀⣠⣤⣤⠤⣤⡼⠶⠄⢤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⣀⣀⣉⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠇⠀⠀⣍⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣸⡆⠀⡀⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣴⣿⣿⣿⣿⣿⣦⡌⢻⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠓⠒⠁⠀⢹⠉⠁⠀⠀⢰⣿⣿⣦⠀⠈⠉⠉⠉⢻⡏⠉⠙⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⠿⠛⠓⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠶⡶⠶⠶⠿⠀⠀⠀⠀⠉⠛⣿⠉⡀⠀⠐⠶⠶⠾⠗⠲⢶⣺⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠭⠭⠿⢿⠿⠟⠿⢽⡆⣻⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⠄⠠⠀⣀⠀⠀⠀⠸⡿⠂⣿⣿⣷⠀⠀⠀⠤⣄⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣦⣶⣾⡇⣼⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠂⠀⢽⣿⡎⠀⠀⠀⡀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣖⡀⠹⣿⣿⣄⣙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⡁⠀⠉⠉⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠈⠉⠉⠉⠂⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣯⣙⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⠷⠒⠒⠛⠂⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠙⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⢀⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⣿⣷⣦⣤⣭⣿⣿⣿⡇⠙⠿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⢰⣐⢠⠤⡤⠀⢠⠤⡀⡤⢼⢠⠤⡠⡦⠠⢤⠠⠤⠄⢠⠁⠸⣿⣿⣿⣿⡟⢉⢀⠀⡀⡀⡘⢻⢿⣿⡏⡟⢻⢿⠃⠀⡀⢀⠉⠛⠻⢿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠘⠀⠘⠀⠃⠘⢸⠐⠃⠃⠸⠘⠨⠃⠃⠈⠘⠀⠀⢀⠂⠀⢺⣿⣿⡏⠀⠏⠁⠀⠈⠤⠆⡧⠼⠸⢸⠇⡣⠭⠸⠄⠏⠅⠘⠀⢠⠁⠀⣿

⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣿

⣿⠿⠿⠿⠿⢿⣿⡿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⢻⠧⠁⢸⡟⣀⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠫⠓⠉⠉⠙⢿⣿⣿⣷⣄⠀⡀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣡⣤⣤⣤⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠙⢿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣿⣷⣷⣶⣶⡄⠉⢿⣿⣿⣿⣿⣿⣿

⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⠪⢄⣤⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣉⢻⣿⠻⠙⠋⢃⢰⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠹⡄⢸⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠙⠀⠰⣽⣿⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣶⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⠛⠙⠙⠒⠀⣸⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣢⣾⢢⣿⣿⡆⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣛⣿⣒⠒⣽⡁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠳⠃⠀⣠⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⠀⠻⣿⠀⣿⣏⠀⠈⢹⣿⣿⡿⠿⠿⠿⣿⣿⣆⡞⣿⣿⣿⣷⣶⠟⠁⠀⠀⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠁⠘⠛⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣡⣠⡏⠀⣿⣿⠀⣤⣾⣿⣿⣧⣄⣀⣠⣾⣿⣿⡇⢸⣿⡟⠋⠁⣠⡆⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠴⠒⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠿⠑⠃⠋⢸⣿⣿⡟⠋⠉⢠⣽⣿⣿⣇⠐⢿⣿⠷⠞⡉⠄⠀⣶⡟⠁⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣤⡀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠒⡀⡀⢀⢀⠀⡠⡀⣀⣄⡆⡀⡈⣯⠛⠇⠀⡀⠀⠀⡀⢸⣿⣿⠀⠀⡄⢀⢿⡿⡋⡴⣂⣤⣤⣀⡎⣈⣒⢠⡹⣗⡀⠀⡀⠀⠈⠻⣿⣿⣿⡿⡿⢛⠋⡁⡀⠁⣇⡹⣿⣇⡆⢀⠀⣠⡀⣠⠀⠸⡙⠻⠿⣿⣿

⣿⠀⠀⠉⠀⠇⠨⠤⠃⡥⠞⠇⠀⠏⠨⠍⠡⠔⠭⠇⠇⠀⡐⠀⢸⣿⣿⠀⠀⠇⣥⠀⠈⠀⠆⡇⠰⡸⠠⡇⠃⣸⠸⠀⠆⠄⠸⠀⢠⠃⠀⣿⣿⡇⣦⠇⡉⠀⠘⢀⠆⣇⡰⢸⠀⡇⠗⣚⠸⡀⢆⠄⠘⢀⢠⢃⡈⣿

⣿⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣬⣿⣧⣼⣿⣿⣿⣤⣤⣤⣼⣿⣿⣤⣤⣼⣯⣤⣤⣤⣤⣥⣦⣴⣥⣤⣤⣤⣥⣤⣤⣤⣤⣤⣥⣤⣤⣿⣿⣯⣤⣦⣬⣥⣬⣤⣤⣥⣤⣤⣬⣼⣥⣦⣤⣤⣤⣦⣤⣬⣥⣤⣷⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠐⠂⠰⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠉⠀⠘⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠀⠈⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣴⣾⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣛⣻⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣤⣭⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠃⠐⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠘⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠿⠿⢿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢱⡠⢴⣿⣿⠟⠁⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⣤⣤⣤⣤⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠈⡀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⣶⡎⠽⠛⠿⠆⠀⠈⢀⠀⠀⡀⡄⠀⠀⣄⠀⠀⠀⠈⠰⢠⠤⣼⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⡀⢀⠀⠀⠀⠘⣆⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⣿⣿⡇⢒⡅⡇⢘⢈⠆⣃⡵⡏⠉⡗⢑⡓⢋⡠⣒⡆⡇⠀⠠⠁⢿⣿⣿⣿⠁⡗⠊⠈⠐⡁⡅⣏⣸⢸⠉⡇⢋⣘⢸⡁⡕⡃⢸⠀⢀⠆⠀⣿⣿⡇⠀⠇⠚⠐⠁⡉⡁⣍⢭⢸⠉⣧⢎⢹⢸⠁⡍⣰⢸⠁⠀⠌⠀⣿

⣿⣿⣷⣮⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣦⣥⣶⣾⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣊⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣁⣀⣲⣾⣷⣄⣭⣀⣀⣀⣀⣀⣀⣊⣀⣀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠇⢠⣶⣾⣿⣿⣿⣶⣶⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⠄⣿⠭⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡷⢶⣿⣔⠰⢶⡶⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⠯⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣶⣿⠿⠯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠗⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⣾⡇⠘⠿⣿⣿⣿⣿⣿⣿⡇⠘⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⢟⠛⢿⣿⣿⣿⣆⠀⠀⠀⢠⠀⠀⠀⡀⢀⢼⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣷⣄⣀⣴⣿⣿⣿⠀⠀⠀⠀⠉⠛⢻⣿⣿⠀⠀⠀⠚⢰⠁⡉⡡⠈⢩⢸⠉⣿⢎⢽⠸⠁⡍⢰⢸⠁⠀⡌⠘⣿⣿⣿⢸⢐⣹⢉⡎⢤⢸⠁⡄⡏⢹⢰⠡⡎⡏⠨⢙⠀⠈⡀⡙⢸⣿⣿

⣿⣿⣿⡟⠋⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⡉⣀⡀⠀⠀⠀⠀⠚⠀⠀⣿⣿⣿⣶⣚⣧⣴⣄⣠⣘⡈⠀⠁⠈⢀⣬⣥⣤⣤⣄⣀⣀⣐⣁⣙⣻⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⡏⠉⠙⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣦⣤⣤⣽⣒⢶⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣤⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⣾⠎⠀⠀⠈⠁⠈⠉⠙⢿⡟⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠼⢿⣿⣿⠿⠟⠂⢤⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡘⣿⣯⣹⣿⣿⣷⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣤⠀⠀⠀⣤⠀⢠⣴⣾⣿⣏⠉⢻⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠐⢂⢿⣇⠀⡉⢙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠘⡟⠁⠀⠀⠈⠉⠁⠀⠈⠻⣿⣿⣧⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⡇⠀⠰⣶⣶⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣺⣿⣟⢻⣷⠏⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠐⠐⠀⠀⠀⠀⣿⣉⠉⠉⠀⠀⣤⣿

⣿⣿⣿⣿⣿⣿⡿⠆⠀⠹⡿⠈⣈⣩⣽⣿⣿⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣷⣼⣿⣿⣿⣿⡶⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣀⠸⣿⣿

⣿⣿⢿⠛⠛⠉⠀⠀⠀⠀⠃⢀⢠⢀⠴⢎⡉⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⠀⠀⣀⡠⣴⣾⣿⣿⣿⣿⣿⢶⣆⠄⠀⣼⠄⠂⣀⣄⡀⠀⠀⠀⣿⣿⡇⠀⣀⡀⠀⠀⠀⣿⣿⡆⠀⠀⡀⠀⠀⡀⢾⣿⣿⣏⡽⡏⢤⣼⣿

⣿⠋⢸⠒⢸⠀⠇⡰⢸⢈⠆⡏⢸⢸⢐⡋⣇⢐⢺⠀⠁⠀⡘⠀⢸⣿⣿⣠⣴⠠⣘⢰⡁⠫⡪⠑⣽⢹⢫⣷⠦⠵⢽⠡⡬⢤⢰⢡⠀⡄⠀⣿⣿⡇⠀⠄⠂⡆⠰⠁⡌⡎⣢⢸⠁⡧⠮⠦⠟⢁⠥⡎⡇⠀⢀⠂⢾⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣴⣿⣦⣿⣮⣵⣋⣭⣾⣾⣿⣶⣭⣴⣥⣮⣬⣮⣾⡑⣀⠀⣿⣿⡇⠀⠀⠀⠁⠀⠉⠀⠋⠁⠁⠀⠁⠈⠁⠤⠁⠉⠁⠀⠀⠂⠀⠀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⣀⣠⣀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣤⣽⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡤⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠋⢁⣋⠀⠀⣀⣂⡁⠀⠀⠀⠀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣔⢉⣻⣟⠉⠍⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⡟⡿⠟⡱⠁⠀⣾⣳⣸⣰⣿⣿⣿⣀⠀⠀⠀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⣿⡿⢿⡿⣿⣿⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⠟⠉⠰⠀⠀⢰⡿⡋⣧⣿⣿⢿⣿⡷⠀⠀⠀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⡩⡶⠒⢻⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣾⠃⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡼⠀⠋⢜⣮⣁⣼⣧⣠⠄⠀⠀⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠙⠿⣶⡶⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⠛⠀⠀⠀⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⣿⣿⣿⡿⣿⠏⠀⠉⣿

⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⣠⠄⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⠄⠀⠀⠀⠀⠀⢀⢴⣿⣿⣿⣿⣿⣏⡗⢀⠀⠀⣿

⣿⣿⡿⣛⣩⣵⣿⣶⡀⡀⠀⠍⠻⠿⠋⠀⠀⣠⣤⣴⣶⣭⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢱⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⢐⡄⢀⣼⣿⣶⠶⠚⠀⠀⠀⠌⠘⠿⠿⢿⣿⣿⣿⠷⠿⠃⠀⣿

⣿⠏⠸⠿⢿⣿⣿⣿⣿⣷⣤⢤⠂⢀⣤⣴⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣇⣄⣈⠛⣽⣿⠗⠒⠀⠀⠀⠀⡀⢀⢀⢀⠀⠀⠈⠀⠀⠀⠀⠁⣿

⣿⠀⠀⣇⡀⡍⢩⠉⡉⡍⢍⢫⠆⣇⡍⣍⢷⠈⣉⡍⠍⠁⠀⡄⢸⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠁⡧⠜⠐⠁⠢⡂⡆⢱⢸⢋⣧⠆⠴⢸⠀⡬⢤⢰⠀⠀⡄⠀⣿

⣿⠀⠄⠃⠀⠃⢘⡐⡁⡗⢊⠘⠀⢃⣀⡒⡘⣊⡒⢃⡀⠀⠘⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣼⠓⠀⢴⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠉⠁⠋⠉⠨⣼⣥⣦⣭⣤⡅⠉⠈⠈⠀⠐⠀⠀⣿

⣿⣾⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣾⣿⣷⣿⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿

⣿⠿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡄⣤⡀⠙⠢⣼⣿⡿⠛⠉⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡗⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣀⣀⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠋⠙⠃⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⢛⡟⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠈⠘⠿⢦⠄⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⢠⣤⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠐⣶⡤⣁⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⣼⡇⣄⣀⣤⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿

⣿⠸⠶⠂⠀⠀⠀⠀⢼⣧⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠉⠈⢻⣷⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠆⢰⠿⠃⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⠏⠀⠀⢸⠿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿

⣿⣀⠀⠀⠀⠀⣀⡀⠘⡁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣄⣈⣉⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠚⠛⠋⠂⠀⠀⠀⠀⡛⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠉⠸⢠⠂⠖⢀⠰⢲⢰⠖⣯⣄⣲⣸⠂⣐⢀⢰⠂⠀⡀⠀⢸⣿⣿⡇⠀⡏⠅⡖⢠⠂⡀⡖⢂⢰⠂⣇⣔⣀⢲⠂⡂⡄⡆⠒⠀⠄⠀⣿⣿⣿⣿⡟⡩⠛⢟⠟⠛⡤⠄⢠⠤⡇⡤⢺⢵⠝⠿⠛⢛⠟⠻⡛⣿⣿

⣿⠀⠀⠀⠈⠀⠐⠁⠐⠚⠘⠀⠋⠀⠒⠀⠀⠑⠈⠈⠀⠠⠁⠀⢸⣿⣿⠃⠀⠁⠀⠁⠈⠐⠁⠗⠋⠘⠀⠃⠀⠒⠈⠊⠐⠁⠁⠀⠌⠀⠀⣿⣿⣿⣿⣃⣶⠀⣏⠨⣃⡧⠜⠸⣠⠇⠋⠭⢘⠌⠣⠂⡈⡸⡰⢡⣿⣿

⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣶⣿⣿⣿⣿⣶⣾⣾⣷⣿⣿⣿⣷⣶⣿⣿⣿

⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⡿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠕⡺⠺⣽⣿⠿⠻⢅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⢀⣉⡉⠊⠀⠀⠀⠀⠀⠀⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⣹⣫⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣷⣶⣿⣿⢠⣦⢂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⢸⡈⠀⠀⠠⠀⠀⠀⠀⠀⢐⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⣟⡿⠿⠟⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠘⢏⡂⠀⢠⢀⠀⠀⠀⠀⣯⣾⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠹⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣖⢿⣯⡭⢀⣴⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⠀⠙⠒⢿⣿⣧⠀⠀⠀⡈⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣿⣿⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⢆⢉⠁⠀⠀⢸⣽⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠙⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⣿⠀⡖⡂⡤⢀⠄⠐⡤⠄⢸⠧⡆⡠⠀⢤⠄⠄⡀⡄⠤⠀⡀⠀⢸⣿⣿⠂⠀⡖⡂⡤⢀⠄⠀⡤⠄⢡⠤⡆⡠⠀⢤⠄⠄⡀⡄⠤⠀⡄⠀⣿⣿⣿⡿⡖⢠⢀⠄⠤⡀⡤⢄⢠⠤⡆⡠⢤⢰⠄⠤⠀⢀⠄⠉⠛⠻⣿

⣿⠀⠃⠀⠃⠘⠠⠃⡧⢞⡸⣀⣏⠉⠭⠘⠔⠡⠃⠃⠀⡐⠀⠀⢸⣿⣿⠀⠀⠃⠀⠃⠘⠠⠃⡧⠞⠸⠀⠏⠉⠭⠘⠔⠡⠃⠃⠀⡐⠀⠰⣿⣿⣿⣟⠃⠀⠀⠀⠠⠂⡧⠼⠸⠀⠟⠉⠭⠘⠄⠫⠘⠘⣰⢠⢃⣤⣿

⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣮⣵⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣶⣼⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣷⣶⣷⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⢀⣄⢸⣏⡀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣻⣿⣿⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠠⣜⣾⣿⠿⠊⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⣉⢙⡋⣉⠉⠁⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢛⣿⡭⠾⠷⢭⣍⡙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢠⠀⠀⠀⠀⠀⠀⣸⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⡿⠷⠷⠶⠿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠐⠀⠀⠀⠀⠀⣰⣯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣭⣭⣾⠟⠁⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠀⠀⠀⢀⡔⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⠀⠀⠈⠉⠁⠀⠀⠀⢰⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢀⣠⣴⣿⠁⠀⢸⣿⠟⠋⠁⠀⢀⡀⠀⠀⠀⠀⠈⠐⠤⡀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠁⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⣿⠿⠛⠀⠀⠈⢀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠁⠀⢀⣊⣉⡙⢻⣧⣄⠀⠀⢠⣗⡟⣁⣠⣈⣙⣿⠄⠂⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣙⣄⣀⣀⣃⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣀⣀⣀⣀⣸⣿⣿⣿⣷⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠤⠀⡄⡐⠁⠀⢸⠀⢸⢀⠜⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠊⠈⠁⠀⠂⠀⠸⠀⠸⠀⠡⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤

⣿⣿⠀⠉⠉⠉⢹⣩⡧⠈⠉⠁⠈⠉⠉⠉⠁⠉⠈⠍⠉⠉⠈⠉⠁⠈⠉⠇⠈⠉⠉⠁⢹⣏⣇⣃⣉⣉⣩⣠⣉⣉⣉⣈⣁⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⢿⠿⠿⠿⢿⠿⢿⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣾⣤⣤⣬⣬⣤⣬⣤⣤⣤⣤⣬⣤⣤⣤⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠈⡗⠘⠉⠙⠙⢉⠙⣹⡇⠀⠋⠙⠉⠉⠉⠙⠋⠀⠋⠙⠉⡁⠚⡉⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣤⣴⣴⣴⣴⣤⣬⣤⣼⣧⣿⣦⣴⣦⣤⣤⣤⣦⣤⣦⣤⣦⣤⣶⣤⣦⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠠⠀⡁⢹⡁⡡⣛⠀⠀⡐⡁⡀⠀⠰⢸⢸⣛⡛⣟⣛⢻⠘⡈⠁⡨⠉⠁⡇⢀⠈⢉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⢡⣼⢋⢹⢉⠙⢸⠋⢹⠉⣿⠋⠙⠁⣾⠀⠈⠋⠙⢈⡏⡏⡏⣙⢉⢹⠉⣿⠁⣅⠈⡁⠈⢡⠘⣿⣏⡀⢉⠀⡋⡄⡿⠇⢐⡷⢀⣾⣿⡁⠈⡁⢸⢡⠸⠿⠀⢈⡇⣲⣿⣇⠂⣃⡈⡃⡌⠿⣶⢰⡇⣿⠉⠉⣿⣿

⣿⣿⠶⠶⠶⠾⠰⠾⠾⠶⠶⠶⠿⠷⠶⠶⠿⠶⠶⠷⠶⠶⠷⠶⠷⠿⠾⠶⠶⠿⠦⠷⠾⠶⠾⠶⠾⠤⠿⠶⠷⠶⠷⠶⠿⠷⠶⠷⠶⠦⠾⠷⠾⠶⠾⠶⠾⠿⠶⠿⠷⠷⠼⠷⠶⠷⠶⠷⠶⠿⠿⠾⠧⠿⠶⠶⠿⠿

⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣀⣉⣩⣩⣉⣅⣉⣉⣉⣉⣉⣹⢀⣩⣉⠉⣉⡁⣏⣡⣡⣉⣭⣝⣹⣈⣉⣹⣉⣨⣘⣀⣊⣏⣁⣁⣏⣄⣼⣉⣍⣁⣁⣳⣾⣍⣉⣋⣍⣉⣁⣈⣉⣏⣉⣉⣽⣁⣉⣍⣀⣘⣉⢉⣏⣈⣉⣭⣹⣉⣉⣉⣉⣿⣉⣉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣿⣿⠝⣿⣿⡍⠉⠩⡍⠉⠉⢹⠉⢉⠉⢙⢉⠉⠉⠉⡋⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣿⣿⡙⣿⣿⡍⠛⠛⡉⠛⠛⢻⠙⠙⠩⢹⢉⠛⠛⠛⠋⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭

⣿⣿⣿⣿⡻⣿⣿⡛⠻⠿⠛⠻⠻⢿⠛⠛⠻⠻⠛⠿⠻⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣵⣿⣿⣷⣶⣶⣷⣶⣶⣾⣶⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠿⣿⣿⠛⠿⠿⠻⠿⠿⢿⠻⠻⠿⢻⠛⠿⠿⠿⡿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣵⣿⣿⣷⣶⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣥⣩⣨⣭⣗⣭⣬⣌⣭⣄⣉⣭⣰⣩⣮⣉⣌⣄⣨⣅⣺⣠⣬⣤⣨⣅⣭⣅⣩⣭⣀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 2711

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/linux-hostile-foundation/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/linux-hostile-foundation/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Rest_Assured_the_Linux_Foundation_Does_Not_Really_Speak_for_Linux_(Not

Anymore)⠀✐

Posted in Free/Libre_Software, GNU/Linux, Kernel, OSDL at 11:23 am by Dr. Roy

Schestowitz

Video_download_link | md5sum d6256f67dc837bd44b75ac7d9d0342cf

Not the Voice of Linux

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/who-bosses-lf.webm

Summary: The employer of Linus_Torvalds, who remains_the_trademark_holder_of

"Linux", is clearly aligned against_the_goals_of_Linux_as_a_project and as a

community

THE Linux_Foundation, as noted in the above video, came about after OSDL had

blown up. The Linux Foundation claims to be older than it really is (the

University of Manchester does the same thing for that matter, cherry-picking

historical dates) and within only a few years it lost its direction. Today, in

2022, the_Linux_Foundation's_Board_of_Directors_is_almost_90%_corporate and

more than 80% proprietary companies (mostly ‘suits’ who don’t even use GNU/

Linux). Judging by the way things change every year, the Board might be over

90% corporate some time soon (maybe as soon as next year) because they

literally sell seats on the Board. They even market it that way (we showed

evidence of this before, based on their own words). You pay for a certain

membership tier and in exchange you get to exercise control over Linux and

more.

“It’s indisputable at this point that it’s just a front group or a shell of

very affluent companies, some of them not even American.”It’s quite frankly a

miracle that the IRS still lets this thing go on without having to pay any

taxes. It’s indisputable at this point that it’s just a front group or a shell

of very affluent companies, some of them not even American.

I’ve said a lot more in the video above as I commented, one by one, on the 26

members of the Linux_Foundation’s_Board_of_Directors. Even outside the Board,

in the management team of the Linux Foundation, there_are_prominent

Microsofters.

There is no simple soluton or quick ‘fix’ to this sordid mess. The Linux

Foundation buying positive media coverage about the Linux Foundation (in

essense corrupting the media) leads to a different kind of backlash and other

sorts of scandals, as we’ve noted here before. They also run_afoul_of_rules,

which means they can get banned. █

                ䷩ 𝚕𝚒𝚗𝚎 2780

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/lxer-not-reachable/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/lxer-not-reachable/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ LXer_Not_Reachable_Since_February_16th_(Updated)⠀✐

Posted in Free/Libre_Software, GNU/Linux at 2:42 am by Dr. Roy Schestowitz

Summary: As of this time, the cause remains a mystery, there is only

speculation at this point and no visible answers

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇LXer_issue⦈_

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇LXer_out⦈_

Update: The culprit now becomes more obvious.

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇wmkt.net_expired⦈_

⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀

⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀

⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀

⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 2967

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/megaphone-for-campinos/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/megaphone-for-campinos/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ [Meme]_Megaphone_of_António_Campinos⠀✐

Posted in Europe, Patents at 2:45 pm by Dr. Roy Schestowitz

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Summary: EPO President António_Campinos helped by a little rigging from Benoît

Battistelli-bribed ‘media’

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣣⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠮⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣟⣓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠈⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠀⠛⠀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠄⠀⠂⠈⠁⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡟⢰⣧⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠿⠟⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠠⠀⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⡍⠉⠈⠭⠭⠜⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡄⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⢿⡽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠀⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⡿⠦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⠙⠈⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠙⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠒⠉⠐⠛⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠄⠀⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡟⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⣻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠁⠂⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⡍⠉⠈⠭⠭⠌⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡄⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⡿⠏⠿⡽⠧⠿⠿⢇⠷⠻⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠿⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠬⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠿⡞⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠁⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣿⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠛⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠀⠀⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣾⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⣻⠿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠁⠾⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⡍⠉⠈⠩⠍⠼⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠧⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⠷⠻⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⡲⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣹⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠟⣀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠁⠀⠀⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠴⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠀⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⡍⠉⠈⠭⠍⠼⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠠⠶⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⠿⡽⠷⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢹⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣻⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⣍⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠓⠇⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠛⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⠁⠀⠐⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣾⢸⠀⠀⡏⢙⣾⣿⣿⠿⠿⠟⠛⠛⢉⣭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠼⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⡿⠏⠿⡽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢨⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠚⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠕⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⡞⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣟⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠂⠉⠐⠿⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠀⠐⠂⠈⠥⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⣉⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠀⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⡍⠉⠈⠩⠍⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠧⠇⠧⠾⡿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣷⣿⣿⣷⣷⣿⣴⣷⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣯⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⢙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⣉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢒⠊⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠓⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠂⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠐⠀⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣾⢸⠀⠀⡏⢙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠹⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠀⠠⠄⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⢹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣟⣓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠄⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄⠘⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⢿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠗⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠐⠀⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣾⢸⠀⠀⡏⢙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠀⠠⠄⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠔⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠧⠇⠧⠾⡿⠏⢿⠽⠷⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⡿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣷⣿⣿⣿⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣯⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⣌⠉⢸⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣍⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⣿⣿⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠂⠉⠐⠿⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠐⠀⠘⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣋⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠛⠛⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠸⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠒⠉⠐⠿⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⠁⠀⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⣿⣿⣭⣭⣿⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⡼⢿⣿⣿⣿⣿⣿⣿⣿⣻⣓⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠈⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⢠⣿⣦⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⢿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣿⣿⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠟⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡁⠀⠐⠀⠈⠅⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠄⠀⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢦⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣾⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⣀⡴⠁⠐⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⢠⣼⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣟⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣟⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠟⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡁⠀⠐⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢙⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⡿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⡿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣍⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣁⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⠌⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⡄⠛⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠸⠁⠀⢀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⣷⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡿⣻⣿⣿⣿⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣹⢿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠗⠀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡁⠄⠀⠂⠈⠅⠈⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡷⢿⣸⡇⢀⣸⡃⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠡⠍⠉⠈⠩⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣯⡟⣹⣿⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣽⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⣰⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠸⠁⠀⢀⠀⠀⠀⠀⢨⣿⠿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⢈⢉⣼⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⣿⣹⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠟⡀⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠀⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢻⣶⡏⠙⢺⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠷⠇⠧⠾⡿⠏⣿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠿⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢩⠀⢲⡀⠀⠃⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⣆⣀⠁⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠸⠁⠀⢀⠀⠀⠀⠐⣻⡟⠃⠀⠀⠀⠀⠀⡏⢺⣿⣿⣷⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢿⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡀⠀⠀⠀⠀⠀⣿⣤⣼⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⡎⠃⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⢻⣿⣿⣹⣿⣿⣽⣯⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠒⠉⠐⠟⡀⣤⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⡁⠄⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢻⢶⡏⠹⢺⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠭⠥⠌⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⡿⠏⣿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣿⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢟⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢿⡿⣿⠻⣿⣿⣿⣿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠽⠿⠿⠛⠭⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⡀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⣍⣝⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⢀⠸⠃⠀⢀⠀⠀⠀⠘⠓⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢿⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠚⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣹⣿⣿⣽⣯⣮⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠐⠉⠐⠟⡀⣤⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠐⠂⠈⠅⠘⠄⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢻⣶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠄⠬⠥⠤⠭⠡⠤⠭⠥⠬⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⢿⠽⢧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣿⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢿⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠽⠿⠿⠛⠩⠝⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⣽⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⡘⠃⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣿⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⢀⠸⠃⠀⢀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢿⣹⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⣯⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣽⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⣯⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠐⠉⠐⠟⡀⣤⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠞⠀⡁⠄⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⣶⡏⠹⢺⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠄⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠍⠈⠩⠭⠤⠬⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⣿⡽⠷⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠂⡀⠂⠈⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢟⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⣿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠽⡿⠿⠛⠭⠽⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣭⣿⣟⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⣸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢩⠀⢲⡀⠀⠃⠀⠀⠀⠀⠐⠋⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⡀⠀⠀⠀⠀⠀⣿⣶⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣿⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢰⢀⠸⠃⠀⢀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢿⣹⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⣯⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠒⠉⠐⠟⣀⣠⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠞⠀⡁⠄⠐⠂⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⣶⡏⠹⢺⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠭⠥⠬⠥⠍⠉⠈⠭⠭⠤⠬⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⣿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠠⠀⠀⠀⠂⠀⠂⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⣿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠿⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣭⡟⣹⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣭⣽⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⢀⣀⠀⣠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠇⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⢠⣀⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣿⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⢀⠸⠃⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠟⡀⣠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞⠀⡁⠄⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠍⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⢿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠂⡀⠂⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⢾⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠰⠃⠀⢀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡏⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠉⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢜⠛⠿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣴⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⣿⣿⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠃⠀⢀⠀⠀⠀⠀⠀⠹⡏⠹⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣟⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠛⠀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠄⠀⠂⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⡲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⡿⠏⢿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⡟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣯⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⢹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣁⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣍⡛⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣸⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣟⣿⣿⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠃⠀⢀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⢟⡿⣹⣇⣏⣽⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⠀⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡁⠄⠀⠆⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡏⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⡿⠏⢿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣾⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⢸⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣟⣿⣿⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⢟⡿⣹⣇⣟⣽⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⠀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠄⠀⠂⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡏⢹⢶⡏⠙⢲⡟⢿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠷⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣣⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢿⣟⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠸⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠀⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣻⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⡍⠍⠈⠩⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣷⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣣⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡏⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⣲⡖⣶⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⣿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣽⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣾⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣭⡟⢹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⣸⢿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢿⠿⠛⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⢠⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣟⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣹⢿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠄⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⡿⠽⠧⠿⢿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⠛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣷⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⢀⠄⠀⠂⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⣸⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⡉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⡀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣹⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⡁⠄⠀⠆⠈⠅⠐⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⢿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠠⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⡿⠽⠧⠿⢿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣷⣮⣽⣟⣻⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⡀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠁⠀⢀⠀⠀⣣⣾⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣾⣷⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣹⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢙⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⡿⡽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢹⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢿⠄⢀⣷⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣹⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠒⠉⠐⠛⡀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞⠀⡁⢄⠀⠆⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⡿⠽⠧⠿⢿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿

⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣵⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣿⣫⣿⣧⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢠⢀⠨⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠷⠶⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠈⢆⣀⠀⣿⡆⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣹⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⣄⠀⠀⠀⡈⠋⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⡁⢄⠀⠆⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠭⠉⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⣿⠽⠯⠿⢿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 4134

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Gemini version at gemini://gemini.techrights.org/2022/02/18/meme-a-social-democracy-where-every-vote-is-for-sale/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ [Meme]A‘Social_Democracy’_Where_Every_Vote_is_for_Sale⠀✐

Posted in Europe, Patents at 7:41 pm by Dr. Roy Schestowitz

       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Will you vote for Campinos? Make me!⦈

Summary: António_Campinos might need to embark on another journey to the

“eastern front” to secure_the_"crown" of EPO (maybe EPO ‘cooperation’ bribe

money will help)

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⡿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣕⣤⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⣿⣮⢟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠔⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⡐⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠐⡀⠀⠀⠀⠀⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠁⢈⠀⠀⠘⢏⡻⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡊⠀⠀⠀⠐⢁⣉⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢓⣠⣿⣿⡿⢮⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠂⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣆⢀⢀⣠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢿⡈⠌⠉⢀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⡛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡆⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣯⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠙⡐⢸⣿⡟⢠⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⠿⣛⣻⣯⣭⣭⣿⣿⣿⣿⣯⣭⣥⣥⣛⠋⠠⠛⢛⣩⠐⡊⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢉⣁⢍⠂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣭⣔⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠀⣼⣿⣿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠒⠄⠀⠀⠀⢬

⣿⣿⣿⣆⣀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢘⣟⠋⡈⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢻⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠻⠮⠞⠿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠨⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⡌⣟⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠻⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢨⢆⢶⠀⠐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠜⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⣿⢣⣿⡟⣤⣤⣴⣴⣿⣿⣷⣿⣷⡶⠊⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⠉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠂⠀⠀⠀⢀⠐⠃⠀⠉⡄⠀⠅⠈⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢂⡀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢔⣤⣁⠀⠀⠀⠀⠀⠀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠂⠉⠂⡟⣦⢇⠡⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣬⣿⣿⣿⠟⠁⠀⠀⠀⠀⠌⠀⠀⣴⠀⢉⡄⠀⠀⠀⠠⠐⢀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣾⣿⣿⣶⣿⣿⡞⠐⠳⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⡁⠀⠀⢸⣿⣿⠿⢁⢙⣫⣿⠛⠉⢋⣑⠐⢀⠠⠀⠈⢀⣠⣶⢟⡙⣤⣄⡃⠐⡀⠀⠀⠀⠠⠐⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢈⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣤⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠠⠀⣐⡀⠀⠀⠀⠀⠀⢀⣉⡀⠀⠀⠈⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⠀⠀⠀⠄⠸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣆⠀⢀⢠⢢⢠⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣽⣿⢫⡈⠌⠉⠁⠨⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣵⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣅⣤⣴⣿⣿⣿⣿⠿⣩⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢭⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⡟⣶⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣏⠙⠀⢸⣿⠟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣷⣿⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠃⠑⣿⡟⠠⠛⢛⣉⠐⡆⠀⠨⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣀⠉⠈⠀⠀⢉⣁⠅⠂⠀⠁⣇⡾⡿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠀⣀⡀⠀⠀⠀⠠⠊⢹⣿⣿⠉

⣿⣿⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠨⣉⣥⣑⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣬⠀⢀⠀⠀⡀⠻⠿⠀

⣿⣿⡄⠀⠀⠠⣬⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠈⢉⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠕⠐⠄⠁⠀⠀⠨

⣿⣿⣿⣆⡀⣀⢄⣤⣶⣶⣶⣶⣖⣤⣭⣥⣤⣄⠀⠲⠶⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⣀⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⡀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢷⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠶⠿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠀⠈⢿⣿⣿⣿⣿⣷⣤⡀

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⠟⡡⠀⣴⣞⡃⠀⠄⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢄⢶⠀⠒⡀⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣻⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣾⣿⣟⣤⣶⣿⣿⣿⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⢿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠙⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣥⣿⠉⡁⠉⢉⣠⠀⢂⣀⣻⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣶⣶⣶⣶⣶⣖⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠓⠂⠀⠀⠀⠀⠐⠀⠀⠈⡀⠀⠄⠈⠀⠐⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠏⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⢔⠐⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢹⣿⣿⣿⣿⣿⣿⣿⡦⠁⣀⣀⠀⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢔⣤⣁⠀⠀⠀⠀⠀⠀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⡠⠂⠉⠂⡟⣦⣇⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣨⣿⣿⣿⠟⠁⠀⠀⠀⠀⠌⠀⠀⣴⠀⢉⡄⠀⠀⠀⠠⠐⢀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣾⣿⣿⣶⣿⣿⡞⠈⠻⠚⠉⢉⠄⠀⠀⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⠁⢙⣫⣿⠛⠉⣋⣑⡀⢈⠠⠀⠈⢀⣠⣶⢟⡙⣤⣅⡁⠐⡀⠀⠀⠀⠠⠐⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠈⢏⡛⠉⠀

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⣐⠀⠁⠀⠀⠀⠀⢀⣁⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡒⠀⠀⢀⡄⠸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣆⠀⢀⡠⢪⢡⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣽⣿⢫⡈⠈⠉⠀⠈⠴⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⡛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣾⣧⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠋⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣁⣤⣴⣿⣿⣿⣿⠿⣩⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣛⣷⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠙⠀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠃⠑⣿⡟⠠⠛⢛⣉⠐⠊⠀⠀⠙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣠⠈⠉⠀⠀⢉⣁⢅⠂⠀⠁⣆⡾⡿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠠⢸⣿⡇⠂⢀⠀⠀⠀⠀⣠⠐⢹⣿⣿⠍

⣿⣿⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠈⡉⣧⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⡬⠀⢀⠀⠀⡀⠻⠿⠀

⣿⣿⡄⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠈⢉⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠵⠐⠄⠀⠀⠀⠨

⣿⣿⣿⣆⡀⢄⢄⣤⣶⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠲⠶⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡄⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣤⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠾⠿⠞⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠀⠈⢿⣿⣿⣿⣿⣷⣤⡀

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⠟⡡⠀⣴⣞⡃⠀⠄⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢄⢶⠀⠒⡀⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣿⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣾⣷⡶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⢿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠙⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣣⣿⡉⡁⠉⢉⣠⠀⢂⣀⣻⢁⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣯⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠓⠂⠀⠀⠀⠀⠐⠀⠀⠉⠄⠀⠅⠀⠀⠀⢈⢭⣹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⡿⠏⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢴⠂⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠰⣶⠊⠳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡦⠁⣀⣀⠀⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢔⣤⣁⠀⠀⠀⠀⠀⠀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⡠⠂⠉⠂⡟⣦⣇⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣨⣿⣿⣿⠟⠁⠀⠀⠀⠀⠌⠀⠀⣴⠀⢉⡄⠀⠀⠀⠠⠐⢀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠓⣷⣾⣿⣿⣶⣿⣿⡞⠈⠻⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⠂⢙⣫⣿⠛⠉⣛⣑⠀⠈⠠⠀⠈⢀⣠⣶⢟⡙⣤⣅⡁⠐⡀⠀⠀⠀⠠⠐⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⢌⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣀⡀⠀⠀⠀⠀⠀⢀⣍⡀⠀⠀⠈⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢁⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⠀⠀⢀⠄⠸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⣠⢪⢠⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡈⠌⠉⠀⠠⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⡛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠉⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠃⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠆⣰⣿⣁⣠⣴⣿⣿⣿⣿⠿⣩⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣛⣶⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠙⠀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣷⣿⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠋⠑⣿⡛⠠⠛⢛⣉⠐⡂⠀⠨⡙⢿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣠⠈⠉⠀⠀⢉⣁⠅⠀⠀⠁⣆⡾⡿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠀⠀⠠⠚⢹⣿⣿⠉

⣿⣿⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠈⡉⣧⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣬⠀⢀⠀⠀⡀⠻⠿⠀

⣿⣿⡄⠀⠀⠠⣬⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⠀⠈⢉⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⠸⠻⣿⣿⣷⠕⠐⠄⠀⠀⠐⠨

⣿⣿⣿⣆⡀⣀⢄⣤⣶⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠲⠶⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⠀⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢟⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠾⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣷⣀⡀

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⢟⡡⠀⣴⣞⠃⠀⠄⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⠐⡀⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣿⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣾⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡟⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣷⢼⣿⢼⣿⡷⢀⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠠⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣥⣿⡉⡁⠉⢉⣢⠀⢂⣀⣓⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡤⣤⣶⣶⣶⣶⣶⣖⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠓⠂⠀⠀⠀⠀⠐⠁⠀⠈⡀⠀⠄⠈⠁⠄⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⡻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠠⠀⠀⠠⠀⠀⠀⠀⢀⡁⠀⠀⠀⠠⢔⠑⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠰⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡤⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣕⣤⣡⢀⠈⠀⠀⠀⢂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⡠⠃⠋⡒⡿⣮⢟⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢉⡄⠀⠀⠀⠠⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣛⡐⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠐⡀⠀⠀⠀⠠⢸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠁⠬⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⣀⡉⠀⠀⠀⠐⢀⣅⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣧⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠆⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⣀⢀⢠⢪⢱⣾⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡡⠌⠉⠐⡈⠤⣢⣶⣾⣿⣿⡿⣿⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⢍⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣏⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠙⡐⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣟⣛⣛⣻⠿⠉⠃⠑⣿⡛⠠⠛⢹⣩⠐⡊⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣬⡈⠀⠀⢉⣁⢍⡂⠀⠁⣇⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢐⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠀⠛⢿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠀⢸⣿⣿⣦⠀⠘⢻⣭⣔⡀⠀⠨⣉⣷⣑⡇⣿⠁⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⡘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣼⡟⣼⣿⣿⣿⣟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⠸⢿⣿⣿⣷⠵⠒⠄⠁⠀⠀⠬

⣿⣿⣿⣆⡀⣄⡔⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢚⣟⠋⡌⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡤⠀⠀

⣿⣿⣿⣟⢿⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⡀⠀⠀⡘⣯⣙⣏⠀⠈⠻⠦⠾⠿⠞⠀⠀⣠⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠊⠨⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣵⣿⣰⣗⠀⠨⣷⣌⣃⠞⠀⠰⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣴⣶⣿⣿⣷⣾⣷⣶⠞⣿⣿⣿⣶⣝⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣟⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠗⠂⠀⠀⠀⠀⠐⠃⠀⠙⡄⠈⠅⠈⠁⠔⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⢖⠙⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⣀⠀⠀⠀⢠⠀⢀⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣔⣤⣡⢀⠈⡁⠀⠀⠂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⡠⠃⠋⡒⡿⣮⢟⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣸⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠀⢉⡤⠀⠀⠈⠡⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⡐⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡁⠐⡀⠀⠀⠀⠡⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠁⠌⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⣀⡉⠀⠀⠀⠀⢀⣁⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠴⢃⣠⣿⣿⣿⢦⣬⣿⣧⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⡛⠿⢿⣿⣿⣯⣇⠀⠀⣠⢪⢱⣾⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢿⡨⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠆⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⢟⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠛⡀⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣟⣛⣛⣻⠿⠛⠃⠑⣿⡋⠠⠛⢛⣉⠐⡊⠀⠹⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢨⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣬⡈⠀⠀⢉⣁⢅⡂⠀⠈⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⢈⢿⣿⣇⠀⠀⢸⣿⡇⠄⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠀⢸⣿⣿⣦⠀⠘⢿⣭⣴⡀⠀⠨⣉⣥⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⠀⠀⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣼⡟⣼⣿⣿⣿⡟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠒⠄⠁⠀⠀⠬

⣿⣿⣿⣆⡀⣄⡄⣸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢚⣟⠋⡐⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⣿⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⡀⠀⠀⡘⣯⣙⣏⠀⠚⠻⠦⠟⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⠘⢫⠈⠨⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣵⣿⣠⣗⠀⠨⣷⣌⣛⠟⠀⠰⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢨⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣴⣿⣿⡏⣤⣤⣴⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣥⣿⠉⡁⠉⢉⣢⠀⢃⣀⣿⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠀⠉⡄⠈⠅⠈⠁⠴⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣄⣴⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡠⠃⠋⡒⣿⣮⣟⠧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣤⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠀⢉⡤⠀⠀⠈⠡⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣿⣿⣿⣶⣿⣿⡟⡘⡻⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠂⡈⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠐⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠰⡀⠀⠀⠈⠡⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠂⠀⠀⠀⠀⠁⠌⠀⠀⠘⢏⡛⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⠀⣐⡀⡁⠀⠀⠀⠐⢀⣅⡀⢀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢃⣠⣿⣿⡿⢮⣬⣿⣧⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣽⣿⣿⣿⠟⠻⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⣠⢪⢹⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢯⡨⠌⠉⢑⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⡻⠿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡑⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⢀⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⢟⣿⡋⣼⣿⣿⣿⡟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣭⡙⠐⢸⣿⡟⢠⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠄⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣩⠐⡎⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠠⢹⣷⢨⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⣗⠍⠂⠀⢁⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠀⣠⠞⢹⣿⣿⠉

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠘⣿⣿⣿⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠗⠄⠁⠀⠐⠬

⣿⣿⣿⣆⣀⣄⡄⠈⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⣈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢿⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣴⣿⠃⠻⢦⠿⡿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⡊⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣿⣭⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣭⣿⣿⣶⡿⠋⠨⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠗⡀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⣄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣥⣿⡉⡁⠉⢩⣦⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣖⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡟⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⢀⠐⠃⠀⠙⣄⠈⠅⠈⠃⠼⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣕⣴⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⢀⠀⡠⠃⠋⡒⣿⣮⣟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠈⠡⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⡿⡘⡺⠚⢋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠐⢀⠠⠀⠀⢀⣠⣶⢿⡙⣼⣕⡋⠰⡀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠐⠁⠈⠀⠀⠘⢏⡻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡋⠀⠀⠀⠀⢠⣉⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢃⣠⣿⣿⡿⢦⣬⣿⣧⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠂⠀⢐⡆⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣂⢀⣠⢪⢳⣾⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡨⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠈⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢫⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣟⣶⡋⣼⣿⣿⣿⡟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠀⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠄⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠀⡳⣀⡛⡉⠐⡊⠈⠹⡙⣿⣿⣿⣿⠏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⣗⢍⠂⠀⠈⣆⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠘⣿⣿⣷⣭⣴⡀⠀⢩⣉⣷⣓⡇⣿⠁⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠓⠄⠁⠁⠀⠬

⣿⣿⣿⣆⡀⣀⡄⠈⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⣈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣴⣷⠃⠹⠦⠾⡿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⡈⠨⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⣿⣿⣿⣯⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣭⣿⣿⣶⡿⠋⠨⠨⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⣿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢈⢆⢶⠀⠐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠠⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠗⠂⠀⠀⠀⠀⠐⠓⠀⠙⣄⠀⠅⠈⠁⠬⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⡿⣿⣿⣿⣿⣿⠿⠋⠁⡀⠀⣇⣦⣡⢀⠈⠀⠀⠀⠂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡠⠃⠉⠒⣿⣮⢟⢥⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣼⣿⣿⣿⠟⠁⠂⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡞⡘⠻⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣑⠐⢈⠠⠀⠀⢀⣠⣶⢿⡙⣤⣕⡣⠐⣀⠀⠀⠀⠀⠸⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠂⠀⠀⠀⠀⠁⠈⠀⠀⠈⢋⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⢿⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⡀⡁⠀⠀⠀⠀⣀⣁⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢁⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⠄⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣧⣇⡀⢀⣠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣽⣿⢫⡨⠌⠉⢀⡈⠤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡂

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢳⣿⣿⠇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⢿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣏⣶⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣏⠫⡀⢸⣿⠟⢠⣿⣧⣴⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠢⠛⢛⣭⠐⡊⠀⠱⡙⢿⣿⣿⣿⢏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⡿⢟⣛⣯⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣬⣈⠀⠀⢉⣁⢅⠂⠀⠁⣆⡾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠀⢀⡀⠀⠠⠀⣠⠖⢹⣿⣿⠍

⣿⣿⠂⠐⠛⢿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣔⡀⠀⠉⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠙⢿⡏⠀⣿⣿⣽⣿⣦⣹⣿⣿⠇⠀⠀⠀⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠓⠄⠀⠀⠀⢬

⣿⣿⣿⣆⡀⣀⠄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡌⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢛⣿⣼⣶⣾⣤⡤⠀⠀

⣿⣿⣿⣟⢿⣿⣿⢰⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠦⠿⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠊⠩⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢒⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣷⡌⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢁⣶⣢⡀⢼⣶⡦⣭⣤⣴⣴⣿⣿⣷⣿⣷⡶⠞⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠟⠛⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠚⢻⣷⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡑⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠀⠙⣄⠀⠅⠈⠁⠔⢈⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣿⠊⢳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠈⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⢀⠉⠻⡿⣿⣿⣿⣿⣿⠿⠋⠁⡀⠀⣇⣦⣡⢀⠈⠀⠀⠀⠂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡠⠃⠉⠒⣿⣮⢟⢥⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣦⣼⣿⣿⣿⠟⠁⠂⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡞⡘⠻⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣓⠐⢈⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡣⠐⣀⠀⠀⠀⠀⠸⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠂⠀⠀⠀⠀⠁⠈⠀⠀⠘⢊⡻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⡀⡁⠀⠀⠀⠀⣀⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠀⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⡀⢀⣠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡨⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡵⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢻⣿⣿⠇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣛⣯⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣏⠻⠀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠢⠛⢛⣩⠐⡊⠀⠱⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⡿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣬⣈⠀⠀⢉⣁⢅⠂⠀⠁⣖⡾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠀⣠⠞⢹⣿⣿⠍

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣄⡀⠀⠩⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠐⢀⠈⠀⡠⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠙⣿⡏⠀⣿⣿⣽⣿⣦⣹⣿⣿⢅⠀⠀⠀⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠓⠄⠁⠁⠈⢬

⣿⣿⣿⣆⠀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡘⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢛⣿⣼⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⣿⣿⣿⢰⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠦⠟⠿⠖⠀⠀⣠⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠊⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢨⢆⢶⠀⠐⡀⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣷⡜⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣣⣾⢁⣶⣢⡀⢼⣶⡤⣭⣤⣤⣶⣿⣿⣷⣿⣷⣶⠊⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢁⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠛⠛⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠊⢻⣷⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢀⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣣⣿⠉⡑⠉⢉⣢⠀⢋⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠗⠂⠀⠀⠀⠀⠐⠃⠀⠙⡄⠈⠅⠈⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠻⣻⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣾⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠀⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣄⣤⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠃⠋⡒⣿⣦⣟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠛⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⡀⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠰⡀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠂⠀⠀⠀⠀⠁⠨⠀⠀⠘⢋⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣐⡀⡉⠀⠀⠀⠐⣀⣉⡂⠀⠀⠉⡨⠁⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢇⣠⣿⣿⡿⢦⣼⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠆⠀⢐⡆⠸⣿⣿⣿⣷⣦⣄⣠⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢬⣾⣿⣿⡿⣿⣿⣿⣿⠟⠛⠟⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⡀⢀⢠⢪⢳⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡉⠌⠉⢑⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⡊

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⡿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣥⠉⢻⣿⣿⡇⣰⣿⢅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠈⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣛⡿⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠿⠐⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠸⣿⣿⣿⣿⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠋⠠⠛⢛⣭⠐⡎⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣁⢍⠂⠀⠁⣇⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍

⣿⣿⠂⠀⠛⣿⢣⣿⣿⢧⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠘⢿⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⢀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣾⠐⢀⠈⠀⡀⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢼⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⠇⠀⠐⠀⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣔⠀⠀⣻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠕⠄⠁⠀⠘⢤

⣿⣿⣿⣆⣀⣠⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢾⣟⠋⣘⢂⠀⠀⠙⢉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣶⣤⡤⠀⠀

⣿⣿⣿⣟⢿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡺⠹⢦⠿⡿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡙⢫⠈⠨⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣾⣿⣿⡄⢿⣷⣂⠀⢵⣮⣋⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠲⠈⣴⣞⡃⠀⠴⠂⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢨⢆⢶⠀⢒⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠭⠉⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠀⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡑⠉⢉⣢⠀⢋⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣟⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠁⠀⢀⠐⠃⠀⠙⣄⠈⠅⠈⠃⠼⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣥⢀⠈⠀⠀⠀⠂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠂⠀⡠⠃⠉⠒⣿⣮⣟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣴⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢉⡤⠀⠀⠈⠡⠐⣀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⢉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠀⢀⠠⢀⠀⢀⣠⣶⢿⡙⣼⣕⡋⠰⣀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠐⠁⠌⠀⠀⠘⢏⡻⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⡀⡊⠀⠀⠀⠐⢡⣉⡀⠀⠀⠉⡩⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⣓⣠⣿⣿⣿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⠆⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣨⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢤⣾⣿⣿⡿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⣂⢀⣠⢪⢺⣿⣿⣿⣿⣿⣿⣏⣹⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢻⡈⠌⠉⢑⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠞⠉⡛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⡉

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⡿⠿⠿⢿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣥⠉⢱⣿⣿⡇⣰⣿⢅⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⢀⢊⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⡿⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠻⣿⣏⠹⠐⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣮⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠋⠢⠛⢹⣭⠐⡎⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣁⢍⠂⠀⢉⣆⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠒⠈⠛⣿⢧⣿⣿⠷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣭⣄⡀⠀⠨⣉⣧⣛⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⡀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡵⠕⠄⠀⠁⠘⢬

⣿⣿⣿⣆⣀⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢞⣟⠋⡘⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡤⠀⠀

⣿⣿⣿⣟⢿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠺⡻⠮⠟⠿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡘⢫⠊⠨⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣷⣂⠀⢵⣮⣋⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠱⠸⣴⣞⡓⠀⠤⠂⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢇⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⢿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⠚⣿⣿⣿⣶⣝⠫⠉⢍⠉⠍⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣄⣽⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡑⠉⢉⣦⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠗⠂⠀⠁⠀⢀⠐⠂⠀⠙⣄⠈⠅⠈⠁⠔⢉⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢂⠀⠀⠀⠸⣿⠊⠷⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠐⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣥⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⢀⠀⡠⠃⠉⠒⣿⣮⢟⠧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡄⠀⠀⠀⠡⠔⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠀⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣅⡋⠐⡀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⠀⣐⡀⠋⠀⠀⠀⠐⢡⣅⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠘⣃⣠⣿⣿⣿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢀⠄⠹⣿⣿⣿⣷⣦⣆⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⡛⠿⢿⣿⣿⣯⣇⢀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢋⣽⣿⢻⡈⠬⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⢛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢹⣿⣿⠆⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢭⢻⣿⣿⣿⣿⣿⢿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣷⣿⣿⣿⣿⣾⣿⠿⣟⣻⣯⣭⣽⣿⣿⣿⣿⣯⣭⣭⣥⣛⠛⠠⠛⢛⣉⠐⡎⠈⠉⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢍⡂⠀⠈⣆⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠀⢀⡀⠀⠀⡀⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣭⣄⡀⠀⠨⣉⣷⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠈⣼⣿⣿⣿⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠵⠒⠄⠀⠁⠀⢨

⣿⣿⣿⣆⡀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢘⣟⠋⡀⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⣿⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⡻⠮⠞⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠨⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⡌⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢃⣿⡏⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢼⡿⣿⡿⣿⢿⣿⠁⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢥⣿⡉⡑⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠗⠂⠀⠀⠀⢐⠐⠃⠀⠉⣀⠈⠅⠈⠁⠕⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢂⡀⠀⠀⠸⣷⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠐⠙⠁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⡿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣥⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⣿⣮⢟⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠈⠡⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡞⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⠂⢙⣻⣿⠛⠉⢛⣛⠀⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠐⣀⠀⠀⠈⠠⢸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠀⠁⠌⠀⠀⠈⢏⡻⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠿⣿⣿⣘⣿⣶⣶⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⣀⡋⠀⠀⠀⠐⢁⣉⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠘⢓⣠⣿⣿⣿⢦⣬⣿⣧⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢐⡄⠹⣿⣿⣿⣷⣦⣦⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⣀⢀⢠⢪⢹⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣿⣿⢻⡈⠬⠉⢀⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⢛⡻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⠀⢏⢻⣿⣿⣿⣿⣿⢿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⢏⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣾⣿⣿⣾⣿⠿⣟⣻⣯⣭⣭⣿⣿⣿⣿⣯⣭⣭⣥⣛⠛⠠⠛⢛⣍⠐⡊⠈⠹⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣭⣄⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠈⣼⣿⢿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣔⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠓⠄⠀⠀⠐⠬

⣿⣿⣿⣆⡀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣧⢸⣟⠋⡐⢂⠀⠀⠘⠉⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢷⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⡻⠮⠞⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠨⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⡎⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠰⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡏⣤⣤⣤⣶⣿⣿⣷⣷⣷⣶⠞⣿⣿⣿⣶⣝⠉⠉⠩⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢼⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡑⠉⢉⣢⠀⢃⣀⣿⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠀⠙⣄⠈⠁⠈⠁⠄⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠁⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢂⠀⠀⠀⠸⣿⠊⢳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠃⡀⠀⠀⠀⢠⠂⢠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣥⠀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡲⣿⣮⢿⢧⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣴⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⣀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣳⣷⣾⣿⣿⣶⣿⣿⡟⡘⡻⠚⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⡿⠛⠉⢛⣛⠀⢈⠀⢀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠐⡀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠂⠀⠀⠀⠐⠁⠈⠀⠀⠈⢏⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣸⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡂⠀⠀⠀⠐⢁⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢓⣠⣿⣿⡿⢦⣼⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢀⡆⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⢀⣠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢻⡠⠬⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣍⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⢛⣾⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠟⠐⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢛⣩⠐⡊⠀⠙⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠠⣠⠉⠈⠀⠀⢉⣁⢍⡂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠏⢹⣿⣿⠉

⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠀⠊⢙⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⡕⠕⠄⠁⠀⠀⢬

⣿⣿⣿⣆⡀⣀⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠒⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡘⢂⠀⠀⠘⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⠦⠞⠿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠪⠿⣿⡿⢟⡱⠠⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢰⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣿⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠈⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡍⡁⠉⢉⣢⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣢⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠗⠂⠀⠀⠀⠀⠐⠃⠀⠙⣄⠀⠁⠈⠁⠴⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠁⠀⠀⠠⣶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣷⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣥⠀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡲⣿⣮⢿⢧⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣴⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠠⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣳⣷⣾⣿⣿⣶⣿⣿⡟⡘⡻⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢃⢙⣻⡿⠛⠉⢛⣛⠀⢈⠀⢀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠐⡀⠀⠀⠈⠠⢸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠂⠀⠀⠀⠐⠁⠈⠀⠀⠈⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡂⠀⠀⠀⠐⢁⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢁⣠⣿⣿⡿⢦⣼⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢀⡆⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢴⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⢀⣠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢻⡠⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠆⣰⣿⢅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⢋⣷⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠝⠀⢸⣿⠟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣾⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠑⣿⡛⠢⠙⢛⣉⠐⡊⠀⠩⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢀⠠⣠⠉⠈⠀⠀⢉⣁⢍⡂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠀⣐⡀⠀⠠⠂⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠈⣉⣵⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠐⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠀⠊⢙⣿⣿⣿⣄⠈⣿⣿⣿⠇⠀⠐⠀⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠗⠄⠁⠁⠀⠬

⣿⣿⣿⣆⡄⣄⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠲⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡌⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⢷⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⢦⠞⡿⠞⠀⠀⣠⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠊⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠪⠿⣿⡿⢟⡱⠠⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢨⢇⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣟⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣾⣿⣟⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⢿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⢙⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡁⠉⢉⣢⠀⢃⣠⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠂⠙⣄⠈⠅⠈⠁⠔⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣷⠊⠻⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣥⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠃⠉⡒⣿⣮⢟⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠀⠡⠐⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣛⠀⢈⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠐⡀⠀⠀⠈⠠⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⡀⠀⠀⢀⠀⠁⠈⠀⠀⠘⢏⡛⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡋⠀⠀⠀⠐⢡⣍⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢦⣼⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣏⣀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢻⡨⠌⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⡛⡻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠈⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣛⣮⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠟⠐⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⢿⣿⣟⣛⣛⣛⠿⠙⠃⠑⣿⡋⠠⠛⢛⣉⠐⡊⠈⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⢅⡂⠀⠈⣇⠾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣶⡀⠙⠃⠐⢸⣿⣿⣦⠀⠈⢿⣭⣄⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⢀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⠀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⡟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠕⠄⠀⠁⠀⠬

⣿⣿⣿⣆⡀⣀⡄⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠐⢾⣟⠋⡔⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢳⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⠀⠀⠀⡘⣯⣽⣋⠀⠙⡻⠦⠞⠿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣷⣿⣻⡿⠿⣟⣷⣿⣰⣗⠀⠨⣷⣌⣛⠏⠀⠣⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⠐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠁⠀⠀⠐⠃⠀⠙⡀⠈⠁⠈⠁⠤⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠻⠋⠁⡀⠀⣅⣥⣥⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠃⠉⠒⣿⣮⢟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡄⠀⠀⠀⠡⠐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢋⣓⠈⢀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠐⡀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠉⡀⠀⠀⠀⠀⠁⠨⠀⠀⠘⢎⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢿⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⡀⡋⠀⠀⠀⠐⢁⣁⡂⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢓⣠⣿⣿⣿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠂⠀⢀⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣋⣿⣿⢫⡨⠬⠉⢐⡈⠤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⡻⠿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢭⢻⣿⣿⣿⣿⣿⢿⣿⣿⠋⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⢻⣷⡋⣼⣿⣿⣿⣟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣁⠐⡊⠀⠱⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣦⡀⠹⠃⠀⢳⣿⣿⡗⢍⠂⠀⠈⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠀⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣄⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠂⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠨⠀⡄⠻⠿⡀

⣿⣿⡄⠐⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠀⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢪⣔⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠕⠄⠀⠀⠘⠬

⣿⣿⣿⣆⡄⣀⡄⢈⣹⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢛⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⣗⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣳⡇⣸⡦⠀⣰⣿⠃⠻⠦⠞⡿⠞⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣧⣤⡄

⣿⣿⣿⣿⣿⣿⣯⣩⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣽⣿⣿⣶⡿⠋⠸⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢐⡀⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣾⣷⡶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣽⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡑⠉⢉⣢⠀⢂⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠂⠙⡄⠈⠅⠈⠁⠔⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⢶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢂⡀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣥⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⢀⠀⡠⠃⠉⡒⣿⣮⢟⠧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⡁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡁⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠐⡀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⡀⠀⠀⠀⠀⠁⠈⠀⠀⠈⢋⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⣀⡃⠀⠀⠀⠐⢁⣉⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠘⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢀⠄⠹⣿⣿⣿⣷⣦⣄⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⣀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡈⠌⠉⢀⡈⠴⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⡻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⢅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⢛⣾⡋⣼⣿⣿⣿⣟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡛⠐⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⡉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣉⠐⡊⠀⠹⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣦⡀⠹⠃⠀⢳⣿⣿⣕⢍⠂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣐⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⡘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠐⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠕⠐⠄⠁⠀⠀⠬

⣿⣿⣿⣆⡄⣀⡄⠈⣹⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢷⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣰⣿⠃⠻⠦⠞⡿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡊⠨⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣯⣩⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣽⣿⣿⣶⡿⠋⠸⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠩⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢿⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣹⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⠉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣢⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠐⠐⠃⠀⠙⡄⠀⠅⠈⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣷⠊⢳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠐⠙⠁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⣯⣦⢏⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠀⢁⡤⠀⠀⠀⠠⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢁⢙⣫⡿⠛⠉⢛⣛⠀⢀⠠⠀⠀⢀⣠⣶⢟⡙⣴⣕⡋⠰⡀⠀⠀⠈⠠⠸⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠨⠀⠀⠘⢏⡻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⣀⡉⠀⠀⠀⠀⣀⣉⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠘⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢐⠄⠹⣿⣿⣿⣷⣦⣆⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⣠⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡨⠌⠉⢐⡈⢥⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣛⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⠀⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣾⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡓⠑⣿⡟⠢⠙⢛⣉⠐⡊⠈⠉⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⡠⠊⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣄⡀⠀⠨⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⣿⣿⡍⠙⢿⡏⠀⣿⣻⣽⣿⣦⣹⣿⣿⠇⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠷⠑⠄⠀⠀⠀⢬

⣿⣿⣿⣆⣀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡈⠂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢻⣿⣿⢰⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠮⠾⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠱⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢒⡠⠹⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣷⡜⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣣⣾⢁⣶⣢⡀⢼⣶⣤⣭⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢅⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢙⣿⠟⠛⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠊⢻⣷⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⠉⡁⠉⢉⣢⠀⢋⣠⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⠀⠐⠃⠀⠙⣄⠈⠅⠀⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣿⠊⠳⢦⣇⡤⢹⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⢀⠀⡠⠃⠉⡒⣯⣦⢏⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠀⢁⡤⠀⠀⠀⠠⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢁⢙⣫⣿⠛⠉⢛⣛⠀⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠰⡀⠀⠀⠈⠠⠸⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢏⡻⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⢀⡋⠀⠀⠀⡀⣀⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠘⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡨⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣛⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠟⠀⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠑⣿⡟⠂⠙⢛⣩⠐⡊⠈⠉⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣽⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⠅⡂⠀⠈⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠀⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣴⡀⠀⠨⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠀⢀⠈⠀⡄⠻⡿⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠙⢿⡏⠀⣿⣻⣽⣿⣦⣹⣿⣿⠇⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠗⠓⠄⠀⠀⠘⠬

⣿⣿⣿⣆⣀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⣈⠂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⣻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢿⣿⣿⢰⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠮⠿⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣯⡄⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠱⠈⣴⣞⡓⠀⠄⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣷⡌⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣣⣾⢁⣶⣢⡀⢼⣶⣤⣭⣤⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠍⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⠟⠛⢻⣿⡿⢿⡿⣿⣿⣿⢿⣷⢚⢻⣷⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⠀⠐⠃⠀⠛⣄⠀⠁⠈⠁⠄⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠂⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣴⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⣯⣦⢯⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣾⣿⣿⣶⣿⣿⡟⡚⡺⠚⠉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢀⢙⣫⣿⠛⠉⢛⣛⠀⠈⠠⢀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠰⡀⠀⠀⠀⠠⠘⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠂⠀⠀⢀⠀⠁⠈⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⠀⡊⠀⠀⠀⠀⢀⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢮⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠀⠀⢀⡄⠹⣿⣿⣿⣷⣦⣆⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣆⠀⢀⣠⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢫⡩⠌⠉⢀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⢛⣶⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠹⠀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠑⣿⡛⠠⠙⢛⣉⠐⡊⠈⠩⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⣠⠉⠈⠀⠀⢉⣁⠅⡂⠀⠀⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠀⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠨⣉⣷⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠀⢀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠐⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠚⠙⠟⢿⣿⠄⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠗⠖⠄⠀⠀⠀⢬

⣿⣿⣿⣆⡀⡀⢀⣀⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⣀⣀⣀⠊⢻⡇⢤⢾⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⠏⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠀⣈⠺⡻⠮⠞⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠨⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⠀⠣⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣧⣤⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠂⢹⣿⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣯⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡑⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⠐⠐⠃⠀⠛⡀⠀⠅⠈⠁⠔⢉⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠁⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣷⠊⠻⢦⣇⡤⢹⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠂⠠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠃⠉⡒⡯⣦⢏⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡳⣷⣾⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⠀⢙⣻⣿⠛⠉⢛⣛⠈⠀⠀⠀⠀⢀⣠⣶⢿⡙⣬⣕⡃⠰⡀⠀⠀⠈⠠⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⡀⠀⠀⠀⠐⠁⠨⠀⠀⠘⢏⡛⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣾⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⡀⡂⠀⠀⠀⡐⢀⣍⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⣿⢮⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⡿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣏⠀⠀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣽⣿⢫⡨⠌⠉⠀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠏⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢪⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣛⣿⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠛⠀⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡛⠠⠙⢛⣩⠐⡊⠈⠩⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠨⣠⠉⠈⠀⠀⢉⣁⢅⡂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣷⡙⢦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠀⢀⠨⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠈⠋⠀⣤⣟⣯⣭⣟⢿⣿⣿⣦⠻⣿⠄⠈⣿⣿⣿⠇⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠗⠄⠁⠀⠀⢨

⣿⣿⣿⣆⣄⢸⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⣿⣿⣿⣷⣻⣿⣿⣇⠹⡇⢤⢾⣟⠋⡈⠂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣊⠺⡻⢮⠾⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣇⢻⣝⡿⠿⠿⣛⠔⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠔⠀⠡⠘⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⡿⢋⣼⡧⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡌⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⠚⣿⣿⣿⣶⣝⠩⠍⠩⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⢼⣿⠻⣿⡿⢄⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠅⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣯⣿⡉⡙⠉⢉⣢⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⠀⠐⠃⠂⠙⡄⠈⠁⠈⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠻⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢂⡀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡯⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠃⠉⡒⡯⣦⢏⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣴⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢁⢙⣫⣿⠛⠉⢛⣛⠈⠀⠀⠀⠀⢀⣠⣶⢟⡙⣬⣕⡃⠰⡀⠀⠀⠈⠠⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⡂⠀⠀⠀⠐⠁⠨⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⠆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⠀⡁⠀⠀⠀⠐⢀⣍⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⣃⣠⣿⣿⣿⢦⣼⣿⣦⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠆⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣆⡀⢀⠠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢫⡨⠬⠉⢀⡈⢴⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣛⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠹⡀⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡛⠢⠛⢛⣉⠐⡊⠈⠉⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠨⣠⠉⠈⠀⠀⢉⣁⢅⡂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣷⡙⢦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠈⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠠⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠈⠋⠀⣤⣟⣯⣭⣟⢿⣿⣷⣦⠹⣿⡄⠈⣿⣿⣿⢅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠷⠗⠄⠁⠀⠐⢬

⣿⣿⣿⣆⡄⢸⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⣿⣿⣿⣷⣻⣿⣿⣇⠹⡧⢤⢞⣟⠋⣈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢛⣿⣴⣶⣾⣤⡤⠀⠀

⣿⣿⣿⣟⣿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣊⠚⡻⠮⠿⠿⠶⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⠫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣇⢻⣝⡿⠿⠿⣛⠔⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠖⠀⠡⠈⣴⣞⡃⠀⠔⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢇⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⡿⢋⣼⡧⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡌⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠰⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⣿⡿⢄⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠁⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⣀⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡁⠉⢉⣢⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⠀⠐⠃⠀⠛⣄⠀⠅⠈⠃⠄⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⠿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠁⠀⠀⠠⣶⠓⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⠻⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡯⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⢠⠀⢀⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⡠⠃⠉⡒⣿⣦⢏⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠈⠡⠔⣀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠈⢀⠀⠀⠀⢀⣠⣶⢿⡙⣼⣕⡋⠰⡀⠀⠀⠈⠡⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠐⠁⠬⠀⠀⠘⢏⡻⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣿⣆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⣐⡀⡋⠀⠀⠀⡐⢡⣍⡀⠀⠀⠉⡩⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢃⣠⣿⣿⣿⢦⣼⣿⣧⣽⣿⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢐⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⠠⢪⢳⣿⣿⣿⣿⣿⣿⣟⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡨⠬⠉⢐⡈⠴⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⢈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⡿⠿⠿⢿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢳⣿⣿⡇⣸⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⢟⡿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠟⡀⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠸⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠢⠛⢛⣉⠐⡏⠈⠑⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣁⠅⡂⠀⠈⣧⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠐⠚⠛⣿⢧⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣭⣔⡀⠀⢨⣉⣧⣓⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠠⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠗⠄⠁⠁⠀⠬

⣿⣿⣿⣆⣀⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢿⣟⠋⡘⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⣿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠻⡻⠮⠾⠿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣷⣂⠀⢵⣮⣃⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠳⠈⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠂⢋⢈⢇⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣿⣎⠻⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⠚⣿⣿⣿⣶⣝⠫⠭⢍⠉⡉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⡛⠿⢿⣿⡿⢿⡯⣿⡿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣯⣿⡍⡑⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠁⠀⢀⠐⠃⠀⠙⡄⠀⠅⠈⠁⠜⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠻⣻⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢂⡀⠀⠀⠸⣾⠊⢳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠐⠙⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⡠⠃⠉⡒⣿⣦⢏⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠈⠡⠔⣀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠈⢀⠀⠀⠀⢀⣠⣶⢿⡙⣼⣕⡋⠰⡀⠀⠀⠈⠡⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠐⠁⠬⠀⠀⠘⢏⡻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⡀⡋⠀⠀⠀⡐⢡⣍⡀⠀⠀⠉⡩⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢃⣠⣿⣿⣿⢦⣼⣿⣧⣽⣿⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢐⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⣠⢮⢳⣿⣿⣿⣿⣿⣿⣟⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡨⠌⠉⢐⡨⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⡿⠿⠿⢿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢻⣿⣿⡇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣟⡾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠝⡐⢸⣿⡟⢠⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠠⠛⢻⣉⠐⡏⠈⠙⡙⣿⣿⣿⣿⢏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣑⢍⡂⠀⢀⣇⡿⣿⣿⡟⢸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠘⠛⣿⢧⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⣻⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⡘⣿⣿⡀⡀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠠⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢼⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠗⠄⠁⠀⠀⢬

⣿⣿⣿⣆⣀⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄⢠⢾⣟⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢻⣿⡇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠸⡻⠮⠟⠿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣧⣂⠀⢵⣮⣃⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠳⠈⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⣇⢶⠀⠐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣿⣎⠛⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⢉⠉⡍⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⡟⠻⢿⣿⡿⢿⡿⣿⡿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⣄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡍⡑⠉⢉⣦⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠟⠂⠀⠀⠀⠀⠐⠒⠀⠻⡆⠈⠅⠈⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⢹⣿⣿⣿⣿⣿⣿⣿⡯⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⡯⣦⢟⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠀⢁⡤⠀⠀⠀⠡⢐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣾⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣛⠀⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠰⡀⠀⠀⠈⠠⠸⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⠂⠀⠀⠀⠀⠁⠬⠀⠀⠘⢏⡻⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⡀⡈⠀⠀⠀⠐⢁⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠜⢃⣠⣿⣿⣿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡀⠌⠉⢐⡀⠥⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣫⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠹⠀⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣷⣾⣿⠿⣟⣻⣯⣭⣽⣿⣿⣿⣿⣯⣭⣭⣥⣛⠛⠠⠛⢛⣉⠐⡊⠈⠉⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠆⢹⣿⣿⠉

⣿⣿⠒⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠐⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠀⢀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠈⣼⣿⣿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠑⠄⠁⠀⠀⠨

⣿⣿⣿⣆⡀⣀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣿⢸⣟⠋⣈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢷⣷⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⡻⠦⠞⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⣿⣯⡌⣟⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠰⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡟⣤⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠩⠭⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣧⢸⣿⢽⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢣⣿⠉⡁⠉⢉⣢⠀⢃⣀⣻⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢀⠐⠃⠀⠙⣄⠀⠅⠈⠁⠘⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠂⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣷⠊⠳⢦⣇⡤⢻⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⢠⠂⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⣯⣦⢏⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣶⣿⣿⡟⣐⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢀⢙⣫⣿⠛⠉⢛⣛⠀⢀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠠⡀⠀⠀⠈⠠⠸⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢋⡻⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡋⠀⠀⠀⡐⣀⣉⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢦⣼⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠀⠀⢐⠄⠹⣿⣿⣿⣷⣦⣆⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣇⠀⢀⠠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣽⣿⢻⡈⠌⠉⢐⡈⠴⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⢈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⢅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣯⣾⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⡀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠑⣿⡛⠠⠙⢛⣭⠐⡊⠈⠉⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢀⠀⣀⠉⠈⠀⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠊⢹⣿⣿⠉

⣿⣿⠂⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠈⣉⢷⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠷⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠚⢙⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⣿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠵⠕⠄⠁⠀⠐⢬

⣿⣿⣿⣆⡀⣀⢄⣬⣶⣶⣶⣶⣖⣤⣭⣥⣤⣄⠀⠒⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⣈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⣻⣿⣴⣶⣾⣤⡤⠀⠀

⣿⣿⣿⣟⢷⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠿⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢩⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠪⡿⣿⡿⠟⡡⠀⣴⣞⡃⠀⠰⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣻⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣏⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠩⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢧⣿⠉⡑⠉⢉⣢⠀⢋⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠟⠂⠀⠀⠀⠀⠐⠃⠀⠛⡀⠈⠅⠈⠁⠄⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣷⠊⢳⢦⣇⡤⢹⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⡀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡂⣿⣤⢟⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠈⠡⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⣛⣓⠀⢈⠐⠂⠀⢀⣠⣶⢟⡙⣴⣕⡋⠀⡀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⡂⠀⠀⠀⠀⠁⠨⠀⠀⠘⠍⡻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⠀⣐⡀⡁⠀⠀⠀⠐⢠⣅⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢦⣼⣿⣧⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠀⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⡯⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⡀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡀⠌⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣟⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠟⠀⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡛⠀⠛⢛⡩⠐⡊⠉⠩⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠉⣀⠈⠈⠀⠀⢉⣁⠅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠊⢹⣿⣿⠉

⣿⣿⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⠀⠨⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠚⢙⣿⣿⣿⣄⠈⣿⣿⣿⠇⠀⠀⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠕⠐⠄⠀⠀⠀⠬

⣿⣿⣿⣆⣀⣀⢄⣬⣷⣶⣶⣶⣖⣤⣭⣥⣤⣄⠀⠲⠶⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣼⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⠦⠗⡿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⠈⠈⢿⣿⣿⣿⣿⣧⣄⡄

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠪⡿⣿⡿⢟⡁⠀⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣟⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣾⣿⣏⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⠄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢧⣿⠍⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠛⠂⠀⠀⠀⠐⠐⠃⠀⠛⣄⠈⠅⠈⠁⠴⢈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⠁⠀⠀⠀⠠⢖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⢳⢦⣇⡠⢹⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠐⠙⢁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⡢⣿⣦⢟⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠉⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠚⠉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⣋⣓⠀⠀⠀⠂⠀⢀⣠⣶⢟⡙⣼⣝⡓⠀⡀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠁⠬⠀⠀⠈⠍⡻⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⡄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⠀⡊⠀⠀⠀⠐⢠⣍⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢀⡆⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣾⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣝⡛⠿⢿⣿⣿⣧⣏⡀⢀⠠⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢫⡨⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣿⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠟⡀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⡿⠿⣿⣟⣛⣛⣛⠟⠋⠃⠑⣿⡛⠠⠙⢛⡉⠐⡊⠁⠹⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⢅⡂⠀⠈⣇⡿⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⢿⣿⣿⡿⣫⣶⣿⣿⣿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠐⢸⣿⣿⣦⠀⠘⢻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡀⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⣏⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠇⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠕⠀⠀⠁⠐⢬

⣿⣿⣿⣆⡀⣀⠄⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢺⣟⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣼⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⣿⣿⣇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⠀⠀⠀⡘⣯⣝⣋⠀⠚⡻⢦⠟⠿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⠫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣵⣿⣠⣗⠀⠨⣷⣌⣛⠏⠀⠲⠨⣴⣞⡃⠀⠰⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢒⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣴⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠍⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣧⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⡍⡑⠉⢉⣢⠀⢊⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠟⠂⠀⠀⠀⢀⠐⠃⠀⠙⣀⠀⠅⠈⠁⠕⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⡻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢻⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠐⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠛⠋⠁⡀⠀⣅⣧⣡⢀⠈⡀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⡂⣿⣦⢟⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠚⠉⢉⠄⠀⠃⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⣋⣑⠐⢀⠰⠂⠀⢀⣠⣶⢟⡙⣼⣝⣓⠀⣀⠀⠀⠀⠠⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠉⠌⠀⠀⠈⢎⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⣀⡂⠀⠀⠀⠐⢀⣉⡀⠀⠀⠉⡩⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⢘⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⡆⠹⣿⣿⣿⣷⣦⣆⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣧⣗⢀⢀⡠⢪⢰⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢻⡠⠌⠉⠀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣯⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡊

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠅⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⣿⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠟⡐⢸⣿⠟⢠⣿⣧⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⠿⣿⣿⣛⣛⣛⠿⠋⠃⠑⣿⡏⠢⠙⢛⡩⠐⡊⠈⠱⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⠿⠿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⠅⡂⠀⠈⣇⡾⡿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⢿⣿⣿⡿⣫⣶⣿⣿⣿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠐⢸⣿⣿⣦⠀⠈⢻⣭⣔⡀⠀⠨⣉⣷⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣬⡟⣼⣿⣿⣿⣏⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠀⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣀⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⠻⣿⣿⣷⡷⠕⠄⠀⠀⠀⠬

⣿⣿⣿⣆⣀⣀⠄⣸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢺⣟⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣢⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣼⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢟⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⠀⠀⠀⡘⣯⣝⣋⠀⠚⠻⢮⠟⡿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⠫⠈⠨⢿⣿⣿⣿⣿⣧⣤⡄

⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣵⣿⣠⣗⠀⠨⣷⣌⣛⠏⠀⠲⠈⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢒⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣤⣶⣿⣿⣷⣾⣷⡶⠚⣿⣿⣿⣶⣝⠋⠉⠍⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣧⢸⣿⢽⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢐⠐⠓⠀⠙⣄⠈⠅⠈⠁⠵⢈⢩⣹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⡻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠐⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⡀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⡂⣿⣦⢟⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣦⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠚⠉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢁⢙⣻⣿⠛⠉⣛⣛⠀⢀⠰⠂⠀⢀⣠⣶⢟⡙⣤⣝⡃⠀⡀⠀⠀⠀⠠⠘⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢍⠻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⠀⡃⠀⠀⠀⠀⢀⣉⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⣃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⠆⠹⣿⣿⣿⣷⣦⣄⣠⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣇⠀⠀⠠⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢿⡀⠬⠉⢀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣟⣥⠈⢱⣿⣿⡇⣰⣿⣁⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠐⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣟⣾⡋⣼⣿⣿⣿⣟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡛⠀⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣉⠐⡊⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠜⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⣗⢅⡂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠊⢹⣿⣿⠉

⣿⣿⠀⠈⠛⢿⣿⣿⣿⣿⡟⣼⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣿⣭⣴⡀⠀⠩⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⡀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡀⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠗⠄⠀⠀⠀⢨

⣿⣿⣿⣆⣀⣀⡄⠈⣻⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢛⣿⣿⣿⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣴⣿⠃⠻⠦⠿⡿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠨⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣯⣩⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣯⣭⣿⣿⣶⣿⠋⠰⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢒⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠩⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠰⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⠻⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢼⣿⢾⣿⡷⠀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡁⠉⢩⣦⠀⢋⣀⣻⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⠀⠐⠃⠀⠙⣄⠈⠅⠈⠁⠕⢊⢩⣹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠰⣷⠊⠳⢦⣇⡠⢹⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠐⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⡿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠁⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⠠⠃⠋⡂⣯⣤⢟⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠈⢁⡄⠀⠀⠀⠠⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⡿⠛⠉⣛⣓⡀⠘⠀⠂⠀⢀⣠⣶⢿⡙⣴⣝⡃⠀⡀⠀⠀⠈⠠⠘⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⢀⠀⠁⠈⠀⠀⠘⠍⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⡀⠈⠀⠀⠀⠀⢀⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⣃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⠆⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⡯⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣖⠀⠀⠠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡠⠌⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣯⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢭⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣟⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡓⠑⣿⡛⠢⠛⢛⡉⠐⡊⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣽⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⠅⠂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢐⡀⠀⠀⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠂⠈⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢻⣭⣔⡀⠀⠩⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⣿⣿⡍⠙⢿⡏⠀⣾⣿⣽⣷⣦⣹⣿⣿⢅⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠖⠄⠀⠀⠀⠬

⣿⣿⣿⣆⡀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⣏⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣼⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⢿⣿⣿⢰⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⢮⠗⡿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠈⣴⣞⡃⠀⠰⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣷⡜⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢁⣶⣢⡀⢼⣾⡦⣭⣤⣴⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠍⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠟⠻⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠊⢻⣷⣿⣿⣿⣿⣷⢼⣿⢽⣿⡷⠄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠛⠂⠀⠁⠀⢀⠐⠃⠀⠛⣄⠈⠅⠈⠁⠄⢈⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠂⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣔⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡉⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡠⢽⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠐⠙⠁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⠠⠃⠋⡂⣯⣤⢋⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠈⢁⡤⡀⠀⠀⠡⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡚⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢁⢙⣫⡿⠛⠉⢋⣑⡀⢈⠠⠂⠀⢀⣠⣶⢟⡙⣴⣝⡃⠀⡀⠀⠀⠀⠠⠘⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⡀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢍⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⡆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⣐⡀⡈⠀⠀⠀⠀⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡝⠄⠀⢀⠄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿⣿⡿⣿⣿⣿⡿⠟⠻⠟⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⠀⢀⠠⢪⢳⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡠⠌⠉⢐⡈⠴⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣟⣾⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠹⠀⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠑⣿⡋⠠⠛⢙⡉⠐⡊⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⠅⠂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠀⠄⣠⠂⢹⣿⣿⠍

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣔⡀⠀⠩⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠷⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⣿⣿⡍⠙⢿⡏⠀⣾⣿⣽⣷⣦⣹⣿⣿⠇⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠐⠄⠀⠀⠀⠨

⣿⣿⣿⣆⡀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢱⣿⣿⣿⣿⡏⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣼⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢿⣿⣿⢰⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠻⠦⠗⠿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⠫⠈⠨⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠩⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⡜⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢁⣶⣢⡀⢼⣶⡦⣭⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠍⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢙⣿⠟⠟⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠊⢻⣷⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⠄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢀⠐⠃⠂⠙⡄⠈⠅⠈⠁⠅⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠁⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⣀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⡂⡯⣦⣛⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢋⣑⠀⠐⠠⠂⠀⢀⣠⣶⢟⡙⣤⣕⡃⠀⡀⠀⠀⠀⠠⠘⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⡂⠀⠀⠀⠀⠀⠈⠀⠀⠘⢍⠻⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⣐⡀⡊⠀⠀⠀⠀⢠⣍⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⠆⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⠀⠀⠠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢻⡠⠌⠉⢐⡀⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣻⣴⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠙⠀⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢹⡉⠐⡋⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⣀⠉⠈⠀⠀⢉⣁⠅⠂⠀⠀⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠩⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠨⠀⡀⠻⠷⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠊⠙⠟⢿⣿⠄⠘⣿⣿⣿⠅⠀⠀⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠕⠑⠄⠀⠀⠀⠬

⣿⣿⣿⣆⡀⡀⢀⣈⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢉⣀⣀⣀⠊⢻⡧⢤⢾⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⡏⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠀⣉⡺⡻⢦⠗⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⠀⠡⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣤⣤⣶⣿⣿⣷⣾⣷⣶⠞⣿⣿⣿⣶⣝⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⢿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡧⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡍⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⠀⠐⠃⠀⠙⣀⠈⠅⠈⠁⠵⢈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡠⣹⣿⣿⣿⣿⣿⣿⣿⣧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⡂⡯⣦⣛⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⢉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢋⣑⠐⢘⠠⠂⠀⢀⣠⣶⢟⡙⣤⣝⡃⠀⣀⠀⠀⠀⠠⠘⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⡀⠀⠀⠀⠀⠁⠌⠀⠀⠈⢍⡛⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⠀⡊⠀⠀⠀⠐⢠⣅⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢀⠆⡹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⡀⠀⡠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡠⠬⠉⢐⡈⠤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⢄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⢿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢙⡍⠐⡋⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⣀⠉⠈⠀⠀⢉⣁⠅⠂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢐⡀⠀⠠⠄⣠⠊⢹⣿⣿⠉

⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠨⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠈⠀⡀⠻⠷⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠊⠙⠟⢿⣿⡄⠘⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠐⠄⠀⠀⠀⠨

⣿⣿⣿⣆⡄⡀⢀⣀⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⣀⣀⣀⠈⠻⡧⢤⢾⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣾⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⡇⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠀⣉⡺⠻⠮⠟⠿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⠀⠡⠈⣴⣞⡃⠀⠤⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⢿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡍⡁⠉⢩⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⠐⠐⠓⠀⠙⣄⠀⠅⠈⠁⠵⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⣧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⡀⠉⠻⠿⣿⣿⣿⣿⣿⠛⠋⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⠂⣯⣦⢏⠧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠠⠐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡟⡚⡺⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣓⠐⢀⠠⠀⠀⢀⣠⣶⢟⡙⣼⣝⡃⠀⡀⠀⠀⠈⠀⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⢀⠀⠁⠈⠀⠀⠈⠎⡛⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⣀⡋⠀⠀⠀⡐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢐⡆⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⡀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢳⡁⠌⠉⢑⡀⠠⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣅⣤⣶⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠠⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⢛⣷⡙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⠐⢸⣿⠟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡋⠠⠛⢛⡉⠐⡋⠀⠱⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠨⣀⠉⠈⠀⠀⢉⣁⢍⠂⠀⠈⣆⡿⡿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣷⡙⢦⣶⣶⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠀⠋⢀⣤⣟⣯⣭⣟⢿⣿⣿⣦⠹⣿⡄⠈⣿⣿⣿⠇⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣔⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠗⠕⠄⠀⠀⠐⢬

⣿⣿⣿⣆⡀⢸⢿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣴⣿⣿⣿⣿⣷⣻⣿⣿⣧⠹⡧⢤⢾⣟⠋⡈⠂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠌⣻⣿⣼⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣊⡸⡹⠮⠿⡿⠞⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠨⢿⣿⣿⣿⣿⣯⣤⡄

⣿⣿⣿⣿⣿⣇⢻⣝⠿⠿⠿⣋⠔⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠔⠀⠱⠘⣵⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢐⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⡿⢋⣼⡧⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡌⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠩⠉⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⣿⡿⣄⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠁⢿⣿⣿⣿⣿⣿⣧⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡍⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢀⠐⠓⠀⠛⣄⠀⠁⠈⠀⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠻⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣿⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠂⢠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣷⣡⢂⠈⠀⠀⠀⠂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⡂⣯⣦⢟⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠀⠡⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠀⢈⠠⠀⠀⢠⣠⣶⢟⡙⣤⣝⡋⠐⣀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠐⠀⠨⠀⠀⠘⢏⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⢻⣿⣿⣸⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⢀⡉⠀⠀⠀⡐⢀⣅⡀⠀⠀⠉⡉⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢓⣠⣿⣿⣿⢦⣬⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠿⠻⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣟⡀⢀⣠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡩⠬⠉⢐⡈⢥⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⡿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⡏⣰⣿⣅⣤⣶⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣟⡿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠝⠐⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣮⣄⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠠⠛⢻⣩⠐⡏⠀⠩⡙⣿⣿⣿⣿⢏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢉⣁⢍⡂⠀⠈⣖⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣆⠀⡀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⢣⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣑⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⡀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢪⣄⠀⠀⢿⢿⡇⠀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠓⠄⠁⠀⠐⠬

⣿⣿⣿⣆⡒⣄⠼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢾⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⣻⣿⣼⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⣻⣿⣇⠛⢁⣤⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡺⡻⠮⠟⡿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡅

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣧⣂⠀⣵⣮⣉⣭⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠳⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢲⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣿⣎⠛⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠞⣿⣿⣿⣶⣝⠋⠩⠉⠉⠍⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡍⡁⠉⢉⣦⠀⢋⣠⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢀⠐⠃⠂⠙⡄⠈⠅⠈⠋⠕⢈⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣷⣡⢂⠈⠀⠀⠀⠂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠂⠀⡠⠂⠋⠂⣯⣦⣟⢧⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠉⠀⣴⠈⢁⡤⠀⠀⠈⠡⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⣘⡺⠚⠉⢉⠄⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠈⢈⠠⠀⠀⢀⣠⣶⢿⡙⣴⣝⡫⠠⣀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠁⠨⠀⠀⠘⢏⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⡀⡋⠀⠀⠀⡐⢡⣍⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢃⣠⣿⣿⣿⢦⣬⣿⣧⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡾⠄⠀⢀⡆⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⡿⣿⣿⣿⣿⠟⠻⠟⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⣀⢀⣠⢪⢰⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡩⠬⠉⠁⡀⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠋⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠋⣀⣼⣿⡿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣟⣥⠈⢳⣿⣿⡇⣰⣿⣅⣤⣶⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣟⡾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠝⠐⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠋⠠⠛⢻⣭⠐⠋⠀⢡⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡂⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢉⣁⢍⠂⠀⠈⣆⡿⣿⣿⡟⣸⡇⠠⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⡄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠈⠛⣿⢧⣿⣿⢷⡀⠈⠁⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣛⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⡘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢪⣔⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⠻⣿⣿⣷⠵⠕⠄⠁⠀⠀⢬

⣿⣿⣿⣆⡀⣄⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢿⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠂⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢰⣀⠉⢿⣿⣼⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⣿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡺⡻⠮⠟⡿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⡌⠈⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣧⣂⠀⣵⣮⣋⣭⣽⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠳⠈⣵⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⣆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⡎⠻⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠍⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠀⢿⣿⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡑⠉⢉⣦⠄⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢀⠐⠃⠀⠙⣆⠈⠅⠈⠉⠴⢈⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⡀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⠒⣿⣦⢞⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠀⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡳⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠀⣀⠀⠀⠀⠠⠘⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢀⠀⠁⠨⠀⠀⠘⢏⡛⠉⠁

⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⠀⡂⠀⠀⠀⠐⢀⣁⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠘⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡚⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⡯⣾⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⡀⢀⢠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢻⡨⠬⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠆⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⠀⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⢻⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣷⣿⣿⣾⣿⣾⣿⠿⣟⣻⣯⣭⣽⣿⣿⣿⣿⣿⣭⣥⣥⣛⠛⠠⠛⢛⡩⠐⡋⠈⠩⠙⣿⣿⣿⣿⢏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢅⠂⠀⠈⣆⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠈⠛⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠨⢻⣭⣴⡀⠀⠨⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠀⣾⣿⣿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠗⠔⠄⠁⠀⠐⢬

⣿⣿⣿⣆⣀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢸⣟⠋⡨⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣼⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⣷⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡹⠦⠟⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⡌⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠲⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢰⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡟⣤⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢀⠐⠃⠂⠙⡄⠈⠅⠈⠁⠔⢉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⢖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⠒⢿⣤⢞⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣴⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠚⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣻⣿⠛⠉⢛⣛⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣝⡃⠐⡀⠀⠀⠀⠠⠘⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⡀⡃⠀⠀⠀⠐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⣿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣀⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⡯⣿⣿⣿⣿⠟⠻⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⡀⢀⣠⢢⢰⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡀⠌⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠋⠛⠻⠿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠇⣰⣿⢅⣠⣴⣿⣿⣿⣿⠿⣩⣾⡁⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢊⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣟⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠙⠐⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠙⣿⡋⠠⠛⢛⡩⠐⡋⠀⢩⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣠⠈⠈⠀⠀⢉⣁⢍⠂⠀⠈⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⡠⠎⢹⣿⣿⠉

⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⣉⣧⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠀⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠊⢙⣿⣿⣿⣄⠈⣿⣿⣿⠇⠀⠀⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⠀⣿⢳⣿⢸⠻⣿⣿⣷⠷⠑⠄⠁⠀⠀⢬

⣿⣿⣿⣆⣀⣄⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⢀⠲⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠉⢻⣿⣼⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠿⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⢟⡡⠀⣴⣞⡃⠀⠠⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⠐⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣟⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢧⣿⡍⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢐⠐⠃⠀⠙⣄⠀⠅⠈⠁⠔⢊⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⢀⠀⡠⠃⠉⠒⢿⣤⢞⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣴⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡻⠚⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢁⢙⣫⣿⠛⠉⢛⣛⠀⠈⠠⠀⠀⢀⣠⣶⢟⡙⣤⣝⡃⠐⡀⠀⠀⠀⠠⠘⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡃⠀⠀⠀⠐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⣿⢆⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢠⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⢀⣠⢢⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡨⠌⠉⢀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠋⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠠⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣏⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠟⠀⢸⣿⠟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢛⣭⠐⡋⠀⠩⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀⠈⠈⠀⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⣉⣷⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠊⢙⣿⣿⣿⣄⠘⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⠀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠒⠄⠁⠁⠀⢨

⣿⣿⣿⣆⡀⣀⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⢀⠲⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡘⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢹⣿⣴⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠗⡿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⢟⡡⠀⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣿⣿⠿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣧⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⡀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢧⣿⡍⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢀⠐⠃⠀⠛⣄⠈⠅⠈⠁⠔⢈⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⢀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠂⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⡠⠂⠉⠒⣿⣦⢞⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⣟⡘⡺⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣛⠀⢀⠠⠀⠀⢀⣠⣶⢟⡙⣴⣝⡃⠐⡀⠀⠀⠀⠠⠘⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⡀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⢀⡂⠀⠀⠀⠐⢠⣅⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⣿⢆⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣕⡀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡠⠌⠉⢀⡈⠤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣯⣼⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠉⢱⣿⣿⠇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⢄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣟⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠛⠐⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠑⣿⡋⠠⠛⢛⡩⠐⠊⠈⠩⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣀⠈⠈⠀⠀⢉⣁⠅⠂⠀⠈⣆⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢐⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠊⢙⣿⣿⣿⣄⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⠻⣿⣿⣷⠗⠖⠄⠁⠀⠐⢬

⣿⣿⣿⣆⡀⣀⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⢀⠲⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢷⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠸⠦⠗⠿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⡿⣿⡿⢟⡡⠀⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣟⣿⠿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣧⣿⣿⣿⣿⣷⢼⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢣⣿⠉⡁⠉⢉⣦⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠂⠀⠀⠀⢀⠐⠃⠀⠙⣀⠈⠅⠈⠃⠔⢈⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⡠⠂⠋⠒⣯⣦⢞⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⡞⡘⡺⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠀⢀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⣃⠀⣀⠀⠀⠀⠠⠘⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠁⠌⠀⠀⠘⢏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⢀⡂⠀⠀⠀⠐⢠⣅⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠜⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠄⠀⢀⠄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣖⣀⢀⣠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡈⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠞⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢮⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣏⣾⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣧⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣛⣛⣻⠿⠋⠃⠑⣿⡋⠠⠛⢛⡩⠔⡋⠀⢹⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⡿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⠅⠂⠀⠈⣇⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠍

⣿⣿⠀⠀⠛⣿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣶⡀⠙⠃⠐⢸⣿⣿⣶⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠂⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣼⠐⢀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⣏⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠇⠀⠀⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠖⠄⠁⠀⠀⠬

⣿⣿⣿⣆⡀⣀⡄⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢾⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣐⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⣻⣿⣼⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢟⣿⣇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⡀⠀⠀⡘⣯⣝⣋⠀⠚⡻⢦⠟⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣷⣿⣰⣗⠀⠨⣷⣌⣛⠏⠀⠣⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⣇⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣄⣼⣿⣿⡏⣴⣤⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠩⠉⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢐⠐⠃⠀⠙⣄⠈⠅⠈⠁⠔⢉⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⡀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⠒⣿⣦⢞⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠀⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡘⡳⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢁⢙⣻⣿⠛⠉⢛⣛⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣝⡃⠠⣀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢀⠀⠁⠨⠀⠀⠘⠏⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⡀⡂⠀⠀⠀⠐⢀⣁⡀⠀⠀⠉⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢓⣠⣿⣿⡿⢆⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢠⡄⡹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠻⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⡀⢀⣠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢳⡠⠌⠉⢀⡈⠴⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢱⣿⣿⡆⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣿⣾⡋⣼⣿⣿⣿⡿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠐⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠃⡲⣀⡛⣉⠔⡋⠈⠩⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣦⡀⠹⠃⠀⢳⣿⣿⣕⢅⠂⠀⠈⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣴⡀⠀⠨⣉⣧⣙⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⠀⠀⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠖⠄⠁⠀⠀⢬

⣿⣿⣿⣆⡀⣀⡄⢈⣹⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⢂⡀⠀⠘⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⣻⣿⣴⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢛⣿⣿⣿⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣳⡇⣸⡆⠀⣰⣿⠁⡹⠦⠟⡿⠖⠀⠀⣠⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄

⣿⣿⣿⣿⣿⣿⣯⣯⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣿⣽⣿⣿⣶⡿⠋⠰⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢲⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠍⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢿⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢐⠐⠃⠀⠙⣄⠈⠁⠈⠃⠔⢈⢝⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠤⡀⠉⠻⠿⣿⣿⣿⣿⣿⠟⠋⠁⡀⠀⡅⣕⣡⢀⠈⡀⠀⠀⢀⠐⠈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⠀⠂⠉⠂⢷⢦⣧⢧⢸⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠈⢁⡄⠀⠀⠀⠠⠐⢀⣁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⣟⡈⢳⠚⠉⢉⢀⠀⠀⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢀⢙⣫⣿⠛⠉⣋⣛⠈⢀⠠⠀⠈⢀⣠⣶⢿⡙⣼⣔⡃⠀⡀⠀⠀⠀⡠⠰⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⡀⠀⠀⢀⠀⢁⢌⠀⠀⠈⢉⡛⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣷⣴⣖⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⢀⠉⠀⠀⠀⠁⢠⣍⡀⡀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣙⠸⢃⣠⣿⣿⣿⢤⣼⣿⣤⣽⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡓⡀⠀⢐⠆⡸⣿⣿⣿⣷⣦⣆⣠⠄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣼⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⠀⢠⢦⢰⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣋⣿⣿⢫⡈⠌⠉⠀⡀⢰⣠⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⢈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣧⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠂⣸⣿⣍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⢿⢋⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣛⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠻⡀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡏⠠⠛⢛⣭⠐⠏⠀⠀⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡂⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⢅⡂⠀⠀⣆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠏⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣴⣀⠀⢨⣉⣥⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣮⠂⢀⠠⠀⡄⠻⠿⠀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠙⢿⡏⠀⣾⣿⣽⣷⣦⣹⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠵⠄⠁⠀⠀⠌

⣿⣿⣿⣆⣐⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡐⠂⠀⠀⠝⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢰⡀⠈⣹⣿⣼⣶⣾⣤⡄⠀⡈

⣿⣿⣿⣟⣿⣿⣿⢐⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⡻⠦⠾⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠌⠈⢿⣿⣿⣿⣿⣿⣤⡅

⣿⣿⣿⣿⣿⣿⣭⡀⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠘⣴⣞⡃⠀⠀⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢶⠀⠱⡀⠙⣿⣿⣿⣿⣷⣬

⣿⣿⣿⣿⣿⣿⣿⣷⡜⠻⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢡⣶⣢⡀⢼⣶⡦⣭⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠟⠟⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠚⢻⣷⣿⣿⣿⣿⣧⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢡⣿⡉⡁⠉⢉⣢⠂⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠟⠂⠀⠀⠀⢀⠐⠁⠀⠉⡀⠈⠅⠈⠁⠔⢈⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠗⠛⠿⢟⠨⠛⣻⠩⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠁⠀⠠⡀⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⠠⢖⡓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡏⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⡉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠘⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⡅⣄⡡⢀⠈⠀⠀⠀⢀⠐⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠂⠉⠂⣷⣦⣁⢣⣰⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠌⠈⠀⣴⠀⢁⡄⠀⠀⠀⠠⠐⢀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢓⣿⣾⣿⣿⣶⣿⣿⣝⡀⠃⠚⠉⠉⢀⠀⠀⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠛⢀⢙⣫⣿⠛⠉⢋⣓⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡁⠀⡀⠀⠀⠀⠠⠐⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠁⢌⠀⠀⠈⠌⡙⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⡟⠻⣿⣿⣐⣿⣶⣴⣔⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣐⢀⠁⠀⠀⠀⠀⢀⣁⡀⠀⠀⠁⡈⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢤⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡗⠀⠀⢀⠄⠸⣿⣿⣿⣷⣦⣄⣀⠄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣧⣗⠀⠀⢠⢠⢲⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢋⣿⣿⢣⡀⠈⠉⠀⡀⠠⣂⣶⣾⣿⣿⡿⣻⡵⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣧⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣧⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠂⣰⣿⢁⣠⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢩⢻⣿⣿⣿⣿⣿⢿⣿⣿⠋⣄⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⢛⣷⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠛⠀⢸⣿⠟⢠⣿⢧⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠀⠀⠀⠀⠉⠩⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡏⠠⠛⢛⣭⠐⠏⠀⠀⠈⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣬⣈⠀⠀⢉⣁⠅⠂⠀⠀⣄⠾⡿⢿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠀⢀⠀⠀⠀⠀⢠⠌⢹⣿⣿⠉

⣿⣿⠀⠀⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣄⡀⠀⢨⣉⣥⣃⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣮⠀⠀⠠⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠙⢿⡏⠀⣾⣿⣽⣷⣦⣹⣿⣿⠁⠀⠐⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⠿⣿⣿⣷⠕⠓⠄⠀⠀⠀⠬

⣿⣿⣿⣆⢀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⠄⠂⠀⠀⠘⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢰⡀⠈⢹⣿⣼⣶⣶⣤⡄⠀⠀

⣿⣿⣿⣟⢿⣿⣿⢠⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠦⠷⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⠫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡀

⣿⣿⣿⣿⣾⣿⣭⡀⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠈⣴⣞⡃⠀⠀⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢖⠀⢐⡀⠙⣿⣿⣿⣿⣷⣬

⣿⣿⣿⣿⣿⣿⣿⣷⡜⠻⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢡⣶⣢⡀⢼⣶⣆⣭⣤⣤⣶⣿⣿⣷⣾⣷⣶⠘⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠟⠛⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠊⢻⣷⣿⣿⣿⣿⣧⢼⣿⢽⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢥⣿⠉⡁⠉⢉⣢⠀⢃⣀⣻⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠓⠂⠀⠀⠀⢀⠐⠀⠀⠉⠀⠀⠁⠈⠀⠐⢈⢌⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠏⠛⠿⣟⠨⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠠⡀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⢔⠑⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⣹⣿⣿⣿⣿⣿⣿⣿⡦⠉⢀⣀⠀⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣧⣡⢀⠈⡀⠀⠀⢀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⠀⠂⠉⠂⣿⣦⢧⢡⣸⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠃⠀⣴⠈⢁⡄⡀⠀⠀⠠⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡟⡘⢳⠛⠉⢉⠀⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣛⠐⢀⢀⢀⠈⢀⣠⣶⢿⡙⣴⣝⡃⠀⡀⠀⠀⠈⠠⠰⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠈⢈⠀⠀⠈⢍⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣤⣔⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⣀⠁⠀⠀⠀⡀⢠⣍⡀⠀⠀⠈⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⣿⢦⣼⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡜⠀⠀⢀⡆⡹⣿⣿⣿⣷⣦⣆⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⠀⢠⢦⢱⣾⣿⣿⣿⣿⣿⣏⣩⣀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢫⡀⠌⠉⢀⡈⠠⣂⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣧⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠇⣰⣿⢉⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣟⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠻⠀⢸⣿⡟⢠⣿⣧⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡹⠁⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡛⠠⠛⢛⣭⠐⠏⠀⠰⡙⢿⣿⣿⣿⠏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢨⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠠⣀⠈⠈⠀⠀⢉⣁⢅⡂⠀⠀⣆⠾⡿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠌⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣤⣀⠀⢬⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠂⢀⠨⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠚⠙⠟⢿⣿⠄⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠷⠄⠁⠁⠀⠨

⣿⣿⣿⣆⡐⡀⢀⣊⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣀⣀⠊⠻⡧⢤⢿⣟⠋⡄⠂⠀⠀⠝⠩⣇⢻⣷⣤⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢰⣀⠈⢻⣿⣼⣶⣾⣤⡤⠀⠈

⣿⣿⣿⣟⠏⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠄⠈⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠙⣉⠘⡻⠦⠿⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡉⢫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⡇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣇⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢠⢆⢖⠀⢱⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣷⣶⣷⣶⠊⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣯⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⡸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢧⣿⡉⡑⠉⢉⣠⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠙⠂⠀⠀⠀⢀⠐⠁⠀⠙⡀⠘⠅⠈⠃⠔⢉⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠨⠛⣻⠉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢈⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⡁⠀⠀⠀⠠⣶⡛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡦⡉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣧⣡⢀⠈⡀⠀⠀⢀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⠀⠂⠉⠂⣿⣦⢧⢡⣸⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠃⠀⣴⠈⢁⡄⡀⠀⠀⠠⠐⢀⠁⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣾⣿⣿⣶⣿⣿⡟⡘⢳⠛⠉⢉⠀⠀⠀⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠟⢂⢙⣿⣿⠛⠉⢛⣛⠐⢀⢀⢀⠈⢀⣠⣶⢟⡙⣴⣜⡃⠀⡀⠀⠀⠈⠠⠰⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠈⢈⠀⠀⠈⠭⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣤⣔⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⣔⠀⠁⠀⠀⠀⡀⣠⣍⡀⠀⠀⠈⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⣿⢬⣬⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡑⡀⠀⢀⡆⠹⣿⣿⣿⣷⣦⣆⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢬⣾⣿⣿⠿⣽⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⠀⣠⢦⢰⣾⣿⣿⣿⣿⣿⣏⣩⣀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢫⡈⠌⠉⠀⡀⢴⣂⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⡄⠀⢈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣧⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣸⣿⣉⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢫⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣛⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠹⠀⢸⣿⡟⢠⣿⣧⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡏⠠⠛⢛⣯⠐⠏⠀⠠⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⣠⠈⠈⠀⠀⢉⣁⢅⡂⠀⠈⢆⠾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠌⢹⣿⣿⠉

⣿⣿⠂⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣤⡀⠀⢬⣉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠂⢀⠨⠀⡤⠿⠿⡀

⣿⣿⡄⠀⠀⠩⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠚⠙⠟⢿⣿⠄⠈⣿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠷⠄⠀⠁⠀⠬

⣿⣿⣿⣆⡐⡀⢀⣈⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢉⣀⣀⣀⠊⠻⡧⢤⢿⣟⠋⡌⠂⠀⠀⠝⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣾⣤⡤⠀⠈

⣿⣿⣿⣟⠏⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠄⠀⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠘⣉⠚⡻⠦⠟⡿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠊⠈⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣇⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢖⠀⢑⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣯⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣠⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠂⠀⠀⠀⢀⠐⠁⠀⠙⡀⠈⠁⠈⠃⠔⢉⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢈⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣴⡓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⡉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠘⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠟⠋⠁⡀⠀⡅⣖⣡⠂⠈⠀⠀⠀⢀⠐⠈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡀⠃⠉⠒⣿⣦⣧⢥⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⢁⡠⠀⠀⠈⠠⠐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⣿⣿⣿⣶⣿⣿⡟⡜⠻⠚⠉⢉⠀⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⣛⣛⡐⠀⢠⢀⠀⢀⣠⣶⢟⡙⣼⣝⡃⠠⡀⠀⠀⠀⠠⠰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠉⢈⠀⠀⠈⠍⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣿⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣷⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⣐⠀⡋⠀⠀⠀⠀⣠⣍⡀⠀⠀⠁⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⣓⣤⣿⣿⣿⣦⣬⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡗⠀⠀⢀⡆⡸⣿⣿⣿⣿⣦⣆⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⠿⠟⠛⠛⢿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⠀⣠⢢⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡛⣽⣿⢣⡈⠌⠉⠀⡈⢠⣠⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠠⠈⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣧⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠆⣰⣿⢍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣖⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⣶⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠻⠐⢸⣿⡟⢡⣿⣧⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠀⠀⠀⠀⠉⠹⣰⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣓⠑⣿⡋⠠⠛⢛⣯⠐⠏⠀⠀⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠠⣠⠈⠈⠀⠀⢉⣑⢍⡂⠀⠈⣆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⠀⠀⠀⠄⡠⠎⢹⣿⣿⠍

⣿⣿⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣧⡙⢦⣶⣶⠀⠸⢻⣭⣤⡀⠀⠬⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠂⠀⠠⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠈⠋⠀⣤⣟⣯⣭⣟⢿⣿⣿⣦⠹⣿⠄⠈⣿⣿⣿⠃⠀⠀⠢⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠷⠄⠁⠀⠈⠬

⣿⣿⣿⣆⡐⢸⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⣿⣿⣿⣷⢻⣿⣿⣇⠹⡇⢤⢞⣟⠋⡜⢂⡀⠀⠹⠩⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⣻⣿⣾⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⡈⠘⡻⢦⠿⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⠫⠊⠉⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣆⢻⣝⡿⠿⠿⣛⠔⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠖⠀⠱⠘⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢠⢆⢖⠀⢐⡀⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣧⡙⠿⣿⡿⢣⣼⡧⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡄⣤⣤⣴⣶⣿⣿⣷⣾⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠍⠉⠍⠉⠉⢀⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⣿⠿⢄⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⠁⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢣⣿⡉⡁⠉⢉⣠⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠂⠀⠀⠀⢐⠐⠁⠀⠙⡀⠘⠅⠈⠂⠔⢈⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⢟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢈⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣲⠛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠸⣿⠊⠷⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡧⣉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠤⣀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠁⡀⠀⡇⣷⣥⠂⠈⡀⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⢀⡠⠃⠉⠒⣿⣦⣧⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠈⢁⡄⡀⠀⠀⠡⠐⢀⡁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣿⣶⣿⣿⣿⡜⠻⠛⠉⢉⠀⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢂⢙⣿⣿⠛⠉⢛⣛⡘⠈⢠⢀⠀⢀⣠⣶⢟⡙⣼⣝⡋⠰⡀⠀⠀⠈⠠⠰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠉⢈⠀⠀⠈⢍⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣿⡆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⣐⢀⡉⠀⠀⠀⡐⢠⣍⡀⣀⠈⠁⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢓⣤⣿⣿⣿⣮⣬⣿⣧⣽⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⢀⡦⡹⣿⣿⣿⣿⣦⣆⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢬⣾⣿⣿⠿⣽⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⡛⠿⢿⣿⣿⣯⣗⢀⠀⣠⢢⢻⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢫⡨⠬⠉⠀⡨⢴⣂⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡅⠠⢈⠙⢿⣻⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡨

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⡿⠿⠿⢿⣻⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣛⡾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠻⠀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠄⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠋⠠⠛⢛⣯⠔⠏⠀⠠⡙⢿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢨⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣑⢍⡂⠀⢉⣦⠿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠞⢹⣿⣿⠍

⣿⣿⠐⠘⠛⣿⢧⣿⣿⠷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⢿⣭⣔⣀⠀⢬⣉⣧⣓⡆⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠀⢀⠠⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⠃⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠷⠄⠁⠁⠈⠬

⣿⣿⣿⣆⣐⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢿⣟⠋⡜⢂⡀⠀⠙⠩⣇⢻⣷⣄⣐⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢸⣀⠌⢻⣿⣼⣶⣾⣤⡤⠀⠀

⣿⣿⣿⣟⣿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠸⡻⢦⠿⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡈⢫⠎⠨⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣷⣂⠀⢴⣮⣃⣭⣿⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠣⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢠⢆⢶⠀⢒⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣿⣎⠻⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠉⠉⠉⠍⠉⠩⠉⠉⣀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠻⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠀⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⢄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢸⣿⠈⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢣⣿⡉⡑⠉⢉⣠⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⣿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣟⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠀⠀⢐⠒⠃⠀⠉⡀⠘⠅⠈⠃⠵⣈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡨⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢉⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⡛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣉⣀⣀⠈⠙⢁⡀⠀⠀⠀⡠⠀⢀⠀⠀⠈⠈⠀⠚⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠤⣀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠁⡀⠀⡇⣷⣥⠂⠈⡀⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⢀⠠⠃⠉⠒⣿⣦⣧⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⢁⡄⡀⠀⠀⠡⠐⢀⡁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣿⣿⣿⣶⣿⣿⡿⡘⢳⠛⠉⢉⠀⠀⠂⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢀⢙⣫⣿⠛⠉⣛⣛⡘⠈⢠⢀⠀⢀⣠⣶⢟⡙⣼⣝⡃⠠⡀⠀⠀⠈⠠⠰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠉⢈⠀⠀⠈⢍⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣷⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠅⠀⣐⢀⡉⠀⠀⠀⡐⣠⣍⡀⢀⠀⠁⣨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢓⣤⣿⣿⣿⣯⣼⣿⣧⣽⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⡀⠀⢀⡦⡹⣿⣿⣿⣿⣦⣆⣀⡆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢬⣾⣿⣿⡿⣿⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⠀⣠⢢⢹⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣿⣿⢫⡈⠌⠉⠒⡈⢴⣢⣶⣾⣿⣿⡿⣻⡽⠞⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠠⢈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡨

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⡿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠻⠀⢸⣿⡟⢡⣿⣧⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠀⠀⠉⠹⣰⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢋⠠⠛⢛⣯⠐⠏⠀⠰⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣑⢅⡂⠀⠉⣤⠿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠄⣠⠜⢹⣿⣿⠍

⣿⣿⠀⠘⠛⣿⢧⣿⣿⠷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠘⢿⣭⣔⡀⠀⢬⣉⣧⣓⡆⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⢀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠂⠀⠨⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿⠇⠀⠐⢪⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠷⠄⠁⠁⠈⠬

⣿⣿⣿⣆⣐⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢾⣟⠋⡜⢂⡀⠀⠹⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢸⣀⠌⣻⣿⣾⣶⣾⣤⣤⠀⠈

⣿⣿⣿⣟⢿⣿⣇⠛⢁⣤⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠺⡻⢦⠿⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠎⠩⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⡀⢿⣷⣂⠀⢵⣮⣃⣭⣿⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠳⠘⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢠⢆⢶⠀⢒⡀⠛⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣿⣎⠻⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠉⠩⠉⠍⠍⠉⠩⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠻⢿⣿⡿⢿⡿⣿⡿⣿⣹⣯⠀⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⢀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢸⣿⠈⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢧⣿⡉⡁⠉⢉⣠⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠃⠀⠀⠀⢐⠐⠃⠀⠙⡀⠈⠅⠈⠃⠴⢈⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡨⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢉⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠠⠠⣴⡛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡦⣉⣀⣀⠈⠙⢁⣀⠀⠀⠀⡠⠀⢀⠀⠀⠈⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠟⠋⠁⡀⠀⡅⣦⣥⠂⠈⠀⠀⠀⢀⠐⠈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⠀⠃⠉⠒⣿⣦⣧⢧⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⢁⡄⠀⠀⠀⠡⠐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⣿⣿⣿⣶⣿⣿⣟⡈⢻⠚⠉⢉⠀⠀⠃⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠁⠀⢸⣿⣿⠟⢀⢙⣫⣿⠛⠉⣋⣛⡀⢈⢠⢀⠀⢀⣠⣶⢟⡙⣴⣝⡓⠠⡀⠀⠀⠈⠠⠰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠉⢈⠀⠀⠈⠍⡻⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠹⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⢀⠋⠀⠀⠀⡀⢠⣍⡀⠀⠀⠉⡸⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⣓⣤⣿⣿⣿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡗⠀⠀⢠⠆⡸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣖⢀⠀⣠⢢⢻⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣿⣿⢣⡨⠈⠉⠀⡈⢤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣧⡈

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠆⣰⣿⣉⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣖⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣏⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠛⠀⢸⣿⠟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡹⠁⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⣾⣿⣾⣿⠿⣛⣻⣯⣭⣭⣿⣿⣿⣿⣯⣭⣭⣥⣛⠋⠠⠛⢛⣯⠔⠏⠀⠨⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⣑⢍⡂⠀⠈⢆⠾⡿⣿⡟⣸⠇⠀⠀⠝⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⠀⠀⠠⠄⣠⠞⢹⣿⣿⠉

⣿⣿⠀⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣭⣴⡀⠀⠬⣉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠋⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠂⠀⠠⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠈⣼⣿⣿⣿⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠃⠀⠀⠢⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⠿⣿⣿⣿⠵⠷⠄⠁⠀⠈⠬

⣿⣿⣿⣆⡀⡄⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢸⣟⠋⡔⠂⡀⠀⠙⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢸⣀⠈⢻⣿⣾⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⢷⣷⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡻⠦⠿⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠊⠈⢻⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⡌⣟⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠠⠘⣴⣞⡃⠀⠠⠀⢿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢶⠀⢒⡀⠛⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣷⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡟⣤⣤⣤⣶⣿⣿⣿⣶⣷⡶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠍⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⣿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢧⣿⡉⡑⠉⢉⣠⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⠂⠀⠀⠀⢐⠐⠁⠀⠙⡀⠘⠅⠈⠂⠴⢈⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠏⠛⠿⣟⠈⠛⣻⠉⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⢈⠁⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⠁⠀⠀⠀⠠⣶⡛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠌⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⡇⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠃⠉⠂⣿⣦⣿⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣦⣸⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣶⣿⣿⡯⡘⢻⠛⠉⢉⢄⠀⠀⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣻⣿⠛⠉⢛⣓⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡋⠰⡀⠀⠀⠈⠠⠰⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠐⠁⠈⠀⠀⠘⢏⡻⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣔⢀⠁⠀⠀⠀⡐⣡⣉⡂⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣙⠸⢓⣠⣿⣿⡿⣦⣬⣿⣦⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⠂⠀⠐⠆⡹⣿⣿⣿⣿⣦⣆⣀⡄⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⢀⢠⢢⢰⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡠⠌⠉⠑⡈⢤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣅⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣅⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣛⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠛⡀⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠐⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠩⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⠿⣛⣻⣯⣭⣽⣿⣿⣿⣿⣯⣭⣥⣥⣛⠋⠠⠛⢻⣭⠐⠏⠀⠸⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⢀⢀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⣑⢅⠂⠀⠀⢇⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⢀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠆⢀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍

⣿⣿⠂⠈⠛⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣭⣔⡀⠀⢨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠐⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠸⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠈⣼⣿⢿⣿⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠕⠄⠁⠀⠈⢬

⣿⣿⣿⣆⡀⡄⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⣻⣿⣿⣿⣿⣷⢘⣟⠋⡀⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣶⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡻⠮⠷⠿⠖⠀⠀⣠⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠘⢿⣿⣿⣿⣿⣿⣤⡅

⣿⣿⣿⣿⣿⣿⡌⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠲⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⢙⠻⠿⢟⣃⠀⢋⢀⣆⢶⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢃⣿⡟⣤⣤⣤⣶⣿⣿⣷⣶⣷⡶⠚⣿⣿⣿⣶⣝⠉⠍⠉⠉⠉⠉⠉⠩⠉⠉⣀⣀⣤⣶⣿⠇⠰⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢥⣿⡍⡙⠉⢉⣢⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠃⠀⠙⣄⠸⠅⠈⠀⠴⣈⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⢖⡓⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡠⣿⣿⣿⣿⣿⣿⣿⣿⣦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠘⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣆⡡⢀⠀⠀⠀⠀⠀⠐⡈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠉⠂⣿⣦⣏⠡⣸⣆⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣠⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⠁⡤⠀⠀⠀⠠⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⣾⣿⣿⣶⣿⣿⡏⠘⠳⠚⠉⢉⠀⠀⠀⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢀⢙⣻⣿⠛⠉⢛⣓⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠀⡀⠀⠀⠈⠠⠰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠐⠀⠈⠀⠀⠘⢋⡛⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣐⣿⣶⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣐⢀⠁⠀⠀⠀⠐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣙⠸⠓⣠⣿⣿⡿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡗⠀⠀⠀⠆⡸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣽⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⠀⠠⢢⢰⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢋⣽⣿⢣⡀⠌⠉⠀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣥⡂

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠆⣰⣿⣅⣠⣴⣾⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⢀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣏⣦⡊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠛⠀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠩⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡋⠠⠚⢛⣡⠐⠏⠀⠀⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⡀⠀⣀⠈⠈⠀⠀⢉⣁⠅⠂⠀⠀⢆⠾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠆⢀⡀⠀⠠⠄⡠⠎⢹⣿⣿⠉

⣿⣿⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠨⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠸⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠊⢉⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠵⠄⠁⠀⠀⠬

⣿⣿⣿⣆⡀⣀⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠲⠶⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡀⢂⡀⠀⠙⢉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣼⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢟⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⢦⠗⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠘⢿⣿⣿⣿⣿⣧⣠⡄

⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⢟⡁⠀⣴⣞⡃⠀⠄⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢇⢶⠀⢰⡠⠉⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣻⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣾⣿⣏⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣇⠹⡿⠛⣿⢣⣿⠉⡉⠉⢉⣠⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⢀⠐⠁⠀⠙⠄⠈⠀⠈⠀⠴⢈⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⢶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⣧⠉⣀⣀⠀⠛⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠘⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣆⡡⢀⠀⠀⠀⠀⠀⠐⡈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠉⠂⣷⣤⣮⠡⣸⣆⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⠁⡤⠀⠀⠀⠠⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣵⣾⣿⣷⣶⣿⣿⡏⠘⢳⠚⠉⢉⠀⠀⠀⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢀⢙⣫⣿⠛⠉⢋⣓⠐⠀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠀⡀⠀⠀⠈⠠⠰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢉⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣐⣿⣶⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣐⠀⠁⠀⠀⠀⠀⢠⣅⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣉⠸⠓⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡗⠀⠀⠀⠆⡹⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣽⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⠀⢠⢢⢰⣾⣿⣿⣿⣿⣿⣏⣡⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢣⡠⠌⠉⠐⡈⢠⣂⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣥⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠃⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣍⣠⣴⣾⣿⣿⣿⠿⣩⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢊⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣏⣷⠊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠛⠀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢛⣭⠐⠏⠀⠈⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⡀⠀⣀⠈⠈⠀⠀⢉⣁⠅⠂⠀⠀⢆⠾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠆⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣬⠂⠀⠈⠀⡄⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠈⢋⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠕⠄⠁⠀⠈⠬

⣿⣿⣿⣆⡀⣀⢄⣤⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠲⠶⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡀⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⠦⠟⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠈⢿⣿⣿⣿⣿⣷⣠⡄

⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠊⠿⣿⡿⢟⠁⠀⣴⣞⡃⠀⠰⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢦⠀⢲⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣛⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣾⣿⣏⣤⣴⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣧⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢡⣿⡉⡁⠉⢉⣠⠀⢃⣀⣿⢁⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⢀⠐⠁⠀⠙⡀⠐⠁⠈⠀⠴⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠏⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⠁⠀⠀⠀⠠⢶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡯⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⡅⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠋⠂⣿⣤⣮⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣨⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣽⣿⣿⣿⣶⣿⣿⡟⡘⢳⠛⠉⢉⢄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢂⢙⣻⣿⠛⠉⢛⣓⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠀⡀⠀⠀⠈⠠⠸⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⡀⠀⠀⠀⠐⠁⠈⠀⠀⠘⢉⡛⠉⠁

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣐⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⣐⠀⠁⠀⠀⠀⡀⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣉⠸⣃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢐⠆⠹⣿⣿⣿⣷⣦⣄⣠⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣟⢀⠀⠠⢢⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢣⡠⠌⠉⠀⡈⢠⣂⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⢋⣷⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠻⠐⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⡀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠁⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣛⣛⣛⠿⠋⠃⠑⣿⡛⠠⠛⢛⣭⠰⠎⠀⠨⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢿⣫⣵⣾⣿⣿⣿⣿⡿⡿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⠅⠂⠀⠀⣇⠿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⢀⢸⣿⡇⠢⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠀⠈⠛⢿⣿⣿⡿⣫⣶⣿⣿⣿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠀⢸⣿⣿⣶⠀⠘⢻⣭⣔⡀⠀⢨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠸⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣮⠂⢀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⣟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠕⠄⠁⠁⠈⠨

⣿⣿⣿⣆⣀⣀⡔⣸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠠⢞⣟⠋⡄⠂⡀⠀⠙⢉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢻⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⠀⠀⠀⡘⣯⣙⣋⢀⠸⠻⠦⠿⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠨⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⣟⣧⣿⣰⣗⠄⠨⣷⣌⣛⠏⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢠⢆⢶⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⢀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢧⣿⡍⡙⠉⢉⣦⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠃⠀⠙⡄⠀⠅⠈⠁⠴⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠗⠛⠿⣟⠈⠛⣻⠹⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣖⠓⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣾⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⣯⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⡅⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠋⠂⣿⣤⣮⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣤⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣽⣿⣿⣿⣶⣿⣿⡟⡘⠻⠛⠉⢉⢄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢀⢙⣻⣿⠛⠉⢋⣓⠐⠀⢠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠠⡀⠀⠀⠈⠠⠸⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠀⢈⠀⠀⠘⢋⡻⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⢀⠁⠀⠀⠀⠀⣠⣉⡂⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣙⠸⢃⣠⣿⣿⡿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠀⠀⠐⠆⡹⣿⣿⣿⣷⣦⣄⣀⡄⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⢀⢠⢢⢠⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢫⡠⠌⠉⠑⡈⢤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣅⠀⠈⠙⢿⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠃⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢱⣿⣿⡆⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⢟⣷⡋⣼⣿⣿⣿⡿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⠙⠀⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⡀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣭⠐⠏⠀⠨⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⡀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢱⣿⣿⡕⠅⠂⠀⠀⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡆⠂⢀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠉

⣿⣿⠀⠀⠛⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣴⡀⠀⠨⡉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⠀⠀⠀⡀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠿⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠕⠄⠀⠀⠈⢬

⣿⣿⣿⣆⡀⣀⡔⠈⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡀⢂⡀⠀⠝⢉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⣿⣿⣶⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡆⠀⣰⣿⠃⠹⠦⠷⠿⠶⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡉⢻⠈⠈⢿⣿⣿⣿⣿⣿⣤⡅

⣿⣿⣿⣿⣿⣿⣯⣭⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣯⣽⣿⣿⣶⣿⠋⠰⠈⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠂⢋⢨⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⣤⣴⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠩⠉⠉⠉⠉⠉⠩⠉⠉⣀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠈⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡙⠉⢉⣢⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢐⠐⠃⠀⠙⡄⠨⠀⠈⠁⠴⣈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⣧⠉⣀⣀⠐⠛⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠌⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⡅⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠋⠂⣿⣤⣮⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣤⣿⣿⣿⠟⠉⠂⠀⠀⠀⠌⠂⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣽⣿⣿⣿⣶⣿⣿⡟⡘⠻⠛⠉⢉⢄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢀⢙⣻⣿⠛⠉⢛⣓⠐⢀⢠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠠⡀⠀⠀⠈⠠⠸⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⡀⠀⠀⠀⠀⠀⢈⠀⠀⠘⢋⡻⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣿⣆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⣔⡀⠁⠀⠀⠀⠀⣠⣉⡂⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣙⠼⠃⣠⣿⣿⡿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢐⠆⡸⣿⣿⣿⣷⣦⣆⣀⡄⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⠀⢠⢢⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢣⡠⠌⠉⠐⡈⢴⣢⣾⣾⣿⣿⡿⣻⡽⠞⠉⠛⠻⢿⣿⣿⣿⣿⣷⣅⠀⠈⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣍⣤⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⣷⡋⣼⣿⣿⣿⣿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠐⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠁⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣭⠐⠏⠀⠘⠙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⡕⢅⡂⠀⠀⣇⠿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠂⣀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣿⡏⣼⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣴⡀⠀⠨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣾⠀⢀⠈⠀⡄⠻⠿⡐

⣿⣿⡄⠀⠀⠨⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣀⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠕⠄⠁⠀⠈⠬

⣿⣿⣿⣆⡀⣀⡔⢊⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡀⢂⡀⠀⠝⢉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢸⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠀

⣿⣿⣿⣟⢿⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡆⠀⣰⣿⠃⠹⠦⠷⡿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢻⠈⠈⢿⣿⣿⣿⣿⣿⣤⡅

⣿⣿⣿⣿⣿⣿⣯⣭⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣭⣿⣿⣶⣿⠋⠠⠘⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠭⠉⠉⠍⠉⠉⠩⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠉⢿⣿⣿⣿⣿⣿⣷⣸⣿⢿⣿⡷⣄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢡⣿⡉⡙⠉⢉⣢⠀⢂⣀⣿⣑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠃⠀⠙⡄⠈⠅⠀⠀⠴⣈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡨⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣾⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⣯⡉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣆⡁⢀⠀⠀⠀⠀⠀⠐⡈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠂⠉⠂⣷⢤⣎⠡⣸⣆⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣦⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠄⠀⠀⣴⠀⠁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⣿⣿⣿⣶⣿⣿⡏⡘⠳⠛⠉⢉⠀⠀⠀⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢀⢙⣻⡿⠛⠉⢋⣓⠀⠀⢀⠀⠀⢀⣠⣶⠟⡙⣤⣄⡃⠐⡀⠀⠀⠈⠠⠰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⡀⠀⠀⠀⠐⠀⠈⠀⠀⠈⢉⡛⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣠⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣐⢀⠀⠀⠀⠀⡐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣉⠸⢓⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡕⠀⠀⠀⠆⡸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣽⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣖⠀⠀⢠⢢⢰⣾⣿⣿⣿⣿⣿⣏⣡⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⣽⣿⢣⡀⠈⠉⠀⡈⠠⣠⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠛⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣾⣿⣼⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢰⣿⣿⠆⣰⣿⣍⣠⣴⣾⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣲⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⣛⣷⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠙⠐⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠩⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣷⣿⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡏⠠⠛⢚⣭⠐⠏⠀⠈⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣬⣈⠀⠀⢉⣁⠅⠂⠀⠀⢆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠆⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣔⡀⠀⠨⡉⣥⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⠀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠛⢿⡏⠀⣾⣿⣽⣿⣦⣹⣿⣿⠁⠀⠀⠀⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⠀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠵⠄⠁⠀⠈⢬

⣿⣿⣿⣆⡀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡀⠂⡀⠀⠙⢉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣶⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⢻⣿⣿⢰⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠹⠦⠗⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⠫⠈⠈⢿⣿⣿⣿⣿⣧⣤⡀

⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠘⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⣇⢶⠀⢰⡀⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣷⡜⠻⣿⣿⣿⣷⣽⣿⣿⣿⢿⣣⣾⢁⣶⣢⡀⢼⣶⣦⣭⣤⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⠟⠛⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠋⢻⣷⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⠀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢡⣿⠉⡉⠉⢉⣠⠀⢂⣀⣿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠓⠂⠀⠀⠀⢀⠐⠃⠀⠉⠀⠀⠅⠀⠀⠴⢈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠗⠛⠿⣟⠈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⢖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡠⢽⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣆⡡⢀⠀⠀⠀⠀⢀⠐⡈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠉⠂⣷⣤⣞⢡⣸⣆⣀⣠⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣦⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠄⠀⠀⣴⠀⠁⡤⠀⠀⠀⠡⠐⢀⠅⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣵⣾⣿⣷⣶⣿⣿⡏⠘⠻⠚⠉⢉⠀⠀⠀⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢀⢙⣻⣿⠛⠉⢋⣓⠀⠀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠀⡀⠀⠀⠈⠠⠰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠁⡀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢉⡛⠉⠀

⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣐⢀⠀⠀⠀⠀⠐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣉⠸⣓⣠⣿⣿⡿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡗⠀⠀⠀⠆⡸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣟⢀⠀⢠⢢⢠⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⣽⣿⢣⡀⠌⠉⠁⡈⢠⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠛⠿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣵⡂

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠆⣰⣿⣅⣤⣴⣾⣿⣿⣿⠿⣩⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣶⣿⣿⣿

⣿⣿⣷⠘⣿⣿⣿⣛⣶⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠻⠐⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡋⠠⠛⢛⣭⠐⠎⠀⠈⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⡿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣬⣈⠀⠀⢉⣁⠅⠀⠀⠀⢆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠄⣀⡀⠀⠠⠄⡠⠎⢹⣿⣿⠉

⣿⣿⠀⠀⠛⢿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢻⣭⣴⡀⠀⠨⡉⣥⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠿⠿⡀

⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠛⢿⡏⠀⣾⣿⣽⣿⣦⣹⣿⣿⠁⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠑⠄⠁⠀⠀⠬

⣿⣿⣿⣆⡀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡀⢂⡀⠀⠙⢉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣶⣤⡄⠀⠈

⣿⣿⣿⣟⢛⣿⣿⢰⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠹⠦⠗⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡉⠫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡄

⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠀⣴⣞⡃⠀⠰⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢀⢇⢶⠀⢲⡠⠙⣿⣿⣿⣿⣷⣬

⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣿⣷⣽⣿⣿⣿⢿⣣⣾⢁⣦⣢⡀⢼⣶⡦⣭⣤⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣁⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⠛⠻⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠚⢻⣷⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢡⣿⡉⡁⠉⢉⣠⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⢤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠓⠂⠀⠀⠀⢀⠐⠃⠀⠙⠀⠐⠁⠈⠀⠴⢈⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠗⠛⠿⣟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⢶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠰⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⡅⣆⣡⢀⠈⡁⠀⠀⠀⠐⡈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠉⠂⣷⣤⣎⢡⣸⣆⣀⣠⣿⢿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣦⣠⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣵⣾⣿⣿⣶⣿⣿⡟⡘⢻⠚⠉⢉⠀⠀⠀⢙⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢀⢙⣻⡿⠛⠉⢋⣓⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠀⡀⠀⠀⠈⠠⠰⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⡀⠀⠀⠀⠐⠀⢈⠀⠀⠘⢋⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣔⢀⠀⠀⠀⠀⠐⢠⣁⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣙⠸⣃⣠⣿⣿⣿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⠀⠀⠀⠆⠸⣿⣿⣿⣷⣦⣄⣀⡄⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣽⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⠀⠠⢢⢰⣾⣿⣿⣿⣿⣿⣏⣡⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢣⡠⠌⠉⠀⡈⢠⣀⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢫⢻⣿⣿⣿⣿⣿⡿⣿⣿⢏⣀⣖⣿⣿⣿

⣿⣿⣷⠘⣿⣿⡿⣯⣶⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠛⠐⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠩⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣷⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡋⠠⠛⢙⣭⠰⠏⠀⠈⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⣠⠉⠂⠀⠀⢉⣁⠅⠂⠀⠀⢆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠢⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠐⠘⢻⣭⣴⡀⠀⠨⡉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣼⠂⢀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠊⠙⠟⢿⣿⠀⠈⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠕⠄⠀⠀⠈⠬

⣿⣿⣿⣆⡀⡄⢀⣀⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢉⣀⣀⣀⠈⠻⡇⢤⢾⣟⠋⡀⢂⡀⠀⠙⢉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠉⢻⣿⣾⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⠏⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣆⠐⣈⡹⠻⠦⠞⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡉⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡄

⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⠀⠢⠸⣴⣞⡃⠀⠀⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢀⢆⢶⠀⢰⡀⠙⣿⣿⣿⣿⣷⣬

⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣤⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⡿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠀⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣯⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⠀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢥⣿⠍⡁⠉⢙⣠⠀⢂⣀⣿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⢀⠐⠁⠀⠙⡀⠐⠀⠈⠀⠴⡈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⢟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⢶⡓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣉⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡠⢿⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠤⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣇⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⡀⠃⠋⠂⣿⢦⣿⠧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣷⣿⣿⣿⣶⣿⣿⡟⡘⠳⠙⠉⢉⢄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣻⣿⠛⠉⣋⣓⠐⠀⠀⠀⠀⢀⣠⣶⢿⡙⣤⣔⡋⠠⡀⠀⠀⠀⠠⠸⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠀⠁⠨⠀⠀⠘⢍⡻⠉⠀

⣿⣽⣿⣿⣿⣿⣿⣿⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣦⣖⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⣀⠁⠀⠀⠀⠀⢀⣍⡀⠀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢓⣠⣿⣿⣿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠞⠀⠀⢀⠆⡸⣿⣿⣿⣿⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣾⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣏⣀⠀⣠⢪⢲⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣿⣿⢫⡉⠌⠉⠀⡈⠠⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⡊

⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡆⣰⣿⣍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⣿⣟⣾⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠛⠐⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠁⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡋⠠⠛⢛⣭⠔⠏⠈⠨⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠠⣀⠉⠈⠀⠀⢉⣑⢅⠂⠀⠀⢇⠿⣿⢿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠃⢐⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉

⣿⣿⠂⠘⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣷⡙⢦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠸⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣾⠂⠀⠈⠀⡤⠻⠿⡀

⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠀⠋⠀⣤⣟⣯⣭⣟⢿⣿⣿⣦⠹⣿⡄⠈⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠕⠄⠀⠁⠈⠨

⣿⣿⣿⣆⡀⢸⢿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⣿⣿⣿⣷⣻⣿⣿⣇⠹⡇⢤⣟⣟⠋⡜⢂⡀⠀⠝⠉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⣻⣿⣶⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣉⡹⡻⠦⠷⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⣿⣆⢻⣝⡿⠿⠿⣛⠄⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠖⠀⠳⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢈⣇⢦⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣦⡙⠿⣿⡿⢋⣼⡧⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡌⣤⣤⣤⣶⣿⣿⣿⣾⣷⣶⠈⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⣿⡿⢄⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠁⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢣⣿⡍⡑⠉⢉⣢⠀⢃⣠⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠁⠀⠹⡄⠀⠄⠈⠀⠴⢈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠏⠛⠿⣟⠈⠛⣻⠹⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⣠⠀⠠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠠⢖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢂⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⡯⠉⣀⣀⠀⠛⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠤⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣇⣧⣡⢀⠈⡁⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡀⠃⠋⠂⣿⢦⣟⠧⣸⣦⣀⣠⣿⢿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠈⢁⡤⠀⠀⠀⠡⠐⢀⡁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⣿⣿⣿⣶⣿⣿⡟⡘⡳⠛⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢋⣓⠀⠀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣄⡋⠠⡀⠀⠀⠀⠠⠰⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠈⠐⠁⠌⠀⠀⠘⢏⡛⠉⠁

⣿⣾⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣠⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣶⣖⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠤⠀⣐⣀⡁⠀⠀⠀⡐⢠⣉⡀⢀⠀⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣙⠸⢃⣠⣿⣿⣿⢦⣬⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢀⠆⡹⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣾⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⠀⢠⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢫⡉⠌⠉⠁⡈⠰⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡊

⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⣿⣷⠘⢿⣿⡿⢟⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠛⡐⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠁⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡓⠑⣿⡋⠠⠛⢛⣭⠐⠎⠈⠸⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢡⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠩⣀⠉⠈⠀⠀⢉⣙⢅⠂⠀⠀⣆⠿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠃⣐⡀⠀⠠⠄⣠⠞⢹⣿⣿⠉

⣿⣿⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣷⡙⢦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠸⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠂⢀⠨⠀⡤⡿⠿⡀

⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠀⠋⠀⣤⣟⣯⣭⣟⢿⣿⣿⣦⠹⣿⡄⠘⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠕⠄⠁⠁⠈⠨

⣿⣿⣿⣆⡀⢸⢿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⣿⣿⣿⣷⣻⣿⣿⣧⠹⡇⢤⣞⣟⠋⡄⢂⡀⠀⡝⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣾⣤⡄⠀⠈

⣿⣿⣿⣟⢿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣊⡹⡻⠦⠷⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⣿⣇⢻⣝⡿⠿⠿⣛⠔⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠖⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢈⢇⢦⠀⢲⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⡿⢋⣼⡯⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡌⣤⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⣿⡿⢄⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠁⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢣⣿⡍⡑⠉⢉⣠⠀⢃⣀⣿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠁⠀⠙⡄⠈⠄⠈⠀⠴⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣠⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⢶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⢳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⣯⡉⣀⣀⠀⠛⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⢀⢳⠀⠀⠃⢀⣂⣥⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠬⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠋⠉⡀⠀⣇⣇⣡⣂⠈⣁⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠃⠋⠂⣿⣦⣿⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⠈⠁⡀⠐⢠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣰⣦⣴⣿⣿⣿⠟⠩⠀⠀⠀⠀⠌⠂⠠⣴⠈⢁⡤⠀⠀⠀⠡⠐⣀⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡜⣻⠛⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿

⠛⣀⣠⣄⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣓⡐⠀⠠⠀⠈⢀⣠⣶⢟⡙⣤⣜⡋⠰⣀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢈⠐⠁⢬⠀⠀⠘⢏⡻⠉⠁

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣯⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡁⠀⠀⠀⠐⢠⣍⡃⢀⠈⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣉⠸⢓⣠⣿⣿⡿⢦⣬⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠂⠀⢐⡆⠽⣿⣿⣿⣿⣦⣆⣀⡆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣼⣿⣿⠿⠟⠻⠟⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣟⣂⠀⣠⢢⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣋⣿⣿⢫⡩⠌⠉⠁⡀⠼⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡅⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡊

⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡆⣸⣿⣍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⠈⢫⣿⣿⣿⣿⣿⡿⣛⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠛⡐⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠐⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠠⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢫⠰⠛⢻⣭⠴⠏⠉⠩⡙⣿⣿⣿⣿⢏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡂⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣑⢅⡂⠀⠁⣇⠿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠃⣘⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍

⣿⣿⠒⠈⠛⣿⢣⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠂⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡠⠀⣸⣿⣃⢰⣿⣿⣾⠂⢀⠨⠀⡤⡿⠿⡐

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠅⠀⠀⠪⣿⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣿⠵⠕⠄⠁⠁⠘⠬

⣿⣿⣿⣆⡀⣄⡸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⣟⠋⡔⢂⡀⠀⠽⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⣻⣿⣶⣶⣾⣤⡤⠀⠈

⣿⣿⣿⣟⢿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡹⡻⠦⠟⡿⠖⠀⠀⣠⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡘⢻⠈⠉⢿⣿⣿⣿⣿⣷⣤⡅

⣿⣿⣿⣿⣿⣿⣿⡄⢿⣷⣂⠀⢵⣮⣋⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠳⠘⣴⣞⡃⠀⠄⠀⢿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⣿⠟⠀⢙⠻⠿⢟⣃⠀⢋⢨⢇⢶⠁⢰⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠄⠀⠐⠛⣿⡿⢉⢇⠀⠘⣿⣿⣿⣶⣝⠉⠍⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⠿⣿⣿⣿⣿⣿⡿⠒⣀⣍⣛⠛⠿⠿⠿⠿⠿⠿⠿⠛⢛⣉⡩⠄⠠⢼⣯⢶⣀⠄⠁⣜⠿⢷⣝⡀⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⢿⣿⣿⣿⡗⣀⡴⡲⢀⠄⠀⠁⡅⠈⣹⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⢰⣶⡆⣴⣶⢲⣶⣶⣶⠀⠀⣶⣶⣶⢰⣶⣶⡆⣶⣶⣶⢰⣶⡶⠀⠀⠀

⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⠛⣿⣧⣶⡍⡙⠉⠁⡢⠀⢃⠠⢿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⡏⢸⣿⣏⣀⠀⠀⣿⣿⣿⣼⣿⣿⡇⣿⣿⣀⠸⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡇⠀⠈⠙⢿⢻⣧⠀⣤⣽⢅⠀⡂⡉⠘⢛⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢻⣿⣿⣿⣧⢸⣿⣿⠛⢀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣷⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠘⠻⣿⡝⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⣿⣴⣿⣿⡎⠀⠛⠿⢶⣾⣆⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣶⠙⡄⣿⣿⢻⣿⢼⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⠏⠛⠿⣗⡀⠀⣠⠠⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠋⠉⠩⣁⠈⠩⠁⠉⠁⠉⢀⠁⠉⠉⠈⠩⢾⡛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠘⠀⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⢀⢳⠀⠀⠃⢀⣂⣵⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠬⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠋⠉⡀⠀⣇⣧⣡⣂⠈⡁⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡠⠃⠋⠂⣿⣦⣿⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿

⠈⠁⡀⠐⢠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣰⣦⣴⣿⣿⣿⠟⠩⠀⠀⠀⠀⠌⠂⠠⣴⠈⣁⡤⠀⠀⠈⠡⠐⢀⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡜⡳⠛⠋⢉⢄⠀⠂⢹⣿⣿⣿⣿

⠛⣀⣠⣄⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢂⢙⣻⣿⠛⠉⢋⣓⡘⠐⠠⠀⠈⢀⣠⣶⢿⡙⣬⣔⡋⠰⣀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢈⠐⠁⢌⠀⠀⠘⢏⡻⠉⠁

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣯⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡉⠀⠀⠀⡐⣡⣍⡁⢀⠈⠉⡨⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⣓⣠⣿⣿⡿⣦⣼⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⠆⠀⢐⡆⡹⣿⣿⣿⣿⣦⣄⣠⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣾⣿⣿⡿⠟⠻⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⠀⣸⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡨⠌⠉⠑⡈⢸⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡅⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡊

⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣴⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿

⣿⠀⢻⣿⣿⣿⣿⣿⡿⣛⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠙⡐⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠄⠀⠉⠹⣴⣿⣿⣿⣿⣿

⣿⡆⠨⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢫⠰⠛⢛⣭⠔⡏⠈⠹⡙⣿⣿⣿⣿⠏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿

⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣓⢅⡂⠀⠁⣆⠿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠣⣐⡀⠀⠠⠄⣠⠟⢹⣿⣿⠍

⣿⣿⠂⠈⠛⣿⢷⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠂⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⡀⠀⠀⠸⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠂⢀⠨⠀⡤⡻⠿⡐

⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿⠅⠀⠀⠪⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣔⠀⠂⣿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠗⠄⠁⠁⠘⠬

⣿⣿⣿⣆⣀⣄⡸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣟⠋⡐⢂⡀⠀⠝⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⣻⣿⣶⣶⣾⣤⣄⠀⠈

⣿⣿⣿⣟⢿⣿⣇⠛⢁⣤⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡹⡻⠮⠷⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡙⢫⠈⠉⢿⣿⣿⣿⣿⣿⣠⡅

⣿⣿⣿⣿⣿⣿⣿⡀⢿⣯⣂⠀⢴⣮⣋⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠳⠘⣴⣞⡃⠀⠤⠀⢿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⢙⠻⠿⢟⣇⠀⢋⢨⢇⢦⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠄⠀⠐⠛⣿⡿⢉⣇⢀⠘⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠩⠉⠉⠉⢀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⠿⣿⣿⣿⣿⣿⡿⠒⣀⣍⣛⠛⠿⠿⠿⠿⠿⠿⠿⠛⣛⣉⡩⠄⠠⠼⣮⢶⡀⠄⠁⣜⠿⢷⢝⡀⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⢿⣿⣿⣿⡟⡀⡴⡢⢂⠀⠀⠡⡍⠈⣹⡾⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⢰⣶⡆⣴⣶⢲⣶⣶⣶⠀⠀⣶⣶⣶⢰⣶⣶⡆⣶⣶⣶⢰⣶⡶⠀⠀⠀

⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⠛⣿⣣⣶⡍⡝⠉⢩⡢⠀⢃⠠⢿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣷⣿⡏⢸⣿⣏⣀⠀⠀⣿⣿⣿⣼⣿⣿⡇⣿⣿⣀⠸⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡇⠀⠈⠙⢿⢻⣧⠀⣤⣿⣅⠀⡂⡉⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⢸⣿⣿⠛⢀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣷⣾⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠘⠛⣿⡝⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⣿⣤⣿⣿⡎⠀⠛⠿⢶⣶⣆⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣶⠙⡄⣿⣿⢻⣿⢼⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⢰⣿⣿⠏⠛⠿⣗⡀⠀⣠⠠⡉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠋⠉⠉⣡⠈⠩⠁⠉⠉⠉⢀⡀⠉⠉⠈⢩⢾⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠘⠀⠙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢔⠈⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⠛⠹⠁⠋⠌⢿⣟⢝⣑⣺⠿⠟⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⣦⡄⠀⠀⠈⠛⠛⠳⠯⠹⠄⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⢹⣻⣿⡥⢀⠀⠀⢶⣤⠀⠀⠈⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⢻⣿⡄⢰⠧⠀⠀⢀⣀⣐⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⢾⡞⢚⣷⣆⣈⣙⡸⢗⣷⡄⢶⡄⢺⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡼⣧⣾⣾⣧⣛⣍⡡⠙⣿⣿⢾⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⠇

⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠨⠜⠿⠟⢷⣹⣯⢼⣹⣿⣿⣿⣵⠄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠻⠥⢦⣼⣅⢻⡞⣹⣿⣿⢿⣿⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣽⣿⣮⣷⣜⣻⠮⣻⡟⠫⢿⣿⠟

⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀⢱⣣⣴⢰⢿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣀⣀⣉⣁⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣼⡣⡨⢛⣿⣿⣿⣿⣿⣿⠩⣿⣿⣉⣯⣼⣦⢠⡘⠛⠋⠁⠀⡡

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣀⣿⣇⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⣴⢼⢿⢦⠅

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣴⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠻⢿⣿⣿⢙⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡋⣀⣼⣿⣿⣳⣟⢻⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣗

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣿⣶⣿⠻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠫⠛⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠙⢦⡀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠊⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⡿⢋⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⢾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⠋⠩⠉⠉⠄⢿⣟⣝⡑⣢⡿⠟⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⣶⡄⠀⠀⠘⠛⠛⠳⠏⠸⠔⠞⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣺⣿⡥⢀⠠⠀⢶⣠⠀⠀⠈⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⡄⠴⠧⠀⠀⢀⣀⣐⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⢾⡟⢚⣷⣦⣈⣙⠸⢇⣷⡄⢶⡄⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡼⣧⣼⣾⣧⣛⣍⡡⠚⡿⣿⢾⣿⣿⣿⣏⣈⣿⣿⣿⣿⣿⣿⠇

⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢠⠜⠿⠿⢗⡽⡭⢼⣹⣿⣿⣿⣵⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠻⡅⢢⣴⣅⢳⡞⣱⣿⣿⢿⣿⣿⣿⣿⡆

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣮⣷⣜⣿⠮⣺⡟⣫⡿⣿⠟

⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡄⠀⢡⣦⣴⢰⢷⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣀⣀⣉⣉⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣸⡃⡨⠛⣿⣿⣿⣿⣿⣿⠉⣿⣯⣈⣯⣼⣇⢠⡘⠙⢋⠁⠀⠠

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣐⣿⣗⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⡴⢾⢿⣦⠁

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⢃⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣬⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠻⢿⣿⣿⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡏⣀⣼⣿⣿⣻⣟⢻⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣷⣶⣿⠻⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠊⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠊⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣵⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⢾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⠛⠙⠁⠉⠄⢿⣟⣝⡗⣮⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⢦⡀⠀⠀⠊⠛⠋⠳⠧⠸⠄⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣺⣿⡤⠠⠠⠀⢶⣠⠀⠀⠈⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⡄⢰⠯⠀⠀⢀⡀⣐⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⢼⡟⢚⣷⣆⣈⣙⠸⢇⣷⣄⢶⡄⢸⣿⣿⢿⣿⣿⣿⣿⣿⡿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡼⣧⣾⣾⣧⣛⣭⡡⠚⣿⣿⣾⣿⣿⣿⡟⣈⣿⣿⣿⣿⣿⣿⠇

⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣯⢢⠜⠿⠿⢗⣻⡯⢼⣹⣿⣿⣿⣵⠆

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠻⡅⢢⣴⣇⢲⡞⢱⣿⣿⢿⣿⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣮⣷⣼⣻⠮⣿⡟⢫⠿⣿⠟

⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀⢡⣦⣴⢰⢷⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣁⣀⣉⣁⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣸⡧⠨⠛⣿⣿⣿⣿⣿⣿⠉⣿⣿⢈⣯⣼⣆⢠⡞⠙⢋⠁⠀⠠

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣰⣿⣟⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⣴⢾⢿⣦⠅

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣬⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠛⢿⣿⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡏⣑⣼⣿⣿⣳⣟⡻⣎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣷⣶⣿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠫⠻⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠙⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠊⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣵⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⢾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⠛⠙⠉⠙⠄⢿⣛⣙⡕⣮⡿⠟⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⣦⡀⠀⠀⠘⠛⠛⠳⠮⠸⠐⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣺⣿⡥⢀⠠⠀⢶⣠⠀⠀⠈⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⡄⠰⠧⠀⠀⢀⣀⣐⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⢾⡟⢚⣷⣆⣈⣙⠸⢇⣷⡄⢶⡄⢺⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡼⣧⣾⣾⣧⢛⣭⡣⠚⡿⣿⢾⣿⣿⣿⡟⣈⣿⣿⣿⣿⣿⣿⠇

⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢢⠜⠿⠿⢗⡹⡯⢼⣹⣿⣿⣿⣵⠆

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠻⡅⢢⣴⣥⢳⡞⢱⣿⣿⢿⣿⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣮⣷⣜⣿⠮⣻⡟⢻⡿⣿⠟

⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢀⣾⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣄⠀⢡⣦⣤⢰⢿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣀⣀⣉⣁⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣸⡇⡨⢛⣿⣿⣿⣿⣿⣿⠉⣿⣿⣉⣿⣼⡆⢠⡚⠙⢋⠁⠀⠠

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣰⣿⣅⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⡴⢾⢿⣦⠅

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣼⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠻⢿⣿⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡏⣁⣼⣿⣿⣻⣟⢻⢏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣿⣶⣿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠊⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠙⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣯⣻⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⣿⡷⣧⣦⡽⢿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣻⣿⣯⣯⣯⣖⣷⣽⣬⣝⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠃⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟

⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣽⣹⣿⣿⣿⣵⡎

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢌⣀⣀⣉⣁⠀⠀⠘⠻⠟⠁⢸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣥⡧

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠐⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⢾⣿⣷⡇

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣹⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣯⣻⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⣿⡷⣧⡦⠽⢿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣸⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⢹⣻⣿⣿⣭⣯⣕⣷⣽⣬⣝⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠃⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠸⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠆

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡆

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠄⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢜⣁⣀⣉⣉⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣥⡥

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢿⣿⣷⡇

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠒⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣿⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⡛⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣷⣿⣿⡷⢧⣦⡽⡿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣻⣿⣿⣭⣾⣆⣷⣬⣮⣙⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣴⡀⠀⠀⢌⣁⣀⣉⣉⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠐⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣹⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⡛⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣷⣿⣿⡷⢧⣦⡽⡿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⢹⣻⣿⣿⣭⣾⣆⣷⣬⣮⣙⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠸⡽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠐⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢜⣁⣀⣉⣉⠀⠀⠘⠻⠟⠁⢸⣿⣿⡇⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⣿⡌⠉⣈⣻⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡆⣴⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⡛⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣷⣿⣿⡷⢧⣦⡽⡿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣻⣿⣿⣭⣾⣆⣷⣬⣮⣙⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇

⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢘⣁⣀⣉⣁⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣻⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣾⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣿⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧

⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⡛⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣷⣿⣿⡷⢧⣦⡽⡿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣻⣿⣿⣽⣾⣆⣷⣬⣮⣙⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⣏⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠐⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢌⣁⣀⣉⣉⠀⠀⠘⠻⠟⠁⢸⣿⣿⡇⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇

⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣻⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡆⣴⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠲⣾⠸⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣷⣶⣿⡿⢿⡿⠀⢀⣶⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡔⣷⣷⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣉⠉⠀⠀⡀⢒⣚⣛⣛⢛⣛⣿⣿⣿⣿⠯⠵⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠷⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣶⣶⣼⡁⠤⠄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⣉⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣛⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢭⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣾⢙⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⢿⣷⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⡀⠻⣾⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⢷⣆⠘⢿⣿⣮⣻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣧⡘⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡦⠀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠈⢻⣶⣿⣿⣦⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⡇⠀⠐⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⣿⣿⣿⣿⠁⠀⠀⣰⡸⠿⣿⣾⣻⣿⣿⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⡄⠀⠀⣽⠟⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣷⣿⣽⣟⢿⣿⠀⢺⣿⣿⣿⣿⣿⣿⡇⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠔⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⡇⠀⠀⠈⠛⠉⠉⡉⣽⣟⣓⣋⣱⣾⣿⣿⣿⣿⣿⡹⣷⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡠⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣛⣿⡃⠀⠀⠀⠀⠀⠀⠈⣿⡿⡿⠻⣠⣽⣿⣿⠿⣿⣿⣷⡘⣿⡌⣿⣿⣿⣿⣿⣻⢛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⢸⣷⢀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡁⠀⠀⠀⠀⠀⠀⠘⢃⠌⢐⣱⡟⣿⣿⣸⣿⣿⣯⣿⣧⣾⣶⣾⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⡇⠀⣾⠟⢠⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⠀⠋⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⢀⡀⣀⣄⣶⢼⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠙⠛⠛⠻⠟⢛⣻⢟⠿⢿⣿⣿⠿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠿⢆⣩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣤⣄⡀⠈⠉⠉⠀⠀⠉⢭⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠋⠻⣿⣿⡛⠿⠯⠛⣿⣿⣫⣟⡁⠀⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠃⣈⡉⣠⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠙⣛⡛⠇⠻⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿

⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢁⠀⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⣆⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⣀⠐⣿⣟⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀

⠀⠀⠁⠀⣹⡿⠆⣀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀

⠀⠀⠀⢠⣿⣷⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀

⠀⢣⣀⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠧⠟⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⠀⠀

⠀⠀⣽⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⠤⣒⠈⠀⠀⠐⠋⠛⠛⢛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀

⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿

⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⡿⠿⠿⠟⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 6031

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/phoronix86-amd/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/18/phoronix86-amd/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ When_AMD_Sends_You_a_Crate_of_CPUs_Worth_(Market_Value_of)Roughly$500,000⠀✐

Posted in Deception, Hardware, Marketing at 4:41 pm by Dr. Roy Schestowitz

Recent: When_Blogs_Become_Marketing_and_Benchmarks_Become_Product_Promotions

Front_page of Phoronix moments ago (screenshots minutes old):

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

Number of employees at Intel: 121,100 (2021)

Number of employees at AMD: 15,500 (2021)

Summary: The apparent bias or the priorities at Phoronix seem to have changed

(no explanation was ever provided for the ‘gifts’); a single job opening at

AMD, for instance, now merits a “news” post and anything that’s not x86 is

mostly ignored as if it’s only a Wintel world

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠚⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣉⣽⣬⣉⣍⣍⣽⣌⣩⣉⣷⣮⣍⣏⣩⣍⣼⣿⣿⣿⣿

⣿⣿⣏⣀⣀⣸⣭⡭⢭⠽⠭⠯⠍⠭⠭⣭⣿⣽⣭⣽⣭⣽⣽⣽⣯⣭⣧⣭⣿⣬⣽⣏⣯⣧⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣭⣭⣯⣭⣭⣭⣿⣯⣹⣽⣽⣭⣭⣭⣯⣿⣽⣿⣿⣿⣿

⣿⣿⣿⣿⣿⠀⠐⠲⡆⠐⠒⠶⣦⠀⠈⣿⠶⠾⠶⠿⠿⡷⠴⠼⢷⠿⠧⠿⠷⡶⠶⠾⠷⠿⠷⡶⠶⡿⣿⢿⡿⠿⠿⠿⠿⠿⢿⠿⢿⠿⠿⣿⣿⣿⡇⣿⢷⠾⠷⡶⡶⠾⠶⠶⣾⡾⢶⣷⣷⣾⣶⣷⣿⣿⣿⣿⣿⣿

⣿⣿⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣓⣛⣛⡒⣺⣒⣳⣿⣶⣿⣿⣷⣿⣿⣿⣷⣿⣷⣷⣾⣷⣷⣷⣿⣿⣷⣿⣿⣿⣾⣿⣾⣿⣾⣿⣿⣿⡇⣿⣻⣛⣛⣻⣛⣻⣟⣻⣻⣟⣛⣻⣛⣛⣿⣛⣟⣛⣿⣿⣿⣿

⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣭⣯⣯⣽⣽⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡾⡼⠼⠿⣿⠶⠮⠷⡴⣿⡾⠵⢷⠽⠮⠷⠴⠾⣷⣤⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣛⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡟⠛⠛⢻⢟⠟⠛⠻⡟⠛⢛⠛⣻⢻⢟⣻⡛⠛⢿⠛⣻⠛⡟⠟⡻⡟⢛⡻⢻⡟⠿⠛⢻⢛⢻⠛⢻⡟⡟⡟⡟⠛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣩⣏⣍⣯⣛⣋⣟⣹⣛⣟⣻⣙⣛⣟⣻⣛⣉⣟⣹⣿⣿⣿

⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣝⣛⣛⣛⣻⣏⣛⣛⣻⣏⣛⣻⣙⣙⣻⣿⣉⣏⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣤⣶⢿⣾⢴⡾⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠤⠤⠯⠤⠬⡽⠴⠤⠤⠤⠥⢬⠤⠯⠤⠤⠤⡤⠯⡭⠼⡤⠤⡯⠭⠤⠦⡧⠼⡤⡼⠤⡥⠽⠿⠿⣿⣿⡇⣿⠖⠶⢒⢳⣿⢷⠳⢲⡲⢶⠶⠲⡻⢷⢶⣶⣶⣶⣿⣿⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣒⡒⣒⣚⣖⣓⣒⣓⡓⣲⣓⣚⣚⣒⣖⣒⣓⣳⣓⣓⣲⣓⣓⣓⡒⣞⣒⡓⣓⣳⣓⣒⣓⡚⡓⣾⣿⣿⡇⣟⣛⣋⣿⣛⣛⣛⣛⣛⣻⣛⣻⣟⣛⣛⣛⣟⣻⣛⣿⣿⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣬⣭⣽⣭⣭⣭⣭⢭⡭⡭⣭⣭⡭⣭⣯⣯⣭⣯⣭⡭⣭⢽⣭⣭⣭⣭⣯⣭⣹⣭⣭⢽⣭⣽⣭⣽⣿⡇⣿⡬⢬⣥⣯⣭⣼⣭⣭⣽⣽⣧⣧⣭⣯⣭⣥⣤⣤⣵⣾⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠚⠒⢒⢲⠒⠒⢶⣷⣶⣾⣶⣶⣶⣶⣶⣷⣷⣾⣾⣶⣾⣾⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣿⣿⣿⡇⣿⠾⠶⠿⠿⠿⢿⡿⡿⠿⠿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣟⣛⣛⣿⣻⣛⣛⣛⣻⣉⣉⣿⣛⣛⣿⣛⣟⣛⣻⣿

⣿⣿⡿⣿⣿⣿⡿⡿⡿⡿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡿⣿⣿⢿⢿⠿⠿⢿⠿⠿⡿⢿⡿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣭⣭⣭⣯⣭⣽⣯⣯⣭⣭⣭⣿⣭⣭⣯⣯⣭⣻⣿⣿

⣿⣿⡷⠷⣾⠷⣷⣷⢶⣿⣾⣷⣶⣾⣶⣿⣷⣶⣶⣵⣾⣾⣷⣶⣿⣷⣿⣷⣶⣶⣾⣶⣶⣶⣾⣾⣿⣷⣶⣿⣷⣶⣶⣶⣷⣷⣶⣿⣷⣾⣶⣿⣿⣿⡇⣿⣶⣦⡶⡶⣶⣷⢾⢶⣶⣷⣾⡶⣶⢶⣶⣷⣶⣾⢿⣿⣿⣿

⣿⣿⣿⠛⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⣿⡿⠿⠿⠿⠿⢿⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⣿⠿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠳⣚⣿⣷⣿⣿⣾⣶⣶⣶⣶⣷⣾⣿⣾⣷⣶⣶⣾⣿⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣋⣛⣛⣉⣉⣉⣽⣛⣻⣛⣛⣛⣛⣛⣛⣻⣛⣙⣛⣟⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣙⣏⣛⣛⣿⣿⣿⡇⣟⣋⣉⣿⣛⣛⣟⣻⣙⣻⣻⣻⣻⣟⣛⣛⣛⣛⣛⣻⣻⣿⣿

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⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣚⣒⣒⣒⣗⣒⣒⣒⣒⣓⣖⣒⣒⣒⣒⣒⡛⣚⣒⣾⣚⣲⣒⣒⢞⣒⣓⣒⣖⣒⣲⣚⣒⣒⣚⣛⣿⣿⡇⣿⣶⣴⣶⣶⣷⣶⣿⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣭⣿⣯⣽⣭⣍⣯⣭⣹⣭⣽⣭⣍⣽⣽⣽⣽⣿⣽⣿⣿

⣿⣿⣧⢴⠧⠷⢥⡧⠼⡽⢤⠯⠮⣥⣯⣧⣽⢯⣼⣤⣧⣤⣷⡼⣿⣽⠬⡥⢧⣥⢧⣷⣥⢷⣤⣶⣶⣤⣯⣦⣤⣿⣮⣾⣴⣧⣴⣽⣿⣿⣿⣿⣿⣿⡇⣿⠶⠷⠿⠶⠷⢾⣶⣶⣶⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⡎⢹⠉⠉⢹⢹⢹⣿⣿⣿⣿⠻⠒⢒⢲⠒⡟⠲⢲⢓⠒⡒⠳⠚⠲⢚⠶⠞⢻⠗⠒⢓⡟⠛⠛⢿⠛⡛⡛⡿⠻⠿⠛⡛⡿⠟⠟⣿⣿⡇⣿⢻⢻⢿⣿⣿⢿⠻⣿⠿⢿⠻⢿⠿⢿⠻⠟⢿⠿⠿⡿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣭⣭⣩⣏⣭⣭⣭⣻⣭⣉⣍⣭⣉⣭⣩⣽⣭⣩⣩⣍⣭⣭⣉⣹⣍⣍⣏⣩⣹⣽⣭⣹⣭⣭⣽⣿⡇⣿⣟⣏⣭⣉⣛⣙⣫⣻⣟⣟⣏⣉⣹⣙⣛⣛⣏⣽⣿⣿⣿⣿

⣿⣿⣷⣾⣷⣶⣶⣶⣾⣶⣷⣶⣶⣼⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⠶⠶⠿⠿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢛⠟⠻⡟⠿⡿⢿⢿⡻⠿⢿⠻⢛⢿⡿⡟⠿⠿⣿⣿⣿⣿

⣿⣿⣧⠤⠤⠼⠽⠦⠴⠯⠵⠤⠴⠦⠾⣮⣤⢵⣴⣯⣶⣥⢼⣬⣴⣾⣤⢧⢤⢶⣴⡼⣤⣼⣷⣥⣶⢴⣧⣴⡼⣤⣧⣼⣦⣷⣼⣮⣶⣤⣴⣼⣿⣿⡇⣿⣯⣹⣙⣯⣍⣹⣝⣭⣻⣽⣿⣏⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⠓⢒⠚⡖⠟⡓⡖⠚⠻⠚⠚⢺⠚⠚⣳⠒⠛⠛⠛⠚⡖⠗⠓⠓⠛⠻⠛⠛⠟⡟⢛⠟⠛⡟⠛⣿⣿⡇⣿⡷⠶⠶⠶⠷⠷⣷⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣩⣭⣭⣹⣩⣭⣏⣭⣩⣭⣯⣭⣍⣭⣻⣭⣭⣭⣭⣩⣭⣍⣏⣩⣽⣭⣭⣩⣯⣭⣭⣹⣿⣿⣿⣿⣿⡇⡿⠛⠛⣿⠿⠛⠿⠟⠿⢟⣿⢿⣛⠿⠿⠛⠿⢿⠻⣿⣿⣿⣿

⣿⣿⡿⠿⠿⡿⠿⢿⠿⠛⠻⠿⠿⠿⠿⡿⠶⠖⠰⠶⠲⢶⠶⠶⡶⠷⠲⠖⡖⠶⠆⠶⠾⢾⡷⡶⡔⠞⢷⠶⠦⠗⠷⠶⠶⢼⠾⠲⡶⠶⠶⣶⣿⣿⡇⣿⣉⣍⣫⣏⣭⣽⣻⣟⣽⣿⣯⣯⣽⣟⣽⣏⣉⣩⣿⣻⣿⣿

⣿⣿⣟⣛⣛⣻⣙⣉⣉⣛⣏⣹⣙⣟⣝⣙⣏⣉⣏⣋⣉⣟⣙⣹⣋⣹⣙⣛⣏⣛⣛⣛⣛⣉⣉⣏⣙⣏⣋⣍⣏⣉⣉⣛⣉⣝⣹⣉⣹⣋⣉⣛⣿⣿⡇⣿⠷⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣧⣦⣴⣤⣼⣴⣼⣤⣤⣤⣦⣼⣶⣤⣬⣤⣼⣴⣤⣤⣴⣤⣤⣤⣧⣤⣴⣤⣼⣴⣴⣼⣤⣤⣦⣮⣧⣤⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 6107

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Gemini_version_available_♊︎

✐ Links_18/2/2022:_EasyOS_3.4.1_Soon,Media_Conflating_Snap_With‘Linux’⠀✐

Posted in News_Roundup at 6:17 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o § Desktop/Laptop⠀➾

            # ⚓ 7_New_Features_to_Try_in_Kali_Linux_2022.1⠀⇛

                   For years, cybersecurity-centric Linux

                   distributions have been revolutionizing penetration

                   testing and security auditing for internal and

                   remote networks.

                   Offensive Security, Kali Linux’s developers, gives

                   you the first major release of 2022 with its newest

                   version. Kali 2022.1 is packed to the brim with

                   innovations and the latest feature additions,

                   making it a power-packed distro for the new year.

                   Here are some exciting new features of Kali Linux

                   2022.1 you need to try right now.

            # ⚓ The_7_Best_Linux_Docks_to_Give_Your_Desktop_a_New_Look⠀⇛

                   Is your Linux desktop cluttered with apps, and you

                   struggle to find an app every time you want to

                   launch it? Well, it turns out, you can use a dock

                   to fix this.

                   Generally speaking, an application dock is a system

                   component on certain desktop operating systems that

                   facilitates multitasking by providing quick access

                   to apps and utilities. Not only that, but it also

                   contributes to the visual appearance of your

                   desktop, making it both functional and appealing.

                   On Linux, there are a variety of apps you can use

                   to get a dock on your desktop. Let’s check out some

                   of these best docks apps for Linux.

            # ⚓ Dell_Latitude_3510_Laptop_10th_Generation_Intel_Core_i5-

              10210U/4GB/1TB_HDD/Ubuntu [Ed: Only noteworthy because Dell

              offers GNU/Linux in India]⠀⇛

                   Planning to buy a new laptop with exceptional

                   features and specifications? Dell Latitude 3510

                   Laptop 10th Generation Intel Core i5-10210U/4GB/1TB

                   HDD/Ubuntu is a good choice that you can go for.

                   The laptop is equipped with a 10th Generation Intel

                   Core i5-10210U with 1.6 GHz clock speed that lets

                   you multitask with ease and experience faster

                   performance

                   [...]

                   You can purchase this Dell Latitude 3510 Laptop

                   10th Generation Intel Core i5-10210U/4GB/1TB HDD/

                   Ubuntu in India at Rs 53,969. Also, you will get a

                   warranty of 1 Year on it from the manufacturer from

                   the date of purchase.

            # ⚓ macOS_vs._Windows_vs._Linux:_Which_OS_Would_You_Buy [Ed:

              Very poorly written and poorly researched, maybe machine-

              generated]⠀⇛

      o § Audiocasts/Shows⠀➾

            # ⚓ Built_to_impress:_but_does_the_SLIMBOOK_TITAN_live_up_its

              COLOSSAL_name?_–_Invidious⠀⇛

                   Thanks to Slimbook for sending us this unit.

                   Overall, Ethan and I were quite impressed with this

                   machine and we really like it.

      o § Applications⠀➾

            # ⚓ Flatpak_App_of_the_Week:_Minder_–_Powerful_Mind_Mapping

              Software_to_Visualize_Your_Ideas⠀⇛

                   With Minder you will be able to easily and quickly

                   create visual mind-maps thanks to an automatic

                   layout system and the plethora of tree layouts to

                   choose from. You can add images and tasks to nodes,

                   create node-to-node connections with optional text

                   and notes, add stickers and node groups, as well as

                   to stylize nodes, links, and connections, or

                   colorize node branches.

                   The interface is quite simple and intuitive

                   featuring tabs so you can open multiple mindmaps,

                   quick search of nodes, as well as connection titles

                   and notes, zoom in and out, undo and redo changes,

                   as well as a Focus Mode to focus on certain ideas

                   and to better view and understand portions of your

                   mind-map.

            # ⚓ GStreamer_1.20:_Embedded_&_WebRTC_lead_the_way⠀⇛

                   Made available earlier this month, GStreamer 1.20

                   is the fruitful result of 17 months of hard work

                   from the entire community. Over 250 developers

                   contributed code to make this release happen, and

                   once again, Collabora had more contributors than

                   any other organization.

                   Our work focused on the two areas in which we

                   believe GStreamer shines the brightest: embedded

                   systems, and network streaming, in particular

                   WebRTC. Below is a summary of the impact our team

                   of engineers had on this latest release.

                   As usual, you can also learn more about the

                   enhancements done by the rest of the community by

                   looking at the project’s 1.20 release notes.

      o § Instructionals/Technical⠀➾

            # ⚓ Three_Examples_to_Increase_Request_Timeout_in_NGINX_–

              LinuxCapable⠀⇛

                   NGINX is one of the best choices for serving long-

                   running requests because it has a robust

                   architecture. However, you might need to increase

                   your request timeout to ensure that NGINX can

                   easily handle these heavy loads.

                   By default, it is set at 60 seconds, but if you

                   cannot serve your entire traffic without hitting

                   this limit, try raising it higher, like 75 or 100

                   milliseconds (or whatever makes sense for how busy

                   the site is). The error “504: Gateway Timeout” will

                   appear if there are not enough resources available

                   on the host machine; however, using some proxy

                   timeout settings should fix these problems –

                   including read/connect delays as well as sending

                   messages alone; before waiting till everyone sends

                   them back!

                   In the following tutorial, you will learn how to

                   increase request timeout in NGINX using

                   proxy_read_timeout, proxy_connect_timeout,

                   proxy_send_timeout directives to fix 504 Gateway

                   Timeout error.

            # ⚓ How_to_Install_Jitsi_Meet_on_Ubuntu_–_OSNote⠀⇛

                   Jitsi Meet is a WebRTC-based video conferencing

                   software that allows you to communicate with

                   others. A Jitsi Meet server allows you to join

                   multi-person video conference rooms that function

                   similarly to a Zoom or Skype meeting. The advantage

                   of a Jitsi conference is that all of your data

                   travels only through your server, and end-to-end

                   TLS is used to secure the connection.

            # ⚓ New_Linux_User?_7_Tips_to_Help_You_Excel_at_Using_the_OS_–

              LinuxBuz⠀⇛

                   Long-time Windows or Mac users may find it

                   difficult to shift to Linux, and in most cases,

                   it’s only due to the professional necessities. So,

                   here in this article, we will make it easier for

                   you to understand Linux in much easier ways so that

                   you can explore more.

                   If you are not a power user, spend some time

                   learning from scratch to grab the little things

                   that can prove to be helpful in the later stage.

                   The more you use it, the more you learn, and the

                   more you get into it.

            # ⚓ How_to_Install_FastPanel_on_Ubuntu_–_VITUX⠀⇛

                   Fastpanel is a web-hosting control panel. It

                   provides web-based intuitive, point-and-click

                   interfaces for common tasks such as transferring

                   files, installing applications, updating PHP

                   versions, and creating email accounts.

                   Fastpanel is written in PHP5, uses the PEAR DB

                   database layer, and includes over 100 database

                   functions (including MySQL-specific functions such

                   as “orelse” or “bcp”) as well as a large number of

                   other useful functions (including file management,

                   image conversion, HTTP authentication, and session

                   handling). Fastpanel is compatible with all major

                   web servers on Unix/Linux platforms: Apache 1.3+,

                   Nginx 0.7+, and Lighttpd 1.5+.

                   Have you ever wanted to install FastPanel on

                   Ubuntu? Have you been scared to try it because you

                   thought it would be a huge pain to get started?

                   We’ve done all the hard work for you. Read this

                   guide, then follow along, step by step. In no time,

                   FastPanel will be up and running on your Ubuntu

                   server in minutes.

            # ⚓ Install_Varnish_7_for_Nginx_on_Rocky_Linux_8⠀⇛

                   Varnish cache is a free and open-source cache

                   accelerator used to speed up your website by

                   caching the content in memory. It is extremely fast

                   and reduces the page load time, which helps with

                   your SERPs and improves user experience. It is used

                   by many organizations including Facebook, Twitter,

                   and Wikipedia. Varnish sits between Nginx and

                   clients that receive requests from clients and

                   forwards them to the backend. This will improve the

                   webserver performance because Varnish will serve

                   content from memory.

                   In this tutorial, I will show you how to install

                   Varnish 7 for Nginx on Rocky Linux 8.

            # ⚓ How_To_Install_LibreOffice_on_AlmaLinux_8_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   LibreOffice on AlmaLinux 8. For those of you who

                   didn’t know, LibreOffice is a free and open-source

                   office suite and is often considered a good

                   alternative to the Microsoft Office suite.

                   LibreOffice includes Writer (word processing), Calc

                   (spreadsheets), Impress (presentations), Draw

                   (vector graphics and flowcharts), Base (databases),

                   and Math (formula editing).

                   This article assumes you have at least basic

                   knowledge of Linux, know how to use the shell, and

                   most importantly, you host your site on your own

                   VPS. The installation is quite simple and assumes

                   you are running in the root account, if not you may

                   need to add ‘sudo‘ to the commands to get root

                   privileges. I will show you through the step-by-

                   step installation of LibreOffice’s free open-source

                   office productivity suite on AlmaLinux 8. You can

                   follow the same instructions for CentOS and Rocky

                   Linux.

            # ⚓ How_To_Install_OpenRGB_on_Ubuntu_20.04_LTS_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   OpenRGB on Ubuntu 20.04 LTS. For those of you who

                   didn’t know, OpenRGB is free and open-source

                   software used to control RGB lighting control that

                   does not require manufacturer software. The project

                   is focused to provide support for multiple hardware

                   manufacturers’ products to reduce the programs

                   load, which is limited to Windows, superfluous.

                   OpenRGB supports ASUS, ASRock, Corsair, G.Skill,

                   Gigabyte, HyperX, MSI, Razer, ThermalTake, and more

                   This article assumes you have at least basic

                   knowledge of Linux, know how to use the shell, and

                   most importantly, you host your site on your own

                   VPS. The installation is quite simple and assumes

                   you are running in the root account, if not you may

                   need to add ‘sudo‘ to the commands to get root

                   privileges. I will show you the step-by-step

                   installation of OpenRGB software for controlling

                   RGB lighting on Ubuntu 20.04 (Focal Fossa). You can

                   follow the same instructions for Ubuntu 18.04,

                   16.04, and any other Debian-based distribution like

                   Linux Mint.

            # ⚓ How_to_Install_MERN_Stack_with_Nginx_on_Debian_11⠀⇛

                   How to install MERN stack with Nginx on Debian 11.

                   MERN stack is a setup with MongoDB, Express, React

                   and Node.js. This is one of the variants of MEAN

                   stack. MongoDB is the database, Express with

                   Node.js is used for backend which communicates with

                   the database, React is the client side or frontend.

                   We will use Nginx reverse proxy to Node.js server

                   and setup Let’sEncrypt SSL.

                   In this guide you are going to learn how to setup

                   MERN stack on your Debian 11 server.

                   This setup is tested on Google Cloud, so it should

                   work fine on other VPS, cloud servers running

                   Debian 11.

            # ⚓ Simple_Way_To_Disable_The_Screen_Lock_On_Your_Ubuntu

              21.10⠀⇛

                   In this tutorial we are going to show you how to

                   disable the screen lock on your Ubuntu 21.01

                   desktop environment using the settings panel.

                   What is lock screen and what are the benefits of

                   having or not having it on?

                   The lock screen option is mainly used by the user

                   when he needs to secure his computer system with a

                   password. The lock screen can lock the screen after

                   user inactivity for a period of time like the

                   default 5 minutes on the Ubuntu desktop environment

                   or by pressing the windows button and L.

            # ⚓ Add,_switch,_delete,_and_manage_Linux_users_in_KDE_|

              Opensource.com⠀⇛

                   Sharing a computer in a household is usually a

                   pretty casual affair. When you need the computer,

                   you pick it up and start using it. It’s simple in

                   theory, and mostly works. That is, until you

                   accidentally grab the common computer and

                   accidentally post screenshots of your server’s

                   uptime to your partner’s cooking blog. Then it’s

                   time for separate user accounts.

                   From the very beginning, Linux has been a multi-

                   user system. It’s designed to treat each user, so

                   long as they log in, as a unique human being, with

                   a desktop all their own, a unique web browser

                   profile, access to their own documents and files,

                   and so on. The KDE Plasma Desktop does a lot to

                   make it easy to switch from one account to another,

                   but first you must set up a user account for each

                   person who you expect to use a computer. You might

                   also set up a special account for guests (I call

                   this account, pragmatically, guest.)

            # ⚓ Install/Upgrade_MariaDB_10.8_on_Ubuntu_20.04_LTS_–

              LinuxCapable⠀⇛

                   MariaDB is one of the most popular open-source

                   databases next to its originator MySQL. The

                   original creators of MySQL developed MariaDB in

                   response to fears that MySQL would suddenly become

                   a paid service due to Oracle acquiring it in 2010.

                   With its history of doing similar tactics, the

                   developers behind MariaDB have promised to keep it

                   open source and free from such fears as what has

                   happened to MySQL.

                   MariaDB has become just as popular as MySQL with

                   developers, with features such as advanced

                   clustering with Galera Cluster 4, faster cache/

                   indexes, storage engines, and features/extensions

                   that you won’t find in MySQL.

                   In the following tutorial, you will learn how to

                   install or upgrade MariaDB 10.8 on Ubuntu 20.04

                   LTS.

            # ⚓ 6_steps_for_migrating_a_PostgreSQL_database_between

              containers_|_Enable_Sysadmin⠀⇛

                   I decided to run Kanboard, an open source project

                   management application, in a rootless Podman pod as

                   a small weekend project. The pod consists of three

                   containers, an infra-container, a kanboard-

                   container, and a postgresql-container. That

                   deployment went well, but eventually, the image I

                   used for the postgresql-container became

                   deprecated, meaning it was no longer receiving

                   updates. It was time to move to a different image,

                   but that meant migrating a database between

                   containers. It sounds intimidating, but the process

                   is actually straightforward. Here’s how to do it.

            # ⚓ Install_Microsoft_Fonts_on_Linux_Mint_20_LTS_–

              LinuxCapable⠀⇛

                   Most Linux Distributions use open-source fonts to

                   substitute Microsoft’s iconic typefaces like Arial,

                   Courier New, and Times. Red Hat created the

                   Liberation family to replace these similar-looking

                   but different sizes — all you have to do is select

                   your preferred font when editing documents so that

                   they’ll be readable without any disruptions!

                   For users who want to install Microsoft fonts and

                   want the option to use them in LibreOffice, the

                   following tutorial will teach you how to install

                   Microsoft fonts on Linux Mint 20 LTS.

            # ⚓ How_To_Install_Akaunting_on_Debian_11_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   Akaunting on Debian 11. For those of you who didn’t

                   know, Akaunting is a free, open-source, and online

                   accounting software for small businesses and

                   freelancers. Akaunting provides an elegant and

                   intuitive UI will all the features and controls

                   needed to stay abreast of your cashflows and

                   transactions.

                   This article assumes you have at least basic

                   knowledge of Linux, know how to use the shell, and

                   most importantly, you host your site on your own

                   VPS. The installation is quite simple and assumes

                   you are running in the root account, if not you may

                   need to add ‘sudo‘ to the commands to get root

                   privileges. I will show you through the step-by-

                   step installation of Akaunting open-source

                   accounting software on a Debian 11 (Bullseye).

            # ⚓ How_to_Install_FFmpeg_5.0_in_Ubuntu_20.04_or_Ubuntu_18.04

              via_PPA_|_UbuntuHandbook⠀⇛

                   The popular FFmpeg multi-media library released

                   version 5.0 recently. Here’s how to install it in

                   Ubuntu 20.04, Ubuntu 18.04 and/or Ubuntu 16.04 via

                   PPA.

            # ⚓ How_to_install_Kali_Linux_2022.1_overview_–_Invidious⠀⇛

                   In this video, I am going to show how to install

                   Kali Linux 2022.1 overview.

            # ⚓ How_to_install_ONLYOFFICE_Desktop_Editors_on_Zorin_OS⠀⇛

                   ONLYOFFICE desktop app is an open-source office

                   suite pack that comprises editors for text

                   documents, spreadsheets, presentations, and forms.

                   Along with offline work, it’s possible to connect

                   the application to the cloud for online document

                   collaboration. The source code of the suite is

                   available on GitHub under the AGPL v.3.0 license.

            # ⚓ How_to_Install_PHP_7.4_on_CentOS_8_|_RHEL_8_–_Unix⠀⇛

                   PHP is a general-purpose scripting language geared

                   towards web development. The PHP reference

                   implementation is now produced by The PHP Group.

                   PHP originally stood for Personal Home Page, but it

                   now stands for the recursive initialism

            # ⚓ Workstation_Failed_Install_on_Ubuntu/CentOS/RHEL_(VMware

              Kernel_Module_Updater_fails)⠀⇛

                   Hi Guys, Sometimes you may have a trouble

                   completing the VMware Installation on a newly

                   installed Ubuntu or RHEL or even CentOS.

            # ⚓ dbus_daemon_fails_with_undefined_symbol:_XML_SetHashSalt

              FiX⠀⇛

                   To be honest, i was busy with this issue for 2

                   days. I have googled everywhere and tried all the

                   suggested solutions, but nothing works. While the

                   system boots, it still hanging with start D-bus

                   messages. It takes too long to reach the console,

                   but even with that, you will not be able to log in

                   with LDAP or ssh Clients. All services using the

                   Dbus are down.

                   The Only Way is to use Rescue mode to handle this

                   issue quickly.

            # ⚓ How_to_manage_users_in_Zorin_OS_–_Real_Linux_User⠀⇛

                   Probably for most people their computer is

                   literally their personal computer. These days lots

                   of children have their own computers, but what if

                   you have one family computer that is being shared

                   by multiple persons. If you allow everyone within

                   the family to use the same account, you can for

                   sure expect problems. There will be chaos in the

                   structure of system and personal files, there will

                   be an abundance of apps installed by different

                   people with different interests, and there will be

                   a great chance that family members mutate or delete

                   each other’s files without being aware of the

                   consequences for others in your household. And

                   maybe worse, with a single user setup, the young

                   kids also have the freedom to use the computer when

                   you are not around. In Zorin OS, just like in any

                   other serious desktop operating system, it is

                   possible to create multiple user accounts. And it

                   is advisable to use it. In this tutorial I will

                   explain how to manage users in Zorin OS.

            # ⚓ How_To_Install_Virtualmin_on_CentOS_8_/_RHEL_8⠀⇛

                   Virtualmin is a domain hosting and website control

                   panel which gives the ability to create and manage

                   many domains, as well as simplify both automation

                   and tasks. It is based on Webmin. Virtualmin is an

                   alternative to cPanel and Plesk

                   Virtualmin is available in two versions. Virtualmin

                   GPL and Virtualmin Professional. The Virtualmin GPL

                   version is fully free and open-source software and

                   does not require monthly fee, compared to the

                   Virtualmin Professional version which requires a

                   monthly or annual fee.

            # ⚓ Adam_Young:_Root_versus_groups⠀⇛

                   If you lock down everything, you either need to

                   hand out keys, or plan on doing everything

                   yourself, and getting overwhelmed.

                   Probably the single most power ful tool in Linux

                   land to keep people from having to be “root” is the

                   group concept. For example, if I want people to run

                   Docker containers, they need to be able to talk to

                   the Docker socket. The root user can do this by

                   virtue of its global access. However, the more

                   limited access approach is to add a user to the

                   docker group.

      o § Games⠀➾

            # ⚓ Proton_Experimental_heats_up_with_fixes_coming,_plus_a_disk

              space_saving_measure_|_GamingOnLinux⠀⇛

                   Now that the huge release of Steam Play Proton 7.0-

                   1 is out, work begins again on Proton Experimental

                   as it pulls in all the latest changes for you to

                   play with. What is Proton? It’s a compatibility

                   layer designed to run Windows games from Steam on

                   Linux. See more about it in our full guide.

            # ⚓ Escape_Simulator_gets_Linux_fixes,_networking_improvements

              –_ready_for_Steam_Deck_|_GamingOnLinux⠀⇛

                   A big update arrived for Escape Simulator, the

                   online co-op puzzle game that managed to sell a lot

                   of copies and so it should be ready for the Steam

                   Deck.

                   This fresh free upgrade brings in The Alchemist set

                   to make rooms with, additional updates to the room

                   editor with new skyboxes and particle effects, new

                   logic items and additions to existing items to

                   create more challenges with and code optimizations.

                   There’s more though, they said they’ve fixed up

                   some graphical issue for Linux and macOS, along

                   with “Steam Deck support” – although they didn’t

                   elaborate on what they did. Some networking

                   improvements were also made, that the developer

                   said “should work much better for the community

                   rooms”. Could be a great game for the Steam Deck to

                   run through a few puzzle rooms!

            # ⚓ Submerged:_Hidden_Depths_–_A_Relaxing_Experience_–_Boiling

              Steam⠀⇛

                   Submerged: Hidden Depths isn’t your typical game,

                   where you explore, fight off enemies, then move on

                   to the next area. The exploration is part of the

                   game’s experience, but there’s no enemies to be had

                   here.

                   Please note that, even though I have access to the

                   full game, I was asked by the publisher to only

                   talk about what goes on during the first hour of

                   gameplay, so as not to spoil the story for

                   potential buyers.

                   Submerged: Hidden Depths is the sequel to

                   Submerged, released in August 2015. Originally a

                   Stadia exclusive, the game will be available on

                   Steam March 10th. You’re in control of a girl named

                   Miku. Along with Miku is her younger brother Taku.

                   Together, they explore a vast, open-world ocean on

                   their fishing boat, where every now and again

                   there’s a spot of land to walk on and discover. So

                   kind of think of it like the sailing that’s done in

                   Zelda: The Wind Waker.

            # ⚓ Caves_of_Qud_gets_a_big_content_upgrade,_improved_gamepad

              and_Steam_Deck_support⠀⇛

                   Here’s a game that will be thoroughly interesting

                   to see on a Steam Deck. Caves of Qud is a fantastic

                   science fantasy roguelike epic and the developers

                   have been busy.

                   In the latest update not only have they added in a

                   ton more content like two minor late-game regions,

                   48 new Achievements, makeovers to multiple areas,

                   new animations and more — they’ve also made big

                   improvements to gamepad support.

                   This new input system isn’t fully ready and so it

                   needs be manually enabled in the control settings

                   under the pre-release option, but even so testing

                   with an Xbox pad today it feels pretty great. It’s

                   good news for the Steam Deck too, as it’s enabled

                   by default if it detects you playing on it and

                   scales things up a bit to be clearer.

      o § Desktop Environments/WMs⠀➾

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ #31_Bit_Windy_·_This_Week_in_GNOME⠀⇛

                         Update on what happened across the GNOME

                         project in the week from February 11 to

                         February 18.

      o § Distributions⠀➾

            # § New Releases⠀➾

                  # ⚓ Easy_3.4.1_coming_soon⠀⇛

                         I built EasyOS 3.4.1RC and did some basic

                         testing. Looks OK.

                         Booted it on a PC with AMD Radeon HD 6870

                         video card and 1024×768 monitor — no problem.

                         Good, the sun in the wallpaper is no longer

                         squashed…

            # § SUSE/OpenSUSE⠀➾

                  # ⚓ AppArmor,_Flatpak,_GStreamer_update_in_Tumbleweed_–

                    openSUSE_News⠀⇛

                         openSUSE’s rolling release Tumbleweed has

                         produced five snapshots since our last

                         review.

                         Snapshots 20220215, 20220214, 20220213,

                         20220212 and 20220210 updated several tools,

                         libraries and clients this week.

                         The latest snapshot, 20220215, updated a

                         couple Python Package Index and RubyGem

                         packages. The package that generates profile

                         reports from pandas DataFrame fixed almost a

                         dozen regressions and reverted a performance

                         speedup to fix a precision regression. The

                         RubyGem package rubygem-faraday, which is an

                         HTTP/REST Application Programming Interfaces

                         client library, updated to a major new

                         version from 1.3.0 to 2.1.0; the package

                         added several new features like backport

                         authorization process, improved documentation

                         and added a policy on inclusive language.

                         Data compression package lzip 1.23 reduced

                         compression times by 5 to 12 percent

                         depending on the file. Text editor vim

                         8.2.4375 fixed a few crashes and a couple of

                         those involved FuncRef. An update of yast2-

                         trans 84.87.20220211 added new pot files for

                         storage, dns-server, nfs and s390.

                         Snapshot 20220214 updated six packages.

                         Flatpak 1.12.5 now detects and removes left-

                         over data from /var/lib/flatpak/appstream and

                         a fix was made with a display bug in Flatpak

                         history; it does not set up an unnecessary

                         polkit agent for flatpak’s history. An update

                         of gnome-maps 41.4 provided some translations

                         and fixed build issues with Meson 0.60. The

                         update of NetworkManager 1.34.0 had multiple

                         additions for Meson builds requirements. The

                         updated NetworkManager also split out

                         NetworkManager-pppoe, which is needed to

                         configure regular PPPoE connections; the

                         changelog states that it’s not very common

                         since most users have PPPoE routers for the

                         DSL connections.

                         Internet Relay Chat client hexchat 2.16.1

                         updated in snapshot 20220213 and received

                         build fixes with OpenSSL 3. The IRC client

                         also fixed Python scripts not being opened as

                         UTF-8. The 4.6.1 GTK4 package has a new API

                         for text shaping engine HarfBuzz and the

                         toolkit also fixes support for the new high-

                         contrast setting with Wayland. The glib2

                         2.70.4 version updated translations and fixed

                         a memory leak. Another packages to update in

                         the snapshot was yast2-installation 4.4.40,

                         which fixed some issue running with Qt 5.15.

                  # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2022/07⠀⇛

                         This week, the major news is a glibc update

                         to version 2.35. This was surprisingly smooth

                         (so far) compared to earlier version updates.

                         Let’s all cross our fingers for this to stay

                         the way it is. In total, Tumbleweed has seen

                         6 new snapshots during this week (0210, 0212,

                         0213, 0214, 0215, and 0216).

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ Fedora_Magazine:_Upgraded_Fedora_shirts⠀⇛

                  # ⚓ Remi_Collet:_PHP_version_7.4.28,_8.0.16_and_8.1.3⠀⇛

                         RPMs of PHP version 8.1.3 are available in

                         remi-modular repository for Fedora ≥ 34 and

                         Enterprise Linux ≥ 8 (RHEL, Alma, CentOS,

                         Rocky…) and in remi-php81 repository for EL

                         7.

                         RPMs of PHP version 8.0.16 are available in

                         remi-modular repository for Fedora ≥ 34 and

                         Enterprise Linux ≥ 8 (RHEL, Alma, CentOS,

                         Rocky…) and in remi-php80 repository for EL

                         7.

                         RPMs of PHP version 7.4.28 are available in

                         remi-modular repository for Fedora ≥ 34 and

                         Enterprise Linux ≥ 8 (RHEL, Alma, CentOS,

                         Rocky…) and in remi-php74 repository for EL

                         7.

                  # ⚓ Friday’s_Fedora_Facts:_2022-07_–_Fedora_Community

                    Blog⠀⇛

                         Here’s your weekly Fedora report. Read what

                         happened this week and what’s coming up. Your

                         contributions are welcome (see the end of the

                         post)!

                         I have weekly office hours on Wednesdays in

                         the morning and afternoon (US/Eastern time)

                         in #fedora-meeting-1. Drop by if you have any

                         questions or comments about the schedule,

                         Changes, elections, or anything else. See the

                         upcoming meetings for more information.

                  # ⚓ Irving_Wladawsky-Berger:_How_Does_AI_Improve_Human

                    Decision-Making?⠀⇛

                         “Artificial Intelligence (AI) is the newest

                         general-purpose technology (GPT),” wrote

                         Sukwoong Choia, Namil Kim, Junsik Kim, and

                         Hyo Kang in a recent paper, How Does AI

                         Improve Human Decision-Making? Evidence from

                         the AI-Powered Go Program. “One remarkable

                         characteristic of AI is its ability to

                         provide humans with high-quality predictions

                         at relatively low cost and to automate a wide

                         range of predictions. AI has already

                         outperformed human professionals in many

                         domains – including strategic gameplay,

                         medical diagnosis, and new drug development.”

                         “Furthermore, as a GPT, the domains where AI

                         outperforms humans are expanding at a fast

                         pace. The rapid development and adoption of

                         AI thus raise an interesting yet pressing

                         question about how AI affects human tasks in

                         these various domains. Studies of AI and

                         human capital, for instance, have examined

                         the performance gap between humans and AI,

                         highlighting AI’s potential for replacing

                         jobs.” However, we should keep in mind that

                         new technologies have been replacing workers

                         and transforming economies for over two

                         centuries. But, over time, these same

                         technologies led to the creation of whole new

                         industries and new jobs, increasing

                         productivity and economic output, raising

                         earnings, and augmenting the demand for

                         labor.

                         Workers can increase their productivity and

                         performance when assisted in their jobs by

                         AI-based tools. But beyond its assistant

                         role, AI can play a major instructional role

                         by training human professionals to make

                         better decisions. Recent technology advances

                         have significantly improved the quality and

                         reduced the cost of AI-based predictions.

                  # ⚓ IT_talent:_6_ways_job_expectations_have_evolved⠀⇛

                         Enterprise IT organizations have been shaken

                         by some tectonic shifts over the past couple

                         of years. Tech professionals who held tight

                         to their seats during the early months of the

                         pandemic are now streaming toward the exits

                         during the Great Resignation. It’s a critical

                         time for IT leaders to realign with their

                         team members.

                         Specifically, it’s more important than ever

                         to not only understand but get ahead of what

                         IT professionals want from their employers,

                         bosses, and teams today. People’s job

                         expectations have shifted significantly over

                         the last year and IT leaders must acknowledge

                         and meet them in order to not only retain

                         their key players but keep them engaged and

                         happy in their roles.

            # § Canonical/Ubuntu Family⠀➾

                  # ⚓ Ubuntu_Touch_OTA-22_lands_with_video_calling

                    improvements_and_FM_radio_daemon⠀⇛

                         The UBports Foundation has announced the

                         availability of Ubuntu Touch OTA-22. It comes

                         with plenty of improvements but among the

                         headlines is that video calling now works in

                         the browser (but not apps just yet) and that

                         an FM radio daemon has been added and that

                         the app should be available in the next

                         release.

                         For those already running Ubuntu Touch on one

                         of their devices, the update can be obtained

                         through the Updates screen of the System

                         Settings. UBports is randomly rolling out the

                         update to devices from today but it won’t

                         push it out to everyone just yet in case the

                         distribution needs to be paused to fix a

                         major issue. If you don’t run Ubuntu Touch

                         yet but have a device lying around that you’d

                         like to try it on, just head over to the

                         Ubuntu Touch devices page for instructions.

                  # ⚓ Multiple_vulnerabilities_put_40_million_Ubuntu_users

                    at_risk_|_TechRadar [Ed: Shoddy media pretending Snap

                    is part of "Linux"]⠀⇛

                         Security researchers have recently found

                         “multiple vulnerabilities” on Ubuntu systems,

                         some of which would allow a threat actor to

                         gain root privileges on the target endpoint.

                  # ⚓ Dangerous_privilege_escalation_bugs_found_in_Linux

                    package_manager_Snap_|_CSO_Online⠀⇛

                         Researchers found an easy-to-exploit

                         vulnerability in Snap, a universal

                         application packaging and distribution system

                         developed for Ubuntu but available on

                         multiple Linux distributions. The flaw allows

                         a low-privileged user to execute malicious

                         code as root, the highest administrative

                         account on Linux.

                  # ⚓ New_Linux_Privilege_Escalation_Flaw_Uncovered_in_Snap

                    Package_Manager⠀⇛

                         Multiple security vulnerabilities have been

                         disclosed in Canonical’s Snap software

                         packaging and deployment system, the most

                         critical of which can be exploited to

                         escalate privilege to gain root privileges.

                         Snaps are self-contained application packages

                         that are designed to work on operating

                         systems that use the Linux kernel and can be

                         installed using a tool called snapd.

      o § Devices/Embedded⠀➾

            # ⚓ Solderable_OSM_module_taps_i.MX8M_Mini⠀⇛

                   Kontron unveiled a 30 x 30mm “OSM-S i.MX8M Mini”

                   OSM module with up to 4GB LPDDR4, which is

                   available with a baseboard and a Linux BSP as the

                   “BL i.MX8M Mini OSM” SBC. Iesy is prepping its own

                   i.MX8M Mini and Rockchip PX30 based OSM modules.

                   The Open Standard Module (OSM) form factor was

                   developed by Kontron, F&S Elektronik Systeme, and

                   Iesy in early 2020 when it was unveiled on F&S’

                   OSM-MX8MM module. Kontron has now followed up with

                   an OSM-S i.MX8M Mini, which similarly combines a 30

                   x 30mm OSM Size-S form factor with an i.MX8M Mini.

                   There is no product page so far, but the datasheet

                   for an OSM-S i.MX8M Mini based BL i.MX8M Mini OSM

                   SBC covers the basics.

            # § Open Hardware/Modding⠀➾

                  # ⚓ Weekly_Update_(7/2022):_Call_and_chat_with

                    +015550199999_or_put_Ubuntu_Touch_OTA_22_on_your

                    libhybris_phone!⠀⇛

                         A rather boring week: People love handhelds

                         with keyboards, an unofficial PinePhone

                         battery case, a translucent backcover and a

                         little bit of software news. Oh, and PINE64

                         shared another community update!

                  # ⚓ Unique_Clock_Is_All_Hands,_No_Dial,_And_Does_The_Worm

                    |_Hackaday⠀⇛

                         Back in the old days, we didn’t have fancy

                         digital clocks. No, we had good analog clocks

                         with a big hand and a little hand, and if you

                         wanted to know the time you had to look at

                         the clock and figure out which number each

                         hand was pointing at, or kind of pointing at.

                         It wasn’t easy, and we liked it that way.

                         So now, along comes an analog clock that’s

                         nothing but the hands — no dial, no numbers,

                         just hands. How is such a thing possible? The

                         clue is in the clock’s name: AKUROBATTO, and

                         in the video below, which shows the acrobatic

                         movements of the clock’s hands as it does its

                         thing. Serial improbable-clock maker

                         [ekaggrat singh kalsi] clearly put a lot of

                         thought into this mechanism, which consists

                         of the hands and a separate base. The hands

                         are joined together at one end and powered by

                         small stepper motors. The base has two

                         docking areas, where servo-driven claws can

                         grasp the hand assembly, either at the center

                         pivot or at the tip of either hand. With a

                         little bit of shuffling around at transition

                         points, the hands sweep out the hours and

                         minutes in a surprisingly readable way.

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ How_to_block_a_number_on_your_Android_Phone_–_Geeky

                    Gadgets⠀⇛

                  # ⚓ 5_easy_ways_to_make_Android_more_ergonomic_|

                    Computerworld⠀⇛

                  # ⚓ Motorola_Moto_G22_Android_smartphone_leaked_–_Geeky

                    Gadgets⠀⇛

                  # ⚓ 5_Simple_Ways_to_Take_Notes_on_Android_While_You’re

                    Offline⠀⇛

                  # ⚓ Samsung_Galaxy_S22_Plus_Review:_the_Best_Android

                    Phone_You_Can_Buy⠀⇛

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

            # § Productivity Software/LibreOffice/Calligra⠀➾

                  # ⚓ GTK4:_Using_GtkMediaStream_in_LibreOffice⠀⇛

                         Today’s GTK4 version of LibreOffice (towards

                         7.4) using the first cut of my efforts to use

                         GtkMediaStream + GtkPicture for video

                         playback. Works a lot better than this video

                         of a video suggests 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇;-)⦈

            # § Programming/Development⠀➾

                  # ⚓ Ruby_3.1.1_Released⠀⇛

                         Ruby 3.1.1 has been released.

                         This is the first TEENY version release of

                         the stable 3.1 series.

                  # § Shell/Bash/Zsh/Ksh⠀➾

                        # ⚓ 7_Must-Know_Linux_File_Manipulation_Commands

                          [Ed: Those are not Linux commands, they’re_mostly

                          GNU_programs]⠀⇛

                               Modern Linux desktops have come a long

                               way in regards to letting you

                               manipulate files on your system.

                               However, because of all the overhead

                               resources used by a GUI (such as GNOME

                               or KDE Plasma), when you need to work

                               with more than one file or directory,

                               the command line is often the fastest

                               and most efficient way to get things

                               done.

                               Learning how and when to take advantage

                               of the Linux command line with just a

                               handful of essential file-manipulation

                               commands will help to enhance your

                               productivity and transform your Linux

                               experience.

                  # § Rust⠀➾

                        # ⚓ Lang_team_February_update⠀⇛

                               Two weeks ago, the lang team held its

                               February planning meeting (minutes). We

                               hold these meetings on the first

                               Wednesday of every month.

* § Leftovers⠀➾

      o § Science⠀➾

            # ⚓ Hello_(Many_Quantum)_World(s)_|_Hackaday⠀⇛

                   Historically, the first program you write for a new

                   computer language is “Hello World,” or, if you are

                   in Texas, “Howdy World.” But with quantum computing

                   on the horizon, you need something better. Like

                   “Hello Many Worlds.” [IonQ] proposes what that

                   looks like and then writes it in seven different

                   quantum languages in a post you should check out.

            # ⚓ Infinity_Mirror_Hypercrystal_Is_As_Beautiful_As_It_Sounds_|

              Hackaday⠀⇛

                   Sometimes, we feature projects that are full to the

                   brim with advanced functionality or solve some

                   tricky little problem for the end-user. Other

                   times, we feature stuff that just looks super damn

                   cool, and the Infinity Mirror Hypercrystal is

                   firmly in that latter category.

                   [...]

                   The result is an infinity mirror piece that looks

                   more advanced, more alien, and more luridly

                   enticing than most we’ve ever seen. The dichroic

                   shift placed on the LEDs goes a long way to

                   elevating this sculpture to new aesthetic heights.

                   Video after the break.

            # ⚓ blog.harterrt.com_–_Data_Intuition_Case_Study:_Grain-free

              Dog_Food⠀⇛

                   My vet told me I should stop feeding my dog grain-

                   free dog food. Apparently, grain-free dog food is

                   linked with a heart condition called Dilated

                   Cardiomyopathy (DCM). This set off my bullshit

                   detector, so I decided to dig deeper.

                   [...]

                   I have a different hypothesis for what’s going on

                   here. I suspect this link between grain-free dog

                   food and DCM is entirely caused by a good old-

                   fashioned sampling bias.

      o § Hardware⠀➾

            # ⚓ Commodore_64_Monitor_Traces_I/O_Calls,_Eases_Debugging_|

              Hackaday⠀⇛

                   Developing for the Commodore 64 can be a rewarding

                   retrocomputing experience, and thanks to [Dave Van

                   Wagner], things are easier with his C64 IO_Monitor

                   project, which opens the door to logging and

                   tracing Kernal I/O calls for closer inspection.

                   That’s not a typo, by the way. Kernal is what

                   handles the C64’s low-level OS routines. Amusingly,

                   as the story goes, it did in fact originate as a

                   misspelling of kernel, but the name stuck.

            # ⚓ Building_A_High-Capacity_Linear_Servo_Actuator_|_Hackaday⠀⇛

                   Linear actuators are useful things, moving things

                   in straight lines rather than annoying circles like

                   so many motors. [Retsetman] recently built a linear

                   servo actuator of his own design with accurate

                   positional control.

                   The design relies on a carriage that moves along a

                   threaded rod, perhaps the most rudimentary design

                   of linear actuator. A large brushed DC motor is

                   used to turn the threaded rod through a 3D-printed

                   9:1 herringbone geartrain, shifting the actuator

                   back and forth. End stop switches are used to

                   disengage the motor to avoid damage to the

                   mechanism. Feedback is via a ten-turn potentiometer

                   driven off the output geartrain to match the range

                   of the actuator to the rotational range of the pot.

            # ⚓ VIA_SOM-9X35_Starter_Kit_features_MediaTek_i350_Arm

              processor_for_edge_AI_devices_–_CNX_Software⠀⇛

                   VIA has just introduced the SOM-9X35 Starter Kit

                   based on MediaTek i350 quad-core Cortex-A53

                   processor with AI accelerator and HiFi4 DSP

                   designed for Edge AI devices in the retail,

                   commercial, and industrial sectors.

                   The kit is comprised of the SOM-9X35 module with

                   MediaTek i350 SoC, up to 4GB RAM, 16GB eMMC flash,

                   and WiFI 5 + Bluetooth 5.0 wireless module, as well

                   as the VIA VAB-935 3.5-inch carrier board, a 7-inch

                   1024×600 touch panel display, a 13MP camera module,

                   two speakers and microphone, and accompanying

                   accessories.

            # ⚓ Early_Hard_Drives:_Really_Big,_Really_Expensive⠀⇛

                   Today in Tedium: Hard drives may be the most

                   fundamental building block of the computer

                   revolution. Hitting the perfect balance between

                   size and cost, it was a defining piece of computer

                   history, one that made our machines more permanent

                   and helped us rethink the way we store information.

                   With a hard drive, we were eventually able to move

                   away from the idea of thinking of our documents in

                   terms of a linear order and a physical space. And

                   that, of the many innovations that came from

                   computing, might be the most important. Now,

                   granted, it wasn’t easy to get to that point—in

                   part because hard drives weren’t always the small,

                   compact platters we have today. In fact, they were

                   bigger. A lot bigger. Today’s Tedium talks early

                   hard drives.

                   [...]

                   If you were to explain to the public what a hard

                   drive was with no prior frame of reference, where

                   would you start? How would you highlight the

                   benefits to the world?

                   That’s an odd, somewhat theoretical problem today,

                   but in 1956, it was legitimately a challenging

                   problem that IBM had to solve. At the time,

                   “business machines” often meant storing information

                   on punch cards and and typewritten pages, which

                   meant that the file cabinet business was doing

                   quite well back in the day.

                   The difference between a punch card and a hard

                   drive is quite similar to the difference between

                   the Dewey Decimal System and microfilm—one

                   organizes content that’s completely physical while

                   the other shrinks the scale enough that it allows

                   for some degree of rethinking how we access the

                   content. With a hard disk, it doesn’t have to

                   necessarily be in order anymore. It adds a layer of

                   separation between you and the information being

                   displayed.

                   In many ways, the IBM 305 RAMAC (Random Access

                   Method of Accounting and Control), which was

                   initially built for the needs of accountants,

                   represented this sort of abstraction. Designed at

                   the behest of the U.S. Air Force, it was meant to

                   provide faster, more efficient storage of

                   information than magnetic drums.

                   “This has been a day of solid achievement,” the

                   first message ever stored on a hard drive stated,

                   according to a 2002 ComputerWorld article.

      o § Integrity/Availability⠀➾

            # § Proprietary⠀➾

                  # ⚓ New_Malware_Found_Infecting_Microsoft_Teams_Meetings

                    [Ed: Microsoft Teams itself is technically malware]⠀⇛

                         You may want to think twice the next time

                         you’re on a conference call. It’s not really

                         a time you can let your guard down. Even when

                         doing something as innocuous as joining a

                         chat with co-workers, you can still get hit

                         with malware. Security experts discovered

                         hackers have been targeting Microsoft Teams

                         meetings with malware.

                  # § Security⠀➾

                        # ⚓ Security_updates_for_Friday_[LWN.net]⠀⇛

                               Security updates have been issued by

                               Debian (chromium and zsh), Fedora

                               (microcode_ctl and zziplib), Mageia

                               (docker-containerd, mariadb, nas,

                               phoronix-test-suite, rlwrap,

                               thunderbird, webkit2, wireshark, zsh,

                               and zxing-cpp), openSUSE (aide,

                               chromium, clamav, expat, htmldoc,

                               libmspack, libsndfile, python-Twisted,

                               qemu, rust, strongswan, tiff,

                               virglrenderer, and xerces-j2),

                               Slackware (mozilla and php), SUSE

                               (aide, clamav, cobbler, expat, kernel,

                               libmspack, libsndfile, python-numpy,

                               python-Twisted, qemu, rust, strongswan,

                               tcpdump, tiff, ucode-intel,

                               virglrenderer, wpa_supplicant, and

                               xerces-j2), and Ubuntu (kernel,

                               libarchive, linux-hwe-5.13, and snapd).

                        # ⚓ This_Week_in_Security:_Chrome_0-day,Cassandra,

                          and_a_Cisco_PoC⠀⇛

                               Running Chrome or a Bhromium-based

                               browser? Check for version

                               98.0.4758.102, and update if you’re not

                               running that release or better. Quick

                               tip, use chrome://restart to trigger an

                               immediate restart of Chrome, just like

                               the one that comes after an update.

                               This is super useful especially after

                               installing an update on Linux, using

                               apt, dnf, or the like.

                               CVE-2022-0609 is the big vulnerability

                               just patched, and Google has

                               acknowledged that it’s being exploited

                               in the wild. It’s a use-after-free bug,

                               meaning that the application marks a

                               section of memory as returned to the

                               OS, but then accesses that now-invalid

                               memory address. The time gap between

                               freeing and erroneously re-using the

                               memory allows malicious code to claim

                               that memory as its own, and write

                               something unexpected.

                               Google has learned their lesson about

                               making too many details public too

                               early, and this CVE and associated bug

                               aren’t easily found in in the Chromium

                               project’s source, and there doesn’t

                               seem to be an exploit published in the

                               Chromium code testing suite.

                        # ⚓ Launchpad_now_supports_SSH_Ed25519_keys_and_RSA

                          SHA-2 signatures_|_Colin_Watson’s_blog⠀⇛

                               As of 2022-02-16, Launchpad supports a

                               couple of features on its SSH endpoints

                               (git.launchpad.net,

                               bazaar.launchpad.net,

                               ppa.launchpad.net, and

                               upload.ubuntu.com) that it previously

                               didn’t: Ed25519 public keys (a well-

                               regarded format, supported by OpenSSH

                               since 6.5 in 2014) and signatures with

                               existing RSA public keys using SHA-

                               2 rather than SHA-1 (supported by

                               OpenSSH since 7.2 in 2016).

                               I’m hesitant to call these features

                               “new”, since they’ve been around for a

                               long time elsewhere, and people might

                               quite reasonably ask why it’s taken us

                               so long. The problem has always been

                               that Launchpad can’t really use a

                               normal SSH server such as OpenSSH

                               because it needs features that aren’t

                               practical to implement that way, such

                               as virtual filesystems and dynamic user

                               key authorization against the Launchpad

                               database. Instead, we use Twisted

                               Conch, which is a very extensible

                               Python SSH implementation that has

                               generally served us well. The downside

                               is that, because it’s an independent

                               implementation and one that occupies a

                               relatively small niche, it often lags

                               behind in terms of newer protocol

                               features.

                        # ⚓ CISA_Compiles_Free_Cybersecurity_Services_and

                          Tools_for_Network_Defenders_|_CISA⠀⇛

                               CISA has compiled and published a list

                               of free cybersecurity services and

                               tools to help organizations reduce

                               cybersecurity risk and strengthen

                               resiliency. This non-exhaustive living

                               repository includes services provided

                               by CISA, widely used open source tools,

                               and free tools and services offered by

                               private and public sector organizations

                               across the cybersecurity community.

                               Before turning to the free offerings,

                               CISA strongly recommends organizations

                               take certain foundational measures to

                               implement a strong cybersecurity

                               program….

                        # ⚓ Linux_developers_patch_security_holes_faster

                          than_anyone_else,_says_Google_Project_Zero⠀⇛

                               There’s a lot of FUD about how Linux is

                               being shown recently to be less secure

                               than proprietary systems. That’s

                               nonsense. But, now there are hard facts

                               from Google’s Project Zero, Google’s

                               security research team, showing Linux’s

                               developers do a faster job of fixing

                               security bugs than anyone else,

                               including Google.

                        # § Privacy/Surveillance⠀➾

                              # ⚓ Can_Pegasus_be_stopped?_|_Inside_Story_–

                                Invidious⠀⇛

                                     The balance between privacy and

                                     security is back in the spotlight

                                     in Europe.

                                     This time its Data Protection

                                     watchdog is sounding the alarm

                                     about the threat posed by

                                     surveillance software.

                                     Specifically, the Israeli Pegasus

                                     spyware – which could allow

                                     governments access to people’s

                                     personal information and decrypt

                                     private communications at will.

                              # ⚓ Digital_borders:_EU_increases_use_of

                                technology_to_monitor_migration_–

                                InfoMigrants⠀⇛

                                     The European Union and its border

                                     agency Frontex are using

                                     increasing amounts of technology

                                     to monitor migration at external

                                     and internal borders across

                                     Europe. Experts say that tracking

                                     technology is often being

                                     deployed to evade legal

                                     responsibilities.

                                     In February, the French

                                     government announced it would be

                                     installing additional cameras

                                     along the Channel coast to help

                                     monitor migrants hoping to cross

                                     the stretch of water towards the

                                     UK. The cameras are paid for by

                                     the British government.

                                     In December 2021, the Italian

                                     navy delivered a fresh

                                     consignment of containers with

                                     monitoring equipment to Libya to

                                     monitor migration across the

                                     Mediterranean. That’s according

                                     to research published by the

                                     investigative magazine

                                     Altreconomia (February issue).

                                     “Camera traps” like speed-

                                     monitoring devices for cars and

                                     people have also been placed on

                                     or near the border between Italy

                                     and Slovenia along the so-called

                                     Balkan route, reported the

                                     magazine.

      o § Environment⠀➾

            # § Wildlife/Nature⠀➾

                  # ⚓ South_America_squid_left_exposed_amid_surge_in_China

                    fishing⠀⇛

                         Negotiators from the U.S., China and 13 other

                         governments failed to take action to protect

                         threatened squid stocks on the high seas off

                         South America amid a recent surge in activity

                         by China’s distant water fishing fleet.

                         The South Pacific Regional Fisheries

                         Management Organization, or SPRFMO, is

                         charged with ensuring the conservation and

                         sustainable fishing off the west coast of

                         South America.

                         At the SPRFMO’s annual meeting that ended

                         Friday, Ecuador and the European Union

                         proposed measures that would require all

                         ships to have observers on board by 2028 and

                         mandate they unload their catches only in

                         ports instead of at sea to giant refrigerated

                         vessels — both considered key tools in

                         limiting illegal, unreported and unregulated

                         fishing.

                         [...]

                         Biologists warn that the boom has left the

                         naturally bountiful Humboldt squid — named

                         for the nutrient-rich current found off the

                         west coast of South America — vulnerable to

                         overfishing, as has occurred in Argentina,

                         Mexico, Japan and other places where squid

                         stocks have disappeared in the past.

                         An investigation by The Associated Press and

                         Spanish-language broadcaster Univision last

                         year revealed how the traditionally lawless

                         area has become a magnet for some of the

                         seafood industry’s worst offenders, many of

                         them Chinese-flagged vessels with a history

                         of labor abuse accusations and convictions

                         for illegal fishing.

      o § Civil Rights/Policing⠀➾

            # ⚓ Amazon_Co-Owns_Airline_Accused_of_Operating_Torturous

              Deportation_Flights⠀⇛

                   Activists are pressuring Amazon to divest from Omni

                   Air International, a company at the center of ICE’s

                   deportation machine.

            # ⚓ PEARL_2_PEGASUS:_Bahraini_activists_hacked_with_Pegasus

              just_days_after_a_report_confirming_other_victims_–_The

              Citizen_Lab⠀⇛

                   Mohammed Al-Tajer is a lawyer known for being

                   outspoken about human rights violations in Bahrain,

                   and for defending political prisoners and

                   activists. Al-Tajer was the president of the

                   Bahrain Human Rights Observatory, a human rights

                   coalition inside Bahrain. Al-Tajer was targeted

                   with FinFisher spyware in 2011 when he received a

                   CD containing a video of himself and his wife

                   recorded from a hidden camera in his beach house.

                   His computer was infected with FinFisher around the

                   same time he received the CD.

                   Al-Tajer’s wife, Dr. Huda, was detained for her

                   activism during the 2011 uprising for providing

                   medical aid to injured protesters. Ultimately, Al-

                   Tajer did not accede to the blackmail demands, and

                   the video was circulated online on pro-government

                   forums and social media accounts.

                   [...]

                   In March 2019, Dr. Siwar conducted an Instagram

                   Live interview with a school student reportedly

                   expelled for dealing Lyrica, a prescription anti-

                   anxiety medication that is sometimes abused to

                   produce a “relaxed and euphoric” high. The student

                   said that she was part of an organized drug-dealing

                   group in Hamad Town Intermediate Girls School. Dr.

                   Siwar said that “powerful people” were implicated

                   in the drug dealing. Bahrain Mirror later revealed

                   that Dr. Siwar was referring to the King’s fifth

                   son, Khalid bin Hamad Al Khalifa.

                   Bahrain’s then Prime Minister announced an

                   investigation into Dr. Siwar’s allegations. The

                   investigative report stated that the Lyrica

                   incident was isolated, and that Dr. Siwar was

                   guilty of slander and defamation. Dr. Siwar was

                   sentenced to a year’s imprisonment in the case.

                   Dr. Siwar also faced other allegations: a pro-

                   government newspaper announced that she would be

                   charged with “covering up a rape,” and she was

                   sentenced to a year in prison for reportedly

                   providing Panadol (a medicine similar to Tylenol)

                   to a mentally ill teenager.

                   Although Dr. Siwar was pardoned by Bahrain’s King

                   in May 2021 after spending several months in

                   prison, the prosecution re-introduced the same case

                   in court again in November 2021. When she was

                   summoned in the case, she fled to the UK and sought

                   asylum. Further, in January 2022, the Ministry of

                   Interior’s General Directorate of Anti-Corruption

                   and Economic & Electronic Security began legal

                   action against Dr. Siwar after several individuals

                   complained that Dr. Siwar’s Instagram video had

                   defamed them. The Directorate also accused Dr.

                   Siwar of practicing medicine without a license,

                   defaming employees of a ministry and spreading

                   false information during her court hearing.

            # ⚓ Civil_society_calls_for_solidarity_with_Ukraine’s_human

              rights_defenders_in_guarding_against_cyber_threats⠀⇛

                   In a statement issued today, Access Now, together

                   with Centre for Democracy and Rule of Law and

                   Digital Security Lab Ukraine, calls on the

                   international community to take swift action in

                   support of civil society in Ukraine, as well as the

                   broader public whose human rights are being

                   undermined by cyberattacks on Ukraine’s critical

                   infrastructure.

                   Following the most recent cyberattacks on January

                   13-14 and February 15, 2022 targeting Ukraine’s

                   essential public service infrastructure, and the

                   ongoing threat of escalating Russian aggression,

                   this is a critical moment for solidarity with

                   Ukrainian civil society.

                   [...]

                   “Cyberattacks are disrupting the ability of

                   Ukrainians to seek medical care and obtain other

                   essential services, and receive important

                   information amidst the intensifying military

                   conflict. The international community must act now

                   to protect Ukraine’s critical infrastructure and

                   human rights defenders from these attacks,” said

                   Anastasiya Zhyrmont, Regional Outreach Coordinator

                   for Eastern Europe & Central Asia at Access Now.

            # ⚓ [Attacks]_on_Ukraine’s_infrastructure_and_civil_society

              violate_human_rights⠀⇛

                   There is a pressing need to provide Ukrainian civil

                   society with technical means to protect both

                   themselves and the sensitive data on their servers

                   and devices, as well as to prevent future attacks.

                   We urge tech companies, nonprofits, and funders to

                   expand their support programs and provide Ukrainian

                   activists with free and secure VPNs, antivirus

                   programs, encryption, DDoS protection, and other

                   essential digital tools, equipment, and services.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ #SocialMediaComplianceWatch:_analysis_of_Social_Media

              Compliance_Reports_for_the_month_of_December_2021⠀⇛

                   Google (including YouTube), Facebook, Instagram

                   (both are now under Meta), ShareChat, Snap, Twitter

                   and WhatsApp have released their reports in

                   compliance with Rule 4(1)(d) of the IT Rules 2021

                   for the month of December, 2021. The latest of

                   these was published by Meta and was made available

                   in late January 2022. The reports contain similar

                   shortcomings, which exhibit lack of effort on the

                   part of the social media intermediaries and the

                   government to further transparency and

                   accountability in platform governance. The

                   intermediaries have yet again, not reported on

                   government requests, used misleading metrics, and

                   also have not disclosed how they use algorithms for

                   proactive monitoring. You can read our analysis of

                   the previous reports here.

      o § Digital Restrictions (DRM)⠀➾

            # ⚓ Bionic_Eyes_Go_Dark⠀⇛

                   If you were blind, having an artificial retinal

                   implant would mean the difference between seeing a

                   few hundred pixels in greyscale and seeing all

                   black, all the time. Imagine that you emerged from

                   this total darkness, enjoyed a few years of

                   mobility and your newfound sense, and then

                   everything goes dark again because the company

                   making the devices abandoned them for financial

                   reasons.

                   This is a harrowing tale of close-source

                   technology, and how a medical device that relies on

                   proprietary hard- and software essentially holds

                   its users hostage to the financial well-being of

                   the company that produces it. When that company is

                   a brash startup, with plans of making money by

                   eventually pivoting away from retinal implants to

                   direct cortical stimulation — a technology that’s

                   in it’s infancy at best right now — that’s a risky

                   bet to take. But these were people with no other

                   alternative, and the technology is, or was,

                   amazing.

                   [...]

                   If we were CEO of SecondSight, we know what we

                   would do with our closed-source software and

                   hardware right now. The company is facing

                   bankruptcy, has lost significant credibility in the

                   medical devices industry, and is looking to pivot

                   away from the Argus system anyway. They have little

                   to lose, and a tremendous amount of goodwill to

                   gain, by enabling people to fix their own eyes.

            # ⚓ Why_is_John_Deere_so_opposed_to_letting_farmers_fix_their

              stuff?_—_The_Repair_Association⠀⇛

                   John Deere is trying to block the agricultural

                   Right to Repair in Nebraska—which affects all of

                   us, not just farmers. When farm equipment goes down

                   in the middle of the season, it can cost farmers a

                   harvest and the rest of us a meal. Everyone that

                   eats has a horse in this race.

                   And Deere is rigging the race. They have filled

                   Nebraska’s unicameral legislature with their

                   lobbyists attempting to block the passage of LB543,

                   the Right to Repair for Agricultural and Ranch

                   Equipment. They are telling senators that Deere &

                   Co. supports farmers repairing their equipment, but

                   they don’t support the “right to modify” When

                   pressed, they proclaim that farmers can already fix

                   98% of their equipment, so there isn’t a problem

                   for legislators to address.

                   Hogwash. Within the 2% of repairs that Deere blocks

                   are many problems that can take a machine down

                   100%. Fixing 98% of something rather than 100% is a

                   farce. Limp mode can be a death sentence for a

                   crop. when a simple problem during key times takes

                   the machine down 100%, not 98%.

                   Plus, repair is not modification. Most farmers have

                   no interest in doing anything with their tractor

                   beyond the job it was designed to do—they just want

                   it to be in good working order. So why is Deere

                   paying lobbyists big bucks to bend the ears of

                   every Nebraskan senator, to keep farmers away from

                   2% of repairs? Why are they fighting 5 antitrust

                   lawsuits already so far this month? What is Deere

                   protecting so fiercely?

<

                ䷩ 𝚕𝚒𝚗𝚎 8024

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Links_18/2/2022:_Bottles_2022.2.14_and_RedNotebook_2.23⠀✐

Posted in News_Roundup at 11:55 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o § Desktop/Laptop⠀➾

            # ⚓ Chrome_OS_Flex_can_be_installed_on_EOL_Chromebooks,_but

              Google_doesn’t_recommend_it⠀⇛

            # ⚓ Lilbits:_Windows_11_Pro_will_require_Microsoft_accounts,

              using_Chrome_OS_Flex_to_keep_old_Chromebooks_alive_–

              Liliputing⠀⇛

                   That could come in handy if you have an older model

                   that’s no longer covered by Google’s Auto Update

                   policy, which means that it’s no longer receiving

                   new builds of Chrome OS with new features or

                   security updates. Chrome OS Flex could provide a

                   way to run an up-to-date build of Chrome OS on old

                   gear… but it’s not without its own risks.

                   Google officially advises against using Chrome OS

                   Flex on Chromebooks that have passed their Auto

                   Update Expiration dates, noting that Google doesn’t

                   officially support this use case and that users may

                   run into issues with the installation process, may

                   have firmware or other hardware compatibility

                   problems, and may not receive updates.

                   That said, a number of users have already reported

                   success installing Chrome OS Flex on older

                   Chromebooks, which, quite honestly is probably

                   better than running a 2-year-old version of Chrome

                   OS without the latest security patches, even if

                   those devices never receive another update.

      o § Audiocasts/Shows⠀➾

            # ⚓ Technically_Speaking_(E11):_You_need_Ops_to_AIOps_–

              Invidious [Ed: Red Hat slinging buzzwords, as usual]⠀⇛

      o § Kernel Space⠀➾

            # ⚓ Btrfs_Vs._Ext4:_Essentials,_Benefits,_And_Disadvantages⠀⇛

                   File systems control where and how your data is

                   stored and retrieved from a storage device. Windows

                   and macOS users have little reason to worry about

                   file systems since NTFS and HFS+ are the only

                   choice of filesystems they have, respectively.

                   Linux users have the flexibility to choose the file

                   system their machine uses since the kernel supports

                   a variety of these. Ext4 is the default option for

                   Linux users. Still, there is another file system

                   called Btrfs you could consider using.

                   With a part of the Linux community pushing for the

                   adoption of Btrfs as the default file system, it’s

                   essential to understand the functionalities,

                   advantages, and disadvantages of both.

            # ⚓ RAID_expansion_comes_to_OpenZFS_at_last⠀⇛

                   ZFS has been around for 16 years and has a solid

                   reputation, but it does have limitations compared

                   to its rivals. One of these is in the process of

                   being lifted: soon it will be possible to add space

                   to an existing ZFS array. As long as you’re using

                   FreeBSD, anyway.

                   Filesystems are one of the core differentiators

                   between enterprise Linux distributions (and other

                   Unix and Unix-like OSes). That means, like anything

                   in the Unix world, there’s “advocacy” – in other

                   words, bitter squabbling about which is best or

                   worst.

                   ZFS was originally developed by Sun for Solaris. At

                   one point, Apple was going to adopt it, but changed

                   its mind. Now, of course, Oracle owns it – but

                   there is OpenZFS, and a very small chance that the

                   situation might change.

      o § Applications⠀➾

            # ⚓ Review:_Harmonoid_–_music_app⠀⇛

                   We’ve reviewed a whole raft of open source music

                   players from tiny command-line players to bloated

                   Electron-based heavyweights. But Linux is endowed

                   with a huge selection, and there’s still a few

                   we’ve yet to put under the microscope.

                   Harmonoid is billed as an elegant music app to play

                   local music and YouTube music. It’s written in the

                   Dart programming language and published under an

                   open source license. Before we see how it fares,

                   let’s briefly cover the installation process.

            # ⚓ Okular:_Signature_verification_User_Interface_added_to

              Okular_mobile_interface⠀⇛

                   Okular has two user interfaces, you can control

                   which one you get when compiling okular by setting

                   the OKULAR_UI cmake variable to desktop (the

                   default) or to mobile (which you can build just

                   fine on the desktop too, there’s nothing “mobile

                   only” in it).

                   The mobile one is built on top of Kirigami and is

                   more oriented to use with touch screens. It also

                   has fewer features, for example, you can’t add

                   annotations nor fill forms. I could say it’s less

                   likely you need those features on a mobile form

                   factor but that’s less and less true as time goes

                   and computing shifts to mobile devices, but that’s

                   a story for another day.

            # ⚓ What_is_XRDP?_|_ITProPortal⠀⇛

                   XRDP is one of the best remote desktop software

                   tools for operating systems other than Windows,

                   such as Linux.

            # ⚓ RedNotebook_2.23⠀⇛

                   RedNotebook is a modern desktop journal. It lets

                   you format, tag and search your entries. You can

                   also add pictures, links and customizable

                   templates, spell check your notes, and export to

                   plain text, HTML, Latex or PDF. RedNotebook is Free

                   Software under the GPL.

      o § Instructionals/Technical⠀➾

            # ⚓ Comparing_lzop_and_plzip_compression⠀⇛

                   I had a fascination with file compression in the

                   2000s, but OpenZFS’s inline compression has spoiled

                   me ever since. When I need to leave its comforting

                   confides though, I turn to the excellent lzop and

                   plzip tools, which have largely replaced gzip and

                   bzip2 for my one off archives.

            # ⚓ What_Is_AAA_Security?⠀⇛

                   Authentication, authorization, and accounting,

                   often called AAA or Triple-A, are sets of services

                   and protocols that enable granular access control

                   over computer networks. Before the popularity of

                   mainstream HTTP-based authentication protocols such

                   as OAuth and SAML, AAA protocols were the primary

                   way to authenticate users or machines to network

                   services. AAA protocols are still commonly found in

                   corporate LAN and WAN networks, ISPs, cellular

                   networks, and network devices such as firewalls,

                   routers, and switches.

            # ⚓ Lurking_complexities_in_a_web_server_that_just_serves

              static_files⠀⇛

                   The essentially mandatory complexity is setting a

                   good Content-Type so that browsers are willing to

                   interpret your HTML and CSS as HTML and CSS. In a

                   dynamic site, this is something the application

                   handles; in a static site, you have a blob of bytes

                   and now you get to figure it out. The traditional

                   answer is to use file name extensions along with a

                   small or big mapping table from extensions to

                   Content-Type, but you’re responsible for that code

                   and that table (either hard-coded or with a way to

                   configure it at runtime and an initial default

                   version).

            # ⚓ Testing_Raspberry_Pi’s_new_Network_Install_feature⠀⇛

                   Like Apple’s Internet Recovery, you don’t have to

                   have any OS installed on your computer to use it.

                   And you don’t need to run a separate server to boot

                   your Pi and image its drive. (Note: There are also

                   some PC vendors who have specific image-over-

                   Internet services for certain devices like the

                   Microsoft Surface, but they’re not universally

                   applicable to all PC builds.)

                   This feature is NOT netbooting. The Pi supports

                   that too. This is similar, in a sense, but this

                   goes deeper.

            # ⚓ How_to_install_and_Use_Tripwire_on_Debian_11⠀⇛

                   Hello, friends. In this post, you will learn how to

                   install and use Tripwire on Debian 11. This

                   intrusion detection system is a vital tool for many

                   sysadmins.

                   [...]

                   Tripwire is an intrusion detection system that will

                   help us to further improve server security.

                   To accomplish this, Tripwire is constantly updating

                   critical system files. In addition to this, it also

                   reports control reports in case they have been

                   modified or deleted by a hacker. In short, it scans

                   sensitive files for changes.

                   Fortunately, Tripwire is an open-source tool with

                   outstanding Linux support. This means that the

                   installation process will be easy to do.

                   Let’s go for it.

            # ⚓ Ceph_Storage_5:_Insert_next_disk⠀⇛

                   Red Hat Ceph Storage 5 introduces cephadm, a new

                   integrated control plane that is part of the

                   storage system itself, and enjoys a complete

                   understanding of the cluster’s current state —

                   something that external tools could not quite

                   achieve as well because of their external nature.

                   Among its many advantages, cephadm unified control

                   of the state of a storage cluster significantly

                   simplifies operations.

                   [...]

                   A failed OSDs in a Ceph Storage cluster can also be

                   replaced by a junior administrator with appropriate

                   role-based access control (RBAC) permissions on the

                   Dashboard. OSD IDs can be preserved while replacing

                   the failed OSDs, which is both operationally easier

                   to manage (by having a fixed set of ID assigned to

                   each host) and optimizes memory usage (OSD ID gaps

                   are undesirable).

                   The Cluster administrator can thus use the

                   Dashboard’s RBAC capabilities to delegate a trainee

                   to replace failed drives, without delegating

                   additional permissions that the junior

                   administrator is not yet qualified to operate, as

                   detailed in the following short video.

            # ⚓ How_to_Install_and_Use_ZSH_Shell_in_Linux⠀⇛

                   A shell is used as an interface between a user and

                   the operating system. On most Linux distributions,

                   bash shell is the default shell used, however, the

                   best part about open source is choice. As users, we

                   can decide to change defaults that came with the

                   system and use other alternatives.

                   In Linux, the most commonly used open-source shells

                   include Bourne Again Shell (bash), tcsh (an

                   enhanced C shell), Korn shell (ksh), friendly

                   interactive shell (fish), and zsh.

            # ⚓ How_to_Install_Budgie_Desktop_on_AlmaLinux_|_Rocky_Linux_8

              –_Linux_Shout⠀⇛

                   Learn the steps to install the Budgie Desktop

                   environment on Almalinux 8 and Rocky Linux 8 using

                   the command terminal.

                   One of the greatest benefits of using Linux OS is

                   we can use multiple Desktop User Interface of

                   choice. This allows users to modify and get the

                   Desktop Interface of their own choice. Well, Gnome

                   is the popular one that comes as a default GUI in

                   both AlmaLinux and Rocky. However, it is not

                   suitable for everyone. Few users want a lightweight

                   but with nice, sleek, and familiar looks. If you

                   are one of the then try the Budgie Desktop

                   environment.

                   Budgie comes as a default GUI in Solus operating

                   systems, an independent Linux. And Budgie is a part

                   of this project. However, as it is published under

                   an open-source license we can install it on any

                   popular Linux either by adding some third-party

                   repository or the system’s base repo.

      o § Wine or Emulation⠀➾

            # ⚓ Bottles_2022.2.14_Release_Lets_You_Easily_Install_Windows

              Apps_on_Linux_–_It’s_FOSS_News⠀⇛

                   You can use Wine to install Windows apps on Linux,

                   but it does not work for all the applications.

                   Moreover, it requires you to configure things

                   manually. So, what are the easy options?

                   While CrossOver has been trying its best to make

                   the process easier, Bottles is another solution.

                   With Bottles’ latest release, it aims to make

                   things seamless to help run your preferred Windows

                   app with minimal tweaking.

      o § Games⠀➾

            # ⚓ Valve_remedies_shader_caching_issues_with_Proton_games

              before_Steam_Deck_launch⠀⇛

                   Shader caching exists to reduce the amount of work

                   your GPU needs to do when running a game. But

                   Proton users have had issues with the way Steam

                   caches them for some time now.

                   Thankfully, the latest Steam beta release from

                   Valve seeks to solve some of these issues, and just

                   in time for when the Proton-dependent Steam Deck

                   begins shipping later this month.

                   [...]

                   Right now, this is just in the beta release of

                   Steam. But by the time later pre-orders of the Deck

                   begin hitting doorsteps, it will likely be moved

                   into the main release. In the meantime, those who

                   have been suffering from shader cache-related

                   issues can opt in to the beta version of Steam

                   within the settings of the Steam client. Once

                   that’s done, Steam should automatically update

                   itself to the latest beta release, complete with

                   all related features.

            # ⚓ An_interview_with_James_Spanos_of_Wormwood_Studios_|

              GamingOnLinux⠀⇛

                   You asked: we delivered. Here’s a chat with game

                   developer extraordinaire James Spanos, who works

                   with Wormwood Studios and publisher Wadjet Eye

                   Games.

                   Q: Could you first introduce yourself and tell us

                   about your games?

                   “My name is James Spanos, I’m a game developer,

                   with the major role of coder for Wormwood Studios,

                   and working for/with Wadjet Eye Games, our

                   publisher. I’ve worked on Primordia and

                   Strangeland, both point and click adventure games

                   released in 2012 and 2021, under Wormwood Studios,

                   but I’ve worked on various titles throughout the

                   years, like The Cat Lady and Downfall by Harvester

                   Games, where I did some interface work for, and

                   Mage’s Initiation, where I worked on the combat

                   system! I’ve been a gamer my whole life, so being

                   able to work full time as a gamedev was always

                   something I aspired to!”

            # ⚓ 1_week_from_release,_Steam_Deck_hits_well_over_640_Playable

              games_|_GamingOnLinux⠀⇛

                   We’re now only a single week away from something

                   amazing, Valve will be officially releasing the

                   Steam Deck. Here’s some updated numbers on what

                   games you can expect to see working well. Looking

                   back, 6 days ago we noted there we 520 games rated

                   as Verified or Playable together and the list has

                   just kept growing.

            # ⚓ Devolver_Digital_announces_save-the-day_adventure_McPixel_3

              |_GamingOnLinux⠀⇛

                   McPixel 3 is coming from Sos Sosowski and Devolver

                   Digital – but what happened to number 2? Guess that

                   one got lost adventuring. Even their official

                   announcement email was confused, telling us to join

                   them in asking “What the hell happened to McPixel

                   2?”.

                   The original released back in 2012 and this follow-

                   up is described as: “Is it a bird? Is it a plane?

                   It’s falling too fast to be either of those. It’s

                   McPixel! A wanna-be hero who keeps getting mixed up

                   in the most unbelievable situations you can

                   imagine. Avert one disaster after another at every

                   turn using unconventional yet entertaining methods

                   of mayhem including – but not limited to –

                   summoning a spider-billionaire, having a BBQ in his

                   pants, punching a T-Rex into outer space, peeing

                   into sports cars, and kicking Fork Parker in the

                   balls.”

            # ⚓ itch.io_has_another_Creator_Day_today,_100%_goes_to

              developers_|_GamingOnLinux⠀⇛

                   Game store itch.io, well known for helping out

                   indies and running Game Jams has today put up

                   another Creator Day.

                   For 24 hours, until midnight Pacific Time (8AM

                   Saturday UTC), itch will give 100% of the revenue

                   to creators (minus taxes and normal fees). It’s a

                   really good way to support some smaller developers!

      o § Distributions⠀➾

            # ⚓ 2021_hardcore_list_of_linux_distributions_without_elogind

              and_other_systemd_parts⠀⇛

                   This list is going to be short and there may be a

                   sublist of distros with a medium strict standard.

                   We shall explain what the object is, below the

                   short list (which we hope the community will assist

                   in making longer as we have not been able to

                   currently review the work of every distro and

                   fork).

            # § BSD⠀➾

                  # ⚓ Debugging_an_ioctl_Problem_on_OpenBSD⠀⇛

                         I was trying to use a V4L2 Ruby module on my

                         OpenBSD laptop but ran into a problem where

                         sending the V4L2 ioctls from this module

                         would fail, while other V4L2 programs on

                         OpenBSD worked fine.

                         Since I got a few questions recently about

                         kernel development and debugging, I thought

                         I’d write up how I finally tracked it down

                         and fixed it. (Spoiler: it was not an OpenBSD

                         problem.)

                  # ⚓ My_journey_from_macOS_to_FreeBSD⠀⇛

                         I would like to share my personal experience

                         with my recent move to the PC world. My

                         journey started on MS DOS and then Windows,

                         as it’s common for many people. Later on I

                         moved to Linux, but only on desktop. When the

                         time came and I needed a laptop, I was

                         fascinated by the hardware and software

                         quality of Macintosh. Back then, it was an

                         era of PowerPC, that was coming slowly to an

                         end. I bought my first MacBook Pro around

                         2007 and I was really satisfied with it. I

                         loved the Unix roots of Mac OS X. It was a

                         combination of Mach kernel and FreeBSD user

                         land that gave it it’s unique strength and

                         architecture. I absolutely fell in love with

                         Aqua interface of Mac OS X Tiger. All those

                         glossy, beautiful buttons and scrollbars

                         really captured my heart.

            # § Gentoo Family⠀➾

                  # ⚓ Gentoo:_Format_of_download_file_signatures_has

                    changed⠀⇛

                         We have simplified the format of the

                         downloadable file (i.e. stage 3 and iso

                         image) signatures. Now, each of these files

                         is accompanied by a detached GnuPG signature

                         where the file itself is signed. The signing

                         key remains unchanged; see our web page on

                         release media signatures for the

                         fingerprints.

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ Nebulon_adds_Ansible_support_for_infrastructure

                    deployment⠀⇛

                         Nebulon has integrated its

                         smartInfrastructure platform with Red Hat’s

                         Ansible software – including a set of modules

                         that allow users to automate Nebulon

                         infrastructure deployment and management by

                         using Ansible Playbooks.

                         The Nebulon Ansible Collection, when combined

                         with the firm’s Nebulon ON cloud-based

                         control plane used for management, is claimed

                         to reduce operational overheads by up to 75

                         per cent compared with operating

                         hyperconverged infrastructure (HCI) or

                         traditional three-tier server infrastructure,

                         according to Nebulon.

                         Nebulon’s infrastructure platform is based on

                         a PCIe card called the Services Processing

                         Unit (SPU), which fits inside server nodes

                         and controls all the storage drives in each

                         node. Each SPU is linked to all the others in

                         a cluster via dedicated Ethernet connections,

                         effectively producing a kind of distributed

                         storage area network (SAN) that is

                         configurable via the cloud-hosted Nebulon ON

                         control plane.

                  # ⚓ IBM_merges_13_APAC_nations_into_one_regional

                    organization [Ed: IBM still cooking the books to hide

                    its constant decline]⠀⇛

                         IBM quietly reorganized its Asian affairs at

                         the start of 2022, creating a region called

                         ASEANZK that means big markets such as

                         Australia and South Korea now report to a

                         regional entity.

                         ASEANZK (gesundheit) comprises the ten ASEAN

                         member countries – Brunei, Cambodia,

                         Indonesia, Laos, Malaysia, Myanmar, the

                         Philippines, Singapore, Thailand, and Vietnam

                         – plus Australia, New Zealand and South

                         Korea. The Register understands that the

                         ASEAN group previously operated as a region,

                         and the three other nations stood alone.

                  # ⚓ IBM_Consulting_assimilates_cloud_firm_for_Azure

                    expertise [Ed: IBM is shilling Microsoft]⠀⇛

                         IBM has acquired Neudesic, a US cloud

                         consultancy services firm specialising in

                         Microsoft’s Azure platform, as part of a

                         continued drive to expand the company’s

                         growth in hybrid multicloud services.

                  # ⚓ SAP_&_IBM_Join_Forces_to_Rev_Up_Workload_Transition

                    to_Cloud [Ed: “Transition to Cloud” as in changing the

                    word server to “CLOUD"]⠀⇛

                  # ⚓ IBM_Cloud_to_offer_Z-series_mainframes_for_first_time

                    –_albeit_for_test_and_dev⠀⇛

                         As IBM tries to address allegations it

                         discriminated against older staff, the IT

                         giant has for the first time brought its

                         oldest computing platform – the mainframe –

                         into the age of infrastructure-as-a-service.

                         The 111-year-old tech institution today

                         announced it will offer the Z mainframe

                         platform on the IBM Cloud, by offering

                         virtual machines running z/OS as-a-service.

                  # ⚓ IBM_HR_chief_insists_‘no_systemic_age

                    discrimination’⠀⇛

                         Memo responds to lawsuit brought by wife of

                         exec who killed himself after layoff

                         IBM’s Chief Human Resources Officer Nickle

                         LaMoreaux on Sunday rejected what she

                         described as “false claims of age

                         discrimination at the company.”

                         “Discrimination of any kind is entirely

                         against our culture and who we are at IBM,

                         and there was (and is) no systemic age

                         discrimination at our company,” said

                         LaMoreaux in a public statement posted to the

                         company’s website.

                         The media reports she references follow from

                         the release of documents in an age

                         discrimination lawsuit against the venerable

                         computing biz, Lohnn v. IBM. The initial

                         complaint was filed in July 2021 [PDF] on

                         behalf of Jorgen Lohnn, who took his own life

                         after being laid off from the company.

                         “Jorgen Lohnn worked for IBM for

                         approximately 15 years until his layoff in

                         2016 at the age of 57,” the initial complaint

                         says. “He worked for IBM as a Client

                         Executive for Sales and Distribution. He

                         committed suicide after his layoff from IBM.

                  # ⚓ Controlling_software_supply_chain_security_will

                    require_new_tools,_automation_and_vigilance

                    ⠀⇛

                         “It’s called a supply chain, and it’s only as

                         strong as its weakest link,” said Vincent

                         Danen, vice president of product security at

                         Red Hat Inc., in an interview with theCUBE,

                         SiliconANGLE Media’s livestreaming studio.

                         “If one company is breached, multiple

                         companies end up being breached as a result

                         of that. I don’t look at it as we’re just

                         securing Red Hat. We’re securing our

                         customers, and we’re also doing that for

                         their customers as well.”

                  # ⚓ Idevnews_|_API_Management_vs._Service_Mesh:_The

                    Choice_Doesn’t_Have_to_Be_Yours⠀⇛

                         As organizations look to keep up with our

                         increasingly digital and cloud-driven world,

                         many are modernizing their IT infrastructure

                         and adopting API-centric and microservices-

                         based architectures to improve speed,

                         agility, and efficiency.

                         Such uses of APIs support the rapid-response

                         expectation of the modern era. In this case,

                         APIs take the weight of a monolithic

                         application and break it down into small

                         microservices—which become independent units

                         that promote agility when managing and

                         scaling applications. Consistent and

                         effective management of these interfaces and

                         services is critical for successful

                         deployment and use.

            # § Debian Family⠀➾

                  # ⚓ A_twisted_maze_of_dependencies⠀⇛

                         My relative inexperience with Debian systems

                         means I’m constantly being delighted to

                         discover that such and such has already been

                         packaged up and is just an apt command away.

                         Things that I would have done by hand in the

                         years up to this point now have someone else

                         worrying about them.

                         Unfortunately, the packagers can only work

                         with what they’ve been given, and in the case

                         of certain ecosystems, that means an

                         explosion of crazy. Case in point: the other

                         night, I was working on some Javascript code

                         (unavoidable for the problem at hand), wanted

                         to see how much I had screwed up, and thought

                         “hmm, there was this jshint thing that would

                         show me where I did something stupid back in

                         the day”. I went looking and didn’t find

                         that, but did find something called “eslint”.

                         I figured, okay, es, ECMAScript, that’s the

                         fancy name for this stuff now, should work,

                         right?

            # § Canonical/Ubuntu Family⠀➾

                  # ⚓ Unlock_Multi-Touch_Gestures_in_Xubuntu_—_Sean_Davis⠀⇛

                         One of the features I’ve grown to appreciate

                         since using macOS, elementary OS, and GNOME

                         4x is multi-touch gestures for switching

                         workspaces. When I came back to Xubuntu, I

                         ran into some roadblocks bringing my favorite

                         feature into Xfce. By disabling the Synaptics

                         driver and installing Touchégg, you can bring

                         Magic Trackpad support and gestures to

                         Xubuntu.

                  # ⚓ Ubuntu_Touch_OTA-22_Rolling_Out_Now_with_Initial_FM

                    Radio_Support,_WebGL_Support⠀⇛

                         Ubuntu Touch OTA-22 is here one and a half

                         months after the OTA-21 update to add yet

                         another layer of improvements, as well as to

                         pave the way for new, upcoming features, such

                         as FM Radio support to allow for real analog

                         radio listening on supported devices. For

                         now, only the daemon implementation landed in

                         the OTA-22 release, while an FM Radio

                         application should be available in the app

                         store in the next few weeks.

      o § Devices/Embedded⠀➾

            # § Open Hardware/Modding⠀➾

                  # ⚓ OPPO_announces_tie-up_with_Hasselblad_for_camera

                    tech⠀⇛

                         Chinese phone manufacturer OPPO has announced

                         a three-year partnership with the famous

                         camera firm Hasselblad to develop camera

                         technology for its flagship Find series.

                  # ⚓ Linking_AI_education_to_meaningful_projects⠀⇛

                  # ⚓ How_to_update_the_Raspberry_Pi_Compute_Module_4

                    Bootloader_/_EEPROM⠀⇛

                         The Raspberry Pi 4 and Pi 400 share the same

                         Broadcom BCM2711 SoC with the Compute Module

                         4. All three devices also share an SPI EEPROM

                         flash chip, which stores the Raspberry Pi’s

                         bootloader.

                         But the Compute Module 4 differs in how you

                         update the bootloader. With the Pi 4 or Pi

                         400, you can use Raspberry Pi imager to write

                         a utility image to a microSD card to update

                         the bootloader. You put in the card, power on

                         the Pi, and the bootloader is updated.

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ List_of_Xiaomi_smartphones_that_will_be_updated_to

                    Android_13⠀⇛

                  # ⚓ ExpressBasics:_How_to_block_unwanted_notifications_on

                    Android_|_Technology_News,The_Indian_Express⠀⇛

                  # ⚓ 5_easy_ways_to_make_Android_more_ergonomic_|

                    Computerworld⠀⇛

                  # ⚓ 7_Best_Android_Email_Apps_to_Use_in_2022_–_TechPP⠀⇛

                  # ⚓ JingPad_A1_bootloader_unlock_tool,_Android_ROM,_and

                    source_code_are_now_available⠀⇛

                  # ⚓ This_Could_Be_OPPO’s_Very_First_Android_Tablet⠀⇛

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

            # § Web Browsers⠀➾

                  # ⚓ Our_Old_Friend,_the_Data_URL⠀⇛

                         I first looked into data URLs seriously after

                         encountering them in Sean Conner’s (now

                         defunct) Gemini client torture test, shortly

                         after I started working on Lagrange. I’ve

                         since seen these being played with here and

                         there.

                         When you think about it, data URLs have

                         untapped potential for Gemini. Due to the

                         stipulation that each user action results in

                         no more than a single network request, the

                         usual way of accessing documents composed of

                         heterogeneous content is unavailable. With

                         data URLs, though, it is possible to embed

                         images, CSV-tables, and whatever else into a

                         perfectly normal, spec-compliant Gemtext file

                         — without any ambiguity or new semantics. And

                         the best part is that since clients normally

                         hide raw URLs for basic readability, this

                         doesn’t cause (well written) clients to

                         misbehave when encountering such a URL.

                  # ⚓ How_Everything_We’re_Told_About_Website_Identity

                    Assurance_is_Wrong⠀⇛

                         This isn’t all going to be in the order in

                         which DigiCert has presented the information,

                         instead I’m going to walk through it in a

                         fashion which systematically breaks it apart

                         and shoots it down in flames. Let’s start

                         here: [...]

                  # ⚓ Web_Security_Basics:_XSS⠀⇛

                         I decided to learn more about areas of web

                         development I don’t know a lot about. You

                         know,…stuff like SEO and web security. I’ll

                         share my findings here on my blog and I’ll

                         try to do as much research as possible, but

                         please keep in mind that I’m a noob

                         concerning these topics.

                         I began watching Feross Aboukhadijeh’s

                         fantastic Web Security lecture, which

                         inspired me to learn more about web security.

                         This first post is about Cross Site Scripting

                         (XSS).

                  # § Mozilla⠀➾

                        # ⚓ Is_Firefox_OK?⠀⇛

                               At the end of 2008, Firefox was flying

                               high. Twenty percent of the 1.5 billion

                               people online were using Mozilla’s

                               browser to navigate the web. In

                               Indonesia, Macedonia, and Slovenia,

                               more than half of everyone going online

                               was using Firefox. “Our market share in

                               the regions above has been growing like

                               crazy,” Ken Kovash, Mozilla’s president

                               at the time, wrote in a blog post.

                               Almost 15 years later, things aren’t so

                               rosy.

                               Across all devices, the browser has

                               slid to less than 4 percent of the

                               market—on mobile it’s a measly half a

                               percent. “Looking back five years and

                               looking at our market share and our own

                               numbers that we publish, there’s no

                               denying the decline,” says Selena

                               Deckelmann, senior vice president of

                               Firefox. Mozilla’s own statistics show

                               a drop of around 30 million monthly

                               active users from the start of 2019 to

                               the start of 2022. “In the last couple

                               years, what we’ve seen is actually a

                               pretty substantial flattening,”

                               Deckelmann adds.

                        # ⚓ The_Talospace_Project:_Firefox_97_on_POWER⠀⇛

                               It was previously reported that WebRTC

                               was broken on OpenPOWER under Fx96,

                               which looks like bug 1738445 (a replay

                               of bug 1465274, which I upstreamed four

                               years ago). I don’t use WebRTC myself

                               due to the way my internal network is

                               configured, so don’t consider this in

                               any way an attestation of

                               functionality, but I was able to build

                               Firefox 97 unmodified with the

                               .mozconfigs and LTO-PGO patch from

                               Firefox 95. Although I have an old

                               build of gn, I tested whether that was

                               the necessary piece by pulling that

                               line out of the configuration, and it

                               still built — at least under gcc. I did

                               do a test clang build (removing the

                               compiler export lines and removing

                               forcing linkage with bfd), and that did

                               fail to build (with or without gn), and

                               –disable-webrtc along with this change

                               to NSS did allow it to compile.

                               However, when started up with ./mach

                               run, the clang build could browse but

                               complained the history and places

                               databases were corrupt and about:

                               support was messed up. Using the same

                               profile with a gcc build was fine. IDK.

            # § FSF⠀➾

                  # § Licensing/Legal⠀➾

                        # ⚓ Can_Open-Source_Software_enforcement_help_save

                          the_planet?⠀⇛

                               The Software Freedom Conservancy (SFC)

                               has sued smart TV manufacturer Vizio

                               for alleged breaches of open-source

                               software (OSS) licenses.

            # § Programming/Development⠀➾

                  # ⚓ Golang_gRPC_Example⠀⇛

                         Welcome back. I’m an experienced developer,

                         learning Golang by building an activity

                         tracker. Last time I added SQLite

                         persistence. Today, I’m going to be porting

                         everything to gRPC.

                         If you’re curious about gRPC – how it works,

                         when to use it, what example code might look

                         like – well, you are in luck because I’m

                         going to be building a grpc client, a grpc

                         server, and the protobuf files for my

                         activity tracker. The full code is on GitHub.

                  # ⚓ Insomnia_is_an_open-source_Postman_alternative_with

                    GraphQL_support⠀⇛

                         Insomnia is a free, open-source API design

                         and test tool for individual developers and

                         enterprises.

                  # ⚓ Recent_updates_in_Conan_package_manager_support⠀⇛

                         In our previous blog post about Installing Qt

                         via Conan Package Manager, we introduced how

                         to use Conan package manager with Qt. Now

                         it’s time to look at the recent enhancements

                         in our Conan story.

                  # § Rust⠀➾

                        # ⚓ Rust_Use_Continues_To_Increase⠀⇛

                               The 2021 Rust Survey, the results of

                               which have just come out, show not only

                               increased use of the language for work

                               purposes but also that developers are

                               gaining confidence for using it for

                               production-ready code.

* § Leftovers⠀➾

      o ⚓ Mitski’s_Ghost_Stories⠀⇛

             Three years ago, during the summer of 2019, Mitski

             announced a hiatus. For the past five years, she’d been

             touring nonstop. The 2016 breakout success of her fourth

             studio album, Puberty 2, had vaulted her from a well-

             loved indie artist to a crossover success story, then

             onward and upward into the firmament of pop stardom.

             Lorde tapped her as an opening act in her 2018 Melodrama

             tour; Iggy Pop name-checked her on his radio show; her

             subsequent album, 2018’s Be the Cowboy, was a perennial

             favorite on year-end lists. She still didn’t have a

             permanent mailing address and stored her things at her

             parents’ house, but no matter—she was, as NPR crowned

             her, the 21st century’s poet laureate of young adulthood,

             and her future, as Pitchfork declared, was “limitless.”  

      o ⚓ Uber_and_Lyft_are_taking_on_healthcare,_and_drivers_are_just

        along_for_the_ride⠀⇛

             Correll is now working as a lawyer. But if he had kept

             driving, he might have run into more situations like this

             one. That’s because, for the past few years, rideshare

             companies Lyft and Uber have been moving into the non-

             emergency medical transportation (NEMT) business,

             offering their networks to healthcare organizations that

             need to schedule rides for patients. Correll isn’t sure

             if his ride was through a formal NEMT program, but it

             could have been: to protect patient privacy, drivers

             aren’t told if their rides are from healthcare

             partnerships or not.

      o § Education⠀➾

            # ⚓ God,_Grades_and_College⠀⇛

                   But one often overlooked demographic factor is

                   religion. The U.S. is the most devout wealthy

                   Western democracy. Does a religious upbringing

                   influence teens’ academic outcomes?

                   Over the past 30 years, sociologists and economists

                   have conducted several studies that consistently

                   show a positive relationship between religiosity

                   and academic success. These studies show that more

                   religious students earn better grades and complete

                   more schooling than less religious peers. But

                   researchers debate what these findings really mean,

                   and whether the seeming effect of religiosity on

                   students’ performance is really about religion, or

                   a result of other underlying factors.

            # ⚓ Book_Notes:_“Millions,_Billions,_Zillions”_by_Brian

              Kernighan⠀⇛

                   Just because there are numbers attached to a

                   presentation of fact doesn’t mean it’s true. Or

                   even based in reality. But we too easily become

                   “number numb”: [...]

      o § Hardware⠀➾

            # ⚓ Semiconductor_market_correction_could_come_in_2024_•_The

              Register⠀⇛

                   The semiconductor world’s continuing roaring sales

                   growth could hit a wall in 2024, an industry

                   research firm has predicted.

                   IC Insights is projecting sustained semiconductor

                   revenue growth in 2022 and 2023, with a market

                   correction due the year after that.

                   “2024 is currently expected to be the next cyclical

                   downturn in the market, and 2025-2026 will return

                   to growth years,” Brian Matas, vice president of

                   market research, told The Register.

                   The semiconductor sector is highly volatile, with

                   up cycles in which chip demand outstrips the supply

                   – as we’re seeing right now – followed by down

                   cycles resulting in oversupply.

            # ⚓ HC32L110_Arm_Cortex-M0+_MCU_is_available_in_a_tiny_1.59_x

              1.436_mm_CSP16_package_–_CNX_Software⠀⇛

                   The microcontroller seems to have been released in

                   2020, and there’s plenty of documentation on the

                   product page. You’ll also find the software

                   development tools, and IAR Embedded and Arm Keil

                   MDK are the recommended/supported IDEs for the

                   microcontroller. Everything is in Chinese, but this

                   may change soon if LilyGO releases the board for

                   the “overseas market”.

            # ⚓ AMD_Completes_Acquisition_of_Xilinx⠀⇛

                   AMD (NASDAQ: AMD) today announced the completion of

                   its acquisition of Xilinx in an all-stock

                   transaction. The acquisition, originally announced

                   on October 27, 2020, creates the industry’s high-

                   performance and adaptive computing leader with

                   significantly expanded scale and the strongest

                   portfolio of leadership computing, graphics and

                   adaptive SoC products. AMD expects the acquisition

                   to be accretive to non-GAAP margins, non-GAAP EPS

                   and free cash flow generation in the first year.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ New_Campaign_Calls_On_Biden_and_Becerra_to_‘Make_Meds

              Affordable’⠀⇛

                   “The choice is clear—it’s our communities or Big

                   Pharma.”

                   “No one should have to choose between buying

                   groceries and paying for medications they need to

                   survive.”

            # ⚓ WHO_Says_Covid_Still_Killing_‘Far,_Far_Too_Many’_as_Pharma

              Hoards_Vaccine_Tech⠀⇛

                   Experts from the World Health Organization said

                   Wednesday that global coronavirus deaths remain

                   stunningly high two years into the pandemic as

                   highly contagious variants—including Omicron and

                   its relative—continue to circulate and possible new

                   mutations loom.

                   “At this point in the pandemic, when we have tools

                   that can save people’s lives, this is far, far too

                   many.”

            # ⚓ Global_Youth_Demand_EU,_UK_‘Unconditionally’_Back_Vaccine

              Patent_Waiver⠀⇛

                   Dozens of youth-led advocacy groups from around the

                   world published an open letter Wednesday urging the

                   European Union, the United Kingdom, Norway, and

                   Switzerland to immediately end their opposition to

                   a proposed patent waiver for coronavirus vaccines,

                   which still remain out of reach for billions of

                   people in poor countries.

                   “Publicly funded vaccines should not be used to

                   make pharmaceutical giants richer.”

            # ⚓ The_Benefits_of_Getting_the_Covid_Vaccine_as_a_Pregnant

              Black_Woman⠀⇛

                   I found out that I was pregnant in the summer of

                   2020 when most of the country was still in pandemic

                   lockdown and racial justice protesters righteously

                   filled the streets to exclaim that Black lives

                   matter. It was a summer of nationwide anxiety and

                   reckoning that touched everyone in different ways.

            # ⚓ If_Inequalities_Persist,_Africa_May_Not_Reach_70%

              Vaccination_Until_Late_2024⠀⇛

            # ⚓ Many_Immunocompromised_People_Feel_Left_Behind_as_US_Lifts

              Pandemic_Measures⠀⇛

            # ⚓ Back_to_Normal?_Many_Immunocompromised_People_Feel_Left

              Behind_as_U.S._Lifts_Pandemic_Measures⠀⇛

                   As U.S. health guidelines start to loosen as COVID-

                   19 cases fall from record-high levels of infection,

                   we look at how there there are still millions of

                   immunocompromised people who face acute risk of

                   illness and feel they have received little to no

                   guidance on how to stay safe in a prolonged COVID-

                   19 world. Pulitzer Prize-winning science writer Ed

                   Yong of The Atlantic spoke to immunocompromised

                   people for his new report and says, “While a lot of

                   the world opens up, their world shuts down, and

                   they feel left behind and abandoned by the

                   government, by their friends, by their workplaces.”

                   Yong notes immunocompromised people “want their

                   lives back, too,” but are just asking for

                   structural solutions to help keep them and non-

                   immunocompromised people safe.

            # ⚓ Bald_eagles_show_signs_of_widespread_lead_poisoning⠀⇛

                   The study, which was published Thursday in the

                   journal Science, evaluated eagles in 38 states,

                   testing their bones, feathers, livers and blood for

                   lead. Researchers found that 46 percent of bald

                   eagles and 47 percent of golden eagles had chronic

                   lead poisoning.

            # ⚓ Lead_contamination_found_in_Philadelphia_schools’_water:

              Report⠀⇛

                   An environmental group said Philadelphia’s school

                   system needs to re-examine and rework its water

                   pipes after a study found major lead contamination

                   in school buildings.

                   The report, which was released by the PennPIRG

                   Education Fund, the PennEnvironment Research &

                   Policy Center and the Black Church Center for

                   Justice and Equality, found that 61% of outlets

                   tested across 65 schools were tainted with lead.

            # ⚓ Extreme_Drought_Is_Crashing_Food_Production_Whether_Russia

              Invades_or_Not⠀⇛

                   Ukraine, a major grain exporter, has also been

                   walloped by droughts in recent years—another

                   climate story with international consequences that

                   has been relatively under-covered. The country has

                   long ranked among the most productive agricultural

                   areas on Earth—under the old Soviet Union, it was

                   the nation’s breadbasket—but climate change is

                   dramatically decreasing output and, by extension,

                   threatening the stability of food prices around the

                   world. A report from the Atlantic Council last year

                   emphasized the impacts of drought on Ukraine’s

                   grain exports, noting that they had “fallen sharply

                   year-on-year during the current season due to

                   smaller harvests caused by severe drought

                   conditions.” When an agricultural power as

                   important as Ukraine suddenly starts producing and

                   exporting much less food, it is a recipe for social

                   dislocation, human suffering, and political unrest,

                   both inside the country and beyond. Less production

                   translates into higher prices. The price of food is

                   something people everywhere care about, which makes

                   it something journalists need to be talking about.

            # ⚓ Why_Doesn’t_Healthcare_Improve_Health?⠀⇛

                   However, I keep being surprised by intelligent and

                   scientifically minded people outright refusing to

                   hear the evidence against medicine being useful.

                   That’s not to say evidence against any particular

                   therapy. There are many things that obviously work,

                   such as emergency intervention for losing a limb in

                   a car crash, where “almost certain death” is the

                   clear outcome. There are many things that obviously

                   work from a statistical perspective, such as

                   vaccination against diseases such as covid, hep A &

                   B, polio, HPV, yellow fever, rabies, and the like.

                   There are also many things that seem to work, with

                   good mechanistic evidence and promising studies,

                   such as PRP for various forms of soft-tissue

                   injury, or prophylactic therapy for HIV.

                   But this therapy-specific evidence is only more

                   damming when viewed in the context of broader

                   findings against medicine. Robin Hanson has written

                   on this ad-nauseam, so I will let him do most of

                   the talking.

      o § Integrity/Availability⠀➾

            # ⚓ Scientists_Warn_That_New_AI-Generated_Faces_Are_Seen_As

              More_Trustworthy_Than_Real_Ones⠀⇛

                   As if the possibility that AI might already be

                   conscious wasn’t creepy enough, researchers have

                   announced that AI-generated faces have become so

                   sophisticated that many people think they’re more

                   trustworthy than actual humans.

                   A pair of researchers discovered that a neural

                   network dubbed StyleGAN2 is capable of creating

                   faces indistinguishable from the real thing,

                   according to a press release from Lancaster

                   University. In fact, in a jarring twist,

                   participants seemed to find AI-generated faces more

                   trustworthy than the faces of actual people.

            # § Proprietary⠀➾

                  # ⚓ Russian_‘Minecraft_bomb_plot’_teen_jailed_for_five

                    years⠀⇛

                  # § Security⠀➾

                        # ⚓ VMware_patches_critical_guest-to-host

                          vulnerabilities [Ed: The security_problem_is

                          VMware,_not_Linux]⠀⇛

                               In an advisory this week, VMware

                               alerted users to guest-to-host

                               vulnerabilities in the XHCI and UHCI

                               USB controllers in its ESXi hypervisor,

                               plus an important flaw fixed in NSX

                               Data Center for vSphere.

                               In all, five vulnerabilities were

                               discovered in VMware’s ESXi,

                               Workstation, Cloud Foundation (ESXi),

                               and Fusion during the Tianfu Cup 2021,

                               a Chinese vulnerability competition, by

                               the country’s Kunlun Lab. Bugs that

                               Kunlun discovered were disclosed

                               privately to VMware – though last year

                               China passed a new law ordering

                               security researchers to reveal findings

                               to the country’s Ministry of Public

                               Security at least two days before

                               anyone else.

                               The vendor said it hadn’t seen any

                               evidence the competition’s findings had

                               been exploited in the wild. Patches

                               have been issued, now it’s up to admins

                               to schedule them. The vulnerabilities

                               range from use-after-free() and double-

                               fetch flaws that can be exploited to

                               execute code on the host, to an old-

                               fashioned denial of service (DoS).

                        # § Privacy/Surveillance⠀➾

                              # ⚓ Head_of_Interior_Ministry_IT_center

                                resigns_over_loss_of_data_device⠀⇛

                                     An internal investigation

                                     concluded that the removable

                                     device in question had been

                                     destroyed, however the

                                     destruction of the device had not

                                     been properly documented. The

                                     device was destroyed at least

                                     four years ago.

                                     Stored on the device were

                                     archival copies of scans of

                                     historical documents involving

                                     family-related events. The

                                     disappearance of the device was

                                     discovered when a scanned file in

                                     the Population Register could not

                                     be accessed and needed to be

                                     replaced with an archived copy.

                                     The device containing the copies,

                                     however, could not be found.

                              # ⚓ Majority_of_EU_states_want_EU-wide

                                blanket_communications_data_retention⠀⇛

                                     While the new German government

                                     has come out against

                                     indiscriminate data retention,

                                     the majority of EU governments

                                     have other goals. A diplomatic

                                     report to the German Foreign

                                     Office, published today by the

                                     news portal Netzpolitik.org,

                                     summarises the wishes and plans

                                     of EU governments on the issue of

                                     data retention. The EU Commission

                                     wants to take action following a

                                     pending decision by the European

                                     Court of Justice.

                              # ⚓ Rights_Groups_Urge_Crack_Down_on_US

                                Prison_Surveillance_Technology⠀⇛

                                     Dozens of rights groups are

                                     demanding a crackdown on an

                                     artificial intelligence system

                                     used to eavesdrop on U.S.

                                     prisoners’ phone calls, after a

                                     Thomson Reuters Foundation

                                     investigation highlighted the

                                     risk of rights violations.

                                     Documents from eight states

                                     showed prison and jail

                                     authorities were using

                                     surveillance software called

                                     Verus, which scans for key words

                                     and leverages Amazon’s voice-to-

                                     text transcription service, to

                                     monitor prisoners’ phone calls.

                                     California-based LEO

                                     Technologies, which operates

                                     Verus, says it has scanned close

                                     to 300 million minutes of calls

                                     going in and out of prisons and

                                     jails in the United States,

                                     describing the tool as a way to

                                     fight crime and help keep inmates

                                     safe.

                              # § Confidentiality⠀➾

                                    # ⚓ Off-The-Record_Messaging_part_1:

                                      the_problem_with_PGP⠀⇛

                                           This is a 4 part series

                                           about Off-The-Record

                                           Messaging (OTR), a

                                           cryptographic messaging

                                           protocol that protects its

                                           users’ communications even

                                           if they get [cracked].

                                    # ⚓ Off-The-Record_Messaging_part_2:

                                      deniability_and_forward_secrecy⠀⇛

                                           This is part 2 of a 4 part

                                           series about Off-The-Record

                                           Messaging (OTR), a

                                           cryptographic messaging

                                           protocol that protects its

                                           users’ communications even

                                           if they get hacked. In part

                                           1 we looked at problems

                                           with common encrypted

                                           messaging protocols, such

                                           as PGP. We also considered

                                           two desirable properties

                                           for messaging protocols to

                                           have: confidentiality and

                                           authenticity. In this post

                                           (part 2) we’re going to

                                           look at two more important

                                           properties – deniability

                                           and forward secrecy – and

                                           see that many protocols

                                           fail to achieve them. We’ll

                                           then be ready to see how

                                           OTR works and how it

                                           provides each of

                                           confidentiality,

                                           authenticity, deniability

                                           and forward secrecy in

                                           parts 3 and 4.

                                    # ⚓ Off-The-Record_Messaging_part_3:

                                      how_OTR_works⠀⇛

                                           This is part 3 of a 4 part

                                           series about Off-The-Record

                                           Messaging (OTR), a

                                           cryptographic messaging

                                           protocol that protects its

                                           users’ communications even

                                           if they get hacked. In

                                           parts 1 and 2 we looked at

                                           problems with common

                                           encrypted messaging

                                           protocols, such as PGP. We

                                           considered four desirable

                                           properties for messaging

                                           protocols to have:

                                           confidentiality,

                                           authenticity, deniability,

                                           and forward secrecy. In

                                           this post (part 3) we’ll

                                           see how OTR works and how

                                           it provides each of these

                                           properties, and then in

                                           part 4 we’ll delve into

                                           some of OTR’s key insights.

                                    # ⚓ Off-The-Record_Messaging_part_4:

                                      key_insights⠀⇛

                                           This is the final part in a

                                           4 part series about Off-

                                           The-Record Messaging (OTR),

                                           a cryptographic messaging

                                           protocol that protects its

                                           users’ communications even

                                           if they get hacked. In

                                           parts 1 and 2 we looked at

                                           problems with common

                                           encrypted messaging

                                           protocols, such as PGP. We

                                           considered four desirable

                                           properties of encrypted

                                           messaging protocols:

                                           confidentiality,

                                           authenticity, deniability,

                                           and forward secrecy. In

                                           part 3 we saw how OTR works

                                           and how it provides each of

                                           these properties, and in

                                           this final part we’ll delve

                                           into some of the protocol’s

                                           key insights.

      o § Defence/Aggression⠀➾

            # ⚓ Numb_to_the_Real_Threats:_Why_are_We_Risking_Nuclear_War

              Instead_of_Striving_for_Peace?⠀⇛

                   Meanwhile, tensions continue to mount at the

                   Ukraine-Russia border, as Putin moves more

                   armaments and fleets around and the US flies its

                   elite 82nd Airborne Division into standby mode in

                   Poland, part of 3,000 US troops now deployed to the

                   region.

                   All of this has sent US nuclear hawks, sounding

                   more and more like General ‘Buck’ Turgidson from

                   Dr. Strangelove, chafing at the bit to justify the

                   further escalation and acceleration of the so-

                   called modernization of the entire US nuclear

                   weapons complex.

            # ⚓ Conspicuous_Destruction:_Three_Generations_of_the_Military-

              Industrial_Complex⠀⇛

                   America’s war in Vietnam was waged during the Cold

                   War in the context of what was then known as the

                   domino theory and the idea of “containing”

                   communism. Iraq and Afghanistan were part of the

                   Global War on Terror, a post-Cold War event in

                   which “radical Islamic terrorism” became the

                   substitute for communism. Even so, those wars

                   should be treated as a single strand of history, a

                   60-year war, if you will, for one reason alone: the

                   explanatory power of such a concept.

                   For me, because of President Dwight D. Eisenhower’s

                   farewell address to the nation in January 1961,

                   that year is the obvious starting point for what

                   retired Army colonel and historian Andrew Bacevich

                   recently termed America’s Very Long War (VLW). In

                   that televised speech, Ike warned of the emergence

                   of a military-industrial complex of immense

                   strength that could someday threaten American

                   democracy itself. I’ve chosen 2021 as the VLW’s

                   terminus point because of the disastrous end of

                   this country’s Afghan War, which even in its last

                   years cost $45 billion annually to prosecute, and

                   because of one curious reality that goes with it.

                   In the wake of the crashing and burning of that 20-

                   year war effort, the Pentagon budget leaped even

                   higher with the support of almost every

                   congressional representative of both parties as

                   Washington’s armed attention turned to China and

                   Russia.

            # ⚓ With_Its_Doomsday_Clock_at_100_Seconds_to_Midnight,_The

              Bulletin_of_the_Atomic_Scientists_Calls_for_Escalating_US

              Aggression_Against_Russia⠀⇛

                   Dropping the A-bombs

                   By the time that the scientists at the top-secret

                   Manhattan Project had developed the atomic bomb and

                   the US military had worked out the logistics for

                   deploying it, World War II was for all intents and

                   purposes over. By early May 1945, Germany had

                   unconditionally surrendered; in large part due to

                   the efforts of the Red Army defeating the Nazi

                   Wehrmacht, but at the horrific cost of 27,000,000

                   Soviet lives. The Japanese too had been defeated

                   militarily and had agreed to “unconditional

                   surrender” with the one caveat that Emperor

                   Hirohito be spared.

            # ⚓ Fascism_is_a_Fire_That_Burns_Down_the_Entire_House⠀⇛

                   Even though the other side is a minority in Canada,

                   there were still many who came out to support the

                   “Freedom Convoy.” They not only convened in parks.

                   They were everywhere. In all honesty, I haven’t

                   felt that uneasy since I lived in the States.

                   Trucks with enormous Canadian flags drove down

                   every street blaring their horns which, for some of

                   the vehicles, was deafening.

                   I had already known that organizers of this convoy

                   had a history of white supremacy and far-right

                   ideologies. However, being present amongst them, it

                   became very clear to this was not a movement, but a

                   mob. The tactics they used were classic fascist

                   bullying. Most didn’t care if people supported them

                   or their cause or were interested in learning more.

                   And most seemed more interested in intimidating

                   people. What was also striking to me is how the

                   authorities were friendly with many of them. I saw

                   some of them chatting with them in a familiar and

                   friendly manner. I’ve never seen that kind of thing

                   happen at any of the protests I’ve attended that

                   were anti-capitalist, against ecocide, antiwar or

                   for Indigenous rights.

            # ⚓ The_Avoidable_Tragedy_of_Road_Deaths⠀⇛

                   After the shootings of a baby, a teenager, and two

                   police officers in New York City, Mayor Eric Adams

                   was quick to respond to the problem of gun

                   violence. He gave a speech on the subject in

                   January and laid out a comprehensive plan for

                   combating violent crime.

            # ⚓ Coalition_Warns_Trump_and_GOP_Allies_Pose_‘Unprecedented’

              Threat_to_Democracy⠀⇛

                   Donald Trump’s recent threat to unleash his

                   supporters on major U.S. cities and suggestion

                   that—if reelected—he would consider pardoning

                   January 6 insurrectionists underscore the dire need

                   to defeat the former president and his far-right

                   GOP allies, both of which represent “a clear and

                   present danger” to democracy.

                   “Little has been done to hold Trump accountable or

                   stop future presidents from similarly abusing their

                   power.”

            # ⚓ In_Face_of_US_Claims,_Moscow_Says_“There_Is_No_‘Russian

              Invasion’_of_Ukraine”⠀⇛

                   Amid global demands for urgent diplomacy to de-

                   escalate the Ukraine crisis, the Russian Ministry

                   of Foreign Affairs on Thursday rebuffed allegations

                   by the Biden administration—along with other

                   Western governments and corporate media—that Russia

                   intends to imminently invade its neighbor.

                   “Rather than invoking a global order that no longer

                   exists, the Biden administration should consider an

                   agreement that offers a path out of this mess.”

            # ⚓ Opinion_|_What_Is_Going_to_Happen_in_Ukraine?⠀⇛

                   Every day brings new noise and fury in the crisis

                   over Ukraine, mostly from Washington. But what is

                   really likely to happen?

            # ⚓ Ex-U.S._Ambassador_to_USSR:_Ukraine_Crisis_Stems_Directly

              from_Post-Cold_War_Push_to_Expand_NATO⠀⇛

                   U.S. officials are accusing Russia of sending more

                   forces to the Ukrainian border just days after

                   Moscow announced it was pulling some troops back.

                   This comes as Ukrainian authorities and Russian-

                   backed separatists are both accusing the other side

                   of violating a ceasefire in the eastern Donbas

                   region of Ukraine. For more on the history behind

                   the present crisis in Ukraine, we speak with one of

                   the last U.S. ambassadors to the Soviet Union prior

                   to the collapse of the USSR, Ambassador Jack

                   Matlock, who says the U.S.-led expansion of NATO

                   following the end of the Cold War helped lay the

                   groundwork for the current standoff over Ukraine.

                   He argues continued escalation could stoke another

                   nuclear arms race, and lays out some of the

                   parallels with the 1962 Cuban Missile Crisis.

            # ⚓ John_Pilger:_War_in_Europe_and_the_Rise_of_Raw_Propaganda⠀⇛

                   Marshall McLuhan’s prophecy that “the successor to

                   politics will be propaganda” has happened.  Raw

                   propaganda is now the rule in Western democracies,

                   especially the US and Britain.

            # ⚓ America’s_Disastrous_60-Year_War⠀⇛

                   In my lifetime of nearly 60 years, America has

                   waged five major wars, winning one decisively, then

                   throwing that victory away, while losing the other

                   four disastrously. Vietnam, Afghanistan, and Iraq,

                   as well as the Global War on Terror, were the

                   losses, of course; the Cold War being the solitary

                   win that must now be counted as a loss because its

                   promise was so quickly discarded.

            # ⚓ As_US_Renews_Support_for_Saudi_War_in_Yemen,_Civilian_Death

              Toll_Nearly_Doubles⠀⇛

                   Two parallel but very different meetings took place

                   recently — one in search of peace, the other to

                   plan more war. In Oman’s capital, Muscat, an

                   official delegation headed by Ansar Allah, met with

                   Omani and European officials to negotiate de-

                   escalation and humanitarian assistance in Yemen.

                   Meanwhile, the United States and the Saudi-led

                   Coalition held meetings to plan a ground escalation

                   in Sana’a and Hajjah province in Yemen’s southeast

                   to coincide with airstrikes against residential

                   neighborhoods in other cities throughout the north,

                   which have killed and injured dozens of people and

                   caused extensive damage to property and

                   infrastructure.

            # ⚓ War_In_Europe_And_The_Rise_Of_Raw_Propaganda⠀⇛

                   Marshall McLuhan’s prophecy that “the successor to

                   politics will be propaganda” has happened.  Raw

                   propaganda is now the rule in Western democracies,

                   especially the US and Britain.

            # ⚓ Ethiopia:_Amnesty_Accuses_Tigrayan_Forces_of_Rape_&_Murder

              in_Latest_Probe_of_War_Crimes_in_Conflict⠀⇛

                   Amnesty International is accusing Tigrayan forces

                   of deliberately killing dozens of unarmed civilians

                   and gang-raping dozens of women and girls in the

                   northern Amhara region of Ethiopia. This comes as

                   the Ethiopian government and Tigrayan rebel forces

                   remain at war, and just last year Amnesty similarly

                   accused the Ethiopian government of subjecting

                   Tigrayan women and girls to rape, gang rape, sexual

                   slavery, sexual mutilation and other forms of

                   torture. “These are deliberate attacks which

                   constitute war crimes and possibly may also

                   constitute crimes against humanity,” says Amnesty’s

                   Donatella Rovera, who led the investigation behind

                   this most recent report. While Amnesty has been

                   barred by the Ethiopian government from

                   investigating these crimes on the ground, she says

                   they have used satellite imagery to corroborate the

                   testimonies of civilians who have escaped attacks

                   by both Ethiopian government and Tigrayan rebel

                   forces that began last July.

            # ⚓ Ukraine_banking_and_defense_platforms_knocked_out_amid

              heightened_tensions_with_Russia⠀⇛

                   NetBlocks metrics confirm the loss of service to

                   multiple banking and online platforms in Ukraine,

                   in a manner consistent with a denial of service

                   attack. The incident comes amid heightened tensions

                   with neighboring Russia.

      o § Transparency/Investigative Reporting⠀➾

            # ⚓ FOIA_Lawsuit_Featuring_A_DC_Police_Whistleblower_Says_PD

              Conspired_To_Screw_Requesters_It_Didn’t_Like⠀⇛

                   It’s no secret government agencies love to screw

                   with FOIA requesters. This is especially true when

                   the responding agency doesn’t care for the

                   requester’s attitude or thinks the release of

                   information might lead to future negative reporting

                   or embarrassment.

      o § Environment⠀➾

            # ⚓ Pharmaceutical_pollution_of_the_world’s_rivers⠀⇛

                   Despite growing evidence of the deleterious effects

                   on ecological and human health, little is known

                   regarding the global occurrence of pharmaceuticals

                   in rivers. Studies assessing their occurrence are

                   available for 75 of 196 countries, with most

                   research conducted in North America and Western

                   Europe. This leaves large geographical regions

                   relatively unstudied. Here, we present the findings

                   of a global reconnaissance of pharmaceutical

                   pollution in rivers. The study monitored 1,052

                   sampling sites along 258 rivers in 104 countries of

                   all continents, thus representing the

                   pharmaceutical fingerprint of 471.4 million people.

                   We show that the presence of these contaminants in

                   surface water poses a threat to environmental and/

                   or human health in more than a quarter of the

                   studied locations globally.

            # ⚓ Climate_change_brings_thinner,_more_unstable_ice_to_the

              Great_Lakes⠀⇛

                   The lakes are also staying frozen for less time

                   each year, and the ice that does form is more

                   unstable thanks to shifting climate patterns and

                   water temperatures, said Jia Wang, a researcher

                   with the National Oceanic and Atmospheric

                   Administration’s Great Lakes Environmental Research

                   Laboratory. Average temperatures in the Great Lakes

                   region rose 2.3 degrees Fahrenheit between 1951 and

                   2017, according to NOAA, and Wang said that warm

                   water temperatures carry over from previous years,

                   creating a feedback loop that builds every winter.

                   It causes ice to form later into the next winter

                   season and leaves less time for it to build up in a

                   thick layer.

            # § Energy⠀➾

                  # ⚓ Study_Exposes_Climate_Claims_by_Big_Oil_as_Corporate

                    Propaganda⠀⇛

                         While continuing to fuel the climate

                         emergency over the past decade, oil and gas

                         majors relied on misleading messages rather

                         than actually taking action to transition to

                         clean energy, according to research released

                         Wednesday.

                         “This study confirms what observers have

                         always known about Big Oil’s climate pledges:

                         They’re all hot air.”

                  # ⚓ Texas’s_Power_Woes_Are_Just_the_Latest_Reminder_of

                    the_Danger_of_Privatization⠀⇛

                  # ⚓ As_Trudeau’s_Crackdown_Shows,_No_Protest_Will_Ever_Be

                    Worthy_Enough_for_the_Left⠀⇛

                         OTTAWA – If you were Canada’s prime minister,

                         what would you be prepared to do to enforce

                         Covid restrictions on large swaths of your

                         population? No one need ask that question any

                         longer. Now we know the answer.

                  # ⚓ Canada’s_banking_industry_will_carry_out_emergency

                    orders_to_stop_trucker_[blockade]⠀⇛

                         Canada’s banking industry says it will follow

                         through with the federal government’s

                         emergency orders targeting the trucker

                         protesters as discussions on how best to

                         implement them continue.

                         The government published details late Tuesday

                         on the requirements covering a wide range of

                         the financial industry including banks,

                         credit unions, insurance companies, portfolio

                         managers and investment counselling services.

                  # ⚓ Snoop_Dogg_Says_Death_Row_Records_Will_Be_an_NFT

                    Label⠀⇛

                         Snoop joined a devoted Clubhouse room

                         yesterday to discuss his purchase of the

                         label. “Death Row will be an NFT label,”

                         Snoop told fans. “We will be putting out

                         artists through the metaverse. Just like we

                         broke the industry when we was the first

                         independent [label] to be major, I want to be

                         the first major [label] in the metaverse.”

                         That sentiment should come as no surprise to

                         anyone who has followed Snoop Dogg over the

                         last five years. The rapper is heavily

                         invested in cryptocurrencies, the idea of the

                         metaverse, and even outed himself as the

                         person behind the wildly popular NFT

                         speculation account, Cozomo di Medici.

                  # ⚓ How_Do_NFTs_Harm_The_Environment?_The_Link

                    Explained⠀⇛

                         Non Fungible Tokens — or NFTs for short — are

                         everywhere in the [cryptocurrency] universe.

                         Everyone wants in on the trend, from

                         legendary tennis players like Serena Williams

                         and Academy Award winner Reese Witherspoon to

                         top music artists like Eminem and

                         quintessentially chill dude Tony Hawk.

                         Climate change activists are tailing the NFT

                         wave too, but for a different reason. The

                         inherent technology powering the whole NFT

                         ecosystem is blockchain, predominantly

                         Ethereum. And just like its more famous

                         creation that the world calls cryptocurrency,

                         the blockchain’s artsy side is an energy

                         guzzler too. Just how significant the impact

                         of digital art is, remains a topic of hot

                         debate.

                  # ⚓ Cryptocurrency,_NFTs_and_the_metaverse_threaten_an

                    environmental_nightmare_–_here’s_how_to_avoid_it⠀⇛

                         As concerns rise and hearings are held in the

                         US about the cryptocurrency industry’s effect

                         on the environment, it’s time to address

                         blockchain’s poor sustainability record. The

                         first port of call should be changing how

                         transactions on the blockchain operate – a

                         move which could cut its energy usage by

                         99.99%.

                         A cryptocurrency is a digital representation

                         of value that, unlike traditional money,

                         isn’t issued by any central bank or agency.

                         Cryptocurrencies are powered by blockchain

                         technology, which allows the exchange of

                         virtual coins like bitcoin and ether.

                  # ⚓ El_Salvador_leader_tells_‘boomer’_US_senators_to

                    stand_down_over_bitcoin_adoption⠀⇛

                         El Salvador’s president rebuked several U.S.

                         senators on Wednesday for introducing

                         legislation targeting the Latin American

                         country’s adoption of bitcoin as legal

                         currency, referring to the lawmakers as

                         “boomers.”

                  # ⚓ FBI_to_form_new_cryptocurrency_unit⠀⇛

                         The FBI is forming a new team dedicated to

                         cryptocurrency, according to the Department

                         of Justice (DOJ).

                         The new team will work closely with the

                         National Cryptocurrency Enforcement Team, the

                         DOJ announced Thursday.

                         Prosecutor Eun Young Choi, who has a

                         background in cyber-related crimes, will

                         serve as the National Cryptocurrency

                         Enforcement Team’s first director.

            # § Wildlife/Nature⠀➾

                  # ⚓ Humanity_Subsidizing_‘Our_Own_Extinction,’_Warns

                    Study⠀⇛

                         Releasing a new study showing that world

                         governments spend at least $1.8 trillion

                         annually to subsidize activities which worsen

                         the climate crisis, global subsidies experts

                         on Thursday said leaders must eliminate or

                         redirect the financial supports as part of an

                         ambitious Global Biodiversity Framework at an

                         upcoming summit in China.

                         “Reforming the $1.8 trillion a year of

                         subsidies that are harming the environment

                         could make an important contribution towards

                         unlocking the over $700 billion a year needed

                         to reverse nature loss by 2030.”

      o § Finance⠀➾

            # ⚓ Who_Will_Audit_the_State?⠀⇛

                   In a nutshell, here’s the way it works. The

                   Legislature writes the laws and appropriates the

                   money for the operation of the executive branch,

                   which is defined in our Constitution as the

                   governor, lieutenant governor, attorney general,

                   secretary of state, and state auditor (Article VI,

                   Section 1). Executive branch officers are charged

                   to follow the law and “keep the public records of

                   his office.” The governor is specifically charged

                   to “see that the laws are faithfully executed.”

                   Given the sheer size of government, one could

                   credibly wonder who keeps an eye on what actually

                   happens after the Legislature leaves town? And in

                   that regard, it is the legislative auditor’s office

                   that is charged with investigating and answering

                   exactly that question for our part-time citizen

                   legislators.

            # ⚓ The_Growing_Wealth_of_the_Billionaire_Class⠀⇛

                   This pandemic has had a devastating impact upon our

                   country. Over 900,000 people have died from COVID,

                   and tens of millions have been made ill. Many

                   thousands of workers have lost their lives simply

                   because they went about doing their jobs, while

                   millions of other workers have chosen to find new

                   employment paths. The education of young people,

                   from child care to graduate school, has been

                   severely disrupted. Elderly people have become

                   increasingly isolated, fearful of catching the

                   virus from grandchildren, friends or family. Mental

                   illness is on the rise, as is drug addiction,

                   alcoholism and domestic violence.

                   These are very difficult times.

            # ⚓ Thoughts_on_Inflation,_After_the_January_CPI_Report⠀⇛

                   The basis for the belief that shipping problems

                   were being fixed was both anecdotal accounts in the

                   media and also the big increases in retail

                   inventories reported for December. It seems stores

                   had ordered (and received) lots of stuff they

                   couldn’t sell. This is a context in which we might

                   normally expect prices to fall, or at least not

                   rise further.

                   That turned out not to be the case. The price index

                   for appliances rose 1.5 percent in January and is

                   now 8.5 percent above its year ago level. The index

                   for apparel rose 1.1 percent in the month putting

                   it 5.3 percent above its year ago level. And, used

                   vehicle prices rose 1.5 percent in January, and are

                   now 40.5 percent above year ago levels. So, there

                   is not much of a story of a turnaround there.

            # ⚓ For_New_York_Home_Care_Workers,_Fair_Pay_Is_Possible⠀⇛

            # ⚓ Opinion_|_Inside_the_Campaign_to_Abolish_Poverty_Wages_in

              25_States_by_2026⠀⇛

                   As the economy recovers from a global pandemic,

                   many business owners are pointing to labor

                   shortages caused by the “Great Resignation” as a

                   source of frustration.

            # ⚓ Opinion_|_Afghanistan_on_the_Brink_of_Catastrophic

              Disaster⠀⇛

                   Gay rights, women’s rights—in reality, these are a

                   nuisance to many U.S. conservatives, but purporting

                   to protect these rights on the other side of the

                   world is a great excuse to play war.

            # ⚓ ‘Cancel_It._Every_Penny’:_Poll_Shows_83%_of_Democrats_Want

              Biden_to_Nix_Student_Debt⠀⇛

                   Polling out Thursday reveals overwhelming support

                   from President Joe Biden’s party for canceling

                   student loan debt.

                   “President Biden canceling student loan debt could

                   be hugely consequential to millions of Americans

                   facing significant financial burdens amidst the

                   pain of rising costs.”

            # ⚓ Sanders_Rips_Into_Billionaires_for_Creating_“Oligarchic”

              Society_in_US⠀⇛

            # ⚓ Big_Food_Producers_Are_Profiteering_Off_Inflation_—_and

              Bragging_About_It⠀⇛

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ Honduras:_The_Political_Context_Missing_from_Corporate

              Media⠀⇛

                   However, if one were to only read the corporate

                   coverage of the issue, one would be complete

                   without the political context for what has happened

                   in Honduras since the 2009 coup. In fact, there is

                   no mention at all from the Associated Press about

                   what happened to former President Zelaya in 2009,

                   the fact that Hillary Clinton led a coup against

                   the elected leftist government which created the

                   conditions for the rise of right-wing criminals

                   like Hernández, but also directly led to the

                   assassinations of activists such as Berta Cáceres

                   and Afro-Indigenous leaders, among others.

                   Given the utter failure of the corporate,

                   mainstream media to properly frame the issue as

                   part of a broader struggle between US-backed right-

                   wing forces and the various left political

                   movements opposing them, it seems an appropriate

                   time to re-publish my piece on Honduras from 2015

                   which covers most of the critical issues.

            # ⚓ Moscow’s_package_deal_The_Russian_Foreign_Ministry’s

              response_to_Washington’s_security_proposals,_in_a_nutshell⠀⇛

                   On Thursday, February 17, the Russian Foreign

                   Ministry issued a written response to Washington’s

                   counter-proposals on security guarantees in Europe.

                   Unlike the response Moscow received from the U.S.

                   and NATO earlier this month, which wasn’t

                   officially made public (though the full text was

                   leaked to Spanish newspaper El Pais), the Russian

                   Foreign Ministry published its 10-page commentary

                   in full. Here’s what it says, in a nutshell. 

            # ⚓ The_professor_and_his_prophecies_Known_for_peddling_wild

              conspiracy_theories,_Valery_Solovey_is_now_wrapped_up_in_a

              felony_hate_speech_investigation⠀⇛

                   On Wednesday, February 16, law enforcement officers

                   raided the Moscow home of political analyst Valery

                   Solovey. Solovey and his son Pavel were then taken

                   to the Russian Investigative Committee for

                   questioning. As it turns out, Solovey is considered

                   a witness in a criminal investigation into felony

                   hate speech. Solovey and his son were released late

                   Wednesday evening after being questioned. According

                   to unofficial reports, the felony investigation is

                   connected to an anonymous Telegram account called

                   “SVR General” — allegedly, Solovey may have been

                   involved in creating content for this channel,

                   which regularly criticizes the Russian authorities.

                   Meduza recounts how Valery Solovey, a former

                   professor at Moscow’s prestigious MGIMO University,

                   became an extravagant political commentator known

                   for his colorful (and increasingly wild) conspiracy

                   theories.

            # ⚓ And_Just_Like_That:_Free_Market_Democracy!⠀⇛

                   That’s because “And Just Like That” is part of a

                   vast communist conspiracy – only capitalist. I know

                   because I obtained security-cam footage from a

                   secret “study session” the girls held at the end of

                   Season One. Here’s the transcript. And, so all you

                   commie-queers can fully comprehend the danger we

                   face, I’ve translated it into post-Soviet Marxist-

                   Leninism.

                   [Scene: corporate boardroom somewhere in

                   Manhattan’s Financial District. Affixed to back

                   wall is large flat-screen TV with sound off, tuned

                   to news channel NY1, which broadcasts weather

                   forecast. Seated at polished rainforest-wood table

                   is Charlotte York Goldenblatt. Looking pertly at

                   the screen, she turns as door opens, revealing

                   group leader Carrie Bradshaw.]

            # ⚓ Trump_Donor_John_Malone_Could_Soon_Be_Calling_Shots_at

              CNN⠀⇛

                   What will CNN become under John Malone?

            # ⚓ Russian_court_re-sentences_father_of_top_Navalny_aide_to

              three_years_in_prison⠀⇛

                   A court in Russia’s Nenets Autonomous Okrug has

                   overturned a three-year suspended sentence

                   previously handed down to Yuri Zhdanov — the 67-

                   year-old father of Alexey Navalny’s top aide Ivan

                   Zhdanov — and replaced it with time in prison. This

                   was reported by Zhdanov’s lawyer Vladimir Voronin

                   on Thursday, February 17.

            # ⚓ Russia_expels_U.S._Deputy_Ambassador_Bartle_Gorman⠀⇛

                   Russia has expelled U.S. Deputy Ambassador Bartle

                   Gorman from the country, RIA Novosti reported on

                   Thursday, February 17, citing embassy spokesperson

                   Jason Rebholz.

            # ⚓ Downhill_From_Here⠀⇛

            # ⚓ Leaked_Audio_Exposes_Amazon’s_Anti-Union_Scare_Tactics⠀⇛

                   During a mandatory anti-union meeting on Wednesday,

                   an Amazon official warned workers at the

                   corporation’s biggest New York City warehouse that

                   if they unionize, pay and conditions could become

                   worse, with salary negotiations possibly starting

                   at “minimum wage.”

                   “It’s against the law and an unfair labor practice

                   to make a threat of reprisal.”

            # ⚓ Just_6%_of_US_House_Seats_Expected_to_Be_Competitive_Thanks

              to_Rigged_Maps⠀⇛

                   In a major blow to the democratic principle that

                   lawmakers are accountable to voters who can remove

                   them from office, the vast majority of seats in the

                   U.S. House of Representatives are becoming non-

                   competitive—a trend that critics say threatens to

                   exacerbate GOP extremism as incumbents in solidly

                   red districts shift further right to fend off more

                   reactionary primary challengers.

                   Several months into the decennial redistricting

                   process, 335 congressional districts have been

                   redrawn as of Thursday. Just 27 of them are

                   considered competitive—meaning neither Democrats

                   nor Republicans have an advantage of more than five

                   points—according to FiveThirtyEight.

            # ⚓ Opinion_|_It’s_Settled_That_Israel_Is_Committing_the_Crime

              of_Apartheid—Now_What_Should_We_Do_About_It?⠀⇛

                   When Amnesty International released its report

                   “Israel’s Apartheid Against Palestinians: Cruel

                   System of Domination and Crime Against Humanity”

                   earlier the month, it was clearly part of a rapidly

                   expanding trend. Palestinian human rights

                   defenders, members of Congress and faith leaders in

                   the United States, academics, and activists of the

                   Palestinian rights movement around the world have

                   long recognized and condemned Israeli apartheid,

                   and called for accountability.

            # ⚓ Trump_Acolyte_LePage_Given_Green_Light_to_Run_for_Third

              Term_in_Maine⠀⇛

                   Former Maine Gov. Paul LePage, a far-right

                   Republican who made openly racist comments about

                   immigrants in the state and compared himself to

                   former President Donald Trump during his time in

                   office, has officially been approved to run for a

                   third term.

                   “We can’t let Paul LePage drag us backward once

                   again.”

            # ⚓ Telex_asked_Orbán_allies:_have_power_and_influence_changed

              Viktor_Orbán?⠀⇛

            # ⚓ Broadcasters_Go_Against_Big_Tech_With_Congress_Forcing

              Negotiations⠀⇛

                   The president of the National Association of

                   Broadcasters is urging Congress to pass legislation

                   that would allow broadcasters and news

                   organizations to negotiate with Big Tech platforms

                   on terms to host their content.

                   Curtis Legeyt said at an event hosted by The Media

                   Institute Tuesday that the Journalism Competition

                   and Preservation Act, sponsored by Senator Amy

                   Klobuchar, D-Minnesota, would help smaller

                   broadcasting stations get their share of the pie

                   and allow them to compete against larger players in

                   the industry.

            # ⚓ Twitter_opens_access_to_anti-abuse_tool_for_millions_of

              users⠀⇛

                   ‘Safety Mode’ temporarily blocks accounts for seven

                   days for using potentially harmful language — such

                   as insults or hateful remarks — or sending

                   repetitive and uninvited replies or mentions. The

                   ‘Safety Mode’ tool is now available in beta for

                   more users across English-speaking markets,

                   including the US, the UK, Canada, Australia,

                   Ireland and New Zealand…

            # ⚓ Christopher_Parsons_Delivers_Testimony_to_the_Standing

              Committee_on_Access_to_Information,_Privacy_and_Ethics⠀⇛

                   Citizen Lab senior research associate Dr.

                   Christopher Parsons provided the following briefing

                   on Monday, February 14, 2022 to the House of

                   Commons’ Standing Committee on Access to

                   Information, Privacy, and Ethics, regarding the

                   collection and use of mobility data by the

                   Government of Canada.

            # ⚓ Scam_Review:_Big_Tech_Bullshit⠀⇛

                   This is a post that I will probably come to regret

                   writing and publishing in the future. The reason

                   for that is simple. This post is going to make a

                   lot of former, current and potentially future co-

                   workers feel like idiots. That’s because the topic

                   for this post is scams being pushed by our friends

                   in Big Tech.

                   So it gets somewhat awkward when you realize that I

                   work in tech and plan to continue doing so for the

                   foreseeable future. It gets way more awkward if you

                   know that when it comes to tech scams / fads,

                   nobody is more susceptible to falling for this

                   stuff than people who work in tech. That’s where

                   all this stuff starts and builds momentum after

                   all. Without buy in from the tech community, almost

                   none of this garbage would exist.

                   Today we are going to briefly touch on three tech

                   fads which are actually scams and I’m going to

                   attempt to give you all a brief explanation as to

                   why they are scams. So without further adieu lets

                   get started.

            # ⚓ Islamists_Take_Advantage_of_Political_Correctness⠀⇛

                   As reported by the Organization for Security and

                   Co-operation in Europe, at least a quarter, though

                   arguably much more, of all hate crimes registered

                   in Europe in 2020 were anti-Christia—representing a

                   70 percent increase in comparison to 2019. As

                   explained by Raymond Ibrahim, Christianity is,

                   furthermore, the religion most targeted in hate

                   crimes, with Judaism at a close second.

            # ⚓ Welcoming_the_New_Zealand_Government_to_Have_I_Been_Pwned⠀⇛

                   Continuing the march forward to provide governments

                   with better access to their departments’ data

                   exposed in breaches, I’m very pleased to welcome

                   the 28th national government onto Have I Been Pwned

                   – New Zealand! They’ll join the other govs around

                   the world that have complete free access to breach

                   information impacting their gov domains and TLDs.

            # ⚓ US,_Allies_Warn_Possible_Russian_Cyberattacks_Could

              Reverberate_Globally [iophk: Windows TCO]⠀⇛

                   “It’s not hypothetical,” Monaco said, pointing to

                   the June 2017 “NotPetya” virus, engineered by

                   Russia’s military intelligence service, the GRU.

                   The virus initially targeted a Ukrainian accounting

                   website but went on to hobble companies around the

                   world, including Danish shipping giant Maersk and

                   U.S.-based FedyEx.

                   “Companies of any size and of all sizes would be

                   foolish not to be preparing right now,” Monaco

                   said. “They need to be shields-up and really be on

                   the most heightened level of alert.”

            # ⚓ As_Russia_amasses_troops,_Ukraine_battles_another_threat:

              Digital_warfare [iophk: Windows TCO]⠀⇛

                   A new wave of cyber operations began in earnest

                   Jan. 13, when computers in Ukraine started showing

                   signs of the first serious hacking campaign since

                   Russia’s troop buildup. Computers at dozens of

                   Ukrainian organizations, including nonprofit

                   groups, information technology companies and more

                   than 70 government websites, were infected with

                   malicious software that appeared to be ransomware,

                   a common criminal tactic to lock up computers.

            # ⚓ US_says_Russian_[crackers]_targeted_defense_contractors

              [iophk: Windows TCO]⠀⇛

                   The U.S. intelligence community says that Russian-

                   sponsored actors have been targeting defense

                   contractors for at least the past two years and in

                   some cases have gained access to sensitive

                   information.

                   In an alert released Wednesday, the FBI, National

                   Security Agency (NSA) and Cybersecurity and

                   Infrastructure Security Agency (CISA) said they had

                   observed “regular targeting” of contractors from at

                   least January 2020 through this month.

      o § Misinformation/Disinformation⠀➾

            # ⚓ Spotify_reportedly_paid_$200_million_for_Joe_Rogan’s

              podcast⠀⇛

                   Spotify reportedly paid Joe Rogan at least $200

                   million to commit to podcasting on the platform

                   exclusively for three and a half years, according

                   to a New York Times report. That number, while

                   astronomical, is double what had previously been

                   reported in The Wall Street Journal as Rogan’s deal

                   price — $100 million — and has continued to be used

                   widely in the media without correction from

                   Spotify’s team.

                   This news comes after a volatile month for the

                   audio company and one in which musicians,

                   podcasters, employees, and the medical community

                   scrutinized the company’s work with the

                   controversial podcaster. In January, a group of

                   medical community members penned a letter to the

                   company asking it to remove a Rogan episode they

                   said peddled COVID-19 misinformation. Musician Neil

                   Young read that letter and subsequently pulled his

                   catalog from the platform in response.

            # ⚓ Twitter_is_bringing_pinned_DMs_to_everyone⠀⇛

                   Twitter is now rolling out pinned DMs, the company

                   announced Thursday. The feature was previously only

                   available to Twitter Blue subscribers, but it’s now

                   coming to everyone on Android, iOS, and the web.

                   The feature doesn’t seem to be fully rolled out

                   just yet. I have access to it on the iOS app, but

                   not on Twitter’s web app. On the iOS app, you can

                   swipe to the side on a conversation to reveal a

                   pin, and if you tap that, the conversation will be

                   moved to a new “Pinned conversations” section at

                   the top of your DM inbox.

      o § Censorship/Free Speech⠀➾

            # ⚓ Whatever_Problem_EARN_IT_Is_Trying_To_Solve,_It_Doesn’t⠀⇛

                   I’ve already talked about the potential 1st

                   Amendment problems with the EARN IT Act and the

                   potential 4th Amendment problems with it as well.

                   But a recent post by Riana Pfefferkorn at Stanford

                   raises an even bigger issue in all of this: what

                   actual problem is EARN IT trying to solve?

            # ⚓ Blackburn_&_Blumenthal_Introduce_Terrible,_Dangerous_Bill

              To_Make_Sure_Children_Are_Constantly_Surveilled_Online⠀⇛

                   Senator Richard Blumenthal is apparently a

                   bottomless well of terrible internet regulation

                   ideas. His latest is yet another “for the children”

                   bill that will put children in serious jeopardy.

                   This time he’s teamed up with the even worse

                   Senator Marsha Blackburn to introduce the Kids

                   Online Safety Act, which as the name suggests is

                   full of a bunch of overbearing, dangerous nonsense

                   that will not protect children at all, but will

                   make them significantly less safe while giving

                   clueless, authoritarian parents much more power to

                   spy on their kids.

            # ⚓ Senator_Blumenthal:_Dismissing_All_Critics_Of_EARN_IT_As

              ‘Big_Tech_Lobbyists’_Shows_Your_Unwillingness_To_Recognize

              The_Massive_Problems_In_Your_Bill⠀⇛

                   In the past, whenever Senator Richard Blumenthal

                   has been called out for his many terrible

                   legislative ideas regarding regulating technology

                   and the internet, he has a habit of dismissing all

                   of the concerns by claiming the complaints are only

                   coming from “big tech lobbyists.” He did this a few

                   years ago with FOSTA, which has since proven to be

                   exactly the disaster many of us warned Senator

                   Blumenthal about at the time. This time around,

                   he’s going straight to the same playbook again, and

                   it’s good to see that he’s getting some pushback.

                   Nathalie Maréchal, from Ranking Digital Rights has

                   published a great piece over at Tech Policy Press:

                   No, Senator Blumenthal, I am not a Big Tech

                   Lobbyist.

            # ⚓ Opinion_|_The_Story_of_How—Many_Years_Ago—I_Unbanned_Maus⠀⇛

                   Sometimes life has a way of making you realize

                   things about yourself. Recently, I discovered that

                   an urge of mine, almost four decades old, had been

                   the very opposite of that of a rural Tennessee

                   school board this January. In another life, I

                   played a role in what could be thought of as the

                   unbanning of the graphic novel Maus.

            # ⚓ Sundance_Film_Festival_Under_Fire_For_‘Islamophobia’⠀⇛

                   The film, which The Wrap called a “hot-button

                   documentary,” is called Jihad Rehab. The 2022

                   Sundance program says that it “film focuses on

                   several men — detained in Guantanamo for years

                   without charge by the United States — after they

                   are placed in what’s billed as the world’s first

                   rehabilitation center for extremists.” The reminder

                   that they were “detained without charge,” with no

                   mention of 9/11 or the global jihad, is the first

                   tipoff that this is not exactly a “right-wing”

                   presentation, which is how it got to Sundance in

                   the first place. But that didn’t stop it from

                   running afoul of the Thought Police.

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

            # ⚓ Tactical_acquittal⠀⇛

                   Holding a citizen accountable by law in a foreign

                   country is an upbeat challenge. WikiLeaks founder

                   Julian Assange is a case in point. Hussain is a

                   proclaimed fugitive since 2015 from the anti-

                   terrorism courts in Pakistan on the charges of

                   murder, targeted killings, treason, inciting

                   violence and hate speeches. But the prosecution

                   couldn’t carry the case under British law. This

                   necessitates a legal valve, which should be

                   analysed at the outset whether framing of charges

                   will stand in a foreign court of law or not. No

                   point in merely playing to the gallery.

            # ⚓ The_Belmarsh_Tribunal_NYC:_Shut_down_Guantanamo._Free

              Assange_—_February_25⠀⇛

                   Classified documents leaked by Chelsea Manning and

                   published by Wikileaks in 2011 revealed the grim

                   contours of the US regime of detention and torture

                   at Guantánamo. Many prisoners — among them a

                   journalist from Al Jazeera — were held for years

                   despite officially posing no threat to the US. Many

                   developed severe mental health problems as a result

                   of their treatment. Some committed suicide.

                   But, today, it is not the perpetrators who face

                   persecution, but the whistleblowers. In April this

                   year, Julian Assange will enter his third year of

                   detention at HMP Belmarsh — a maximum-security

                   prison, sometimes referred to as “Britain’s

                   Guantánamo”, that was infamously used to detain

                   terrorist suspects without trial — as he seeks to

                   appeal a court decision to extradite him to the US.

                   That is why the Progressive International is

                   **bringing the Belmarsh Tribunal to the belly of

                   the beast. On 25 February 2022, at the People’s

                   Forum in New York City, we will convene legal

                   experts, UN representatives, whistleblowers,

                   journalists, and many others to investigate and

                   expose the crimes of the so-called War on Terror,

                   to seek justice for its victims, and to demand the

                   closure of the concentration camp at Guantánamo

                   Bay.

      o § Civil Rights/Policing⠀➾

            # ⚓ Mexican_Forces_Evict_Indigenous_Activists_Who_Took_Over

              Water_Bottling_Plant⠀⇛

            # ⚓ Free_Crack_Pipes?_Time_to_Pardon_Tommy_Chong⠀⇛

                   While “harm reduction” is the stated goal of  that

                   federal program, the Biden administration continues

                   to ignore the vast harms caused by federal drug

                   prohibitions, despite record numbers of deaths from

                   drug overdoses last year.

                   The latest federal drug war farce should be a

                   reminder of one of the biggest drug war publicity

                   stunts of this century. On the eve of George W.

                   Bush’s invasion of Iraq, Attorney General John

                   Ashcroft announced the most decisive federal attack

                   ever made on pipes and bowls often used for smoking

                   marijuana, tobacco, and other substances. Ashcroft

                   bewailed, “The illegal drug paraphernalia industry

                   has invaded the homes of families across the

                   country without their knowledge.” Ashcroft did not

                   offer any evidence that pipe sellers, unlike

                   government agents, were planting evidence in

                   people’s homes.

            # ⚓ Time_for_a_Show_Trial⠀⇛

                   The Washington Post reported that Rep. Adam Schiff

                   (D-CA) said that the House’s Select Committee

                   on January 6th will hold public hearings to “tell

                   the whole story” about the attack. “I think we will

                   want [public hearings] to tell the whole story,”

                   Schiff said. “Security at the Capitol, the

                   intelligence leading up to the attacks, lack of

                   intelligence, the role of social media, the former

                   President’s role, the role of those around him, and

                   tell it in an era fashion so the public knows

                   exactly what’s going on.”

                   Evidence is mounting that the attack on the U.S.

                   Capitol on January 6th was not an isolated, impulse

                   act by well-meaning, if uninformed, citizens.  No,

                   January 6th was but one aspect of an incoherent,

                   poorly planned and even more poorly executed coup

                   d’état.  It failed and Joe Biden became president.

            # ⚓ The_Josh_Hawley_Mug:_It_Makes_Him_An_Asshole,_But_Shouldn’t

              Make_Him_A_Copyright_Infringer⠀⇛

                   Josh Hawley, the waifish fascist Senator from

                   Missouri, has made it onto our pages several times

                   in the past. When he’s not advocating breaking up

                   Twitter because he doesn’t like how a private

                   company is run (fascist), or breaking up lots of

                   other companies he simply disagrees with (fascist),

                   you can typically find him pretending the First

                   Amendment works the exact opposite of how it does

                   in reality or explaining in published books and

                   newspaper pages how much he’s been silenced and

                   canceled. It might all look very stupid on its

                   face, but it isn’t. It’s actually quite

                   diabolical.  

            # ⚓ California_Sheriff,_US_DOJ_Sued_For_Seizures_Of_Cash

              Generated_By_Legal_Pot_Businesses⠀⇛

                   A lawsuit filed against both California and federal

                   law enforcement agencies claims the San Bernardino

                   County Sheriff’s Department is exploiting the

                   disagreement between state and federal marijuana

                   laws to stop and seize cash being transported from

                   legal marijuana dispensaries.

            # ⚓ Opinion_|_It’s_Time_to_Get_Loud_on_Abortion_Rights⠀⇛

                   Earlier this year, a small group of women and I

                   gathered to post artwork around Washington, D.C. We

                   were celebrating the 49th anniversary of Roe v.

                   Wade, which protected women’s constitutional access

                   to abortion.

            # ⚓ 55+_US_Prosecutors_Join_in_‘Inexorable_Conclusion’_That

              Death_Penalty_Must_End⠀⇛

                   A bipartisan group of 56 elected prosecutors came

                   together in a new joint statement calling for “a

                   more fair, just, and accountable criminal legal

                   system” in the U.S. that includes bringing a

                   permanent and complete end to the death penalty.

                   “It is time to work together toward systemic

                   changes that will bring about the elimination of

                   the death penalty nationwide.”

            # ⚓ Opinion_|_San_Francisco_Rape_Kit_Controversy_Will_Have

              Chilling_Repercussions⠀⇛

                   This week, San Francisco District Attorney Chesa

                   Boudin came forward with a stunning claim: That the

                   San Francisco Police Department’s crime lab uses

                   DNA evidence obtained from rape kits and entered

                   into a DNA database to try to identify suspects in

                   other crimes.

            # ⚓ Amazon_Warehouse_Workers_Want_to_Feel_Safe⠀⇛

                   Edwardsville, Ill.—On December 10, a tornado

                   flattened an Edwardsville, Ill., Amazon

                   distribution center building, killing Etheria S.

                   Hebb and five others. Arnetra Rhodes, 18, didn’t

                   learn Etheria was her cousin until her mother and

                   family began to mourn. After Rhodes found out what

                   happened, she couldn’t shake the feeling that

                   Etheria should still be alive. “It would’ve been

                   different if they let them know what’s going on.… I

                   know that they heard the sirens.” Rhodes told me.

            # ⚓ Opinion_|_Africa-EU_Summit_Will_Not_Be_Successful_Unless_It

              Addresses_the_Abhorrent_Neo-Colonialism_of_Past_and_Present⠀⇛

                   The climate crisis does not exist in a vacuum. It

                   cannot be solely seen through a physical and

                   environmental lens as it has been both created by a

                   particular group of people, and has been impacting

                   certain communities disproportionately.

            # ⚓ Amir_Locke’s_funeral:_Mom_says_son_was_‘executed,’_Sharpton

              delivers_powerful_eulogy⠀⇛

                   The Rev. Al Sharpton delivered a powerful and

                   emotional eulogy at Thursday’s funeral for Amir

                   Locke, a 22-year-old who was shot and killed by

                   Minneapolis police officers executing a “no-knock”

                   search warrant.

                   Locke, who was fatally shot on Feb. 2, was not

                   named in the “no-knock” warrant.

            # ⚓ No-Knock_Warrants:_What_Are_They_and_How_Are_They_Used?⠀⇛

                   “They’re not functionally doing anything to keep

                   people safer or reduce crime. They are, in fact,

                   doing more harm than good by allowing law

                   enforcement to largely enter people’s homes with

                   impunity, without any consequence, with little

                   oversight, and with little reason or rationale that

                   actually has any impact on reducing harm,” says

                   Katie Ryan, chief of staff for Campaign Zero, an

                   organization focused on reducing police violence,

                   including putting an end to no-knock raids.

                   The practice has received renewed attention in

                   recent years, especially after a 2014 incident in

                   which police entered a Georgia home with a no-knock

                   warrant and threw a grenade into a 19-month-old’s

                   crib. The grenade left the toddler in an induced

                   coma with severe burns. The suspect and the drugs

                   they were searching for were not found in the home.

            # ⚓ Employers’_uphill_fight⠀⇛

                   Yes, but: 61% of teleworkers are working from home

                   because they’re choosing to, per a new Pew Research

                   study. Just 38% are home because their workplaces

                   are closed or unavailable.

                   There’s a disconnect between leadership and rank-

                   and-file workers. Executives are three times as

                   likely as employees to want to return to work, per

                   a recent Future Forum survey.

            # ⚓ Court_frees_brother_who_confessed_to_killing_social_media

              star_Qandeel_Baloch⠀⇛

                   The brother of murdered social media star Qandeel

                   Baloch has been freed by a Pakistan appeals court,

                   three years after he was convicted of killing her

                   for “bringing dishonor” to the family.

                   Baloch’s murder in 2016 sparked a national outcry

                   and promoted changes in the country’s so-called

                   ‘honor killing’ laws.

                   Waseem Baloch’s lawyer, Sardar Mehmood, confirmed

                   the acquittal with CNN Tuesday but did not provide

                   further details. A court order has not yet been

                   made public.

            # ⚓ Christian_killed_by_a_group_of_Muslims_in_Lahore⠀⇛

                   Akhtar Bhatti, Pervez’s uncle, told AsiaNews that

                   the next day a group of 150 to 200 Muslims came to

                   the Christian area of ​​Lahore, some with guns, and

                   started insulting and beating people, including

                   Pervez.

                   Despite his uncle’s attempts to stop the beating,

                   the attackers dragged Pervez away to torture him

                   with sticks and bricks, threatening that they would

                   not leave him alive.

            # ⚓ Syrian_wanted_to_kill_sister_in_Germany:_“If_I_can’t_kill

              my_sister_today,_I’ll_do_it_tomorrow._If_I_can’t_do_it

              tomorrow,_I’ll_do_it_the_day_after_tomorrow…”.⠀⇛

                   The slender, small defendant (18 years, 1.60

                   metres) who is said to have said these words hides

                   his face behind a briefcase. Since Friday, he has

                   been standing trial for attempted murder at the

                   Dortmund Regional Court.

            # ⚓ Police_Destroy_FOUR_MILLION_Bottles_of_Beer⠀⇛

                   Concerned about the government overstepping its

                   bounds and asserting increasing control over

                   aspects of life it has no business interfering

                   with? You should be. And in many parts of the

                   world, governments are providing daily object

                   lessons in what happens when citizens allow self-

                   serving, power-mad officials to arrogate too much

                   power to themselves and overstep all rational

                   restraints. In Nigeria on Wednesday, for example, a

                   state government destroyed nearly four million

                   bottles of beer. Four million bottles of beer,

                   gone, sacrificed to fanaticism and the brutal

                   arrogation of power by unfeeling elites.

            # ⚓ Union_Busting:_What_Are_Some_of_the_Most_Common_Tactics

              Employers_Use?⠀⇛

                   The blowback to Starbucks’ actions isn’t surprising

                   when you look at the numbers. A 2021 Gallup poll

                   puts public approval of unions at 68%, and for

                   people aged 18-34, the approval rating sits even

                   higher at 77%. In the past year alone, graduate

                   student workers all over the country have launched

                   union drives, won union recognition, or secured

                   contracts. Tech workers at Google, congressional

                   staffers on Capitol Hill, ACLU employees, and the

                   staff at several major museums have all waged their

                   own union campaigns. Even social media influencers

                   now have the option to join the union wave.

                   But no matter how popular the public perception of

                   unions might be, winning union recognition remains

                   an uphill battle. Employers determined to prevent

                   their workers from successfully unionizing

                   typically rely on a series of anti-union tactics

                   often referred to as “union busting.”

                   Teen Vogue spoke with Mindy Isser, a Philadelphia-

                   based labor organizer, and Dr. John Logan, the

                   department chair of labor and employment studies at

                   San Francisco State University, to cover some of

                   the basic union-busting tactics and tools employers

                   use to crush unions.

            # ⚓ A_Student_Sleuth_Found_Evidence_that_Our_University

              Practices_Reverse_[sic]_Racism._Here’s_Why_I_Advised_Him_Not

              to_Publish_It⠀⇛

                   Daniel explained that he and his friend wanted to

                   find a measure of academic achievement that they

                   could track statistically. A student’s GPA is not

                   public information, but the Dean’s List is; so they

                   were able to use that as a discrete variable—Dean’s

                   List, yes or no—as a rough proxy for achievement.

                   Daniel explained to me that it would have been

                   better to use a continuous variable (like GPA), but

                   he and his friend had to work with what they had.

                   Daniel explained that he and his friend had

                   performed various kinds of statistical analysis on

                   the data, and had concluded that admission to the

                   honors program was closely related to Dean’s List

                   status within certain groups. However, there were

                   large differences in acceptance rates across those

                   groups. Overall, he told me, the factor that

                   explained the most variance in admissions outcomes

                   was (as he’d suspected) the race or ethnicity of

                   the applicant. The patterns were quite stark.

                   African Americans who weren’t on the Dean’s List

                   had a better overall chance of being admitted to

                   the honors program than whites or Asians who were

                   on the Dean’s List.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ Cloud_Innovation_Ltd_loses_appeal_against_AFRINIC⠀⇛

                   TL;DR — AFRINIC has won. A dramatic legal battle

                   that started in March of last year, can be probably

                   said to be concluded now.

            # ⚓ Who_is_squatting_IPv4_addresses?⠀⇛

                   For the case of this post, I will define IP address

                   squatting as “using IP addresses that are not

                   RFC1918 defined and not your unicast space issued

                   by a RIR”. The first thing that instantly comes to

                   mind is Cloudflare obtained the addresses 1.1.1.1

                   and 1.0.0.1 to run a DNS resolver on, but had to

                   fight back against a huge amount of network and

                   home routers squatting on those addresses

                   internally (I do also wonder if the last unicast /

                   24 block has similar issues)

                   This problem is not that surprising though, your

                   local friendly sysadmin might be able to tell you

                   of a story where they have caught their colleagues,

                   customers, or even parents squatting on addresses.

                   But how big of an issue is this? If only we had a

                   large amount of well known IP address blocks that

                   we can make a safe bet on not being used.

      o § Digital Restrictions (DRM)⠀➾

            # ⚓ Gift_Of_Sight_Stolen_As_Medical_Implant_Company_Implodes⠀⇛

                   Techirt has long discussed how in the modern era,

                   the things you buy aren’t actually the things you

                   buy. And the things you own aren’t actually the

                   things you own. Things you thought you owned can be

                   downgraded, bricked, or killed off entirely without

                   much notice. That game console with backward

                   compatibility? It no longer has backward

                   compatibility. That smart home hub or smart speaker

                   at the heart of your living room setup you’ve

                   enjoyed for years? It not long works. The movies

                   and books you thought were permanently in your

                   personal catalog? Sorry, they aren’t anymore. That

                   perfectly good two-year-old phone? It no longer

                   gets security updates, putting you and your data at

                   risk.

      o § Monopolies⠀➾

            # § Copyrights⠀➾

                  # ⚓ Apple_v._Corellium_Demonstrates_a_Clear_Example_of

                    Fair_Use_–_Public_Knowledge⠀⇛

                         Public Knowledge has been tracking the

                         lawsuit by Apple against Corellium for a

                         while. Corellium is a company that offers

                         various services for software developers and

                         security researchers. Some of these involve

                         creating virtual iPhones for testing and

                         research purposes, which involves making

                         copies of Apple’s iOS software. Apple sued,

                         arguing both that Corellium violated the

                         “anticircumvention” provisions of the Digital

                         Millennium Copyright Act (DMCA) by simply

                         accessing iOS, and substantive copyright law,

                         by making new copies of it.

                  # ⚓ Auguste_Rodin’s_Sculptures_Are_In_The_Public_Domain;

                    3D_Scans_Of_Them_Should_Be,_Too⠀⇛

                         Auguste Rodin is without doubt one of the

                         greatest sculptors in history. Equally

                         without doubt, his works are now in the

                         public domain, since he died in 1917.

                         Unfortunately, the situation in France is a

                         little more complicated, for reasons the

                         artist and public domain campaigner Cosmo

                         Wenman explains:

                  # ⚓ EFF_to_Court:_Security_Research_Is_a_Fair_Use⠀⇛

                         Apple is putting that principle at risk in

                         its lawsuit against Corellium. Corellium

                         created a virtualization of Apple’s iOS

                         operating system that allows developers and

                         researchers to test iOS for vulnerabilities

                         without having to get permission from Apple

                         or pay for the privilege of finding flaws in

                         the system. Apple sued, and lost in district

                         court on fair use grounds. Apple’s hoping for

                         a different ruling on appeal.

                         It shouldn’t get one. EFF, along with Public

                         Knowledge and a number of security experts,

                         filed an amicus brief with the court

                         explaining one reason why: the public’s

                         interest in greater security, more

                         innovation, and more competition in mobile

                         software. We can’t protect ourselves from

                         security flaws if independent testers aren’t

                         allowed to find them.

                         Companies use legal threats, like a threat of

                         suing over copyright infringement, to silence

                         researchers and keep users from knowing that

                         there’s something wrong with their devices.

                         Without meaningful protection from such

                         claims, organizations like Corellium cannot

                         develop research tools, researchers cannot

                         conduct independent testing, and the public

                         loses out on the benefits of innovation and

                         competition to enhance security.

                  # ⚓ Twitter_and_Facebook_Must_Speak_Out_Against_Ghana’s

                    Repulsive_Anti-LGBTQI+_Bill⠀⇛

                         Both Twitter and Facebook have invested

                         heavily in Ghana, which holds itself out to

                         be a constitutional democracy with a strong

                         commitment to human rights. Twitter announced

                         last year it was establishing a headquarters

                         in the Ghanaian capital Accra, citing Ghana

                         as “a supporter of free speech, online

                         freedom, and the Open Internet.” Meanwhile

                         Meta (née Facebook), has long trumpeted its

                         success in bringing connectivity to Ghana

                         through programs like Free Basics and Express

                         Wi-Fi.

                         But now, the Ghanaian parliament has

                         introduced the “Promotion of Proper Human

                         Sexual Rights and Ghanaian Family Values

                         Bill,” a draconian measure that would

                         undermine the Ghanaian Constitution’s core

                         guarantees of freedom of thought and

                         expression. Pulling no punches in a press

                         statement, a group of professors,

                         journalists, and advocates described the bill

                         as “an Orwellian nightmare fraught with

                         stigmatization, bigotry, intolerance,

                         repression, authoritarianism, violation of

                         the fundamental human rights of LGBTQ+

                         persons and those who defend their human

                         rights, false piety, cruelty to, and lack of

                         empathy, for difference in our society.”

                         While Ghanaian law has long criminalized

                         same-sex sexual activities, the new proposal

                         goes much further by threatening up to five

                         years in jail for publicly identifying as

                         LGBTQ or “any other sexual or gender identity

                         that is contrary to the binary categories of

                         male and female.” The sentence increases if

                         the offending person expresses their gender

                         beyond or identifies outside of the so-called

                         “binary gender.”

                  # ⚓ Episode_6:_Open_Culture_VOICES_–_Biyanto_Rebin⠀⇛

                  # ⚓ Police_Arrest_Man_For_Uploading_‘Parasite’_Movie_Edit

                    to_YouTube⠀⇛

                         Police in Japan have just arrested another

                         man for posting 10-movie summaries to YouTube

                         including the hit Korean drama ‘Parasite’.

                         The 48-year-old gave a media interview last

                         year talking about his ‘legal’ work but then

                         complained that it had been edited down,

                         carried on with his work, and then got

                         raided.

                  # ⚓ Supreme_Court_Rejects_Appeal_of_Sports_Streaming_Site

                    Rojadirecta⠀⇛

                         Popular sports streaming site Rojadirecta

                         will remain outlawed in Spain for now. The

                         Supreme Court has denied a hearing of the

                         site’s appeal against a previous order which

                         required the site to block Spanish visitors.

                         Meanwhile, criminal prosecution against

                         several Rojadirecta defendants is also about

                         to start.

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