𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, May 27, 2023

┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅

Generated Sun 28 May 02:53:04 BST 2023

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

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

The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈

Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔

Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕

Gemini index for the day: gemini://gemini.techrights.org/2023/05/27/

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

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

QmeK7zHQpdcwHbx8uR26LkVDXBdvbMng9z4pLo73jfH5QF

QmXLWcERaT62jk6Wo1AD9b8Q68FXMYD367JovbY1ULwntt

QmdZh6yx6XHSGUjNv8hpHYHaPD1tD43gBVHqGXHrajNVyN

QmTF2pMBvBP5Dk3fq4pyka8M4P8oM4BWugLvejCa15k8va

QmW3azBnU7buqhayP66v2xJeRySHJSgNkCJo11LNaUdUut

QmXaswZ1iitN6RTpnpNFN6o7kQXkpopdAhoV6EHhdN52mn

QmPA2gUGrxUHnaSzGwZTa6xsWZRMKqETbvrMmtiNZtJvDA

QmXunK1VfrszdbZV3eLVtiEztrbpHXotzsSs5FidJqHzYd

QmPUbf7suaQniw1646dasmSY6bnK39TXxEV8ULg4u7at86

QmPtdTJXoyGAiBp24ch57o9jAzqAfro8Lh2BcCMZEYztSi

QmcpSETydPVbunSXmzCVgzuCQ777DRLwnusWHKNSEvS1vV

QmPsoAJFgURJZUxZU7m4mBwyBHMrJKTzEY7Ma4Rcmn1bTt

QmaeGXiDDeQqLVHkcfuYJsMR5gkG2KfL8obZ3e39wo9X89

QmRej75aRh5cQjV4EkpTtNhGCL4Ea8gLTYE6afRU4AT8SA

QmXJbVjMgJLV5E7dFhoZEBSRNCRpMoAYeiQ2x94WwVCAE3

QmZNHM6zwJz4HumZeNxKEckXrmY5Mn2R47Zf2ejRtHj763

QmdikaRip3RgsHbg5S4LuJvPizfJB7fh2rKp7uQ8dhxicC

QmQu3g2B85BK7JwmQzcr2cd7XoDdiF92Gy9xcxqS6sf27G

QmUA66kgebedAfGsk5HFXX1YCuCWp2J51StBuNVvAvFwwS

QmYBPCcUR7ecniepZDK6iEaWqzEdVWvK9GovhnZadXHtW8

QmX2VFCGCawxbCCUo2h1FKvHmTmxLRFAdDLmVDjFaZoLpw

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

⦿ European Patent Office (EPO) Management Not Supported by the EPO’s Applicants, So Why Is It Still There? | Techrights

⦿ Geminispace Continues to Grow Even If (or When) Stéphane Bortzmeyer Stops Measuring Its Growth | Techrights

⦿ HMRC: You Can Click and Type to Report Crime, But No Feedback or Reference Number Given | Techrights

⦿ One Week After Sirius Open Source Was Reported to HM Revenue and Customs (HMRC) for Tax Fraud: No Response, No Action, Nothing... | Techrights

⦿ IRC Proceedings: Friday, May 26, 2023 | Techrights

⦿ Social Control Media Needs to be Purged and We Need to Convince Others to Quit It Too (to Protect Ourselves as Individuals and as a Society) | Techrights

⦿ Anonymously Travelling: Still Feasible? | Techrights

⦿ German Media About Industry Patent Quality Charter (IPQC) and the European Patent Office (EPO) | Techrights

⦿ EPO Applicants Complain That Patent Quality Sank and EPO Management Isn’t Listening (Nor Caring) | Techrights

⦿ With EUIPO in Focus, and Even an EU Kangaroo Tribunal, EPO Corruption (and Cross-Pollination With This EU Agency) Becomes a Major Liability/Risk to the EU | Techrights

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

	http://techrights.org/2023/05/27/european-patent-office-ga-de/#comments

	http://techrights.org/2023/05/27/geminispace-growing/#comments

	http://techrights.org/2023/05/27/hmrc-you-can-click-and-type-to-report-crime-but-no-feedback-or-reference-number-given/#comments

	http://techrights.org/2023/05/27/hm-revenue-and-customs-mum/#comments

	http://techrights.org/2023/05/27/irc-log-260523/#comments

	http://techrights.org/2023/05/27/social-control-networks-need-to-be-purged/#comments

	http://techrights.org/2023/05/27/some-privacy-still-feasible/#comments

	http://techrights.org/2023/05/27/stuttgarter-zeitung-epo/#comments

	http://techrights.org/2023/05/27/stuttgarter-zeitung-thomas-magenheim-on-epo/#comments

	http://techrights.org/2023/05/27/suepo-and-epo-articles/#comments

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

	http://techrights.org/2023/05/27/40th-anniversary-gnu/#comments

	http://techrights.org/2023/05/27/goodbyes-to-tina-turner/#comments

	http://techrights.org/2023/05/27/new-wine-and-more/#comments

                ䷩ 𝚕𝚒𝚗𝚎 76

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/european-patent-office-ga-de/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/european-patent-office-ga-de/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ European_Patent_Office_(EPO)_Management_Not_Supported_by_the_EPO’s

Applicants,_So_Why_Is_It_Still_There?⠀✐

Posted in Europe, Patents at 5:57 am by Dr. Roy Schestowitz

More translations (with more languages) available in the site of the EPO‘s

union, SUEPO

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

The European Patent Office in Munich. Experts criticise the practice of

                     granting inventor protection.

                         Photo: dpa/Sven Hoppe

Summary: This third translation in the batch is an article similar to the prior

one, but the text is a bit different (“Patente_ohne_Wert”)

A BIT less than a week before the EPO wanted (or merely hoped) to open an

illegal and unconstitutional kangaroo court, in violation of international

conventions, some condemnation came from the German press. This project will

destabilise the EU by discrediting the EU, so Germany’s government needs to

sober up and listen to the warning signs. EPO corruption is highly contagious

and it has been left to flourish for over a decade already. Here’s the latest

of the batch from SUEPO:

 § Criticism of the European Patent Office Patents without value⠀➾

 Munich – To increase its revenues, the European Patent Office grants

 questionable patents, say critics. Transparency International sees

 structures that favour corruption.

 By Thomas Magenheim-Hörmann

 The example described by the Munich patent attorney makes it clear

 what is at stake. A pharmaceutical company developed a pill against

 infertility, had it protected at the European Patent Office (EPO) and

 invested in its marketing. Then a rival entered the market with an

 alleged plagiarism. The patent holder went to court and lost. The

 alleged imitator was able to show a US patent that Epa examiners had

 overlooked. This rendered their property right worthless. “In extreme

 cases, this can cause millions in damages,” explains the patent

 attorney, who wishes to remain anonymous. He works for one of the

 largest patent law firms in Europe. Patenting for several countries

 alone consumes a six-figure sum, and many times that amount is

 invested in production in reliance on the patent.

 There is a system of lame searches, the expert complains. Examiners

 are encouraged to grant more and more patents because they maximise

 the office’s income. Quality research falls by the wayside. Michael

 Heisel puts the grievances even higher. “We see structural problems

 at the EPO that facilitate corruption,” says the Bavarian head of the

 anti-corruption organisation Transparency International.

 39 countries represented in the Council

 An element of this is the Epa Board of Directors, in which 39

 European countries are represented and which is supposed to control

 the management of the office. But this is called into question by a

 conflict of interests, warns Heisel. On the one hand, the office

 takes over the patent examination for many countries. On the other

 hand

 the states shares of the Office’s income for granted patents. “The

 Administrative Council is not independent of the party being

 controlled, and that can’t be good,” Heisel criticises. Epa service

 instructions support this view. “Productivity has to improve, very

 soon, … because productivity is the only thing that guarantees that

 our payroll will be paid on the 26th. of each month,” writes an Epa

 director. The clarity of a patent is not a priority, the inventive

 step is not to be examined in depth, it continues. It is to be

 examined quickly, decided positively and recognised a lot, it means.

 This practice is also a thorn in the side of Siemens patent chief

 Beat Weibel. His company is the largest German patent applicant and

 the initiator of an industry initiative with the abbreviation IPQC.

 20 major international companies such as Siemens, Bayer and Nokia,

 but also smaller firms, have joined forces because they fear for

 effective patent protection. “We have nothing if patent examiners

 can’t find the state of the art and can only do incomplete research

 due to internal time pressure,” complains Weibel. Siemens has also

 had similar experiences with Epa patents. Representatives of IPQC and

 Office 2023 have met twice to discuss and resolve problems. But that

 already fails in terms of awareness. “The Office’s management has

 denied that there are any quality deficiencies,” says the Siemens

 expert regretfully. The

 Critics, meanwhile, remain silent. “We ask for your understanding

 that Epa does not wish to comment on this,” a spokesperson explains

 succinctly when asked. Data speak a clear language.

 For example, Siemens has documented an increase in the time spent on

 patent applications by one third in the last decade. At the same

 time, according to internal EPO statistics, the time available to

 examiners per patent search has almost halved. As a result, those who

 challenge patents are becoming more successful. From 2015 to 2021,

 the revocation rate climbed from 41 to 46 per cent, according to

 Siemens.

 For 2022, a study by the Chair of Intellectual Property at the

 University of Osnabrück has determined a revocation rate of the Epa

 Board of Appeal of almost 50 percent. A further almost 40 percent of

 contested patents were marginally to substantially restricted. It is

 striking that not even one in ten revocations was based on documents

 that could not be found in the Epa patent database, the study authors

 write. In nine out of ten contested cases, the

 We need reliable patents, and examiners need enough time and

 experience for this,” emphasises a patent expert from the Roche

 pharmaceutical company in Switzerland. He too is a member of th IPQC.

 Epa staff representatives support the accusations from industry and

 research. To the outside world, the management claims that everything

 is fine and plays down or completely ignores quality deficiencies,

 they explain. Only four out of five examiners who leave the office

 are replaced, despite an increase in work. “The Office must provide

 more examiners and more examination time,” the Munich patent attorney

 also demands. A few years ago, several large patent law firms wrote

 an incendiary letter to the Office criticising the declining patent

 quality. This has been negated by the office. “Nothing happened,”

 regrets the expert. Like Tranparency International, he sees the Epa

 Board of Directors as problematic. “There are States, for them this

 is a significant source of income,” Weibel also criticises.

 Patent trolls have also recognised this and use it for themselves.

 These are applicants who apply for protective rights for superficial

 patents, which are also granted if the examination is inadequate,

 explains Heisel. These patents then block competitors. “China in

 particular applies for a large number of patents, and if they are not

 carefully examined, this can deprive German companies of innovation

 opportunities,” warns Heisel.

 Patents: More and more applications from China

 The European Patent Office, with its headquarters in Munich, is a

 supranational organisation and not an EU organisation. The management

 of the Office, under President Antonio Campinos, is controlled by the

 EPO Administrative Council. It is made up of representatives of the

 39 European states that have acceded to the European Patent

 Convention. Germany is represented by a State Secretary for Justice.

 In particular, patent applications from China have been on the rise

 at the European Patent Office for years . In 2022, the increase on

 this basis was a good 15 percent to more than 19,000 requests for

 protection by Chinese inventors. mho

All of a sudden all those EPO photo ops with China don’t quite look the same.

And much can be said about the EPO doing so much business with Belarus

(outsourcing_parts_of_the_EPO_to_Vladimir_Putin's_'oblasts'). █

⠀⠀⠀⠀⠀⣴⡌⢻⣿⣿⣿⣿⡆⢿⣿⣿⣿⣾⡇⢧⡅⣾⣿⣿⣿⣯⠁⢀⠄⠅⠀⣄⠆⠀⠀⠰⠏⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣿⢧⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⡟⠁⠀⠻⢿⣿⠿⣿⡜⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⢧⣴⣿⣷⣀⡀⠃⠀⡂⡀⠑⣠⣼⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⡐⢁⡀⢐⡀⠀⣽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣾⣿⣆⣠⣤⠀⣤⣥⣄⣸⣧⡈⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣧⢤⣾⣧⣶⣾⣿⠀⠀⠀⢸⣷⣆⠀⠀⢀⣥⣶⣦⣾⣭⠠⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣿⡈⣿⣿⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⡇⣿⣿⣧⠀⠀⠈⠙⢹⠛⢙⠴⠋⠀⠀⠀⢠⡄⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⣛⣛⣃⠀⠀⢿⠛⠛⣿⣟⣛⣻⣿⣷⠀⠁⢉⣿⣿⠷⠀⡄⠀⠂⠀⠀⠀⢀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣭⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⢛⣛⡋⠉⠩⠭⢴⣒⡀⣒⣩⣭⣥⣽⣶⣶⣶⣶⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠀⠀⠀⠀⣀⣀⢨⣭⣭⣵⡄⢶⣶⣿⣶⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⡄⠘⣿⣿⠿⠿⠿⠛⠛⠃⢹⣿⡿⠛⠁⠀⠀⠀⢀⣀⣀⣿⣶⣟⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⣭⣿⠶⠶⠿⢿⣟⣛⣻⣿⣯⠭⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢾⡗⠚⠛⠛⠉⡉⠈⠁⣀⣴⠀⡀⢀⣤⣾⡿⠕⠓⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡯⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⠚⡗⢻⡟⠙⢁⣠⣴⣿⣿⣿⡆⠿⠛⠋⠃⣄⣠⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠬⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠁⠀⣶⣿⣿⣿⣿⣿⣿⡇⢰⣜⣲⠿⠃⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⠷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⣄⣀⣀⣤⣤⣢⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⡀⠐⠛⠛⠛⠉⠉⠀⢸⠈⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠃⠛⠙⠏⠉⢉⡁⣄⣤⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠄⢀⣀⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢸⣲⣷⣶⣾⡸⣸⠏⡟⡼⡽⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣀⣸⣀⣄⣀⣀⣸⣿⣯⣭⣽⠓⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣀⣤⣤⣤⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣤⠤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡟⠅⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠿⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 277

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/geminispace-growing/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/geminispace-growing/

Gemini_version_available_♊︎

✐ Geminispace_Continues_to_Grow_Even_If_(or_When)_Stéphane_Bortzmeyer_Stops

Measuring_Its_Growth⠀✐

Posted in Protocol at 4:30 am by Dr. Roy Schestowitz

Video_download_link | md5sum f726c3cf0bd8fe90ec207a68fa9544b8

Gemini is Growing, But Growth Not Measured

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/tracking-size-of-gemini.webm

Summary: A Gemini crawler called Lupa (Free/libre software) has been used for

years by Stéphane Bortzmeyer to study Gemini and report on how the community

was evolving, especially from a technical perspective; but his own instance of

Lupa has produced no up-to-date results for several weeks

THE work of Stéphane_Bortzmeyer, notably Lupa, has helped us estimate the

growth of Gemini in general (as a protocol). But the Botond/Bortzmeyer-led

capsules (the former charts the latter) stopped updating their numbers that

track Gemini’s growth; maybe it’s just too big and expensive for Stéphane to

track all the time, as it’s not 2020 anymore and many thousands of capsules

exist, counting subsites (in the domain sense) too.

“It’s perfectly plausible and possible that Bortzmeyer isn’t aware of the issue

and has just accidentally let the job fail (Botond uses a cron job at 1AM UTC

since last year).”The video above explains that, based on our own experience,

Gemini continues to grow. Even in the absence of crawlers estimating and

reporting this growth, we’re optimistic and last month was record_traffic_for

us. We’re talking about lots and lots of Gemini pages (about half a million

pages in one month). It’s perfectly plausible and possible that Bortzmeyer

isn’t aware of the issue and has just accidentally let the job fail (Botond

uses a cron job at 1AM UTC since last year). radia.bortzmeyer.org is definitely

active this month. Either way, tracking the growth of Geminispace has become a

computationally expensive (and thus financial burdensome) task. It did help a

lot — a very positive contribution. █

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

Stéphane_Bortzmeyer (see image licence in Wikipedia). One of the more essential

   voices of Gemini, up there with "Skyjake", Sean, and Solderpunk.

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠋⠙⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉

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

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣋⣙⣉⣉⣉⣉⣩⣍⣉⣩⣭⣭⣭⣭⣭⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣙⣉⣭⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⠉⠉⠉⠉⠉⠉⠉

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣦⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⣿⣿⣿⡿⠿⠿⣿⠛⠉⠉⠁⠀⢙⠛⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠺⠟⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⣈⢃⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢀⠀⠀⠠⣀⡄⣸⣿⣌⠲⠦⠬⢿⣛⣼⣷⠀⠀⠀⠉⢱⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠉⠉⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⠀⠀⠀⢠⡠⠶⠶⠛⠋⢰⠿⠛⠻⠷⡀⠲⣶⣿⣿⣿⡇⠀⠀⢀⣙⣋⣉⣙⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠁

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠘⢿⣇⣴⣶⣣⣦⣀⠀⠀⣴⣿⣷⡌⢹⣿⣿⣷⡆⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⡀⠀⠉⠉⠙⠿⠿⠻⠐⠚⠛⠙⠋⠉⣾⣿⣿⡟⠁⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤

⣀⣀⣠⣤⣤⣤⣤⣤⣬⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣆⠀⠀⣦⠀⢀⣤⠶⠒⠺⢿⣿⣆⠋⠻⣿⡇⣀⣨⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀

⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡆⠈⠀⠀⠀⠀⢠⣿⣧⣀⣀⣠⣾⣿⣿⡆⠀⠛⡔⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⢻⣿⠿⠿⠛⠛⠿⠏⠁⢀⣼⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⣛⣛⣛⣛⣿⣛⣛⣿⣛⣛⣛⣛⣛⣻⣛⣛⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣽⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤

⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⡟⢿⣿⡟⢭⡏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣰⣍⣇⣿⣿⣧⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⢻⡿⡻⡟⣟⠿⣧⡍⣯⣯⡎⡆⡗⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣧⠣⢸⣿⡆⣺⣧⡷⣵⣷⡿⢿⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛

⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⢻⣿⣿⡿⣇⡻⣸⢸⣸⣹⣸⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⡟⣿⣿⣿⣿⣿⣿⡟⠂⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄

⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠖⢉⡏⣿⣿⣿⣿⣿⣧⠸⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉

⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠮⠤⠛⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛

                ䷩ 𝚕𝚒𝚗𝚎 370

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/hmrc-you-can-click-and-type-to-report-crime-but-no-feedback-or-reference-number-given/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/hmrc-you-can-click-and-type-to-report-crime-but-no-feedback-or-reference-number-given/

Gemini_version_available_♊︎

✐ HMRC:_You_Can_Click_and_Type_to_Report_Crime,_But_No_Feedback_or_Reference

Number_Given⠀✐

Posted in Finance, Fraud, Free/Libre_Software at 2:38 am by Dr. Roy Schestowitz

Video_download_link | md5sum 3658fca2df7acb84de0dde460f814926

HMRC Useless UI, No Reference

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/sirius-hmrc-inaction.webm

Summary: The crimes of Sirius_‘Open_Source’ were reported 7 days ago to HMRC

(equivalent to the IRS in the US, more or less); but there has been no visible

progress and no tracking reference is given to identify the report

THE system of accountability (“checks and balances” is the motto) isn’t

working. The matter is now being escalated to a political level.

“…HMRC inaction would say a lot about the system and reinforce the widespread

belief that enforcement is done only/mostly against foes of “the system”.”The

video above deals with HMRC. I don’t have much to say about the progress; I

have received no reference code/number, they did not get in touch (phone, E-

mail, post), and it’s not clear if they’re doing anything at all to hold Sirius

accountable. As noted earlier, HMRC inaction would say a lot about the system

and reinforce the widespread belief that enforcement is done only/mostly

against foes of “the system”. Irrespective of severity, scale, and strength of

evidence.

Setting up a UI in a Web page is only the first step; does HMRC do anything

with what’s collected in this UI? it’s certainly not designed for anonymous

reporting. █

                ䷩ 𝚕𝚒𝚗𝚎 424

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/hm-revenue-and-customs-mum/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/hm-revenue-and-customs-mum/

Gemini_version_available_♊︎

✐ One_Week_After_Sirius_Open_Source_Was_Reported_to_HM_Revenue_and_Customs_

(HMRC)_for_Tax_Fraud:_No_Response,_No_Action,_Nothing…⠀✐

Posted in Deception, Finance, Fraud, Free/Libre_Software at 12:01 am by Dr. Roy

Schestowitz

It’s like writing to zombie agencies that exist only on paper or selectively

enforce (based on special interests)

🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Regulators_and_enforcers_asked_to_tackle_the_crimes;_No

                             action....⦈_

Summary: One_week_ago we reported tax_abuses of Sirius_‘Open_Source’ to HMRC;

we still wait for any actual signs that HMRC is doing anything at all about the

matter (Sirius has British government clients, so maybe they’d rather not look

into that, in which case HMRC might be reported to the Ombudsman for

malpractice)

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣤⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠒⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣯⢘⣳⣤⣤⣿⣷⣿⣿⣧⣿⣿⠀⣺⡗⣹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠛⠙⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠖⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⣾⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⡀⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⡿⠁⠀⠈⠉⠙⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣟⣿⠟⠉⠀⠀⠀⠀⣿⡏⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡇⠀⠀⠀⠀⠀⠀⣼⠓⠛⣿⣄⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣣⠀⠀⠀⠀⠀⣰⠃⠐⠀⠘⣿⣿⣶⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠻⡛⣛⠀⠀⠀⠀⠀⠉⡇⠀⠀

⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣄⣀⣴⣿⣿⣄⣀⣤⣡⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⢀⡏⠙⢷⣦⣄⡀⣀⣴⣧⠀⠀

⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⢀⣴⣿⡅⢀⣄⣿⣿⣿⣿⣏⠈⠀⠀

⣷⣶⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀

⣿⣯⣿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⣿⣿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡯⣿⠾⠿⠿⠿⠋⠋⠉⢸⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡹⠋⠟⠋⠋⠉⠁⠉⠉⢿⡇⠀⠀

⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣻⣷⡄⠀⠈⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡀⠀⢀⣀⣤⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣀⠀⠀⢠⣼⡇⠀⠀

⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠹⢿⣿⣿⡶⣾⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⣟⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⠔⠀⠀⣿⡇⠀⠀

⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⣿⣽⠋⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⡿⠛⣁⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠤⠀⣀⡀⣤⣾⣿⣿⠀⠀

⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣏⣥⠀⠀⠀⠀⣠⣿⣿⣟⠿⣷⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠚⠭⠷⠿⠛⢹⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣯⣿⣿⣿⡿⢻⡆⣀

⠈⠙⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡶⠃⠀⠀⢰⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⠛⠉⣉⣉⡉⠒⠂⠀⠀⠀⠀⠟⣿⠨⠿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣛⣿⣷⣦⠄⠀⠀⢀⣤⣽⠟⠋⢉⣑⠴⢿⣛⣿

⣤⣤⣾⣿⣿⣿⠿⠿⠿⠿⣿⣶⣦⣄⣴⣿⡿⠷⠀⣀⡀⠒⠀⠀⣿⣿⣿⣿⣧⠀⣼⣿⣿⣇⣤⣀⣀⣀⣈⠙⠀⣀⣀⣀⡀⢀⣠⣤⣶⡿⠟⠛⣉⣭⣵⣶⣾⣿⣿⣿⠀⢩⠀⢺⣿⣶⣶⣟⠋⠁⠀⠀⢢⣤⣾⣿⣿⠿

⠛⠛⢩⣿⡷⠀⠀⠀⠀⢀⣬⣽⣿⡅⠉⣩⣤⡀⣀⣀⣀⡤⠔⢻⣿⣿⠟⠙⠉⠀⣿⣿⡛⣩⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠛⠉⠁⠐⠚⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠋⠀⠘⣿⣷⡯⡻⡇⣠⣤⣤⣶⡿⠉⠀⠀⢀

⣀⣴⣿⡿⠃⠀⠀⠀⢠⢾⣿⣿⣿⠇⠀⢿⡿⠗⠈⠉⠀⣶⣶⣿⣿⣧⠀⠀⡠⢊⠽⣿⡆⠿⣿⣿⣿⣿⣿⠿⠋⠋⠉⠀⠀⠀⠐⠊⠁⣠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⣿⠹⣿⣿⢰⣿⣿⣿⣿⢀⣤⣤⣶⡿

⠙⠁⠹⣿⠄⠀⢀⡴⠟⡛⢸⣿⣟⠐⠂⣶⡆⠒⠒⠶⠒⢛⣿⣿⢻⣿⣷⣾⠁⠀⠀⠙⢿⡀⠹⢿⠛⠛⢁⣾⣷⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠁⣸⣿⣿⣿⣿⣿⠟⣻⡇⠀⢀⣿⣏⡄⠈⠉⠁⠉⠛⠛⠁⠈⠋⠉⠀⠀

⣐⣦⣼⡿⠀⡴⠁⠀⢠⣿⣾⣿⡿⠤⠤⣤⡀⠠⢤⣤⣤⣿⣿⣯⡾⢻⣿⣿⣿⣤⣶⣶⣾⣷⣤⣄⡀⠐⠻⠛⠉⠉⠉⠀⠁⠀⠀⣀⡄⠚⠓⢲⣿⣿⣿⣿⡿⠋⠀⡍⡿⠀⠘⣿⡇⢷⣤⣤⣀⢺⣿⣿⣿⠂⠀⠀⠀⠀

⠛⠛⢻⣧⠞⠁⠀⠀⢸⣿⣧⣿⣷⠀⠀⠉⠇⠠⠀⠀⣾⣿⡟⠙⣿⢼⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡛⠁⢸⣿⠀⠀⠀⠀⠀⠐⠈⠁⣀⣼⣶⣿⣿⣿⣿⣿⠃⠀⠀⢨⣿⡇⠀⢻⣿⠀⠛⠛⠻⢿⣿⣥⣤⠐⠾⠿⢿⠿

⠀⣦⣾⣷⠯⢶⠄⠰⣾⠷⢿⣿⣿⢀⠀⠉⠁⠀⠀⢸⣿⡿⠹⠟⡟⢸⣿⣿⣷⣿⣝⠻⢿⣈⡙⠛⠃⠀⢿⣿⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⠟⠋⠈⣿⣿⡆⠀⠀⣾⣿⠇⠀⠀⣿⣦⣀⣀⡀⠘⠲⠽⠟⠀⠀⠀⠀⠀

[29A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠒⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⣤⣤⣿⣷⣿⣿⣧⣿⣿⠀⣻⡗⢼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣟⣿⠟⠁⠀⠀⠀⠀⣿⡍⣭⡅⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⣼⠓⠛⣿⣄⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣼⠇⠐⠀⠘⣿⣿⣶⣤⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠻⡛⣛⠀⠀⠀⠀⠀⠉⡇⠀⠀

⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣄⣀⣴⣿⣿⣄⣀⣤⣡⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⢀⡏⠙⢷⣦⣄⡀⣀⣴⣧⠀⠀

⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⢀⣴⣿⡁⢀⣄⣿⣿⣿⣿⣏⠈⠀⠀

⣷⣶⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀

⣿⣯⣿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⣿⣿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⠾⠿⠿⠿⠋⠋⠉⢸⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠋⠟⠋⠋⠉⠁⠉⠉⢿⡇⠀⠀

⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢻⣷⡄⠀⠈⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⡀⠀⢀⣀⣤⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⣀⣀⠀⠀⢠⣼⡇⠀⠀

⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⣿⣽⠋⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⠿⠛⣁⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠤⠀⣀⡀⣤⣾⣿⣿⠀⠀

⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣏⣥⠀⠀⠀⠀⣠⣿⣿⣟⠿⣷⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠈⠭⠷⠿⠛⢹⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣯⣿⣿⣿⡿⢻⡆⣀

⠈⠙⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡶⠃⠀⠀⢰⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⠛⠉⣉⣉⡉⠒⠂⠀⠀⠀⠀⠟⡿⠨⠿⣿⣿⣶⣤⣶⣶⣿⣿⣿⣿⢿⢛⣿⣶⣦⠄⠀⠀⢀⣤⣽⠟⠋⢉⣑⠴⢿⣛⢿

⣤⣤⣾⣿⣿⣿⠿⠿⠿⠿⣿⣶⣦⣄⣴⣿⡿⠷⠀⣀⡁⠒⠀⠀⣿⣿⣿⣿⣧⠀⣼⣿⣿⣇⣤⣀⣀⣀⣈⠙⠀⣀⣀⣀⡀⢀⣀⣤⣶⡿⠿⠋⣉⣭⣽⣶⣶⣿⣿⣿⠀⢩⠀⣺⣿⣶⣶⣟⠋⠉⠀⠀⠢⣤⣾⣿⣿⠿

⠛⠛⢩⣿⡷⠀⠀⠀⠀⢀⣬⣭⣿⡅⠉⣩⣤⡀⣀⣀⣀⡤⠔⢻⣿⣿⠏⠙⠉⠀⣿⣿⡛⣩⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠛⠉⠁⠐⠚⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠋⠀⠘⣿⣷⡟⡻⠇⣠⣤⣤⣦⡿⠋⠀⠀⢀

⣀⣴⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⢿⡿⠗⠈⠉⠀⣶⣶⣿⣿⣧⠀⠀⡠⢊⠽⣿⡆⠻⣿⣿⣿⣿⣿⠿⠉⠋⠉⠀⠀⠀⠐⠚⠀⣠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⣿⠹⣿⣿⢠⣿⣿⣿⣿⢀⣤⣤⣶⡿

⠙⠁⠹⣿⠄⠀⢀⡴⠟⡛⢸⣿⣟⠐⠂⣴⡄⠒⠒⠶⠒⢻⣿⣿⢻⣿⣿⣾⠁⠀⠀⠙⢿⡀⠹⢿⠛⠛⢁⣾⣷⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠁⣸⣿⣿⣿⣿⣿⠟⣻⡇⠀⢀⣿⣏⡄⠈⠉⠁⠙⠙⠛⠁⠈⠋⠉⠀⠀

⣐⣦⣼⡿⠀⡴⠁⠀⢠⣿⡾⣿⣿⠤⠤⣤⡀⠤⢤⣤⣤⣿⣿⣯⡾⢻⣿⣿⣿⣤⣶⣶⣾⣷⣤⣄⡀⠐⠻⠛⠉⠉⠉⠀⠁⠀⠀⣀⡄⠚⠓⢲⣿⣿⣿⣿⡿⠋⠀⣎⡿⠀⠘⣿⡇⢷⣤⣤⣀⢸⣿⣿⣿⠂⠀⠀⠀⠀

⠛⠛⢻⣧⠞⠁⠀⠀⢸⣿⣷⣿⣿⠀⠀⠉⠇⠠⠀⠀⣾⣿⡟⠙⣿⢼⣿⣿⠻⣿⣿⣿⣿⢿⣿⣿⡛⠁⢸⣿⠀⠀⠀⠀⠀⠐⠈⠁⣀⣼⣶⣿⣿⣿⣿⣿⠃⠀⠀⢨⣿⡆⠀⢻⣿⠀⠛⠛⠻⢿⣿⣤⣤⠰⠾⠿⠿⡿

⠀⣦⣾⣷⠏⢶⠄⠰⣾⠷⢾⣿⣿⢀⠀⠉⠁⠀⠀⢨⣿⡿⠹⠟⡟⢸⣿⣿⣷⣾⣝⠻⢿⣈⡙⠛⠃⠀⢿⣿⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⠟⠋⠈⣻⣿⡆⠀⠀⣿⣿⠇⠀⠀⣿⣦⣀⣀⡀⢘⠣⠽⠟⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠒⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣿⢘⣳⣄⣠⣯⣷⣿⣿⣧⣿⣿⠀⣹⡗⢾⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⣶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠟⠉⠉⠙⠛⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣻⡿⠛⠁⠀⠀⠀⢹⣯⢩⣭⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⠁⠀⠀⠀⠀⠀⢨⡟⠘⢿⣦⡀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⠀⠀⢠⡿⠀⠆⠀⢿⣿⣶⣤⣤⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡿⠟⠛⠛⠟⢛⠋⠀⠀⠀⠀⠉⢻⠀⠀

⡁⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣀⣀⣶⣿⣧⡀⣠⣄⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣸⠛⠻⣶⣄⡀⠀⣠⣾⡄⠀

⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣠⣾⡟⠀⣀⣹⣿⣿⣿⣿⠉⠁⠀

⣿⣦⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡓⢾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀

⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢀⠼⠿⣿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢯⣩⣽⡿⣿⠿⠟⠛⠉⠁⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠟⢻⠛⠛⠉⠉⡉⠙⠻⣿⠀⠀

⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⢹⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⡀⣀⣠⣴⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⢀⣀⡀⠀⠀⣤⣿⠀⠀

⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠙⢿⣿⣿⣦⣴⣎⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠉⠀⡠⠖⠀⢸⣿⠀⠀

⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠟⢰⣯⡾⠁⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠿⣿⣿⣿⣿⠿⠋⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡀⠀⣀⢀⣠⣾⣿⡆⠀

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⡅⠀⠀⠀⠀⣸⣿⣿⡿⣿⣦⣤⡀⠀⠀⢀⣀⠀⠀⠀⠚⠋⠽⠷⠶⠋⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣤⣼⣽⣿⣿⣿⠟⣷⠄

⠉⠙⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢭⡔⠀⠀⠀⣾⣿⣿⣿⣯⡈⢻⣿⣿⣿⡟⠛⠋⢉⠋⠒⠲⠀⠀⠀⠀⠰⢿⡏⠻⢿⣿⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⢿⣶⣦⣤⠀⠀⠀⢀⣭⡿⠛⢛⣩⢡⠾⣟⠿

⣀⣤⣤⣿⣿⣶⣶⣶⡶⠿⣷⣶⣦⣤⣠⣶⣾⡾⠍⠁⠒⠁⠤⠀⢹⣿⣿⣿⣿⡅⢀⣿⣿⣿⣀⣀⡀⠈⠉⠙⠂⠀⣀⣀⠀⠀⢀⣀⣤⣴⡿⠟⠋⣉⣭⣽⣿⣿⣿⣿⡖⠈⡁⠀⣿⣶⣠⣴⠟⠋⠁⠀⠀⠤⣵⣾⣿⣿

⠿⠟⠛⣻⣿⡇⠀⠀⠀⠀⢨⣿⣿⣟⡈⣉⣭⣄⢀⡈⢉⣀⣠⠖⣾⣿⣿⠏⠛⠃⢸⣿⣟⢛⣽⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠛⠉⠁⠰⢆⣾⣿⣿⣿⣿⣿⣿⣿⠁⠸⠃⠀⢻⣿⣿⡛⢿⠀⣀⣀⣴⡾⠟⠉⠀⠀

⠀⣀⣴⣿⡟⠀⠀⠀⠀⣤⣿⣿⣿⡿⠀⠸⣿⡿⠊⠉⠉⢡⣶⣶⣿⣿⣉⠀⢀⡔⠉⢿⣧⠸⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠁⠀⠀⠐⠊⢀⣤⣿⡿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⡯⢿⣷⣆⣸⣿⣿⣿⡇⣀⣤⣤⣶

⠛⠛⠉⢿⣧⠀⠀⣠⡴⠿⠏⣿⣿⡗⠲⢠⣭⠠⠄⠤⠤⠾⣿⣿⡿⣿⣿⣦⡟⠀⠀⠘⢿⣇⠈⢿⡿⠿⠛⣡⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠋⠀⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⢸⣿⢣⠀⠉⠉⠘⠛⠛⠛⠀⠛⠋⠉⠁

⠀⣢⣠⣾⡏⢀⡞⠁⠀⣸⣷⣿⣿⡧⠤⣬⣥⠀⢤⣤⣤⣰⣿⣿⣡⡿⣿⣿⣷⣦⣤⣴⣶⣾⣤⣄⡀⠀⠴⠿⠛⠛⠉⠁⠉⠉⠁⠀⣠⠐⠒⠶⣼⣿⣿⣿⣿⠟⠁⢰⢻⡇⠀⢺⣿⢸⣦⣄⣀⡀⣷⣶⣿⡷⠀⠀⠀⠀

⠛⠿⠟⢯⣠⠎⠀⠀⠀⣿⡿⣼⣿⡇⡀⠈⠙⠂⠀⠈⢩⣿⣿⠟⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⣾⡆⠀⠀⠀⠀⠀⠐⠊⠁⣀⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⣿⣷⠀⠘⣿⡇⠙⠛⠿⠿⣿⣯⣭⡄⠴⡶⢶⣶

⠀⠆⣲⣾⠿⢶⠄⠠⢶⡿⠷⢿⣿⡇⢀⠀⠈⠀⠀⠈⣽⣿⡟⠶⢾⠃⣿⣿⣿⣿⣯⡻⢿⣇⡙⠻⠛⠀⠰⣿⣷⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⡿⠟⠋⢙⣿⣷⠀⠀⢰⣿⡿⠀⠀⢸⣷⣄⡀⠀⠀⠗⠿⠿⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠢⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣽⣿⡇⣿⣯⢘⣳⡄⣠⣏⣷⣿⣿⣧⣿⣿⠀⣽⡗⣽⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⢛⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠛⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣷⣶⣤⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠁⠀⠀⠙⣿⡛⣛⡃⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⣿⠏⠀⠀⠀⠀⠀⠀⣿⠇⢿⣧⡀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡄⠀⠀⠀⠀⠀⣰⠇⠠⠀⢻⣿⣶⣤⣀⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⡿⠿⠿⢿⠿⠟⠉⠀⠉⠉⠉⠻⡆⠀

⡟⠀⠈⠙⢿⣿⣿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⠀⠀⣤⣴⣿⡀⠀⣐⢀⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠏⠁⠀⠀⠀⢀⡗⠻⣦⣄⡀⠀⠀⣰⣇⠀

⣿⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣠⣿⠁⠀⣘⣿⣿⣷⣿⡟⠙⠀

⣿⣤⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⢤⣾⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⡄⠀

⣿⣿⠿⣿⡟⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣛⣟⣿⣿⣿⣿⠿⠟⠛⢹⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⢛⡿⠟⠛⠛⠋⠛⢻⣿⠃⠀

⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠘⢿⣏⠀⠈⠛⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠈⠀⠀⣀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀

⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⣶⣾⣿⣧⣠⣴⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡗⡷⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠉⢉⡤⠂⠈⣿⡇⠀

⢛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⠋⡿⣢⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⣿⣿⠿⠋⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠈⠀⣀⣴⣿⣷⠀

⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢟⠀⠀⠀⠀⢀⣾⣿⡿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣯⣷⠶⢺⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣈⣟⣿⣿⣿⡿⢻⡄

⠒⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣾⣿⣫⠄⠀⠀⢠⣿⣿⣿⣿⡈⠻⣿⣿⣶⣶⠿⠟⠛⠓⠢⠤⠄⠀⠀⠀⠀⣺⣿⢛⣿⣿⣶⣄⣀⣤⣤⣶⣾⣿⣿⣶⡶⢶⣤⣄⡀⠀⠀⠀⣉⣿⡿⠛⠛⠋⣠⣾⢷

⠀⣀⣀⣹⣿⣤⣤⣤⣤⣶⣶⣦⣤⣀⡀⣠⣤⣿⣏⠒⠡⠐⢀⡀⠘⣿⣿⣿⣿⣏⠀⣹⣿⣿⡏⠀⠀⠉⠉⠒⠢⠀⠀⠀⠀⠀⠀⠁⣀⣤⣿⣿⠿⠛⢛⣻⣭⣭⣿⣿⣿⠉⢛⠀⣽⣶⣤⣤⠾⠛⠋⠀⠀⢌⢑⣤⣾⣿

⣿⣿⠿⠿⣿⣿⠉⠁⠀⠀⠈⣻⣻⣿⠋⠚⢛⣁⠀⠀⠒⠁⠀⣠⢦⣿⣿⡿⠻⠻⠀⣿⣿⠿⢛⣿⣿⣷⣶⣶⣦⣴⣿⣿⣿⣶⣾⠿⠟⠋⠡⠴⢰⣿⣿⣿⣿⣿⣿⣿⡟⠀⡟⠀⠸⣿⣯⡿⢿⡆⢀⣀⣀⣤⣿⠛⠉⠁

⠀⠀⢀⣾⣿⠏⠀⠀⠀⢀⣼⣿⣿⣿⡇⠈⣿⣿⡇⠛⠚⠋⣩⣤⣾⣿⠏⠁⠀⢀⠔⣻⣿⡀⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⠉⠉⠀⠠⠴⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⢻⣿⣶⢡⣿⣿⣿⣿⠀⣀⣀⣤

⠶⠾⠟⢻⣷⡀⠀⠀⣀⣼⠿⢻⣿⡿⠤⡄⣈⡋⡀⢀⣀⣤⣿⣿⣿⣿⣿⣦⣴⠃⠈⠀⢿⣷⠈⢻⣿⠿⡿⠋⣴⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⠿⠃⢸⣿⣿⣿⣿⣿⡿⢿⡆⠀⠀⣿⡏⡀⠙⠛⠈⠛⠿⠿⠋⠘⠟⠛⠉

⠀⠠⡀⣠⣿⠃⢠⠞⠁⠀⣷⣼⣿⣿⣀⣀⣛⠁⢀⣀⣀⣀⣼⣿⣟⣸⣿⣿⣿⣤⣀⣠⣤⣭⣧⣀⠉⠀⠠⢾⠿⠟⠛⠛⠙⠛⠉⠉⠁⡉⠤⢤⣤⣿⣿⣿⣿⣿⠟⠀⡟⣷⠀⢰⣿⡏⣧⣀⣀⠀⢰⣶⣶⣶⡄⠀⠀⠀

⠶⠾⠿⢿⡋⡠⠋⠀⠀⢰⣿⣿⣿⣿⠀⠈⠛⡇⠀⠉⠛⣻⣿⡿⠿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⢰⣶⠀⠀⠀⠀⠀⠠⠔⠊⠁⣰⣤⣾⣿⣿⣿⣿⠇⠀⠀⢱⣷⡄⠀⢿⣿⠘⠿⠿⢿⣾⣿⣋⣉⡠⣶⠶⣶

⠀⠆⠲⣶⡿⢶⠄⠠⠴⣾⠿⢻⣿⣿⠈⠀⠀⠂⠀⠁⢲⣿⣿⢣⣤⡿⢹⣿⣿⣾⣽⡿⣿⣿⠙⠻⠿⠇⠀⣼⣿⣄⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⠟⠙⣿⣿⡄⠀⠀⣼⣿⡇⠀⠈⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⣄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⣾⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣶⣤⣄⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⡿⠟⠉⠀⠀⠈⣿⡟⣛⡋⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣷⡟⠁⠀⠀⠀⠀⠀⢸⡿⠿⣷⣀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢧⠀⠀⠀⠀⠀⢀⡟⠀⠀⠘⣿⣷⣤⣀⣠⣴⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠻⠿⡿⠿⠋⠀⠈⠉⠉⠙⢇⠀

⠛⠁⠈⠙⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡄⠀⢠⣴⣾⡅⠀⢀⠂⣽⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠉⠀⠀⠀⠀⡸⠛⢶⣤⣀⠀⠀⢀⣿⠀

⣿⡆⠀⠀⠀⠘⣿⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⣾⡇⠀⣀⣻⣿⣿⣿⡿⠉⠃

⣿⣧⣀⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣦⣶⣿⣿⣷⣾⡿⣿⣿⣿⣿⣿⣦⠀

⣿⣿⡿⢿⣿⠛⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⣟⣿⣻⣿⣿⣿⡟⠟⠛⢫⣷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠹⠟⣿⠿⠛⠛⢋⠛⠛⣿⡏⠀

⣿⣿⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠻⣿⡁⠈⠙⢿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠁⠀⢀⣀⣤⡼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀

⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠾⢶⣶⣿⣷⣄⣠⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢾⢶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⠀⠉⠉⣡⠔⠀⢹⣿⠀

⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠻⡟⢹⢷⡿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢾⣿⣿⣿⣿⣿⡿⠟⣩⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⡁⢀⣠⣾⣿⡄

⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⡁⠀⠀⠀⠀⣰⣿⡿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢟⣻⣵⡶⠶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣅⣹⣻⣿⣿⣿⠿⣦

⠗⠒⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⡥⠀⠀⠀⣼⣿⣿⣿⡇⠙⢿⣯⣷⣶⡶⠿⠛⠓⠒⠤⠤⠀⠀⠀⠀⢰⣿⡏⣻⣿⣶⣦⣀⣤⣤⣴⣶⣿⣿⣷⣶⢶⣦⣤⣀⠀⠀⠀⢈⣹⣿⠛⠛⠛⢁⣼⡿

⠀⠀⢀⣘⣿⣧⣤⣤⣤⣤⣶⣦⣤⣀⡀⢀⣤⣼⣿⡐⠊⠄⠂⣀⠀⢿⣿⣿⣿⣗⡀⢈⣿⣿⣿⠁⠀⠈⠉⠓⠲⠄⠀⠀⠀⠀⠀⠈⢀⣠⣼⣿⠿⠛⠛⣛⣯⣭⣽⣿⣿⡏⠙⠋⢨⣷⣦⣤⡴⠟⠛⠁⠁⠠⡁⣠⣶⣿

⣾⣿⡿⠿⢿⣿⡋⠉⠉⠀⠀⢙⣿⣿⡟⠙⠛⣋⠀⠀⠐⠂⠀⢀⡴⣼⣿⣿⠟⠿⠇⢸⣿⡿⠟⣻⣿⣷⣶⣶⣶⣤⣾⣿⣿⣶⣶⡿⠿⠛⠉⠤⠆⣾⣿⣿⣿⣿⣿⣿⣿⠁⠸⠃⠈⣿⣿⣽⠿⣷⠀⣀⣀⣠⣽⡟⠋⠉

⠁⠀⢀⣰⣿⡿⠀⠀⠀⠀⣠⣿⣿⣿⣿⠈⢹⣿⣷⠚⠒⠚⢉⣭⣴⣿⡿⡁⠀⠀⡠⠺⣿⡇⢸⣿⣿⣿⣿⣿⣿⡟⠿⠛⠋⠉⠁⠀⠤⠂⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣟⣿⣾⡎⣼⣿⣿⣿⡇⢀⣀⣤

⠴⠶⠿⠻⣿⡆⠀⠀⢀⣠⡿⠛⣿⣿⠧⢠⣈⣛⢁⢀⣀⣀⣼⣿⣿⣿⣿⣷⣠⡞⠀⠁⠸⣿⡄⠹⣿⡿⡿⠟⢡⣶⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠟⠀⣿⣿⣿⣿⣿⣿⠿⣣⠀⠀⢸⣿⣃⠈⠛⠓⠹⠻⠿⠟⠁⠻⠛⠉

⠀⠀⢀⢀⣼⡟⠀⡴⠋⠁⢸⣤⣿⣿⣄⣀⢘⡋⠀⣀⣀⣀⣠⣿⣿⣃⣿⣿⣿⣧⣄⣀⣠⣬⣵⣀⡈⠁⠀⢴⡿⠿⠟⠛⠋⠛⠋⠉⠉⢈⠡⠤⣤⣼⣿⣿⣿⣿⡿⠃⢸⢿⡄⠀⣿⣿⢻⣄⣀⡀⢰⣶⣶⣶⡦⠀⠀⠀

⠶⢶⣾⡿⣟⢁⠜⠁⠀⠀⣿⣿⣿⣿⡀⠀⠙⢳⠀⠈⠙⢻⣿⣿⠿⢿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠀⣶⠆⠀⠀⠀⠀⠀⠤⠚⠉⢀⣤⣴⣿⣿⣿⣿⡿⠀⠀⠈⣾⣧⠀⠸⣿⡏⠛⠿⠿⣷⣿⣟⣉⣁⣴⣶⣶

⠀⠆⠲⣶⣿⢷⠄⠠⠴⢶⡿⠹⣾⣿⡏⠁⠀⠐⠀⠀⠐⣾⣿⣟⣤⣼⠇⣿⣿⣷⣭⡿⠿⣿⡟⠛⠿⠿⠀⢸⣿⣧⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⡿⠋⢻⣿⣧⠀⠀⢨⣾⣿⠀⠀⢻⣧⡀⠀⠀⠀⠿⣿⣿⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣽⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⢛⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣷⣦⣤⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⣿⡿⠋⠁⠀⠈⢻⣿⢛⣛⠁⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⠋⠀⠀⠀⠀⠀⠈⣿⡾⣿⣆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⡀⠀⠀⠀⠀⠀⣼⠃⠀⠈⢿⣷⣦⣄⣀⣤⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⠿⠿⢿⠿⠟⠁⠀⠉⠉⠉⢻⡀

⠛⠟⠉⠉⠻⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡄⠀⠀⢤⣴⣏⠀⠀⡐⢸⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠁⠀⠀⠀⢀⠞⢷⣦⣄⠀⠀⠀⣼⡅

⣿⣧⠀⠀⠀⠈⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣴⣿⠀⢀⣙⣿⣿⣶⣿⠏⠑

⣿⣿⣀⣀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⢴⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⠀

⣿⣿⣿⠿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣻⣟⣿⣿⣿⣿⠿⠟⠛⣿⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⡿⢻⡿⠿⠛⠛⠙⠛⢻⣿⠀

⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠸⣿⡏⠈⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠉⠀⠀⢀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀

⣤⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠦⣶⣾⣿⣆⣀⣴⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⡶⣶⣾⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠈⠉⢉⡤⠀⠸⣿⡆

⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠭⠿⢿⠋⡿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣷⣿⣿⣿⣿⣿⣿⠿⢛⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⢀⠀⢈⠀⣀⣼⣿⣇

⣶⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⠠⣾⣿⣷⣶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠩⠝⣛⣯⣥⠶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⣘⣟⣿⣿⣿⡿⢷

⡿⠒⠢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⣾⣗⣫⠄⠀⠀⢠⣿⣿⣿⣷⠉⢻⣿⣽⣦⣶⠶⠾⠓⠲⠤⢤⡀⠀⠀⠀⠀⣿⡿⠻⣿⣷⣦⣄⣀⣠⣤⣴⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡛⠛⠛⠋⣠⣿

⠀⠀⠀⠀⣻⣷⣄⣤⣤⣤⣤⣤⣤⣀⡀⠀⣠⣤⣿⣇⠐⠡⠀⣀⡀⢸⣿⣿⣿⣿⢀⠀⢻⣿⣿⡋⠀⠐⠒⠒⠒⠤⠀⠀⠀⠀⠀⠀⠁⣀⣨⣽⣿⠿⠛⢛⣻⣿⣭⣿⣿⣯⠙⠛⠉⣽⣦⣤⣤⠾⠟⠃⠀⠀⠍⣁⣴⣾

⣶⣾⣿⣿⠿⣿⣟⠛⠉⠉⠉⠉⡿⠿⣿⠓⠻⠟⠋⠀⠀⠒⠀⠀⣠⣤⣿⣿⡟⠿⠿⢠⣧⡿⡿⢛⣿⣷⣶⣶⣶⣆⣴⣿⣿⣷⣶⣾⠿⠟⠋⢡⡤⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⡟⠀⢹⣿⣿⠿⢷⡆⢀⣀⣀⣤⣿⠛⠉

⠉⠁⠀⢀⣼⣿⠇⠀⠀⠀⢀⣸⣿⣿⣿⡇⠐⣿⣿⡖⠒⠒⠚⣩⣅⣾⣿⠏⠀⠀⢀⠜⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠋⠉⠀⠠⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣷⣖⢡⣿⣿⣿⣿⠀⣀⣀

⡤⠦⣶⠿⢿⣯⠀⠀⠀⢀⣼⣿⢻⣿⡿⢄⣀⣙⠋⡀⣀⣀⣠⣿⣿⣿⣿⣾⣅⣴⠃⠈⠈⢿⣧⠈⢿⣿⣿⡿⠋⣵⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⡿⠃⣻⣿⣿⣿⣿⣿⡿⢿⡄⠀⢀⣿⣇⠀⠙⠛⠈⠟⠿⠿⠋⠸⠟⠋

⠀⠀⢀⠀⢸⣿⠀⢠⠞⠉⢁⣦⣼⣿⣇⠀⠀⢛⠁⠀⣀⠀⢀⣼⣿⡟⣸⣿⣿⣿⣤⢀⣀⣠⣽⣄⡈⠉⠀⢠⣾⠿⠿⠟⠛⠙⠛⠋⠉⠉⡉⠤⢤⣄⣿⣿⣿⣿⣿⠟⠀⣿⣧⠀⢸⣿⡟⣆⣀⣀⠀⣶⣦⣶⣶⠄⠀⠀

⠶⠶⣶⣿⣿⡋⣠⠏⠀⠀⢸⣿⣿⣿⡇⠀⠉⠟⡆⠈⠙⠛⣿⣿⡿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢠⡦⠀⠀⠀⠀⠀⠀⠤⠊⠁⣠⣤⣾⣿⣿⣿⣿⠇⠀⠀⢹⣿⡄⠈⢿⣷⠙⠿⠿⣿⣿⣿⣛⣉⢠⣴⣶

⠀⠆⠲⣶⢿⣿⠇⠠⠴⠶⣾⡟⢿⣿⣿⠉⠀⠤⠃⠈⠀⠰⣿⣿⣧⣤⡿⢸⣿⣿⣮⣿⢿⣿⣿⠛⢿⡿⠆⠀⣿⣿⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠟⠛⣿⣿⡄⠀⠀⣾⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣤⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⢛⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠙⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⣿⡿⠋⠁⠀⠈⢻⣿⢛⣛⠁⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣾⠋⠀⠀⠀⠀⠀⠈⣿⡾⣿⣆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡀⠀⠀⠀⠀⠀⣼⠃⠀⠈⢿⣷⣦⣄⣀⣤⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⠿⠿⠿⠿⠟⠁⠀⠉⠉⠉⢻⡀

⠛⠟⠉⠉⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡄⠀⠀⢤⣴⣏⠀⠀⡐⢸⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠁⠀⠀⠀⢀⠞⢷⣦⣀⠀⠀⠀⣼⡅

⣿⣧⠀⠀⠀⠈⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣴⣿⠀⢀⣙⣿⣿⣶⣿⠏⠱

⣿⣿⣀⣀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⣴⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⠀

⣿⣿⣿⠿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣻⡛⣿⣿⣿⣿⠿⠟⠛⣿⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⡿⢻⡿⠿⠛⠛⠙⠛⢻⣿⠀

⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠸⣿⡏⠀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠉⠁⠀⢀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀

⣤⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⣶⣾⣿⣆⣀⣴⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⡶⡶⣶⣾⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠈⠉⢉⡤⠀⠸⣿⡆

⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠭⠿⢿⠋⡿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣵⣿⣿⣿⣿⣿⣿⠿⢛⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⢀⠀⢈⠀⣀⣼⣿⣇

⣶⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠏⠀⠀⠀⠀⠠⣾⣿⣷⣶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠩⠝⣛⣯⣥⡶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⣜⣿⣿⣿⣿⡿⢷

⡿⠒⠲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⣾⣗⣫⠄⠀⠀⢠⣿⣿⣿⣷⠉⢻⣿⣽⣦⣶⠶⠶⠓⠲⠤⢤⡀⠀⠀⠁⢀⣿⡿⠻⣿⣶⣦⣄⣀⣤⣤⣶⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡛⠛⠛⠏⣠⣿

⠀⠀⠀⠀⣻⣷⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⣀⣤⣿⣗⠐⠡⠀⣀⠀⢸⣿⣿⣿⣿⢀⠀⢻⣿⣿⡋⠀⠐⠒⠒⠒⠤⠀⠀⠀⠀⠀⠀⠁⣀⣨⣽⣿⠿⠛⢛⣻⣿⣭⣿⣿⣯⠑⠛⠉⣽⣦⣤⡤⠾⠟⠃⠈⠀⠍⣁⣴⣾

⣶⣾⣿⣿⠿⣿⣛⠛⠉⠉⠉⠉⡿⠿⣿⠓⠛⠟⠋⠀⠀⠒⠀⠀⣠⣤⣿⣿⡟⠿⠿⢠⣷⣿⡿⢛⣿⣷⣶⣶⣶⣦⣴⣿⣿⣶⣶⣾⠿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⡟⠀⢹⣿⣿⡿⢷⡆⢀⣀⣀⣤⣿⠛⠉

⠉⠉⠀⢀⣼⣿⠏⠀⠀⠀⢀⣸⣿⣿⣿⡏⠐⣿⣿⡖⠒⠒⠚⣩⣅⣾⣿⠏⠀⠀⢀⠜⢿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠋⠉⠀⠠⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣷⣖⢩⣿⣿⣿⣿⠀⣀⣀

⣤⠦⣾⠿⢿⣯⠀⠀⠀⢀⣼⣿⢿⣿⡿⢄⣀⣙⠋⣀⣀⣀⣠⣿⣿⣿⣿⣾⣅⣴⠃⠈⠈⢿⣇⠈⢿⣿⣿⡿⠋⣵⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⡿⠃⣻⣿⣿⣿⣿⣿⡿⢿⡄⠀⢀⣿⣇⠀⠙⠛⠉⠟⠿⠿⠋⠸⠟⠋

⠀⠀⢀⠀⢸⣿⠀⢠⠞⠉⠁⣦⣼⣿⣇⠀⠀⢛⠁⠀⣀⠀⠀⣼⣿⡟⣸⣿⣿⣿⣤⢀⣀⣠⣽⣄⡈⠉⠀⢠⣾⠿⠿⠟⠛⠙⠛⠋⠉⠉⡉⠤⣤⣄⣿⣿⣿⣿⣿⠟⠀⣿⣧⠀⢸⣿⡟⣆⣀⣀⠀⣶⣤⣶⣶⠄⠀⠀

⠶⢶⣶⣿⣿⡋⣠⠏⠀⠀⢸⣿⣿⣿⡇⠀⠉⠟⡆⠈⠙⠛⣿⣿⡿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢠⡦⠀⠀⠀⠀⠀⠀⠤⠊⠁⣠⣤⣾⣿⣿⣿⣿⠇⠀⠀⢸⣿⡄⠀⢿⣷⠙⠿⠿⣿⣿⣿⣛⣉⢠⣴⣶

⠀⠆⠲⣶⢿⣿⠅⠠⠲⠶⣾⡟⢿⣿⣿⠉⠀⠠⠃⠈⠀⢠⣿⣿⣧⣤⡿⢸⣿⣿⣮⣿⢿⣿⣿⠛⢿⡿⠆⠀⣿⣿⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠟⠛⣿⣿⡄⠀⠀⣾⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⣈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣹⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣶⣤⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠟⠉⠀⠀⠙⣿⡟⣛⡋⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣷⡟⠁⠀⠀⠀⠀⠀⢹⢧⢿⣧⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⢠⡟⠠⠀⠹⣿⣦⣄⣀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡿⠿⠿⠿⡿⠿⠋⠀⠉⠉⠉⠙⣇

⡙⠟⠏⠉⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⣤⣾⡁⠀⠀⠂⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠉⠀⠀⠀⠀⡰⠻⣶⣄⡀⠀⠀⢠⣯

⢰⣿⡄⠀⠀⠀⠹⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢠⣾⡇⠀⣈⣻⣿⣷⣾⡿⠉

⢸⣿⣇⡀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣗⢦⣶⣿⣿⣷⣾⣻⣿⣿⣿⣿⣿⡆

⣼⣿⣿⣿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⣟⣛⣻⣿⣽⣿⡿⠿⠛⢻⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠻⠟⣿⠿⠟⠛⢋⠛⠛⣿⡇

⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠊⠉⡉⢿⣿⠉⠉⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠉⠁⠀⠀⣀⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇

⣤⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⢴⣴⣿⣧⣀⣠⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⢶⣴⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠉⠉⣡⠄⠀⢿⣷

⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠭⠿⢿⡟⢹⢧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⣾⣿⣿⣿⣿⣿⡿⠟⣋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡀⠀⡁⢀⣠⣾⣿

⣥⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠃⠀⠀⠀⠀⢰⣾⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⢛⣻⣭⡤⢶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣅⣻⣻⣿⣿⣿⠿

⣿⠿⠥⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⣿⣚⡅⠀⠀⠀⣴⣿⣿⣿⡎⠙⣿⣯⣶⣤⡶⠶⠖⠲⠦⠤⣄⠀⠀⠀⠁⢰⣿⠟⢿⣷⣶⣤⣀⣀⣤⣤⣶⣾⣿⣶⣶⢶⣤⣄⡀⠀⠀⠀⢈⣹⣿⠛⠛⠛⢁⣼

⡆⠀⠀⠀⢙⣿⣆⣀⣠⣤⣤⣤⣤⣀⣀⠀⢀⣠⣴⣿⡉⠛⠠⢀⡀⠀⣿⣿⣿⣿⡇⡀⠘⣿⣿⣟⠁⠀⠒⠒⠒⠢⠄⠀⠀⠀⠀⠀⠈⢀⣀⣭⣿⡿⠟⠛⣛⣿⣭⣽⣿⣿⡅⠙⠋⢩⣷⣤⡤⠴⠿⠛⠁⠀⠀⢁⣠⣶

⣴⣶⣾⣿⣿⢿⣿⡛⠋⠉⠉⠉⠻⠿⠿⡿⠺⠿⠛⠉⠁⠐⠒⠀⢀⣤⣼⣿⣿⢟⠿⠇⣸⣿⣿⡟⢿⣿⣶⣶⣶⣶⣠⣾⣿⣷⣶⣶⣾⠿⠛⠉⣥⠄⣾⣿⣿⣿⣿⣿⣿⣿⠁⢸⠀⠈⣿⣿⣿⠿⣶⢀⣀⢀⣠⡸⡟⠋

⠛⠉⠉⠀⢠⣿⣿⠁⠀⠀⠀⢀⣾⣿⣿⣷⠀⢺⣿⣷⠒⠶⠒⢚⣉⣠⣿⡿⠉⠀⠀⡠⠻⣿⡇⢼⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠀⠠⠄⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⡿⣿⣶⡀⣾⣿⣿⣿⡇⢀⣀

⣤⡤⢴⡾⠿⣿⡅⠀⠀⠀⣀⣿⡛⣻⣿⣇⣀⡈⡛⢁⣀⣀⣀⣸⣿⣿⣿⣷⣧⣀⡞⠀⠁⠹⣿⡌⠹⣿⣿⣿⠟⢉⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⠟⠈⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⢸⣿⣁⠈⠛⠓⠙⠻⠿⠟⠁⠿⠛

⠀⠀⠀⡀⠀⣹⡗⠀⣠⠚⠉⢰⣀⣻⣿⡀⠀⠸⠛⠀⠀⠀⠀⢠⣿⣿⢃⣿⣿⣿⣇⡄⢀⣀⣭⣷⣀⠉⠁⠀⣠⣿⠿⠿⠛⠛⠛⠛⠋⠉⢉⠩⢤⣄⣸⣿⣿⣿⣿⡿⠃⢸⣿⡄⠀⣿⣿⢻⣀⣀⠀⠠⣶⣴⣶⣦⠀⠀

⠤⢤⣴⣾⣿⣿⠃⡴⠁⠀⠀⣾⣿⣿⣿⡁⠈⠻⢷⠈⠙⠛⢻⣿⣿⡿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⣤⠄⠀⠀⠀⠀⠀⠠⠔⠉⠀⣤⣴⣿⣿⣿⣿⡿⠀⠀⠘⣶⣧⠀⠹⣿⡆⠻⠿⠿⣷⣿⣟⣋⡁⣤⣶

⠀⠆⠲⣶⠋⣿⠎⠠⠰⠶⢶⣿⠻⣿⣿⡇⠀⠠⠬⠀⠁⠀⢼⣿⡿⣤⣼⠇⣿⣿⣧⣽⡿⣿⣿⡟⠻⣿⠷⠀⢸⣿⣆⣀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⡿⠛⢻⣿⣧⠀⠀⢸⣿⣿⠀⠀⢹⣧⡀⠀⠀⠀⠿⣿⣿⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⢿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⢈⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣴⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣷⣦⣤⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⠿⠋⠁⠀⠉⢻⣿⢛⣛⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣼⣿⠃⠀⠀⠀⠀⠀⢘⣿⡸⣿⣄⠀⠀⠀⠀⠀⢀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⠀⠀⠀⠀⠀⠀⣼⠃⠄⠈⣿⣷⣤⣀⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⠿⠏⠀⠀⠉⠉⠉⢻

⣘⠻⠿⠉⠛⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⢠⣼⣇⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠋⠀⠀⠀⠀⢀⠟⢳⣦⣄⠀⠀⢀⣼

⠃⣾⣇⠀⠀⠀⠈⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣷⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣴⣿⠀⢀⣹⣿⣿⣿⣿⡏

⠀⣿⣿⣀⠀⠀⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⢴⣿⣿⣿⣶⣟⣿⣿⣿⣿⣿⣷

⣤⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢛⣛⣿⣿⣿⣿⠿⠛⠋⣿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠿⢻⡿⠛⠛⠙⡉⠙⢻⣿

⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠹⣿⡏⠉⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀⢀⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⠀⠀⠀⢀⣸

⣤⣭⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣦⣼⣿⣄⣀⣰⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣦⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠉⢉⡤⠀⠸⣿

⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠽⠿⣿⠛⡿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣴⣿⣿⣿⣿⣿⣿⠿⢛⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢄⢀⠀⢀⠀⣀⣼⣿

⣭⣴⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⠠⣾⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢙⣛⣯⣥⡴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⣜⣿⣿⣿⣿⡿

⣿⡿⠭⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣷⣋⠀⠀⠀⢠⣾⣿⣿⣷⠙⢿⣿⣵⣦⣶⠶⠶⠒⠶⠤⢤⡀⠀⠀⠁⢀⣿⡟⠻⣿⣶⣦⣄⣀⣤⣤⣶⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡟⠛⠛⠋⣠

⣶⡀⠀⠀⠈⢻⣷⣀⣀⣀⣠⣤⣤⣄⣀⡀⠀⣀⣄⣾⣏⠙⠋⠄⣀⠀⢸⣿⣿⣿⣿⢀⠀⢻⣿⣿⡋⠀⠐⠒⠒⠒⠤⠀⠀⠀⠀⠀⠀⠁⣀⣨⣽⣿⠿⠛⢛⣻⣿⣭⣿⣿⣯⠙⠋⠉⣽⣦⣤⡤⠾⠟⠋⠈⠀⢈⣉⣴

⣡⣴⣶⣿⣿⣿⣿⣟⠛⠋⠉⠉⠙⠿⠿⣿⠒⠿⠿⠋⠉⠀⠒⠂⠀⣠⣤⣿⣿⡟⡿⠿⢠⣯⣿⡿⠻⣿⣷⣶⣶⣶⣆⣴⣿⣿⣶⣶⣶⡿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⡟⠀⢹⣿⣿⡛⢷⡆⢀⣀⣀⣤⣿⠋

⠏⠋⠉⠉⠀⣸⣿⡏⠀⠀⠀⠀⣰⣿⣿⣿⡆⠐⣾⣿⡖⠶⠶⠒⣋⣁⣾⣿⠏⠀⠀⢀⠜⢿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⢻⣷⣶⢠⣿⣿⣿⣿⠀⣀

⣤⣤⠤⣶⡿⢿⣯⠀⠀⠀⢀⣸⣿⣿⣿⣿⣀⣀⠙⠋⡁⣀⣀⣀⣿⣿⣿⣿⣾⣄⣰⠋⠈⠈⢿⣇⠈⢿⣿⣿⡿⠛⣱⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⡿⠃⢸⣿⣿⣿⣿⣿⡿⢿⡀⠀⠀⣿⡏⡀⠙⠛⠋⠟⠿⠿⠋⠘⠟

⠀⠀⠀⢀⠀⢈⣿⠆⢀⡴⠋⠉⣦⣨⣿⣧⠀⠀⠿⠃⠀⠀⠉⠀⣼⣿⡟⣸⣿⣿⣿⣠⠀⣀⣨⣽⣆⡈⠉⠀⢀⣼⡿⠿⠟⠛⠛⠛⠛⠉⠉⡉⠤⢤⣄⣿⣿⣿⣿⣿⠟⠀⡿⣧⠀⢸⣿⡟⣧⣀⣀⠀⢴⣦⣶⣶⡆⠀

⡤⣤⣤⣴⣿⣿⠟⢀⠞⠀⠀⢰⣿⣟⣿⣯⠉⠙⠿⡆⠉⠛⠛⣻⣿⣿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢠⡤⠀⠀⠀⠀⠀⠀⠤⠚⠁⢠⣤⣾⣿⣿⣿⣿⠇⠀⠀⢰⣿⡄⠀⢿⣿⠙⠻⠿⢿⡾⣿⣛⣉⢠⣴

⠀⠆⠲⣶⠉⢾⣷⠣⠰⠶⠆⣸⡟⢻⣿⣿⠀⠀⠠⠅⠈⠀⠠⣿⣿⢧⣤⡿⢹⣿⣿⣮⣿⢿⣿⣿⠙⢿⣿⠆⠀⣾⣿⣄⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠛⢿⣿⡄⠀⠀⣼⣿⡇⠀⠈⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢻⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⢹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⢛⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣷⣦⣄⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⠿⠋⠁⠈⠙⣿⡿⣟⡛⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣾⣿⠁⠀⠀⠀⠀⠀⢸⣷⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣃⠀⠀⠀⠀⠀⢀⣾⠀⡀⠹⣿⣶⣄⣀⣀⣤⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠿⠿⠿⠿⠋⠀⠈⠉⠉⠉

⠀⠿⢿⡿⠛⠻⢿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⣠⣾⡇⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⠋⠀⠀⠀⠀⢸⠛⢷⣦⣀⠀⠀⢀

⡾⠇⣶⡆⠀⠀⠀⠙⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣱⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣴⡯⠀⢀⣹⣿⣿⣿⣿

⠀⠀⣿⣇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡲⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿

⣤⣠⣿⣿⣿⣷⣾⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣿⢟⣛⣿⣭⣿⣿⠿⠻⠋⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠙⡿⢻⠿⠛⠛⠙⡉⠙⢻

⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⢻⣿⡏⠉⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⠉⠉⠉⠀⠀⢀⣀⣴⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⣀

⣌⣉⣉⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣷⡀⢀⡸⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢴⣴⣴⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠉⢁⠴⠀⢸

⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢙⡛⢿⣿⢛⡷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣾⣶⣿⣿⣿⣿⣿⠟⢋⣵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⡀⠀⢀⢀⣠⣾

⣛⣋⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⢠⣶⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢛⣯⣤⡴⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣜⣻⣿⣿⣿

⣿⣿⣿⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⢇⠀⠀⠀⢠⣾⣷⣿⡎⠙⢿⣯⣷⣤⣴⡶⠶⠲⠦⠤⣤⠀⠀⠀⠀⢠⣿⡟⠻⣷⣶⣤⣀⣀⣠⣤⣶⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣙⣿⡟⠛⠛⠍

⣭⣭⠁⠀⠀⠉⣿⣦⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣿⡏⠽⡋⠄⡀⠀⢸⣿⣿⣿⣿⠂⠈⢿⣿⣿⠋⠀⠐⠒⠒⠢⠄⠀⠀⠀⠀⠈⠈⠁⣀⣩⣽⣿⠿⠛⢛⣻⣯⣽⣿⣿⣯⠘⠋⠉⣽⣦⣠⡤⠾⠟⠃⠈⠀⢉⣡

⣿⣩⣤⣴⣶⣾⣿⡿⠿⠟⠛⠛⠙⠛⢿⣿⣿⠶⠿⠿⠋⠁⠀⠤⠀⠉⣁⣨⣿⣿⡟⡿⠟⢠⣿⢿⡿⠻⣷⣶⣶⣶⣶⣄⣴⣾⣶⣶⣶⣶⡿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⢻⣿⣿⡻⢷⡆⣀⣀⣀⣄⣿

⣿⠟⠛⠋⠉⠁⣸⣿⡇⠀⠀⠀⠀⣰⣿⣾⣿⠂⠰⣾⣷⡤⠦⠤⠖⣚⣁⣾⣿⠟⠁⠀⢀⠼⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⢀⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⢿⣿⣗⢸⣿⣿⣿⣿⠁

⣀⣀⣀⣤⣴⡾⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⠻⠟⡁⠀⠀⣰⣿⣿⣿⣿⣾⡀⣰⠃⠈⠈⣿⣆⠙⣿⣿⣿⡿⠋⣱⣄⣠⣤⣀⣀⣀⣠⣤⣶⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢟⡀⠀⢀⣿⣇⠀⠙⠛⠈⠟⠻⠿⠋⠸

⠉⠉⠀⠀⠈⠀⢸⣿⠀⢀⡴⠛⠉⡇⣸⣿⡇⠀⠙⠿⠀⠁⠉⠉⠉⣼⣿⡟⣸⣿⣿⣿⣀⠀⣀⣈⣻⣀⠈⠋⠀⢀⣼⡿⠿⠟⠛⠛⠛⠛⠉⠉⡩⠥⣤⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⢸⣿⡟⣦⣀⣀⠀⢴⣦⣶⣶⠄

⣤⣤⣤⣤⣬⣷⣾⠟⢀⠞⠀⠀⢸⣿⣿⣿⡏⠉⠓⠿⡄⠘⠛⠿⣿⣿⣿⣿⣏⢹⣿⡻⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⢠⡤⠀⠀⠀⠀⠀⠀⠤⠊⠁⢠⣤⣾⣿⣿⣿⣿⠃⠀⠀⢹⣿⡄⠈⢿⣧⠙⠻⠿⢿⣞⣿⣙⣉⢠

⠀⠆⠲⣶⠋⢿⠽⡷⠿⠶⠆⠀⢸⡟⣿⣿⣿⠒⠀⠀⠇⠀⠀⢤⣿⣿⢇⣠⣿⢸⣿⣿⣝⣿⢿⣿⣿⠹⢿⣿⠆⠀⣿⣧⡀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠛⣿⣿⡀⠀⠀⣿⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⠿⣿⡿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣸⡗⣼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⢛⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣷⣦⣄⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠁⠈⠙⣿⡿⣟⡛⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⠁⠀⠀⠀⠀⠀⢸⣷⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢀⡾⠀⠀⠹⣿⣶⣄⣀⣀⣤⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠿⠿⠿⠿⠋⠀⠈⠉⠉⠉

⠀⠻⢿⡿⠛⠻⢿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡀⠀⠀⣠⣾⡇⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠋⠀⠀⠀⠀⢸⠛⢷⣦⣀⠀⠀⢀

⠾⠇⣶⡆⠀⠀⠀⠙⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣵⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣴⡯⠀⢀⣹⣿⣿⣿⣿

⠀⠀⣿⣧⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡲⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿

⣤⣠⣿⣿⣿⣷⣾⡿⠟⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣟⣟⣻⣿⣽⣿⡿⠿⠻⠋⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠙⡿⢻⠿⠛⠛⠙⡉⠙⢻

⣿⣿⣿⣿⢿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⢻⣿⡏⠉⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠉⠉⠉⠀⠀⢀⣀⣴⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⣀

⣌⣉⣉⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣷⡀⢀⡸⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢴⣴⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠉⢁⠴⠀⢸

⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢙⡛⢿⣿⢛⡷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣾⣾⣿⣿⣿⣿⣿⠟⢋⣵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢄⠀⠀⢀⢀⣠⣾

⣛⣋⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠏⠀⠀⠀⠀⢠⣶⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡻⣛⣯⣤⡴⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⣤⣜⣻⣿⣿⣿

⣿⣿⣿⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⢇⠀⠀⠀⢠⣾⣿⣿⡎⠙⢿⣯⣷⣤⣴⡶⠶⠒⠦⠤⣤⠀⠀⠀⠀⢠⣿⡟⠻⣶⣶⣦⣀⣀⣠⣤⣶⣶⣿⣷⣶⠶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡟⠛⠛⠍

⣭⣭⠁⠀⠀⠉⢿⣦⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣿⡏⠽⡋⠄⠀⠀⢸⣿⣿⣿⣿⠂⠈⢿⣿⣿⠋⠀⠐⠒⠒⠢⠄⠀⠀⠀⠀⠈⠈⠁⣀⣨⣽⡿⠿⠛⢛⣻⣿⣽⣿⣿⣯⠙⠋⠉⣿⣦⣤⣤⠾⠟⠃⠈⠀⢉⣡

⣿⣩⣤⣴⣶⣾⣿⣿⠿⠟⠛⠛⠛⠛⢿⣿⣿⠶⠿⠿⠋⠁⠀⠤⠀⠉⣁⣬⣿⣿⡿⡿⠟⢠⣟⣿⡿⠻⣷⣶⣶⣶⣤⣄⣴⣾⣷⣶⣶⣶⡿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⢻⣿⣿⡿⢷⡆⣀⣀⣀⣄⣿

⣿⠟⠛⠋⠉⠉⣰⣿⡇⠀⠀⠀⠀⣰⣿⣾⣿⠀⠲⣾⣷⡤⠦⠤⠖⣚⣁⣾⣿⠟⠁⠀⢀⠼⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⢀⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣷⡗⢸⣿⣿⣿⣿⠀

⣀⣀⣀⣤⣴⡾⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⡀⠻⠟⠁⠀⠀⣰⣿⣿⣿⣿⣶⡀⣰⠃⠈⠘⣿⣆⠙⣿⣿⣿⡿⠋⣱⣄⣠⣤⣄⣀⣀⣠⣤⣶⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢟⡀⠀⢀⣿⣇⠀⠙⠛⠛⠟⠿⠿⠋⠸

⠉⠁⠀⠀⠉⠀⢸⣿⠀⢀⡴⠛⠉⣅⣹⣿⡇⠀⠘⠿⠀⠁⠉⠉⠉⣽⣿⡟⣹⣿⣿⣿⣀⠀⣀⣈⣻⣀⠈⠃⠀⢀⣼⡿⠿⠟⠛⠛⠛⠛⠉⠉⡩⠥⣤⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⢸⣿⡟⣦⣀⣀⠀⢲⣶⣶⣶⡄

⣤⣤⣤⣤⣬⣷⣾⠟⢀⠞⠀⠀⢸⣿⣿⣿⡏⠉⢓⠿⡄⠘⠛⠿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⢠⡤⠀⠀⠀⠀⠀⠀⠤⠚⠁⢠⣤⣾⣿⣿⣿⣿⠃⠀⠀⢻⣿⡄⠈⢿⣷⠙⠿⠿⢿⣾⣿⣋⣉⢠

⠀⠆⠲⣶⠋⢿⠽⡷⠿⠶⠆⠀⢼⡟⣿⣿⣿⠐⠀⠀⠃⠀⠀⢤⣿⣿⢇⣠⣿⢸⣿⣿⣝⣿⢿⣿⣿⠻⢿⣿⠆⠀⣿⣷⡀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠛⣿⣿⡄⠀⠀⣾⣿⡇⠀⠘⣯⣄⠀⠀⠀⢸⢿⣿⡿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢻⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣻⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣷⣦⣄⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠉⠉⠙⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⣷⡿⠁⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡿⢀⠀⢹⣿⣦⣄⣀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠿⠿⡿⠿⠋⠀⠀⠉⠉

⠀⠀⠿⣿⡿⠻⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣄⠀⠀⢀⣠⣾⡃⠀⠀⠄⣻⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠉⠀⠀⠀⠀⡸⠛⢷⣦⣀⠀⠀

⣠⣼⢇⣾⡄⠀⠀⠈⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣷⣶⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢠⣼⡇⠀⣀⣻⣿⣿⣿

⠋⠀⠈⣿⡇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⣶⣿⣿⣿⣾⡿⣿⣿⣿⣿

⣤⣄⣀⣿⣿⣷⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣿⣿⣿⣿⣿⡿⠿⠻⢻⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠟⢻⠿⠛⠛⢉⡉⠛

⣿⣿⣿⣿⣿⣯⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢿⣿⠛⠛⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠈⠉⠉⠈⠀⢀⣠⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠀⠀⠀

⣉⣉⣉⣛⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣌⣿⣧⠀⠀⡸⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢴⣤⣴⣶⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠈⠉⢡⠔⠀

⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢛⣿⣿⣿⢻⣧⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣾⣾⣿⣿⣿⣿⣿⠿⢋⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⡀⠀⢀⢀⣠

⠿⠿⣛⣩⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣷⠏⠀⠀⠀⠀⢠⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡿⣿⣯⣥⡴⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣜⣻⣿⣿

⣿⣿⣿⣿⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣿⡴⢆⠀⠀⠀⣠⣾⣿⣷⡍⠻⣿⣿⣦⣤⣤⣶⠶⠶⠤⢄⣀⠈⠉⠉⠀⢠⣿⡟⢿⣶⣶⣤⣀⣀⣠⣤⣴⣶⣿⣷⣶⡶⣦⣄⣀⠀⠀⠀⢀⣹⣿⡛⠛⠛

⣉⣉⣽⠁⠀⠈⠙⣷⣦⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⣿⡏⠽⢋⠄⠀⠀⢿⣿⣿⣿⣷⠆⠘⣿⣿⣿⠃⠀⠀⠒⠢⠤⡄⠀⠀⠀⠀⠈⠈⠁⢈⣩⣽⣿⠿⠛⢛⣛⣿⣿⣿⣿⡭⠘⠋⠉⣿⣦⣤⡤⠿⠛⠃⠁⠀⢉

⣿⣿⣋⣤⣤⣶⣶⣿⣿⡿⠿⠛⠛⠛⠻⣿⣿⣷⠴⣿⡿⠛⠃⠀⠤⠀⠉⣀⣸⣿⣿⡿⡿⡇⢰⣟⣿⣿⢶⣶⣶⣤⣤⣤⣀⣴⣶⣶⣶⣴⣶⡿⠟⠛⣩⡤⣰⣿⣿⣿⣿⣿⣿⣿⡇⠐⠇⠀⢻⣿⣟⠻⢷⡆⣀⣀⣀⣬

⣿⣿⠿⠟⠛⠋⠉⣹⣿⡇⠀⠀⠀⠀⣰⣶⣾⣷⠀⢠⣶⣶⡠⢤⠤⠴⢒⣉⣿⣿⠟⠀⠀⢀⠸⣿⣗⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁⢀⡤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⢿⣿⡅⢰⣿⣿⣿⣿

⣉⠁⡀⣀⣀⣠⣶⣿⣟⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣦⡀⣰⠋⠀⠹⣿⡄⠙⣿⣿⣿⡿⠟⣵⣄⣀⣀⣀⣀⣀⣀⣤⣶⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⣇⠀⠙⠛⠊⠟⠿⠿⠋

⠛⠛⠉⠉⠀⠉⠀⢸⣿⠀⠀⡠⠞⠋⡁⢻⣿⡇⠉⠨⠿⠀⠉⠉⠉⠉⣽⣿⡟⣹⣿⣿⣯⡀⠀⢀⣉⣻⡀⠉⠋⠀⢀⣼⣿⠿⠿⠿⠛⠛⠛⠋⠉⡩⢥⣤⣀⣿⣿⣿⣿⣿⠟⠀⣿⡇⠀⢸⣿⡿⣆⣀⣀⠀⢶⣶⣶⣶

⣀⣀⣀⣀⣀⣨⣶⣾⡟⢀⡜⠀⠀⢸⣿⣿⣿⡇⠀⢲⡾⡀⠒⠳⠶⣾⣿⣿⣾⣏⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⣩⡄⠀⠀⠀⠀⠀⢀⠠⠚⠁⢤⣠⣾⣿⣿⣿⣿⠁⠀⠀⢸⣷⡄⠀⢿⣿⠙⠿⠿⢿⣞⣿⣏⣉

⠀⠆⠲⣾⠛⢿⠟⠹⡷⠾⠆⠀⠀⢸⡟⣿⣿⣷⠐⠀⣀⠃⠐⠀⢠⣿⣿⣇⣨⣿⢸⣿⣿⣝⣿⣿⣿⡿⠻⣿⣿⠀⠀⣿⣧⡀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⠟⠻⣿⣿⡀⠀⠀⣿⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⢿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣼⡗⢾⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⣘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣻⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣶⣤⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠟⠋⠉⠙⢿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣹⣾⠋⠀⠀⠀⠀⠀⠘⣿⣻⣿⡀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠀⠀⠀⠀⠀⠀⣸⠃⡀⠘⣿⣶⣄⡀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⠿⠿⠿⠿⠟⠁⠀⠈⠉

⠀⠀⠸⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣧⡀⠀⠀⣀⣴⡏⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠏⠁⠀⠀⠀⢀⡟⠻⣦⣄⡀⠀

⢀⣤⣶⣰⣅⠀⠀⠀⠙⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣶⣿⣿⣿⣶⣾⣷⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⣴⣿⠀⢀⣘⣿⣿⣿

⡿⠋⠀⢹⣿⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣖⢶⣾⣿⣿⣶⣿⢿⣿⣿⣿

⣧⣀⡀⣸⣿⣷⣶⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢿⡿⣿⣿⣿⣿⢿⠿⠟⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠻⠻⡿⠟⠛⠋⣉⠉

⣿⣿⣿⣿⣿⣿⣭⣿⠃⠀⠀⠀⠀⠀⠀⠀⠜⠛⢻⣿⡿⠛⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠋⠉⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢀⠀⠀⠀

⢉⣉⡙⢛⣛⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⣀⣹⣿⡄⠀⢀⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡶⣦⣤⣶⣾⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠉⢉⡤⠂

⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠙⣻⣿⣿⡞⣿⣔⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣵⣷⣿⣿⣿⣿⣿⡿⠟⣩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⣀⠀⠀⡀⣀

⠿⠿⠿⢛⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡾⠁⠀⠀⠀⠀⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢿⣻⣭⣤⢾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⣛⣿⣿

⣭⣿⣿⣿⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣧⡶⡀⠀⠀⠀⣴⣿⣿⣿⠙⢿⣿⣷⣤⣤⣴⡶⠶⠤⢄⣀⡈⠉⠉⠉⠀⣼⣿⠻⣷⣶⣦⣄⣀⣀⣤⣤⣶⣾⣿⣶⣶⣶⣤⣄⡀⠀⠀⠀⣉⣿⡟⠛⠛

⣉⣉⣛⡛⠀⠀⠉⢻⣦⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣼⣿⠛⠟⠁⠀⠀⠸⣿⣿⣿⣿⡖⠀⢻⣿⣿⡟⠀⠀⠐⠒⠤⢄⠀⠀⠀⠀⠀⠁⠋⠀⣉⣭⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⡍⠛⠉⢹⣷⣤⣠⠼⠿⠛⠀⠀⠈

⣿⣿⡟⣃⣠⣤⣴⣾⣿⣿⡿⠿⠛⠛⠛⢿⣿⣷⡦⣾⣿⠟⠛⠀⠠⠄⠈⢁⣀⣿⣿⣿⢿⣿⠀⣾⣿⣿⡷⣶⣶⣤⣤⣤⣄⣠⣶⣶⣶⣤⣴⣾⠿⠛⢋⣥⢄⣾⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠸⣿⣿⡛⠿⣶⢀⣀⣀⣤

⣿⣿⣿⡿⠟⠛⠛⢉⣿⣿⠀⠀⠀⠀⢀⣶⣶⣿⡧⠀⣴⣶⣄⢤⣤⠤⠖⡊⣹⣿⡿⠇⠈⠀⢀⢿⣿⡆⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠀⣠⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣾⠀⣿⣿⣿⣿

⠛⠉⠁⠀⢀⣀⣴⣾⣿⡋⠀⠀⠀⠀⣾⢿⣿⣿⡇⠀⠸⡿⠋⠀⠀⠀⣾⣿⣿⣿⣷⣔⢀⡔⠁⠈⢻⣧⠈⢿⣿⣿⣿⠿⢋⣄⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⣸⣿⡄⠉⠛⠓⠹⠻⠿⠟

⠝⠛⠛⠉⠉⠉⠉⠈⢻⡇⠀⢀⡴⠚⢋⠘⣿⣿⠉⠁⢶⠆⠈⠉⠙⠉⢉⣿⣿⠋⣿⣿⣿⣇⠀⠀⢈⣛⣇⠈⠙⠁⠀⣠⣿⡿⠿⠿⠟⠛⠛⠛⠉⢉⠭⣤⣀⣸⣿⣿⣿⣿⡿⠃⢸⣿⠄⠀⣿⣿⢳⣄⣀⡀⠐⣶⣶⣶

⣀⣀⣀⣀⣀⣀⣱⣴⣿⠇⣠⠋⠀⠀⣾⣾⣿⣿⠐⠒⢶⣆⠐⠲⠶⢶⣾⣿⣿⣾⡋⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣦⡄⢈⣥⠀⠀⠀⠀⠀⠀⡀⠴⠋⠀⣄⣴⣿⣿⣿⣿⡯⠀⠀⠀⣿⣧⠀⠹⣿⡞⠻⠿⠿⣷⣻⣯⣉

⠀⠆⠺⣿⠏⢿⠟⠻⢷⡶⠗⠀⠀⠀⣿⢿⣾⣿⡆⠀⢀⣘⠀⠂⠀⣸⣿⣿⣀⣹⡇⣿⣿⣏⣻⣿⣿⣿⡟⢿⣿⣧⠀⢸⣿⣄⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⠟⢿⣿⣇⠀⠀⠀⣿⣿⠀⠀⢻⣧⡀⠀⠀⠀⠿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣻⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⢘⣫⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡆⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣿⣿⣶⣦⣄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣿⣿⠿⠛⠉⠉⠻⣿⠿⠿⠇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⣿⡟⠁⠀⠀⠀⠀⠀⣿⣟⣿⣇⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡇⠀⠀⠀⠀⠀⢀⡟⢀⠈⢻⣷⣤⣀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⣿⡿⠿⠿⠿⠿⠿⠋⠀⠀⠀

⠀⠀⠈⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣠⣾⠁⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠉⠀⠀⠀⠀⡘⠛⢶⣦⣀⠀

⠀⣀⣴⣆⣮⡀⠀⠀⠉⢿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣾⣿⣿⣷⣴⣿⣶⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣠⣾⡇⠀⣀⣻⣿⣿

⣾⠟⠁⠘⣿⡇⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠢⣶⣿⣿⣷⣾⣿⣿⣿⣿

⣿⣀⡀⢀⣿⣿⣶⣤⣴⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⡿⣿⢿⣿⣿⣿⡿⡿⠿⢻⣥⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⠟⢿⠿⠛⠋⢉⡉

⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠠⠛⠛⣿⣿⠛⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠘⠉⠉⠉⠀⢀⣠⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀

⡈⢉⡙⠛⠛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣂⣈⣿⣆⠀⠀⡹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣶⣤⣴⣶⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠈⠉⣡⠔

⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠻⣿⣿⣷⢿⣇⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⣼⣾⣿⣿⣿⣿⣿⠿⢋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢄⡀⠀⢀⢀

⠿⠿⠿⠟⣋⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠏⠀⠀⠀⠀⢠⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣯⣥⠴⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣘⣻⣿

⣍⣽⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⢆⠀⠀⠀⢠⣾⣿⣿⡍⠻⣷⣟⣦⣠⣤⣤⡶⠦⠤⣀⣀⠈⠉⠉⠀⢠⣿⡟⢿⣶⣦⣤⣀⣀⣠⣤⣴⣶⣿⣷⣶⢶⣦⣤⣀⠀⠀⠀⢀⣹⣿⠟⠛

⣉⣉⣛⣛⠋⠀⠈⠻⣶⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣿⠟⠻⠋⠀⠀⠀⢿⣿⣿⣿⣷⠄⠘⣿⣿⣿⠃⠀⠀⠐⠤⠤⡈⠀⠀⠀⠀⠈⠘⠁⢉⣩⣿⣿⠿⠛⢛⣻⣿⣿⣿⣿⣭⠙⠋⠉⣿⣦⣠⣤⠾⠟⠃⠈⠀

⣿⣿⣿⢛⣀⣠⣤⣴⣿⣿⣿⠿⠿⠿⠻⠿⣿⣷⣶⢤⣿⣿⠟⠃⠀⠤⠀⠁⢀⣸⣿⣿⡿⣿⡇⢰⣿⣿⣿⢶⣶⣦⣤⣤⣤⣀⣴⣶⣶⣦⣤⣶⡿⠟⠛⣩⡤⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⢿⣿⣟⡻⢷⡆⣀⣀⣀

⣿⣿⣿⣿⠿⠟⠛⠋⢹⣿⡇⠀⠀⠀⠀⢠⣾⣿⣿⠀⢠⣶⣦⣠⣤⣤⠤⠖⠋⣿⣿⠟⠀⠁⠀⡸⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⠋⠁⢀⡤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⡿⢿⣷⡇⢸⣿⣿⣿

⠛⠛⠉⠀⠀⣀⣠⣴⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣦⡀⣠⠊⠐⠙⣿⡄⠹⣿⣿⣿⡿⠟⣡⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⠀⣿⣇⠀⠙⠛⠊⠟⠿⠿

⣿⠛⠛⠛⠋⠉⠉⠁⠙⣿⠀⠀⣠⠶⠛⡉⢸⣿⡏⠉⠑⣶⠀⠁⠙⠛⠉⣹⣿⡟⢻⣿⣿⣿⡀⠀⠀⣙⣻⡀⠙⠋⠈⢀⣼⣿⡿⠿⠿⠻⠛⠛⠋⠉⡉⢥⣄⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⢸⣿⡟⣧⣀⣀⠀⢰⣦⣶

⢀⣀⣀⣀⣀⣀⣀⣦⣼⡿⠀⡼⠁⠀⢰⣷⣿⣿⡗⠒⠲⣶⡀⠒⠶⠶⣶⣿⣿⣷⣟⢻⣿⣿⣿⣾⣿⣿⣿⣿⣷⣦⣤⠈⣩⡄⠀⠀⠀⠀⠀⢀⠠⠞⠁⢠⣠⣾⣿⣿⣿⣿⠇⠀⠀⢹⣿⡄⠀⢿⣷⠝⠿⠿⢿⣞⣿⣏

⠀⠖⠺⣿⠛⢿⠟⠻⠻⣶⠞⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢀⡇⠀⠀⢀⣿⣿⣇⣈⣿⢸⣿⣿⣹⣿⣿⣿⣿⠻⣿⣿⡅⠀⣿⣧⡀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠿⠻⣿⣿⡀⠀⠀⢻⣿⡇⠀⠈⣿⣄⠀⠀⠀⠸⠽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢻⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⣋⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣇⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣷⣶⣤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⡿⠛⠋⠉⠛⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣾⣿⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢏⠀⠀⠀⠀⠀⠀⣼⠃⡀⠹⣿⣦⣄⡀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠻⠿⠿⠋⠀⠀⠀

⠀⠀⠀⢹⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⣀⣼⡏⠀⠁⠄⢹⣿⣿⣟⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠋⠀⠀⠀⠀⢨⠛⠳⣶⣄⡀

⠀⠀⣠⡶⣨⡅⠀⠀⠈⠻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⣿⣷⣦⣾⣷⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣴⣿⠀⢀⣘⣿⣿

⣶⡿⠋⠁⣿⣿⠀⠀⠀⠀⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡲⢶⣿⣿⣿⣶⣿⣿⣿⣿

⣿⣅⣀⠀⣸⣿⣶⣦⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⢿⡿⣿⣿⣿⣿⢿⠿⠟⣯⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠿⢻⡿⠟⠛⠉⣉

⣿⣿⣿⣿⣿⣿⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠼⠛⢻⣿⡟⠛⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋⠋⠉⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀

⣈⠉⠛⠛⠻⢟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⣻⣷⡀⠀⢈⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠈⠉⢉⡤

⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⡾⣿⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣥⣷⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠤⣀⠀⠀⡀

⡿⢿⣿⠿⢛⣩⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠀⣯⡿⠁⠀⠀⠀⠀⣤⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡻⢿⣿⣭⣤⢾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⣛⣿

⣌⣹⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡴⠀⠀⠀⢀⣴⣿⣿⣯⠛⢿⣾⣲⣄⣤⣤⣤⠦⠤⢄⣀⡈⠉⠉⠁⠀⣼⣿⠻⣶⣶⣤⣄⣀⣀⣤⣤⣶⣾⣷⣶⣶⢶⣤⣄⡀⠀⠀⠀⣉⣿⡿⠛

⣈⣉⠛⢛⡛⠉⠉⠙⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢓⠞⠁⠀⠀⢸⣿⣿⣿⣿⡄⠀⢻⣿⣿⡟⠀⠀⠄⠢⠤⢄⠁⠀⠀⠀⠀⠁⠋⠈⣉⣽⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⠍⠛⠉⢹⣷⣤⣠⠼⠿⠛⠀⠁

⣿⣿⣿⡟⢃⣀⣤⣤⣼⣿⣷⣿⡿⠿⠿⠿⣿⣷⣶⣤⣼⣿⡿⠓⠀⠈⠄⠘⠀⣀⣿⣿⣿⢿⣿⠀⣾⣿⣿⡷⣶⣶⣤⣤⣤⣄⣠⣶⣶⣶⣤⣴⣾⠿⠛⢋⣥⢤⣾⣿⣿⣿⣿⣿⣿⣿⠀⡾⠀⠸⣿⣿⡛⠿⣶⢀⣀⣀

⣿⣿⣿⣟⡿⠿⠟⠛⠋⣿⣷⠀⠀⠀⠀⠀⣼⣽⣿⡅⠤⣴⣶⡄⣤⣤⡤⠴⠚⢹⣿⡿⠇⠈⠀⢀⢿⣿⠋⣴⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠛⠉⠀⣠⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣿⠿⣿⣶⠀⣿⣿⣿

⡛⠛⠋⠁⠀⠀⣀⣠⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠸⡿⠋⠀⠀⠀⣾⣿⣿⣿⣷⣄⢀⡔⠁⠊⣻⣧⠙⢿⣿⣿⣿⠿⢋⣄⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⢸⣿⡀⠈⠛⠃⠙⠻⠿

⣿⡟⠛⠛⠛⠋⠙⠋⠉⣿⡇⠀⢀⡴⠞⢋⠘⣿⣿⠉⠁⢶⡆⠈⠐⠒⠋⢉⣿⣿⠛⣿⣿⣿⡃⠀⠀⠈⣛⡆⠈⠛⠉⠁⣠⣿⣿⠿⠿⠟⠟⠛⠛⠉⢉⠩⣤⣀⣸⣿⣿⣿⣿⡿⠃⠘⣿⡀⠀⣿⣿⢳⣀⣀⡀⠰⣶⣶

⠁⣀⣀⠀⠀⣀⣀⣢⣤⣿⠇⢠⠏⠀⠀⣾⣾⣿⣿⠒⠲⢶⣆⠐⠲⠶⣶⣾⣿⣿⣾⠛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣤⡄⠉⣡⠀⠀⠀⠀⠀⠀⡀⠴⠋⠠⣄⣴⣿⣿⣿⣿⡿⠀⠀⠀⣽⣧⠀⠸⣿⡾⠻⠿⠿⣷⣻⣿

⠀⠖⠳⣿⠟⢿⠟⠻⠻⢿⡶⠃⠀⠀⠀⣿⣿⣿⣿⡆⠀⠁⣸⠀⠀⢀⣸⣿⣿⣈⣹⡇⣿⣿⣟⢿⣿⣿⣿⡿⢿⣿⡯⠀⢸⣿⣄⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⠟⢿⣿⣇⠀⠀⢰⣿⣿⠀⠀⢹⣧⡀⠀⠀⠀⠽⢽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢽⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⢼⡗⣹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡗⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⣛⣿⣼⣿⣿⣿⣿⣿⣿⣿⣾⣧⣛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣤⣶⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠋⠉⠻⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⣝⣿⠋⠀⠀⠀⠀⠀⢹⣷⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⣼⠉⠈⠹⣷⣦⣀⠀⢀⣠⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⠿⠛⠻⠿⢿⠋⠀⠀

⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣄⠀⠀⠀⢀⣼⡇⠀⠁⠄⢹⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡪⠋⠀⠀⠀⠀⢨⠛⠻⣶⣤

⠀⠀⠀⢀⡌⣩⡋⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⣶⣿⣿⣷⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢀⣴⣿⠀⢀⣘⣿

⣤⣴⣾⠟⠁⣿⣷⠀⠀⠀⠀⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣲⢶⣿⣿⣿⣶⣿⣿⣿

⣿⣿⡇⠀⠀⢻⣿⣦⣤⣤⣴⣿⠁⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⢿⡿⣿⣻⣿⣿⣿⠿⠟⣯⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠿⢻⡿⠛⠋⠉

⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠉⠀⠀⠀⠀⠀⠀⠼⠟⢿⣿⡿⠿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠛⠛⠛⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣀⡀

⢀⠉⠛⠛⠿⠿⠿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⣻⣧⠀⠀⢘⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠈⠉⠉

⣼⣿⣶⣿⣷⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠉⠿⢿⣿⣷⡶⣿⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣷⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠁⣀⠀⠀

⠻⣿⣿⣿⣿⠟⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⣯⡿⠁⠀⠀⠀⠀⣤⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⢻⠿⣟⣩⣤⢾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⣛

⣦⣉⢒⣶⣶⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣏⡵⠀⠀⠀⠀⣴⣿⣿⣯⠻⣿⣶⣦⣄⣠⣤⣤⠤⢤⣀⣀⡈⠉⠉⠁⠀⣼⣿⠻⣶⣶⣤⣀⣀⣀⣤⣤⣶⣾⣿⣶⣶⢶⣤⣄⡀⠀⠀⠀⣈⣽⣿

⣈⠉⠛⠛⠿⠿⠉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣒⠶⢁⠀⠀⢸⣿⣿⣿⣿⡀⠈⢿⣿⣿⡟⠁⠀⠤⠤⠤⣈⠁⠀⠀⠀⠀⠁⠋⠀⣈⣽⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⡍⢛⠉⢹⣷⣤⣠⠴⠟⠋⠀

⣿⣿⣿⣿⡿⠇⢀⣀⣤⣬⣿⣷⣶⣶⠾⠿⠿⣷⣶⣶⣄⣼⣿⡿⠓⠀⣈⡀⠐⠂⡀⣿⣿⣿⣿⣷⠀⣾⣿⣿⡷⣶⣦⣤⣤⣤⣄⣠⣴⣶⣦⣤⣴⣶⡿⠟⢋⣡⠄⣾⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠘⣿⣿⣟⠿⣶⠀⣀

⣿⣿⣿⣿⣷⡿⡿⠿⠿⠛⣿⣿⠀⠀⠀⠀⠀⣬⣭⣿⡅⠀⣡⣦⡄⣀⣀⣠⠤⠞⢹⣿⣿⠛⠈⠈⢀⣿⣿⠏⣴⣾⣿⣿⣿⣿⣿⡿⡿⠿⠟⠛⠉⠀⣠⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣾⡄⣾⣿

⡉⠻⠿⠛⠋⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠸⣿⠟⠀⠀⠀⣾⣿⣿⣿⣧⡤⢀⡴⠁⠊⣻⣧⠙⢿⣿⣿⣿⡿⢋⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⠿⣃⠀⠀⢸⣿⢅⠈⠛⠋⠙⠻

⣿⣿⣶⠶⠲⠒⠒⠛⠛⠉⢿⣇⠀⠀⣠⠾⢛⠚⣿⣿⠋⠂⣶⡆⠐⠒⠒⠚⢛⣿⣿⠟⣿⣿⣾⡇⠀⠀⠈⠻⡆⠈⠛⠋⠁⣠⣿⣿⡿⠿⠟⠿⠛⠛⠋⢉⢩⣤⣀⣸⣿⣿⣿⣿⡿⠃⠸⣿⡀⠀⣿⣿⢹⣄⣀⣀⠀⣶

⠿⠋⠁⠀⠀⠀⠀⠀⢢⣠⣾⡏⢀⡞⠁⠀⣸⣶⣿⣿⠂⠠⢤⣆⠀⠶⣶⣦⣾⣿⣿⣾⠛⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣤⣀⠉⣁⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣄⣴⣿⣿⣿⣿⣿⠀⠀⠀⣏⣧⠀⠸⣿⣯⠛⠿⠿⢷⣿

⠿⠖⠻⣿⠿⢿⠟⠻⠿⠿⢿⣠⠎⠀⠀⠀⣿⣿⣿⣿⡆⠀⠈⠸⠀⠀⢀⣸⣿⣿⠉⣹⡇⣿⣿⣟⠻⣿⣿⣿⡿⣿⣿⣯⠁⢰⣿⣄⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⠟⢻⣿⣧⠀⠀⢀⣿⣿⠁⠀⢸⣧⣀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⢛⣻⣼⣿⣿⣿⣿⣿⣿⣿⣾⣧⣟⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣿⣿⠟⠛⠉⠛⢿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢻⣽⠟⠁⠀⠀⠀⠀⠘⣿⣼⣿⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠀⠀⠀⠀⢰⠏⡁⠙⣿⣦⣄⡀⠀⣀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⠟⠛⠿⠿⠟⠁⠀

⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⣠⡿⠀⠀⠠⠸⣿⣿⣿⣿⣿⣿⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠟⠁⠀⠀⠀⠀⡟⠛⢶⣤

⠀⠀⠀⠀⣠⢭⣝⠁⠀⠉⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣗⣤⣴⣾⣿⣿⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣠⣿⡇⢀⣈⣿

⣤⣤⣴⡿⠋⢸⣿⡄⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⢶⣾⣿⣿⣷⣿⣿⣿

⣿⣿⣏⠀⠀⢸⣿⣧⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢿⡿⣿⣻⣿⣿⣿⡿⠿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠻⠟⣿⠟⠛⠉

⢛⣿⣿⣿⣷⣾⣿⣿⡟⣿⡿⠉⠁⠀⠀⠀⠀⠀⡠⠿⠿⣿⣿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠟⠛⠙⠋⠉⠀⢀⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⢀⡀

⠀⠉⠛⠻⠻⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢹⣿⡄⠀⠈⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⣤⣴⣴⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡥⠀⠀⠉⠉

⣶⣿⣷⣶⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠹⠿⣿⣿⡶⢾⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣣⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡨⢀⡀⠀

⠻⢿⣿⣿⣿⡿⢟⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⣺⣼⠏⠀⠀⠀⠀⢠⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡻⡿⢿⣋⣥⡴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣘

⢠⣉⠒⣶⣶⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⣩⠄⠀⠀⠀⢠⣾⣿⣯⡛⢿⣷⣶⣄⣀⣤⣤⡤⢤⣄⣀⡀⠉⠉⠉⠁⢨⣿⡿⢷⣶⣤⣄⣀⣀⣠⣤⣴⣶⣿⣶⣶⣶⣦⣄⣀⠀⠀⠀⢀⣹⣿

⠈⠉⠛⠛⠿⠿⠟⠉⠓⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣷⠊⠀⠀⠀⣿⣿⣿⣿⣇⠀⠹⣿⣿⡿⠋⠀⠤⠤⠤⢄⡉⠀⠀⠀⠀⠈⠘⠉⢁⣹⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⡭⠙⡋⠉⣿⣦⣄⡤⠿⠛⠁

⣿⣿⣿⣿⣾⠿⠀⢀⣀⣠⣿⣿⣶⣶⡶⠾⠿⢿⣶⣦⣤⣠⣾⣿⠿⠂⢀⣉⠐⠒⠀⢹⣿⣿⡿⣷⡆⢰⣿⣿⡿⣶⣶⣤⣤⣤⣤⢀⣤⣶⣶⣤⣤⣶⡾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⠐⠇⠀⢿⣿⣟⠻⢷⡆⣀

⣿⣿⣿⣿⣿⣾⣿⡿⠿⠟⢻⣿⡏⠀⠀⠀⠀⢨⣭⣽⣯⠀⢉⣥⣄⢀⣀⣀⣤⠴⠋⣿⣿⠟⠀⠁⠁⣸⣿⡏⢡⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⢀⡤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼⣿⣿⣷⡇⢸⣿

⡉⠻⠿⠿⠛⠁⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠀⠈⣿⡿⠃⠈⠀⢰⣾⣿⣿⣿⣄⠀⣠⠎⠐⢛⣷⡌⢻⣿⣿⣿⣿⠟⣡⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⣟⡀⠀⠀⣿⣧⠀⠙⠛⠉⠛

⣿⣿⣶⠶⠶⠶⠒⠛⠛⠋⢻⣷⠀⠀⢀⡴⠞⠃⢻⣿⡏⠒⢰⣶⠀⠒⠒⠒⠚⣻⣿⡟⢻⣿⣷⣏⠀⠀⠀⠙⢷⠀⠛⠏⠉⢁⣼⣿⣿⠿⠿⠿⠟⠛⠛⠉⡉⣥⣀⣀⣿⣿⣿⣿⣿⠟⠀⢻⣇⠀⢸⣿⡟⣦⣀⣀⠀⢰

⠿⠟⠉⠀⠀⠀⠀⠀⠀⣄⣴⣿⠀⣰⠋⠀⢰⣷⣾⣿⡇⠄⢤⣵⠀⠤⣤⣤⣴⣿⣿⣷⡟⢻⣿⣿⣷⣶⣿⣿⣿⣷⣶⣤⣄⡈⢉⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢀⣠⣾⣿⣿⣿⣿⠅⠀⠀⢨⣽⡄⠈⢿⣿⡟⠿⠿⢿⣾

⡾⠷⠺⣿⠿⢿⠿⠻⠿⠿⠿⣇⡴⠁⠀⠀⢸⣿⣿⣿⣧⠀⠈⠉⠇⠀⠀⣀⣿⣿⡏⢙⣿⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡍⠀⣿⣇⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⡿⠻⣿⣿⡀⠀⠀⣾⣿⡇⠀⠀⣿⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣺⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⣛⣼⣷⣿⣿⣿⣿⣿⣿⣾⣷⣿⡀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡆⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣤⣶⣶⣾⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠛⠋⠛⢻⣿⡿⠿⠏⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿

⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣯⡿⠋⠀⠀⠀⠀⠀⢿⡿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢀⡾⢁⠈⢻⣷⣤⣀⠀⢀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⠿⠛⠻⠿⢛⠋⠀

⠛⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢀⣼⠃⠀⠀⠄⢿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠉⠀⠀⠀⠀⣸⠛⢻⣶

⠀⠀⠀⠀⢀⡭⣛⡋⠀⠉⠛⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣾⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢠⣼⣇⠀⣀⣹

⣤⣤⣤⣶⠟⠁⣿⣇⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⣶⣿⣿⣿⣾⣿⣿

⣹⣿⣿⡃⠀⠀⣿⣿⣤⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡿⣿⢿⣿⣿⣿⣿⣿⠿⢟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢉⠟⢻⡿⠛⠋

⠙⣿⣿⣿⣿⣶⣿⣿⣿⢟⣿⠟⠉⠀⠀⠀⠀⠀⢀⠼⠿⢿⣿⡿⠿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠛⠋⠛⠉⠁⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⣀

⠀⠈⠙⠛⠿⠿⢿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣆⠀⠀⢹⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⣠⣤⣦⣶⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠉

⣿⣾⣿⣶⣶⣶⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠿⣿⣿⣷⢶⣿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⣸⣿⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⣀⠀

⠛⢿⣿⣿⣿⣿⠿⢋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢐⣯⡿⠁⠀⠀⠀⠀⣠⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⣿⠿⣟⣩⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤

⠀⣌⡑⢺⣯⣶⣾⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣏⡥⠀⠀⠀⠀⣬⣿⣽⣝⠻⣷⣶⣦⣀⣀⣤⣤⠤⣄⣀⣀⠀⠉⠉⠛⠀⣿⣿⠿⣶⣦⣤⣀⣀⣀⣤⣤⣶⣾⣷⣶⣶⣶⣤⣄⡀⠀⠀⠀⣈⣽

⠀⠉⠛⠛⠿⠿⠿⠛⠓⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡶⢁⠀⠀⢸⣿⣿⣿⣿⠀⠘⢿⣿⣿⡟⠁⠠⠤⠤⠤⣈⠁⠀⠀⠀⠈⠉⠃⠉⣈⣿⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⠁⢛⠉⢹⣷⣄⣤⡞⠟⠋

⣸⣿⣿⣿⣶⡿⠇⠀⣀⣀⣸⣿⣧⣶⣶⣶⠾⢿⣶⣶⣤⣄⣴⣾⡿⠷⠀⣀⡁⠒⠀⠘⣿⣿⣿⣿⣴⠀⣾⣿⣿⢷⣶⣤⣤⣤⣤⡄⣠⣴⣶⣦⣤⣤⣶⡿⠟⢋⣡⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠾⠀⠸⣿⣿⣟⠿⡶⢀

⣿⣿⣿⣿⣿⣷⣾⣿⡿⠿⠟⣿⣿⠁⠀⠀⠀⠀⣹⣿⣿⣅⢉⣩⣤⡀⣀⣀⣀⡤⠜⢻⣿⡿⠋⠈⠉⢀⣿⣿⠍⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⣀⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⡿⣿⣾⡀⣾

⠉⠛⠿⠿⠟⠋⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢹⣿⠟⠈⠁⠀⣴⣷⣿⣿⣧⡀⢀⡴⠁⠚⣿⣇⠙⢿⣿⣿⣿⡿⢋⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⣸⣿⡄⠈⠛⠓⠙

⣿⣿⣷⣶⠶⠶⠶⠶⠻⠟⠛⣿⡆⠀⠀⣠⡴⢟⠙⣿⣿⠓⠒⣦⡄⠐⠒⠒⠒⢛⣿⣿⠟⣿⣿⣾⡁⠀⠀⠈⠻⡆⠘⠻⠉⠁⣠⣿⣿⡿⠿⠿⠿⠟⠛⠋⢉⢩⣅⣀⣸⣿⣿⣿⣿⡿⠃⢸⣿⡄⠀⣿⣿⢹⣄⣀⣀⠀

⠻⠿⠟⠁⠀⠀⠀⠀⠀⢠⣀⣼⡇⢀⡞⠁⠀⣼⣶⣿⣿⠤⠠⣬⡄⠠⢤⣤⣤⣾⣿⣿⣼⠛⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⣤⣀⠉⣁⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⣴⣿⣿⣿⣿⡯⠀⠀⠘⣽⣧⠀⠘⣿⣯⠛⠿⠿⣷

⣶⣶⠶⣿⠿⢿⠾⠿⠿⠿⠿⢿⣁⠞⠀⠀⠀⣿⣿⣿⣿⡄⠀⠈⠹⠀⠄⠀⢸⣿⣿⠉⣻⡇⣿⣿⣟⢿⣿⣿⣿⡿⣿⣿⣯⠁⢸⣿⡄⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠟⢿⣿⣧⠀⠀⠀⣿⣿⠀⠀⢸⣧⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣿⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣾⡗⣾⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⢛⣸⣧⣿⣿⣾⣿⣿⣿⣾⣷⣿⣀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿

⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⠿⠛⠙⠛⣿⣿⠿⠿⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿

⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⣿⠟⠁⠀⠀⠀⠀⢸⣷⢾⣷⡀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⠀⠀⠀⠀⠀⠀⣰⠏⠈⠹⣿⣦⣀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⠟⠛⠿⠟⡛⠁

⠞⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣠⡟⠀⠁⠠⢹⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⠁⠀⠀⠀⢀⡟⠛⣶

⠀⠀⠀⠀⠀⢨⢝⡛⠃⠈⠙⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣴⣾⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣴⣿⡁⢀⣈

⣆⣀⣠⣴⡾⠛⢸⣿⠀⠀⠀⠀⢹⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⢶⣾⣿⣿⣷⣿⣿

⢈⣿⣿⡟⠀⠀⢸⣿⣦⣀⣀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢿⣿⡿⣿⣟⣿⣿⣿⡿⠿⣻⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠌⣻⠛⡿⠟⠛

⠈⢻⣿⣿⣾⣷⣾⣿⣿⡟⣿⡿⠋⠁⠀⠀⠀⠀⠀⣠⠾⢿⣿⣿⠿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠟⠛⠛⠋⠉⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⢀

⠀⠀⠉⠻⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣷⡀⠀⠈⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣄⣤⣤⣴⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠉

⣿⣦⣿⣦⣶⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻⣿⣿⣷⣤⣾⡅⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣣⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢀⡀

⠙⠿⣿⣿⣿⣿⣿⠟⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠇⣾⣽⠏⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡻⡿⢿⣋⣥⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤

⠀⢠⣑⠻⢭⣭⣶⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣫⠄⠀⠀⠀⢠⣽⣯⣽⠛⢿⣶⣶⣄⣀⣠⣤⣤⢤⣀⣀⡀⠈⠉⠙⠁⢸⣿⠿⢷⣶⣤⣄⣀⣀⣠⣤⣴⣶⣿⣶⣶⣶⣦⣤⣀⠀⠀⠀⢀⣩

⠀⠈⠙⠛⠿⠿⠿⠟⠒⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣷⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢻⣿⣿⡿⠋⠀⠤⠤⠤⣀⡉⠀⠀⠀⠀⠈⠙⠈⢁⣹⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⡍⠛⡋⠉⣿⣦⣤⣴⠿⠛

⢀⣽⣿⣲⣶⣶⡿⠀⠀⣀⣀⣿⣷⣤⣶⣶⣶⣶⣶⣶⣤⣄⣀⣶⣾⠿⠌⠀⣈⠐⠂⠀⢻⣿⣿⣿⣧⡆⢰⣻⣿⡷⣶⣤⣤⣤⣤⣄⢀⣤⣶⣦⣤⣤⣴⣾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⢰⠇⠀⢿⣿⣟⡻⢿⠆

⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⢻⣿⡏⠉⠀⠀⠀⢈⣿⣿⣟⣈⣉⣥⣄⢀⣀⣀⣠⠴⠛⣿⣿⠿⠋⠉⠁⣸⣿⡏⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⢀⡠⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⡿⢿⣷⣄⢀

⠉⠛⠻⣿⠿⠟⠋⠀⠀⠀⣀⣾⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠀⠘⣿⡿⠋⠉⠁⢠⣾⣾⣿⣿⣄⠀⣠⠎⠐⢻⣷⡘⠻⣿⣿⣿⣿⠟⣡⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢿⠀⠀⢀⣿⣇⠀⠙⠛⠊

⣿⣿⣷⣶⣶⠶⠴⠶⠲⠿⠟⢻⣷⡀⠀⢀⣠⠾⡟⢿⣿⡟⠒⠂⣬⠀⠒⠲⠶⠚⣻⣿⡟⢿⣿⣷⡏⠀⠀⠈⠛⢷⠀⠛⠏⠉⢁⣼⣿⣿⡿⠿⠿⠿⠛⠛⠉⡋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⠸⣿⡟⣧⣀⣀⠀

⠙⠿⠿⠋⠀⠀⠀⠀⠀⠠⣀⣠⣿⠁⢰⠋⠀⢠⣷⣾⣿⡇⠄⢤⣭⠀⠤⣤⣤⣴⣿⣿⣥⡟⢿⣿⣿⣷⣶⣾⣿⣿⣷⣶⣤⣄⠈⢉⣁⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣠⣾⣿⣿⣿⣿⠇⠀⠀⢻⣿⡄⠀⢿⣿⡝⠿⠿⢿

⣶⣶⡶⣶⠿⢷⠶⠶⠶⠿⠿⠿⡏⡰⠃⠀⠀⢸⣿⣿⣿⣧⡀⠀⠉⠇⠀⠀⠀⣿⣿⡏⠙⣿⢸⣿⣿⢻⣿⣿⣿⣿⢿⣿⣿⠉⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠻⣿⣿⡄⠀⠀⢸⣿⡇⠀⠀⣿⣄⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣻⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⢛⣘⣧⣿⣿⣾⣿⣿⣿⣾⣷⣿⣄⡙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿

⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠋⠛⢿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿

⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠹⣿⡿⠋⠀⠀⠀⠀⠈⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡁⠀⠀⠀⠀⠀⢀⡟⠉⠉⢿⣶⣄⡀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡿⠟⠛⠻⠟⢛⠁

⡴⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⢀⣾⠁⠈⠀⠌⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠁⠀⠀⠀⠀⣸⠙⠻

⠀⠀⠀⠀⠀⠀⡍⡛⠛⠈⠉⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣤⣤⣾⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢠⣾⡿⠀⣀

⢷⣀⣀⣠⣴⠝⠃⣿⡇⠀⠀⠀⠈⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⢶⣿⣿⣿⣾⣿

⠀⣹⣿⣿⠃⠀⠀⣿⣷⣄⣀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⡿⢿⣿⣿⣿⣿⣿⠿⢟⣧⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢙⠟⢻⠿⠛

⠀⠙⢿⣿⣷⣶⣴⣿⣿⣿⢿⣿⠟⠋⠀⠀⠀⠀⠀⢀⡴⠿⣿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⠛⠛⠛⠉⠁⠀⢀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀

⡄⠀⠙⠻⠿⠿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣆⠀⠈⢹⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣠⣤⣦⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠈

⣿⣶⣼⣶⣴⣶⣶⣴⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⢿⣿⣿⣦⣴⣏⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣜⣼⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠄⣀

⠈⠻⢿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠿⢰⣯⡿⠁⠀⠀⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⢿⣟⣉⣤⣾⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦

⠀⠀⣔⠛⢭⣭⣥⣶⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⡥⠀⠀⠀⠀⣬⣿⣭⡟⠻⣷⣶⣤⣀⣀⣤⣤⠤⣄⣀⢀⠐⠉⠉⠋⠀⣿⡿⠿⣶⣦⣤⡀⣀⣀⣤⣴⣶⣿⣷⣶⡶⣶⣤⣤⡀⠀⠀⠀⣈

⠀⠀⠙⠛⠾⢿⣿⡿⠒⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⡷⠀⠀⠀⢸⣿⣿⣿⣷⠀⠘⣿⣿⣿⠟⠁⠠⠤⠤⢄⣉⠀⠀⠀⠀⠈⠉⠃⠉⣉⣿⣿⡿⠟⠛⣛⣻⣯⣿⣿⣿⠅⢛⠁⢹⣷⣤⣤⡴⠟

⡀⣸⣧⣶⣶⣶⣶⡆⠀⢀⣀⣸⣿⣦⣤⣶⣶⣶⣶⣶⣤⣤⡄⣴⣶⡿⠧⠁⢀⡁⠒⠀⠘⣿⣿⣿⣿⣴⠀⣞⣿⣿⢶⣤⣤⣤⣤⣤⡈⣠⣴⣶⣤⣤⣴⣶⠿⠛⢋⣡⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠺⠀⠸⣿⣿⣟⠿⢷

⣺⣿⣿⣿⣿⣿⣧⣶⣿⣿⡿⠿⣿⣿⠉⠁⠀⠀⠀⣹⣟⣿⣃⣉⣩⣤⡀⣀⣁⣀⡠⠜⢻⣿⡿⠇⠈⠉⢀⣿⣿⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⣀⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⡿⣿⣿⡆

⡟⠛⠛⣿⣿⠿⠛⠀⠀⠀⢀⣰⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢻⣿⠟⠉⠉⠁⣴⣶⣿⣿⣧⡀⢀⡴⠁⠘⣿⣆⠙⣿⣿⣿⣿⡿⢋⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⢿⣃⠀⠀⣸⣿⡂⠈⠙⠛

⣿⣿⣿⣶⣦⣤⣤⠤⠶⠲⠿⠛⣿⡆⠀⠀⣀⣴⠿⠹⣿⣿⠓⠆⣤⡅⠐⠒⠶⠖⢛⣿⣿⠟⣿⣿⣾⠁⠀⠀⠙⠻⡆⠘⠻⠉⠉⣠⣿⣿⣿⠿⠿⠿⠟⠛⠋⢙⢩⣁⣀⣸⣿⣿⣿⣿⡿⠃⠘⣿⡀⠀⢿⣿⢻⣄⣀⣀

⠉⢻⣿⠟⠃⠀⠀⠀⠀⠀⢄⣀⣼⡏⠀⡜⠁⠀⣸⣶⣿⣿⠤⠤⣭⡅⠠⢤⣤⣤⣾⣿⣿⣼⠿⣿⣿⣿⣶⣶⣿⣿⣿⣶⣦⣤⣀⠉⣁⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⣴⣿⣿⣿⣿⣿⠀⠀⠘⣟⣧⠀⠸⣿⣿⠛⠿⠿

⠶⣶⣶⣶⠿⢷⠶⠶⠶⠶⠿⠿⢿⢁⠞⠀⠀⠀⣿⣿⣿⣿⣄⡀⠊⠹⠀⠀⠀⢸⣿⣿⠉⢻⡇⣿⣿⣟⢿⣿⣿⣿⡿⢿⣿⣏⠁⢸⣿⡄⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠟⢿⣿⣧⠀⠀⠀⣿⣿⠀⠀⢸⣧⣄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⣘⣣⣿⣿⣶⣿⣿⣿⣾⣷⣿⣤⡙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿

⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿

⢰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡿⣿⠟⠁⠀⠀⠀⠀⢹⣷⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⣸⠋⠉⠻⣷⣤⣀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠛⠿⡛⡋

⢀⠾⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄⠀⠀⠀⢀⣰⡏⠀⠁⡀⢹⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠀⠀⠀⠀⢀⡏⠛

⠀⠀⠀⠀⠀⠀⣘⠛⠿⠋⠉⠛⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⣤⣼⣿⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣴⣿⠀⢀

⠿⣄⣀⣀⣠⡾⠛⢼⣷⠀⠀⠀⠀⢻⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣗⠶⣾⣿⣿⣷⣿

⡀⢉⣿⣿⡟⠀⠀⢸⣿⣄⣀⣀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠟⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢻⠛⡿⠟

⡇⠘⠿⣿⣿⣶⣦⣼⣿⣿⡿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠟⠛⠛⠋⠉⠀⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀

⣧⠀⠈⠛⠿⢿⣿⣿⣿⣟⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣧⠀⠀⠙⡟⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣄⣄⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀

⢹⣷⣤⣶⣦⣤⣤⣤⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⢻⣿⣿⣷⣤⣾⡁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣣⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠠⢀

⠈⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠻⠇⣿⣵⠏⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣋⣡⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷

⠀⠀⢀⠋⠭⣭⣭⣵⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣫⠄⠀⠀⠀⢀⣿⣿⣿⠻⣿⣦⢦⣀⣀⣠⣤⣤⣄⣀⡀⡁⠊⠙⠛⠁⢸⣿⠿⣷⣦⣤⣄⢀⣀⣠⣤⣴⣶⣿⣶⣶⢶⣦⣤⣄⠀⠀⠀⢀

⠀⠀⠘⠛⠶⢿⣿⣿⡗⠒⠢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢭⠆⠀⠀⠀⣿⣿⣿⣿⣆⠈⢻⣿⣿⡿⠋⠁⠤⠤⠤⣈⠁⠀⠀⠀⠀⠉⠙⠀⢈⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡏⠛⠋⠉⣷⣦⣀⣴⠾

⣄⢀⣵⣶⣶⣶⣴⣦⠀⠀⠀⣈⣿⣷⣤⣤⣤⣶⣶⣶⣤⣤⣄⢠⣶⣾⠿⠍⠑⠂⠐⠀⠀⢿⣿⣿⣿⣧⡆⢠⢿⣿⣷⣤⣤⣤⣤⣀⣀⢁⣤⣶⣦⣤⣤⣴⣾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⢰⠇⠀⣿⣿⣿⡻⠿

⢩⣿⣿⣿⣿⣿⣿⣴⣶⣿⣿⠿⢿⣿⡏⠉⠀⠀⠀⢙⣛⣛⣟⢉⢙⣭⡀⢀⡈⢁⣀⡤⠛⣿⣿⠿⠙⠉⠁⣻⣿⡍⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⢀⡠⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⢿⣿⣆

⣮⠛⠛⢻⣿⡿⠿⠋⠉⠁⠀⢀⣾⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠀⠸⣿⡿⠋⠉⠉⢠⣶⣾⣿⣟⡄⠀⢠⠎⠌⢿⣷⡘⢿⣿⣿⣿⣿⠟⣡⠀⠀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⣿⠀⠙⠛

⢻⣾⣷⣶⣦⣤⣤⡤⠤⠶⠾⠟⢿⣧⠀⠀⠀⣠⡿⠏⢿⣿⡟⠢⢠⣭⠀⠄⠤⠴⠞⣿⣿⡿⢿⣿⣷⡏⠀⠀⠈⠻⢧⠀⠻⠟⠉⠁⣼⣿⣿⡿⠿⠿⠿⠟⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⢿⣇⠀⠸⣿⡏⣧⣀⣀

⠉⠛⣿⣿⠛⠁⠀⠀⠀⠀⠀⡀⣨⣿⠀⢠⠎⠁⢀⣷⣾⣿⡧⠀⣈⣭⠀⢠⣤⣤⣤⣿⣿⣧⡿⣿⣿⣿⣷⣴⣶⣿⣿⣷⣶⣤⣀⠈⢋⡁⠀⠀⠀⠀⠀⠀⣠⠜⠁⢀⣈⣽⣿⣿⣿⣿⠇⠀⠀⢲⣿⡄⠀⢿⣿⡝⠻⠿

⣶⣶⣶⣶⠿⢶⠶⠶⠶⠶⣶⣿⢿⡋⣠⠋⠀⠀⢸⣿⣿⣿⣇⣀⠐⠋⡇⠀⠈⠉⣿⣿⡏⠛⣷⢸⣿⣿⠻⣿⣿⣿⣿⢿⣿⣿⡉⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠻⢿⣿⡄⠀⠀⢸⣿⡏⠀⠀⣿⣤⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⢤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡅⣿⠢⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⣃⣻⣿⣶⣿⣿⣿⣾⣷⣿⣤⣝⡋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿

⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿

⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣟⣿⠏⠁⠀⠀⠀⠀⢿⡦⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿

⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡇⠀⠀⠀⠀⠀⠀⡼⠉⠉⢻⣷⣄⡀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⠟⠛⠛⠟⠛

⠀⢀⡾⠿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢳⡀⠀⠀⠀⠀⣴⡇⠀⠀⡄⢻⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠋⠀⠀⠀⠀⢠⠋

⠀⠀⠀⠀⠀⠀⠀⢘⠿⠿⠋⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⣿⣿⣧⣤⣴⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣴⣿⠀

⠰⢷⡀⠀⢀⣠⣶⠟⣼⣧⠀⠀⠀⠈⢿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣒⠶⣿⣿⣿⣷

⠀⠀⢙⣿⣿⡟⠁⠀⢸⣿⣀⠀⠀⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠟⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠛⡿

⢀⡇⠘⢿⣿⣷⣴⣤⣼⣿⣿⡿⣿⡿⠟⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠟⠛⠛⠋⠉⠀⠀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀

⢸⣦⠀⠘⠛⠿⣿⣿⣿⣿⡟⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠘⢿⣇⠀⠈⠙⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⣄⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀

⠀⢹⣦⣤⣰⣄⣤⣤⣬⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⢾⣾⣿⣧⣤⣾⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣭⣿⣿⣿⣿⣿⣿⣿⠿⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠡

⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠛⠿⠃⣿⣳⠏⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⡿⣿⣋⣡⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠫⢟⣛⣫⣥⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣋⠀⠀⠀⠀⢠⣿⣿⣿⠿⣷⣤⣤⣀⣀⣠⣤⣤⣄⣀⠀⠁⠊⠙⠋⠁⢸⣿⠿⣷⣦⣤⣄⢀⣀⣠⣤⣶⣶⣿⣶⣶⢶⣦⣤⣀⠀⠀⠀

⠀⠀⠀⠘⠳⢶⣿⣿⣿⡿⠥⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⠿⢭⠆⠀⠀⠀⣿⣿⣿⣿⣄⠈⢿⣿⣿⡿⠉⠉⠠⠤⢀⣉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡏⠛⠋⠈⣷⣦⣠⣤

⣤⣀⠀⣲⣦⣤⣤⣤⣆⠀⠀⠀⢈⣿⣧⣤⣤⣤⣤⣶⣦⣤⣄⣀⢠⣴⣾⣿⠌⠁⠂⠠⠄⠀⢿⣿⣿⣿⣧⡄⢨⢿⣿⣧⣤⣤⣤⣀⣀⣀⢁⣤⣦⣤⣤⣤⣴⣾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⢰⠇⠀⢿⣿⣟⣻

⠈⢉⣾⣿⣿⣿⣿⣿⣥⣶⣾⣿⣿⢿⣿⡛⠋⠉⠀⠈⢙⣻⣿⡟⠙⢛⣉⡀⠀⠈⢁⣀⡤⠞⣿⣿⠿⠙⠉⠁⣿⣿⡝⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⢀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼⣿⢿⣿

⣶⣬⠻⠿⢿⣿⣿⡿⠛⠉⠉⠀⢀⣾⣿⠇⠀⠀⠀⢀⣿⣿⣿⣿⠀⠸⣿⡿⠍⠉⠉⢡⣶⣾⣿⣟⡄⠀⢠⠎⠈⢿⣧⠘⢿⣿⣿⣿⣿⠟⣡⠀⠀⢀⠀⠀⠀⣀⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⣷⡀⠉

⠙⢻⣶⣶⣦⣭⣤⣤⢤⣤⠤⣶⠿⢿⣧⠀⠀⠀⣀⣽⢟⢿⣿⡧⠤⢠⣭⠀⠤⠤⠤⠾⣿⣿⡿⢿⣿⣶⡏⠀⠀⠈⠻⣧⠀⠿⠏⠋⢁⣼⣿⣿⡿⠿⠿⠿⠟⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⢿⣇⠀⠸⣿⡟⣧⣀

⠀⠘⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢨⣿⠀⢠⠞⠉⢠⣦⣼⣿⡇⠀⣈⣩⠀⣀⣤⣤⣤⣿⣿⣥⡿⣿⣿⣿⣧⣴⣶⣿⣿⣶⣦⣄⣀⠈⢋⡁⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣨⣽⣿⣿⣿⣿⠇⠀⠀⢻⣿⡄⠀⢿⣷⡜⠻

⠳⢶⣶⣶⣯⢶⠶⠶⠶⠶⢶⣶⣿⣿⡏⣠⠏⠀⠀⢸⣿⣿⣿⣇⠀⠘⠛⡆⠀⠉⠉⣿⣿⡟⠻⣷⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⠋⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠻⣿⣿⡀⠀⠀⢺⣿⡏⠀⠀⣿⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡆⢠⣏⣷⣿⣿⡇⣿⣿⠀⣽⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⢃⣛⣯⣴⣿⣿⣿⣾⣷⣿⣦⣽⣋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿

⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿

⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣿⡟⠉⠀⠀⠀⠀⠸⣷⢾⣿⡀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿

⠀⠐⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⠀⠀⠀⠀⠀⠀⢰⠏⠈⠹⣷⣦⣀⠀⠀⣀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⠛⠛⠻⠛

⠀⠀⣰⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣆⠀⠀⠀⠀⣠⡿⠀⠁⢠⠸⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠟⠁⠀⠀⠀⢀⡘

⠀⠀⠁⠀⠀⠀⠀⠀⡟⢿⠟⠙⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣤⣿⣿⣿⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣰⣿⡇

⠀⢾⣄⠀⠀⢀⣤⡾⢷⣿⡄⠀⠀⠀⠹⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⡲⢾⣿⣿⣿

⠀⠀⠘⢻⣿⣿⠋⠀⠈⣿⣇⡀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⡟⠻

⠀⣰⠀⢿⣿⣿⣦⣤⣠⣿⣿⣿⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠿⠛⠛⠛⠉⠁⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀

⠀⣿⡄⠀⠺⢻⢿⣿⣿⣿⣿⢧⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠻⣿⡀⠀⠉⢿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣄⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄

⠀⠈⣷⣄⣢⣤⣠⣤⣅⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠲⣶⣿⣿⣤⣤⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣽⣿⣿⣿⣿⣿⣿⡿⠟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆

⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛⠻⠟⢸⣟⡾⠁⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣟⣉⣤⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠨⠿⣛⣛⣫⣥⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⡁⠀⠀⠀⠀⣸⣿⣿⡻⢿⣦⣤⣄⠀⣀⣤⣤⣤⣀⡀⢈⠑⠉⠛⠉⢀⣿⡿⢿⣶⣤⣄⡀⣀⣀⣤⣴⣶⣿⣷⣶⡶⢶⣤⣤⡀⠀⠀

⠀⠀⠀⠀⠻⠦⣴⣿⣯⣿⠭⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⡿⢯⡵⠀⠀⠀⢼⣿⣿⣿⣧⡄⠹⣿⣿⣿⡟⠉⠁⠤⢄⣈⡉⠀⠀⠀⠀⠈⠙⠃⠈⣙⣿⣿⡿⠟⠟⣛⣻⣿⣿⣿⣿⠉⢛⠉⢹⣶⣤⣤

⣤⣀⡀⢠⣶⢤⣤⣤⣽⡁⠀⠀⠀⢹⣷⣄⣤⣤⣤⣤⣤⣤⣤⣀⡀⣤⣴⣿⡧⠈⠐⠀⠤⠀⠸⣿⣿⣿⣿⣤⠀⡽⣿⣿⣤⣤⣤⣀⣀⣀⡈⣠⣴⣤⣤⣤⣤⣶⡿⠟⢋⣡⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⡾⠀⠸⣿⣿⣟

⠈⠉⢱⣿⣿⣿⣿⣿⣯⣥⣶⣾⣿⡿⣿⣟⠛⠉⠉⠉⠉⣛⣿⣿⠋⠛⢛⣁⠀⠀⠉⢀⣀⡴⢲⣿⡿⠏⠋⠉⢸⣿⣯⠋⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⡿⣿

⣶⣤⡟⠿⠿⣿⣿⣿⠿⠛⠉⠉⠀⣠⣿⡿⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⢿⣿⡿⠙⠋⠉⣴⣶⣿⣿⣧⠀⠀⡴⠂⠽⣿⡄⠻⣿⣿⣿⣿⡿⢋⡄⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⢸⣿⣂⠈

⠙⠿⣳⣶⣶⣬⣭⣤⣀⣀⣤⣤⡾⠿⣿⡅⠀⠀⢀⣠⡿⠻⣿⣿⠧⠄⣈⡏⠠⠤⠤⠴⢿⣿⣿⠿⣿⣿⣾⠁⠀⠀⠙⢿⡄⠘⠿⠛⠋⣠⣿⣿⣿⠿⠿⠿⠿⠟⠋⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⣿⡄⠀⢿⣿⢸⣤

⡀⠀⠚⢿⣿⡿⠟⠉⠀⠀⠀⠀⡀⠀⣹⡇⠀⡴⠋⠁⣰⣤⣿⣿⣀⢀⣙⡁⢀⣀⣀⣀⣼⣿⣟⣴⠿⣿⣿⣷⣤⣶⣾⣿⣷⣶⣤⣀⡀⠙⣉⠁⠀⠀⠀⠀⠀⢀⡤⠊⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠈⣿⣧⡀⠘⣿⣿⠙

⠛⠶⣶⣶⣯⣶⠶⢶⣶⣶⣶⣤⣾⣿⣿⠃⡴⠁⠀⠀⣿⣿⣾⣿⡀⠀⠙⢳⠀⠈⠉⢹⣿⣿⠛⢿⡆⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢸⣿⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠻⣿⣧⠀⠀⠀⣿⣿⠁⠀⢸⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣻⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⣛⣫⣤⣿⣿⣿⣾⣷⣿⣶⣽⣋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣖⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿

⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿

⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⣿⣿⠏⠁⠀⠀⠀⠈⣿⡶⣾⡇⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿

⠀⠀⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡇⠀⠀⠀⠀⠀⠀⡾⠉⠉⢿⣶⣄⡀⠀⢀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⠟⠛⠛⠟

⠀⠀⢀⣼⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠀⠀⠀⠀⢀⣼⠇⠈⠀⡌⣿⣿⣿⣻⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠀⠀⠀⠀⣠

⠀⠀⠈⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣠⣤⣿⣿⣦⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣼⣿

⠀⠰⣧⠀⠀⠀⣀⣴⠿⣾⣦⠀⠀⠀⠙⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣒⠶⣿⣿⣿

⠀⠀⠈⠻⣿⣿⡟⠁⠀⢹⣿⡀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⠛

⠀⢀⡇⠸⣿⣿⣧⣤⣄⣼⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠞⠟⠛⠛⠉⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂

⠀⢸⡤⠀⠘⠿⣿⣿⣿⣿⣿⣿⣥⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢀⠘⣿⣏⠀⠈⠻⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠈⢻⣄⣠⣤⣄⣀⣉⣉⣩⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⣶⣾⣿⣦⣠⣴⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣭⣿⣿⣿⣿⣿⣿⣿⠿⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱

⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠛⠿⠇⣿⣻⠏⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣋⣁⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠽⣛⣛⣛⣩⣴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢋⠀⠀⠀⠀⢀⣿⣿⣟⠿⣷⣤⣤⡀⢀⣀⣀⣀⣀⣀⠀⠙⠚⠙⠋⠉⢸⣿⠿⣷⣦⣤⣄⠀⣀⣠⣤⣶⣾⣿⣶⣶⢶⣦⣤⣄⠀⠀

⠀⠀⠀⠀⠸⢶⣤⣾⣿⣿⡯⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣯⠆⠀⠀⠠⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⠋⠉⠀⢤⣈⣉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡍⠙⡋⠉⣷⣦⣤

⣤⣀⡀⠀⣤⣤⣤⣤⣭⣍⠀⠀⠀⠙⣿⣦⣀⣠⣤⣤⣤⣤⣤⣀⣀⢀⣤⣼⣿⠀⠁⠀⠠⠄⠀⢿⣿⣿⣿⣧⡄⢨⣿⣿⣧⣤⣤⣀⣀⣀⣀⢁⣤⣤⣤⣄⣤⣴⣾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⠰⠇⠀⢿⣿⣿

⠀⠉⢙⣾⣿⣿⣿⣿⣿⣩⣤⣶⣾⣿⣿⣿⡟⠛⠉⠉⠉⠙⡿⢿⡟⠙⠛⣋⡀⠀⠈⠉⢀⣠⠶⣾⣿⡿⠛⠋⠁⣿⣿⡟⢡⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⢻

⣶⣤⣴⠿⠿⢿⣿⣿⣿⠟⠛⠋⠉⠀⣼⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⠀⠹⣿⣿⠎⠛⠉⢩⣶⣾⣿⣿⡄⠀⢀⠔⡩⢿⣧⠘⢿⣿⣿⣿⣿⠟⣁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⠀⣿⡿⡄

⠉⠻⢿⣴⣶⣬⣍⣁⣀⣀⣀⣤⣴⡿⢿⣯⠀⠀⠀⢀⣼⡟⢿⣿⡿⠤⢄⣙⢁⠤⠤⠤⠼⢿⣿⡿⣿⣿⣶⡏⠀⠀⠈⠻⣧⠀⠿⠟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⣿⣧⠀⠸⣿⡇⢧

⣀⠀⠘⠿⣿⣿⡿⠋⠉⠉⠁⠀⠀⠀⢈⣿⠀⢀⠞⠉⢀⣦⣼⣿⣇⣀⣈⣛⠀⣀⣀⣀⣠⣿⣿⣣⡿⣿⣿⣿⣦⣤⣶⣾⣿⣶⣤⣄⣀⠈⢛⣉⠀⠀⠀⠀⠀⠀⣀⠔⠃⢀⣈⣽⣿⣿⣿⣿⡇⠀⠀⢹⣿⣆⠀⢻⣿⡟

⠛⠷⢶⣶⣯⣷⠤⣴⣴⣶⣦⣤⣤⣷⣿⡟⢀⠞⠀⠀⢰⣿⣷⣿⣇⠀⠈⠛⡆⠀⠉⠉⣿⣿⡟⠻⣷⢸⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡋⠀⣾⣧⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠛⢿⣿⡄⠀⠀⢸⣿⡟⠀⠀⢿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣺⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡏⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⣋⣠⣽⣿⣿⣾⣷⣿⣶⣿⣯⣘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿

⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿

⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⡿⠋⠁⠀⠀⠀⠘⣷⣴⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿

⠀⠀⠀⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⠃⠀⠀⠀⠀⠀⢀⡿⠉⠙⣿⣦⣄⠀⠀⢀⣠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⠟⠛⠛

⠀⠀⠀⢀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⣼⠃⠈⠀⡈⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⠁⠀⠀⠀⠀

⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⣿⣿⠛⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣴⣿⣿⣦⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢠⣾

⠀⠀⢠⣆⠀⠀⠀⢀⣴⡿⣼⡆⠀⠀⠀⠙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⢶⣿⣿

⠀⠀⠀⠙⠷⣶⣾⡟⠁⠀⣿⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⣿⡿⣿⣿⣿⣿⢿⠟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿

⠀⠀⢀⡇⠼⣿⣿⣧⣠⣀⣼⣿⣿⣷⣶⣿⠿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠾⠾⠟⠛⠛⠁⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅

⠀⠀⢸⡇⠀⠹⠿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠀⠀⠀⠀⠀⠀⠐⠉⢁⠹⣿⡇⠀⠉⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⣀⣀⣤⣴⣾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠈⢿⣄⣠⣠⣀⣉⣉⣙⣫⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣶⣾⣿⣄⣠⣼⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣘⣿⣿⣿⣿⣿⣿⣿⠿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠭⠿⢿⠋⣿⣾⠇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⢿⣿⣿⣋⣁⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⢛⣿⠿⢟⣋⣵⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⠀⠀⠀⠀⢀⣿⣿⣻⢿⣶⣤⣄⡀⢀⣀⣀⣀⣀⡀⠈⠑⠚⠛⠋⠁⣸⣿⠿⣶⣦⣤⣀⠀⣀⣠⣤⣶⣾⣿⣶⣶⢶⣦⣤⣄⠀

⠀⠀⠀⠀⠀⠺⣶⣤⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣾⣿⣯⠆⠀⠀⢠⣿⣿⣿⣿⣀⠙⣿⣿⣿⡿⠋⠉⣀⣀⣈⡉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡍⠛⡋⢈⣷⣦

⢦⣄⣀⠀⠀⣠⣤⣈⣉⣉⡍⠁⠀⠀⠙⣿⣆⣀⣀⣀⣤⣤⣤⣀⣀⡀⢠⣤⣾⣿⠐⠡⠐⠠⠀⠀⣿⣿⣿⣿⣧⡄⣸⣿⣿⣧⣤⣤⣀⣀⣀⣈⢀⣤⣤⣤⣤⣤⣴⣾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⢸⠇⠀⢿⣿

⡀⠉⠛⠛⣶⣿⣿⣿⣿⣿⣋⣤⣴⣶⣾⣿⡿⠟⠛⠋⠉⠉⠻⠿⣿⡟⠛⠟⣋⠀⠀⠀⠁⢀⣠⠶⣿⣿⡟⠙⠙⠁⣿⣿⡟⢡⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⢀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿

⢿⣦⣤⣰⠿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⣼⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⠈⢸⣿⣷⠚⠛⠋⢩⣤⣼⣿⣟⡀⠀⢀⠔⡙⢿⣇⠹⢿⣿⣿⣿⣿⠟⣃⠁⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠉⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⡟

⠀⠉⠻⣿⣤⣤⣬⣙⣉⣀⣀⣀⣠⣴⡾⣿⣏⠀⠀⠀⢀⣿⣿⣿⣿⡯⢤⣌⣛⢁⠀⣀⣤⠼⣿⣿⡿⣿⣿⣴⡏⠀⠀⠘⠿⣇⠈⠿⠟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⡿⣧⠀⠸⣿⣇

⣄⡀⠀⠰⢿⣿⣿⡿⠋⠉⠉⠉⠁⠉⠀⢸⣿⠂⢀⡴⠋⢁⣌⣼⣿⡇⠀⠘⣛⠀⣀⣀⣀⣰⣿⣿⣃⡿⣿⣿⣷⣦⣤⣶⣶⣿⣶⣤⣄⡀⠘⢋⡉⠁⠀⠀⠀⠀⠀⣀⠔⠃⢀⣉⣽⣿⣿⣿⣿⡇⠀⠀⢹⣿⣄⠀⠿⣿

⠛⠿⠷⣶⣧⣿⣏⠠⣴⣶⣦⣤⣤⣤⣷⣾⡟⢀⡞⠀⠀⢸⣿⣿⣿⡇⠀⠩⠛⡆⠀⠉⠉⣿⣿⡟⠻⣷⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠻⣿⣿⡄⠀⠀⢸⣿⡟⠀⠀⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⢋⣀⣽⣿⣾⣾⣷⣿⣶⣿⣯⣜⡛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿

⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿

⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⣿⠟⠁⠀⠀⠀⠀⢿⣦⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿

⠀⠀⠀⠸⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⡟⠀⠀⠀⠀⠀⠀⣸⠛⠉⢻⣷⣤⡀⠀⠀⣀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡿⠟⠛⠛

⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⣰⡏⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⠀⠀⠀⠀

⠀⠀⠀⠰⠉⠀⠀⠀⠀⠘⣿⣿⡟⠻⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣤⣿⣿⣧⣀⣴⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⣴

⠀⠀⠀⣴⡀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⠘⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠶⣿⣿

⠀⠀⠀⠈⠳⣶⣶⣿⠟⠀⢸⣿⡇⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹

⠀⠀⠀⢸⠠⣿⣿⣿⣀⣄⣀⣿⣿⣶⣶⣾⡿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠷⠿⠛⠛⠋⠀⠀⣀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⣟⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠊⠉⡈⢿⣟⠁⠉⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣄⣀⣠⣴⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠹⣧⡀⣄⣈⢈⣉⣉⣛⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠤⡼⢴⣶⣿⣧⣀⣤⡇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣃⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠽⠿⡟⢹⢳⡿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣛⣁⣤⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠙⣿⠿⠿⢛⣩⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡁⠀⠀⠀⠀⣺⣿⣟⡿⣷⣦⣤⣀⠀⣀⣀⣀⣀⣀⠀⠉⠓⠛⠛⠉⢀⣿⡿⢷⣦⣤⣄⡀⣀⣀⣤⣴⣶⣿⣷⣶⠶⣶⣤⣤⡀

⠀⠀⠀⠀⠀⠀⢶⣤⣽⣿⣿⣿⣓⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣟⡥⠀⠀⠀⣾⣿⣿⣿⣇⡈⢻⣿⣿⣿⠟⠉⢁⣀⣁⣉⠉⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⡿⠟⠟⣛⣻⣿⣿⣿⣿⠉⢛⠁⢹⣷

⠷⣤⣀⡀⠀⢠⣄⣀⣉⣉⣩⠋⠀⠀⠉⢻⣶⣀⣀⣀⣀⣤⣤⣄⣀⡀⠀⣤⣼⣿⡗⠊⠄⠂⠄⠀⢹⣿⣿⣿⣿⣤⢀⣿⣿⣿⣤⣤⣄⣀⣀⣀⡁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⡿⠀⠾⠀⠸⣿

⡄⠈⠛⠛⢣⣾⣿⣿⣿⣿⣟⣡⣤⣶⣶⣾⣿⡿⠟⠛⠋⠉⠛⠿⠿⢿⠛⠻⢟⡁⠀⠀⠊⠀⣀⡴⢾⣿⣿⠏⠏⠋⢸⣷⣿⠋⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿

⢻⣶⣤⣀⡾⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢡⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⡏⠁⣿⣿⡖⠛⠛⠉⣥⣤⣿⣿⣧⡄⠀⡰⢊⠻⣿⡈⠿⣿⣿⣿⣿⡿⢛⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢹⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⢸⣿

⠀⠈⠙⢿⣧⣤⣤⣉⣋⣉⢀⣀⣀⣤⣴⣿⣿⡁⠀⠀⠀⣰⣿⢿⣿⣿⠥⣀⣘⡋⡀⢀⣠⡤⢿⣿⣿⢿⣿⣶⣾⠁⠀⠀⠻⢷⡀⠹⠿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢿⡄⠀⢿⣿

⣤⣀⠀⠀⠻⣿⣿⣿⠿⠋⠉⠉⠉⠉⠁⠀⢻⡇⠀⣠⠞⠉⢨⣤⣿⣿⠀⠀⢛⡃⢀⣀⣀⣀⣼⣿⣟⣸⢿⣿⣿⣶⣤⣴⣶⣾⣷⣦⣄⣀⠐⠛⣋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣈⣩⣿⣿⣿⣿⣿⠀⠀⠈⣿⣧⡀⠘⣿

⠙⠟⠿⣶⣯⣾⣟⡡⣴⣶⣦⣀⣠⣤⣼⣶⣿⠇⣰⠃⠀⠀⣿⣿⣿⣿⠀⠈⠝⢳⠀⠈⠉⢻⣿⣿⠻⢷⡆⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⠟⠿⣿⣧⠀⠀⠀⣿⣿⠇⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣸⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⣀⣹⣿⣾⣾⣷⣿⣶⣿⣯⣜⡛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾

⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿

⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⡿⠋⠀⠀⠀⠀⠸⣷⣲⣶⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠁⠀⠀⠀⠀⠀⢠⡟⠋⠙⣷⣦⣀⠀⠀⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⠿⠛⠛

⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⠀⠀⠀⠀⢀⣾⠁⠐⢀⠘⣿⣿⣟⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠁⠀⠀⠀

⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⢿⣿⣿⠻⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣄⣠⣼⣿⣿⣤⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠

⠀⠀⠀⢠⣄⠀⠀⠀⢀⣰⡞⣼⡅⠀⠀⠈⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡳⢾⣿

⠀⠀⠀⠈⠙⢶⣶⣶⡿⠉⠀⣿⣧⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣇⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈

⠀⠀⠀⢀⡆⢾⣿⣿⣅⣀⠀⣽⣿⣷⣶⣶⣿⡿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠿⠺⠟⠛⠛⠁⠀⢀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣸⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠀⠀⠀⠀⠀⠀⠐⠉⢉⠻⣿⡋⠉⠙⢿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣠⣀⣠⣤⣶⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⣿⡄⠠⣀⡉⣉⡛⠛⣛⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⣤⣧⣦⣿⣷⣄⣀⣜⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣸⣿⣿⣿⣿⣿⣿⡿⠟⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠽⠿⣿⠉⡟⣾⠇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣠⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠙⣻⠿⠿⠿⣛⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢏⠀⠀⠀⠀⢐⣿⣿⡿⢿⣦⣤⣄⠀⢀⣀⣀⣀⣀⡀⠈⠑⠚⠛⠋⠁⣸⣿⢿⣶⣤⣤⣀⢀⣀⣤⣤⣶⣾⣿⣶⡶⢶⣦⣤⣄

⢀⠀⠀⠀⠀⠀⠶⣤⣌⣽⣿⣿⣟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣿⣫⠄⠀⠀⢰⣿⣿⣿⣿⠀⠙⣿⣿⣿⡿⠋⠉⣀⣈⣉⡉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⡿⠿⠿⢛⣛⣿⣿⣿⣿⡇⠙⡃⠀⣿

⠻⣦⣀⡀⠀⠀⣤⣀⣉⣉⣙⡟⠁⠀⠈⠻⣷⡄⢀⣀⣀⣀⣤⣄⣀⡀⠀⢀⣤⣾⣟⠒⠡⠐⢠⠀⠈⣿⣿⣿⣿⣧⡀⣸⣿⣿⣧⣤⣄⣀⣀⣀⡈⢀⣤⣤⣤⣤⣤⣴⡾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⠸⠃⠀⢿

⣧⠈⠙⠿⠷⣴⣿⣿⣿⣿⣿⣛⣠⣤⣶⣶⣿⣿⠿⠛⠛⠛⠙⠻⠿⢿⡗⠻⠿⡋⠀⠀⠒⠂⠀⣠⠶⣿⣿⡿⠙⠛⠀⣿⣾⡛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼

⠻⣷⣤⣄⣰⣿⣿⣿⣿⣿⣿⠻⠟⠛⠉⠉⣼⣿⡇⠀⠀⠀⢀⣾⣿⣿⣷⠈⢸⣿⣷⠞⠒⠛⢩⣤⣼⣿⡟⣄⠀⢀⠔⡙⢿⣇⠻⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠉⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⣿

⠀⠈⠙⢿⣿⣤⣤⣈⣛⣋⠁⠀⣀⣀⣤⣾⣿⣏⠀⠀⠀⢀⣾⡿⣿⣿⡏⣀⣈⣛⢁⣀⣀⣠⡼⣿⣿⡿⣿⣷⣶⡏⠀⠀⠘⢿⣆⠈⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⡯⣧⠀⠸⣿

⣦⣄⡀⠀⠸⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠀⢸⣿⠀⢀⡴⠛⢉⣄⣽⣿⡇⠀⠘⣛⠀⢀⣀⣀⣠⣿⣿⣃⡿⣿⣿⣷⣦⣤⣶⣶⣿⣶⣤⣀⡀⠚⢛⡉⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀⣉⣽⣿⣿⣿⣿⡇⠀⠀⢡⣿⣆⠀⢻

⠙⠟⠿⣷⣯⣶⣟⣻⠰⣶⣦⣀⣀⣀⣠⣷⣾⡿⢀⡞⠀⠀⢸⣿⣿⣿⣇⠀⠹⠟⡆⠈⠙⠛⣿⣿⡟⠿⣦⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣿⣇⠀⠀⠀⠀⠀⠁⣀⣠⣴⣿⣿⣿⡿⠛⣿⣿⡄⠀⠀⢸⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⢀⣙⣿⣽⣾⣷⣿⣶⣿⣯⣼⣛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾

⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿

⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⠟⠁⠀⠀⠀⠀⣿⡶⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⢻⣶⣄⡀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡿⠟⠛

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣳⡀⠀⠀⠀⠀⣰⡇⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⠀⠀⠀

⠀⠀⠀⠀⠰⠋⠉⠉⠀⠀⠹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣀⣤⣿⣿⣧⣄⣴⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀

⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣴⢺⣯⠀⠀⠀⠙⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠲⢿

⠀⠀⠀⠀⠙⠳⣶⣶⣾⠟⠁⢸⣿⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⠠⣾⣿⣿⣀⡀⢈⣿⣷⣶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠷⠿⠛⠛⠋⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⣿⣿⠉⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣄⣀⣠⣴⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠻⣧⡀⡄⣈⠙⠛⠛⠛⣻⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣿⣧⣀⣠⡇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⢿⡟⢹⢷⡿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣟⣉⣠⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⢙⣿⠿⠿⢟⣋⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡃⠀⠀⠀⠀⣸⣿⣿⡿⣷⣦⣤⣀⠀⣀⣀⣀⣀⣀⠀⠉⠒⠛⠛⠉⢀⣿⡿⣿⣶⣤⣄⡀⣀⣠⣤⣴⣶⣿⣿⣷⢶⣶⣦⣤

⡀⢀⠀⠀⠀⠀⠀⢦⣬⣽⣿⣿⣿⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣞⡡⠀⠀⠀⣼⣿⣿⣿⣇⡈⢻⣿⣿⣿⡟⠉⢁⣀⣁⣉⠙⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⡿⠟⢛⣛⣻⣽⣿⣿⣷⠈⢉⠀⢸

⠛⢦⣄⡀⠀⠀⢀⣀⣈⣉⣙⣛⠋⠀⠀⠉⢻⣦⡀⢀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣤⣿⡇⠚⠥⠂⣄⡀⢹⣿⣿⣿⣿⣤⢀⣿⣿⣿⣤⣤⣀⣀⣀⣀⡁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⡿⠀⠺⠀⠈

⣿⡆⠉⠛⠿⢦⣼⣿⣿⣿⣿⡟⣃⣠⣴⣶⣾⣿⣿⠿⠟⠛⠛⠛⠿⣿⣿⠞⠿⠟⠃⠀⠀⠒⠀⢀⡴⢶⣿⣿⠟⠟⠋⢸⣿⣿⠋⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀

⠘⢿⣦⣄⣀⣸⣿⣿⣿⣿⣿⣿⠛⠟⠛⠉⢉⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⣿⣿⡶⠓⠒⠋⣩⣤⣾⣿⢇⠀⠀⣠⢊⠻⣿⡈⠿⣿⣿⣿⣿⣿⢛⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⢸

⠀⠀⠉⠻⣿⣷⣠⣈⣙⠛⠋⠁⠀⢀⣀⣴⣾⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⢇⡀⢘⡋⢀⣀⣀⣤⠿⣿⣿⣿⣿⣷⣼⠃⠀⠀⠻⢿⡄⠸⠿⠛⠋⢀⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢰⢹⡇⠀⢸

⣦⣄⣀⠀⠀⠿⣿⣿⣿⡿⠛⠛⠋⠉⠉⠉⠀⢹⣷⠀⢠⠞⠋⢩⣉⣿⣿⠀⠀⠙⡃⠀⣀⣀⣀⣼⣿⣿⣠⠿⣿⣿⣶⣤⣤⣶⣶⣷⣦⣤⣀⡀⠛⢋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣪⣿⡄⠈

⠉⠟⠻⣿⠿⣶⣌⢻⡻⢶⣦⣀⣀⣀⣀⣸⣶⣿⠏⢠⠏⠀⠀⣼⣿⣿⣿⡅⠈⠻⢳⠀⠉⠛⢻⣿⣿⠿⢿⡆⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢠⣿⡅⠀⠀⠀⠀⠀⢁⣀⣤⣶⣿⣿⣿⠿⠻⣿⣷⡀⠀⠀⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⢙⣛⣽⣼⣷⣿⣶⣿⣿⣾⣿⣃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴

⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⠟⠁⠀⠀⠀⠈⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿

⠀⠀⠀⠀⠀⡸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡇⠀⠀⠀⠀⠀⠀⡿⠋⠉⢿⣦⣄⡀⠀⠀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⡿⠟

⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠀⠀⠀⠀⠀⣼⠇⠈⠀⡈⢿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀

⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠈⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣀⣤⣿⣿⣦⣀⣴⣦⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀

⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣴⢩⣍⠀⠀⠈⠹⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠲

⠀⠀⠀⠀⠈⠙⢷⣤⣤⣾⠟⠁⢹⣿⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⢰⢠⣿⣿⣯⠀⡀⢸⣿⣷⣦⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠖⠟⠛⠛⠋⠀⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢧⠀⠀⠀⠀⡿⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⣿⣟⠉⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣔⠀⠀⠀⠈⢻⣆⠀⡀⡙⠙⠛⠛⠿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣼⣿⣆⣀⣠⠃⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣃⣿⣿⣿⣿⣿⣿⣿⠿⢛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠻⢿⡏⣻⢧⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣛⣁⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⢛⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁⠀⠀⠀⠀⣺⣿⣿⠿⣷⣤⣤⡀⠀⣀⣀⣀⣀⡀⠀⠉⠓⠛⠛⠉⢀⣿⡿⢷⣶⣤⣄⡀⣀⣠⣤⣶⣾⣿⣿⡷⢶⣶⣦

⣄⠀⢀⠀⠀⠀⠀⠠⣤⣉⣲⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣞⡡⠀⠀⠀⣼⣿⣿⣿⣇⠈⢿⣿⣿⣿⡟⠉⢁⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⣶⠉⢛⠁

⠉⠳⢧⣀⠀⠀⠀⢀⣈⣉⡛⠛⢛⠛⠉⠉⠙⢷⣦⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣴⣿⡇⠛⠡⠂⣀⡀⢻⣿⣿⣿⣿⡄⢀⣿⣿⣿⣤⣤⣀⣀⣀⣀⠁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠚⠀

⠀⣶⡄⠙⠻⠷⢆⣼⣿⣿⣿⣿⡿⢃⣀⣤⣴⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⠖⠿⠿⠋⠁⠀⠒⠀⢀⡴⣼⣿⣿⠏⠟⠋⢸⣿⣿⠛⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

⠀⠸⢿⣦⣀⡀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⣿⣿⠀⠀⠀⠀⢠⣶⣿⣿⡆⠀⣾⣿⣶⠒⠒⠛⣩⣤⣿⣿⢇⡀⠀⡠⢊⢻⣿⡈⠿⣿⣿⣿⣿⡿⢛⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀

⠀⠀⠀⠙⠻⣿⣿⣈⣉⡛⠟⠛⠁⠀⠀⣀⣤⣾⣿⡋⠀⠀⠀⢀⣿⣿⣿⣿⣇⣀⠙⡋⢁⣀⣀⣠⣿⣿⣿⣿⣿⣦⣼⠃⠀⠀⠻⣿⡀⠹⢿⠛⠋⢀⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢹⡆⠀

⣷⣦⣄⡀⠀⠈⣽⣿⣿⣿⣿⠟⠓⠛⠛⠛⠋⠀⢻⣷⠀⢀⠴⠋⢩⣈⣿⣿⠀⠈⠻⠃⠀⠀⠀⠀⣸⣿⣿⣰⡿⣿⣿⣶⣤⣤⣶⣶⣷⣤⣄⣀⠀⠛⢋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⡄

⢀⡟⠻⣿⢿⢶⣄⡹⠿⠿⢆⣀⣀⣀⣀⣀⣱⣤⣾⡏⢠⠏⠀⠀⢸⣿⣿⣿⡉⠉⠻⢧⠈⠙⠛⢻⣿⣿⠿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢠⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠻⣿⣧⡀⠀⠀⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢾⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⢙⣛⣼⣼⣷⣿⣶⣿⣿⣾⣿⣃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⠟⠁⠀⠀⠀⠈⣿⡷⣶⡆⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿

⠀⠀⠀⠀⠀⡸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡇⠀⠀⠀⠀⠀⠀⡿⠋⠉⢿⣦⣄⡀⠀⠀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⣿⡿⠟

⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢧⠀⠀⠀⠀⠀⣼⠇⠈⠀⡈⢿⣿⣿⣻⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀

⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠉⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣀⣤⣿⣿⣦⣀⣴⣤⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀

⠀⠀⠀⠀⠈⠛⢷⣤⣤⣾⠟⠉⢹⣿⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡀⠀⠀⠀⠀⢰⢠⣿⣿⣯⢀⡀⢸⣿⣷⣦⣤⣶⣿⠅⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠖⠟⠛⠛⠋⠀⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢧⠀⠀⠀⢀⡗⠀⠹⣿⣿⣿⣿⣿⣿⣿⣏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⣿⣟⠉⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣔⠀⠀⠀⠈⢻⣆⠀⡀⡙⠙⠛⠛⠿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣿⣆⣀⣠⠃⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢇⣿⣿⣿⣿⣿⣿⣿⠿⢛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠻⢿⡏⣻⢧⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⣛⣁⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⢛⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁⠀⠀⠀⠀⣺⣿⣿⠿⣷⣤⣤⡀⠀⣀⣀⣀⣀⡀⠀⠉⠒⠛⠛⠉⢀⣿⡿⢷⣶⣤⣄⡀⣀⣠⣤⣶⣾⣿⣿⣷⢶⣶⣦

⣄⢀⠀⠀⠀⠀⠀⠠⣤⣉⣳⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣞⡡⠀⠀⠀⣼⣿⣿⣿⡇⠈⢻⣿⣿⣿⡟⠉⢁⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⣶⠉⢛⠁

⠉⠳⢧⣀⠀⠀⠀⢀⣈⡉⠛⠛⢛⠛⠉⠉⠙⢷⣦⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣴⣿⡇⠚⠡⠂⣀⠀⢻⣿⣿⣿⣿⡄⢀⣿⣿⣿⣤⣤⣀⣀⣀⣀⠁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠚⠀

⠀⣶⡄⠙⠻⠷⢆⣼⣿⣿⣿⣿⡿⢃⣀⣤⣴⣾⣿⣿⠿⠟⠛⠛⠻⢿⣿⣿⠖⠿⠿⠋⠁⠀⠒⠀⢀⡴⣾⣿⣿⠏⠟⠋⢸⣿⣿⠛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

⠀⠸⢿⣦⣀⡀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⣾⣿⡶⠒⠒⠛⣩⣤⣿⣿⢏⡀⠀⡠⢊⢻⣿⡈⠿⣿⣿⣿⣿⡿⢛⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀

⠀⠀⠀⠙⠻⣿⣿⣈⣉⡛⠟⠛⠁⠀⠀⣀⣤⣾⣿⡋⠀⠀⠀⢀⣿⣿⣿⣿⢃⣀⠙⡋⢁⣀⣀⣠⣿⣿⣿⣿⣿⣦⣼⠃⠀⠀⠻⣷⡀⠹⢿⠛⠋⢀⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢻⡆⠀

⣷⣦⣄⡀⠀⠈⡽⣿⣿⣿⣿⠛⠓⠛⠛⠛⠋⠀⢻⣷⠀⢀⠴⠋⢩⣈⣿⣿⠀⠀⠻⠃⠀⢀⠀⠀⣼⣿⣿⣰⠿⣿⣿⣶⣤⣤⣶⣶⣷⣤⣄⣀⠀⠛⢋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣺⣿⡄

⣀⡟⠻⣿⢿⢶⣄⡹⠿⠿⢆⣀⣀⣀⣀⣀⣱⣤⣾⡏⢠⠏⠀⠀⢸⣿⣿⣿⡉⠉⠻⢧⠈⠙⠛⢻⣿⣿⠿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢠⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠻⣿⣧⡀⠀⠀⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡏⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⣹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⣛⣹⣼⣷⣿⣶⣿⣿⣾⣿⣇⡙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⢂⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿

⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠛⠁⠀⠀⠀⠘⣿⣴⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⣿⣿

⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⠃⠀⠀⠀⠀⠀⢀⡿⠋⠙⣿⣦⣀⠀⠀⢀⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⠿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣼⠃⠘⠀⡈⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀

⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⣀⣤⣿⣿⣦⣠⣴⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣬⢹⡋⠀⠀⠉⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿

⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣶⠟⠉⢻⣿⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⢠⢠⣿⣿⣏⠀⠀⢸⣿⣶⣤⣤⣴⣿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠾⠟⠛⠛⠋⠀⠀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣆⠀⠀⠀⠀⡇⠈⢻⣿⣿⣿⣷⣿⣿⣿⣟⣿⠏⠉⠀⠀⠀⠀⠀⠀⠚⠉⡻⣿⡟⠉⠛⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⡜⠀⠀⠀⠈⢿⡄⠀⡉⠛⠛⠻⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣽⣿⣄⢀⣠⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣋⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠁⠀⠀⠀⠀⠘⣿⣷⣿⣷⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⣛⠻⣿⡟⣿⢦⡟⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⣛⣁⣴⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡈⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⢛⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠁⠀⠀⠀⠀⣾⣿⣿⢶⣶⣤⣄⡀⠀⣀⣀⣀⣀⡀⠈⠉⠒⠛⠛⠁⢸⣿⡿⣷⣶⣤⣄⣀⣀⣠⣤⣶⣾⣿⣿⣿⢿⣶

⣤⣀⡀⠀⠀⠀⠀⠀⢰⣬⣙⣲⣶⣾⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣞⡅⠀⠀⠀⣾⣿⣿⣿⡄⠙⢿⣿⣿⣿⠟⠉⣁⣈⣉⣉⠁⠀⠀⠀⠀⠊⠙⠃⠈⣛⣿⣿⠿⠛⢛⣻⣿⣭⣿⣷⣶⠉⢉

⠉⠙⠷⣅⡀⠀⠀⠀⢀⡉⠙⠛⠛⢻⠋⠉⠉⠻⣶⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣰⣿⡋⠛⠡⢀⣀⠀⢿⣿⣿⣿⣿⡄⢈⣿⣿⣿⣤⣄⣀⣀⣀⣈⠁⣠⣤⣤⣤⣠⣴⣶⠿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⡟⠀⠟

⠀⠀⣶⡌⠛⠿⣶⣄⣴⣿⣿⣿⣿⡿⢆⣀⣤⣤⣾⣿⣿⠿⠿⠟⠛⠻⣿⣿⣿⠶⠿⠿⠋⠁⠀⠒⠀⢀⣴⣼⣿⣿⠏⠟⠃⢸⣿⣟⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀

⠀⠀⠹⣷⣄⣀⠀⣹⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⢋⣿⣷⠀⠀⠀⠀⢠⣶⣿⣿⡖⠒⣾⣷⡔⠶⠖⠚⣩⣤⣿⣿⢋⠀⠀⡠⢊⢻⣿⡘⢿⣿⣿⣿⣿⡿⢋⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠇⢹⣿⣿⣿⣿⣿⣿⠿⣇⠀

⣄⠀⠀⠈⠛⠿⣿⣧⣉⣉⠻⠿⠛⠉⠀⠀⢀⣤⣾⣿⠃⠀⠀⠀⢰⣿⣿⣿⣿⣃⣀⠻⠟⣁⣀⣀⣠⣿⣿⣿⣿⣿⣦⣼⠁⠀⠀⠻⣷⡀⠻⢿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢹⡆

⠻⣷⣤⣀⠀⠀⠉⣿⣿⣿⣿⣿⠷⠒⠛⠛⠛⠋⠈⢿⡇⠀⢀⡴⠋⣩⣉⣿⣿⠀⠉⠿⠃⠁⠀⠀⠀⣸⣿⡟⣸⢿⣿⣿⣶⣠⣤⣶⣾⣷⣤⣄⣀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡤⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿

⣀⣎⠻⣿⠿⣶⠆⡰⠻⠿⠟⢁⣀⠀⠀⢀⣀⣰⣤⣾⡇⢠⠏⠀⠀⣿⣿⣿⣿⠉⠙⠻⢧⠈⠙⠛⢻⣿⣿⠿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠟⠻⣿⣷⡀⠀⠀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡟⣿⣿⠀⣿⡗⣻⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⢛⣙⣼⣧⣿⣶⣿⣿⣾⣿⣧⣙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣾⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾

⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣿⡿⠋⠀⠀⠀⠀⢿⣷⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⡟⠀⠀⠀⠀⠀⠀⣸⠛⠙⢻⣶⣄⡀⠀⠀⣀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿

⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢰⡟⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠀

⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣠⣼⣿⣧⣄⣠⣦⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡭⣟⠁⠀⠈⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿

⠀⠀⠀⠀⠀⠀⠚⢧⣄⣠⣤⡾⠟⠹⣿⡆⠀⠀⠀⢘⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⡿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⡀⠀⠀⠀⠀⠀⡄⣽⣿⣿⠁⠀⠀⣿⣷⣤⣤⣤⣾⡏⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⡷⠿⠻⠛⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣷⡀⠀⠀⠀⢸⠁⠙⣿⣿⣿⣿⣶⣿⣿⣿⢻⡿⠉⠁⠀⠀⠀⠀⠀⠰⠛⠛⣿⣿⠋⠙⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⣠⠃⠀⠀⠀⢻⣦⠀⢈⠙⠛⠿⠿⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣣⣬⣿⣦⡀⣀⡜⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣹⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⡟⠀⠀⠀⠀⠀⢻⣿⣾⣿⣶⣶⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⢛⣻⣿⣿⢻⡷⣼⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣟⣋⣠⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠇⠀⠀⠀⠀⢰⣿⣿⣷⣶⣦⣤⣀⠀⢀⣀⣀⣀⣀⠀⠉⠑⠚⠛⠋⠁⣿⣿⢿⣶⣦⣤⣀⢀⣀⣤⣴⣶⣿⣿⣿⡿⣷

⣮⣄⡀⠀⠀⠀⠀⠀⠀⣦⣉⡒⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣋⠀⠀⠀⢰⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⠋⢉⣀⣉⣉⡉⠂⠀⠀⠀⠐⠉⠛⠀⢉⣻⣿⡿⠟⠛⣛⣻⣭⣽⣿⣷⡎⠉

⠈⠙⠳⢦⣁⠀⠀⠀⠀⡈⠙⠛⠛⠿⡿⠋⠉⠑⢶⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣾⡿⠙⠋⠄⣀⡀⠸⣿⣿⣿⣿⣧⠀⣸⣿⣿⣇⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣄⣤⣴⣾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⠰

⠀⠀⢰⣄⠙⠻⣶⣦⣠⣿⣿⣿⣿⣿⠷⠀⣀⣤⣤⣿⣿⣿⠿⠿⠟⠛⢿⣿⣿⡷⠾⠿⠟⠉⠀⠐⠂⠀⢠⣤⣿⣿⡿⠹⠛⠀⣿⣿⡟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⢀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀

⡄⠀⠈⢿⣦⣀⠀⢀⣿⣿⣿⣿⣿⣿⣾⣿⠿⠟⠛⢻⣿⡆⠀⠀⠀⠀⣴⣾⣿⣷⠐⢰⣿⣦⡶⠶⠖⢋⣥⣼⣿⡟⡁⠀⢀⠔⡙⣿⣇⠻⣿⣿⣿⣿⣿⠟⣃⠁⠀⠀⠀⠀⠀⢁⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡄

⣧⡀⠀⠀⠙⠿⣿⣿⡍⠉⠛⠿⠿⠛⠁⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⣺⣿⣿⣿⣟⡀⠈⠿⠋⢀⣀⣀⣼⣿⣿⣿⣿⣯⣤⡏⠀⠀⠘⢿⣆⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⣮⣿

⠻⢿⣦⣀⠀⠀⠈⢹⣿⣿⣿⣷⡶⠶⠖⠚⠛⠛⠋⠹⣿⡀⠀⣠⠞⠛⣍⣹⣿⡇⠈⠹⠿⠈⠀⠈⠁⢀⣿⣿⢇⣿⣿⣿⣷⣄⣠⣤⣶⣿⣦⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⢀⣈⣽⣿⣿⣿⣿⡇⠀⠀⢸⣿

⣀⣎⠻⣿⢿⣷⣦⢸⠻⠿⠿⠋⠀⠀⠀⠀⠀⢀⣦⣴⣿⠁⡸⠁⠀⢀⣿⣿⣿⡏⠀⢒⠿⡄⠉⠛⠛⣿⣿⡿⢿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣿⣏⠀⠀⠀⠀⠀⠈⣀⣠⣴⣾⣿⣿⡿⠟⢿⣿⣇⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⣟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣏⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⢙⣸⣧⣿⣶⣿⣿⣾⣿⣧⣝⡋⠘⠛⠛⠃⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣦⡖⣶⠀⣶⠂⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡾⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣾⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶

⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⡿⠋⠁⠀⠀⠀⢹⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿

⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣼⣿⠁⠀⠀⠀⠀⠀⢠⡟⠋⠻⣷⣤⣀⠀⠀⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿

⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⢀⣾⠁⠐⢀⠸⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠁

⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣀⣶⣿⣿⣄⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣼⣿⡛⠀⠈⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠘⠿⣄⣀⣠⣴⡿⠉⣿⣷⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣿⣿⣿⡿⣿⣿⣿⣿⢿⠿⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣀⠀⠀⠀⠀⠀⣀⣸⣿⣿⡏⠀⠀⢸⣿⣦⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢷⠾⠟⠟⠛⠃⠁⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⣿⡆⠀⠀⠀⢀⡇⠈⢻⣿⣿⣿⣷⣿⣿⣿⡟⣿⠏⠉⠀⠀⠀⠀⠀⠀⠞⠛⢻⣿⡟⠙⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⢀⡜⠀⠀⠀⠘⣷⡄⠀⠉⠛⠿⠿⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣤⣽⣷⣄⢀⣨⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣛⣯⣿⣿⣿⣿⣿⣿⠿⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⠃⠀⠀⠀⠀⠸⣿⣶⣿⣷⣶⣶⣶⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠜⠑⠛⣻⣿⣿⡟⣿⢼⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⢿⣿⣿⣛⣁⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡜⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⢟⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⣶⣦⣀⣄⠀⠀⢀⣀⣀⣀⠀⠈⠙⠒⠛⠛⠉⣸⣿⠿⣷⣶⣤⣄⣀⣀⣠⣤⣶⣾⣿⣿⡿⢿

⣶⣅⣀⠀⠀⠀⠀⠀⠀⢰⣌⠛⢿⣷⣶⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣞⡄⠀⠀⠀⣾⣿⣿⣿⡀⠙⢿⣿⣿⣿⠟⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠊⠛⠀⠉⣻⣿⣿⠿⠛⢛⣛⣯⣽⣿⣷⣶⠉

⠈⠉⠛⢶⣄⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠟⠉⠙⠲⣶⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣰⣿⠉⢛⠡⢀⡀⠀⢿⣿⣿⣿⣟⡄⢈⣿⣿⣯⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣤⣠⣴⣶⠿⠟⣋⣥⢰⣾⣿⣿⣿⣿⣿⣿⡟⠀

⠀⠀⠀⣦⡉⠻⣶⣦⣄⣼⣿⣿⣿⣶⡿⠆⢀⣠⣤⣽⣿⣶⣿⡿⠿⠟⠿⣿⣿⣷⠶⢿⠿⠋⠁⠀⠒⠀⠀⣤⣼⣿⣿⠟⠟⠃⢸⣿⣟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀

⣤⠀⠀⢻⣷⣄⠀⠁⣻⣿⣿⣿⣿⣿⣷⣿⡿⠿⠛⢛⣿⣷⠀⠀⠀⠀⢠⣶⣿⣿⡄⠲⣾⣷⡴⠶⠶⠚⣩⣤⣿⣿⢋⠀⠀⡠⢊⢿⣷⡘⢿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⠈⣀⣤⣾⣿⠇⢹⣿⣿⣿⣿⣿⣿⢿⣧

⣾⣄⠀⠀⠈⠻⢿⣷⣟⠙⠛⠿⠿⠟⠋⠁⠀⢀⣠⣾⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣁⠀⠻⠟⡁⣀⣀⣰⣿⣿⣿⣿⣿⣇⣼⠁⠀⠀⠻⣷⠀⠻⢿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢿

⠙⢿⣦⣄⡀⠀⠀⠙⣿⣿⣿⣿⣶⠶⠶⠖⠛⠛⠛⠙⢿⡇⠀⢀⡴⠟⣫⣟⣿⣿⠈⠉⠿⠇⠁⠈⠉⠀⣼⣿⡟⣸⢿⣿⣿⣴⣀⣤⣴⣾⣷⣤⣄⣀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣈⣩⣿⣿⣿⣿⣿⠀⠀⠀⣿

⣀⣆⡻⣿⠿⣷⣦⠰⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⢢⣤⣾⡇⢠⠏⠀⠀⣿⣿⣿⣿⠀⠐⡾⢧⠈⠛⠛⢻⣿⣿⠿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⠀⠀⠀⠀⠀⠀⢁⣀⣤⣶⣿⣿⣿⠟⠻⣿⣷⡀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⢙⣘⣧⣿⣶⣿⣿⣾⣿⣧⣽⣋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⢐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴

⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⣿⠟⠁⠀⠀⠀⠈⣿⣵⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡏⠀⠀⠀⠀⠀⠀⣿⠓⠛⢿⣦⣄⠀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠀⠀⠀⠀⠀⣰⡇⠈⠀⡈⢿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⣠⣾⣿⣧⣀⣴⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡

⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣠⣟⡛⠁⠀⠉⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠻⢆⣀⣀⣠⣾⠛⢸⣿⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⡿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠈⣿⣧⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⡶⠿⠻⠛⠛⠈⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⠀⠀⠀⠀⢸⠀⠛⣿⣿⣷⣷⣾⣿⣿⣿⢿⡿⠋⠁⠀⠀⠀⠀⠀⠰⠛⠛⣿⣿⠋⠛⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢦⡀⣨⠃⠀⠀⠀⢿⣆⠀⠉⠙⠻⠿⠿⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⣨⣿⣆⠀⣀⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢉⣻⣿⣿⣿⣿⣿⣿⡿⠟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⡟⠀⠀⠀⠀⠀⣿⣷⣾⣿⣴⣶⣶⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠚⢛⣻⣿⣿⢻⣧⣿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⣿⣿⣟⣋⣠⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⠃⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠇⠀⠀⠀⠀⢸⣿⣿⣷⣶⣄⣄⡀⠀⢀⣀⣀⣀⡀⠀⠉⠓⠚⠛⠋⢀⣿⡿⢿⣶⣦⣤⡀⣀⣠⣤⣴⣾⣿⣿⣿⡿

⣶⣮⣀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠻⣭⣶⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡶⣣⠀⠀⠀⢰⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠘⠙⠃⠀⢙⣿⣿⡿⠟⠛⣛⣯⣭⣿⣿⣶⡆

⠀⠉⠛⠷⣵⡁⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠋⠉⠓⢶⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣾⡏⠝⡋⠄⣀⠀⢸⣿⣿⣿⣿⣃⠀⣹⣿⣿⣅⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣄⣤⣶⡾⠟⢛⣡⡄⣾⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⢠⣌⠙⢷⣶⣤⢀⣿⣷⣾⣶⣾⠧⠀⣀⣀⣤⣿⣷⣶⡿⠿⠿⠿⣿⣿⣾⡶⢾⡿⠟⠉⠀⠐⠂⠀⢠⣤⣿⣿⡿⠽⠛⠀⣿⣟⡛⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⢀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆

⢀⡄⠀⠘⣿⣦⡀⠈⢀⣿⣿⣿⣿⣿⣷⣾⣿⠿⠿⠛⣻⣿⡆⠀⠀⠀⠀⣴⣿⣿⣧⠒⢶⣷⣦⠶⠶⠖⢊⣥⣼⣿⣟⡁⠀⢀⠔⡻⣿⡆⠻⣿⣿⣿⣿⣿⠟⡁⠁⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠀⣿⣿⣿⣿⣿⣿⡿⢻

⣺⣧⠀⠀⠀⠙⠿⣿⣾⡉⠛⠻⠿⠿⠛⠉⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣟⡀⠘⠿⠋⠀⡀⣀⣾⣿⣿⣿⣿⣯⣠⡏⠀⠀⠸⣿⡆⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⠏

⠘⠻⣷⣄⣀⠀⠀⠈⢻⣿⣿⣿⣶⡶⠶⠶⠶⠛⠛⠋⠹⣷⠀⠀⣠⠶⢛⣅⣻⣿⡇⠉⠸⠿⠈⠀⠉⠁⢀⣿⣿⢃⡿⣿⣿⣧⣆⣠⣤⣶⣷⣤⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⢀⣈⣽⣿⣿⣿⣿⡇⠀⠀⢸

⣀⣆⡺⣿⠿⢿⣶⡴⠾⠿⠿⠿⠋⠀⠀⠀⠀⠀⠐⣤⣴⣿⠀⡼⠁⠀⢸⣿⣿⣿⡇⠀⢒⡿⡄⠙⠛⠛⣿⣿⡿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣇⠀⠀⠀⠀⠀⠈⣀⣠⣴⣾⣿⣿⡿⠛⢿⣿⣆⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⣿⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠋⠛⠋⠀⠙⠛⠙⢘⣃⣿⣤⣽⣿⣾⣿⣧⣽⣏⡘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠟⠁⠀⠀⠀⠘⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⡇⠀⠀⠀⠀⠀⠀⡿⠃⠙⢿⣦⣀⠀⠀⢀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⣼⠇⠈⠀⡈⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⣀⣠⣿⣿⣄⣀⣴⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣸⢟⡟⠁⠉⠙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢿⢆⣀⣀⣠⣾⠟⢺⣿⠀⠀⠀⠀⢹⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⡀⠀⠀⠀⠀⠀⢀⢈⣽⣿⣿⠁⠀⠸⣿⣦⣄⣀⣠⣾⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡽⡶⠿⠿⠛⠛⠈⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣧⠀⠀⠀⠀⣸⠈⠻⣿⣿⣶⣶⣴⣿⣿⡿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠴⠛⠻⣿⡿⠛⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⣀⣠⣤⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⢅⠀⢉⠂⠀⠀⠀⢯⡆⠀⠙⠻⠿⠿⡿⣿⣿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣹⣿⣄⠀⢀⡏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢏⣿⣿⣿⣿⣿⣿⣿⡿⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠶⠾⣿⡟⠀⠀⠀⠀⠈⣿⣶⣮⣶⣴⣶⣶⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠙⢻⣿⣿⡿⢻⣧⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣟⣉⣠⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠀⢨⠃⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⢋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣾⠇⠀⠀⠀⠀⢰⣿⣿⢶⣶⣄⣄⡀⠀⠀⣀⣀⣀⡀⠀⠉⠑⠛⠛⠋⢀⣿⡿⢿⣶⣦⣤⡀⣀⣠⣤⣶⣾⣿⣿⣿

⣶⣦⣎⡀⠀⠀⠀⠀⠀⠀⠐⣀⡚⠭⣭⣵⣾⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⢃⠀⠀⠀⣰⣿⣿⣿⣇⠉⢿⣿⣿⣿⡟⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠘⠙⠃⠈⢙⣿⣿⡿⠟⠛⣛⣿⣿⣿⣿⣶

⠈⠉⠙⠻⢧⣔⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠓⠓⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡏⠽⣋⠄⣀⠀⢸⣿⣿⣿⣿⣁⠀⣹⣿⣿⣄⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣀⣤⣶⡿⠟⢋⣡⠄⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⡍⠻⢶⣤⣄⢀⣷⣶⣶⣶⣶⡧⠀⢀⣀⣬⣿⣷⣶⣶⠿⠿⠿⣿⣿⣶⡶⣾⣿⠟⠉⠀⠤⠂⠀⢠⣤⣿⣿⡟⡿⠛⠠⣿⣿⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⢀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠘⣿⣄⠀⠁⢑⣿⣿⣿⣿⣿⣷⣶⣿⡿⠿⠟⣻⣿⡅⠀⠀⠀⠀⣼⣿⣿⣧⠀⣴⣷⣦⠴⠴⠖⢚⣁⣼⣿⡏⠁⠀⢀⠔⡻⣿⡄⢿⣿⣿⣿⣿⣿⠟⡁⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠀⣿⣿⣿⣿⣿⣿⡿

⠀⢜⣧⠀⠀⠈⠻⢿⣶⣾⡟⠛⠻⣿⠿⠟⠉⠀⠀⢀⣠⣿⡿⠁⠀⠀⠀⣶⣿⣿⣿⣏⠀⠸⠿⠋⠀⠀⣀⣿⣿⣿⣿⣿⣾⣠⡏⠀⠀⠸⣿⡄⠘⢿⡟⠛⠁⣼⣿⣿⣿⡿⡿⠿⠿⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀

⠀⠘⠾⣷⣄⡀⠀⠀⠈⢻⣿⣿⣷⣶⡶⠶⠶⠶⠞⠿⠋⢻⣷⠀⠀⣠⠶⢛⡩⢿⣿⡏⠉⠻⠿⠈⠉⠉⠉⢠⣿⣿⢃⣿⣿⣿⣧⣄⣠⣤⣶⣿⣤⣤⣀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠁⢀⣨⣽⣿⣿⣿⣿⡇⠀⠀

⣀⠆⠲⣾⠿⢿⣷⣶⡶⠾⠿⢻⡿⠏⠁⠀⠀⠀⠀⠀⣄⣰⣿⠀⡰⠁⠀⢸⣿⣿⣿⡇⠂⢲⡿⡀⠙⠛⠿⣿⣿⡿⢿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⠛⢿⣿⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢾⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⣃⣻⣤⣽⣿⣾⣿⣷⣽⣯⣘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡿⣿⡿⠋⠀⠀⠀⠀⢿⣷⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰

⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⢸⠟⠙⢻⣷⣄⡀⠀⠀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢠⡿⠀⠃⢀⢹⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣀⣼⣿⣷⣄⣠⣦⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣹⡿⠟⠈⠉⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⢀⣀⣴⡾⠃⣿⡇⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣇⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡏⠀⠀⢿⣿⣄⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢯⢷⠾⠿⠟⠛⠃⠁⢀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⡄⠀⠀⠀⠀⡇⠙⢿⣿⣷⣶⣤⣾⣿⣿⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠞⠛⢿⣿⠟⠛⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢀⣀⣤⣴⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠩⡀⠈⡱⠀⠀⠀⠸⣥⠀⠈⠛⠿⠿⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣈⣿⣧⡀⠀⣸⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡹⣙⣿⣿⣿⣿⣿⣿⣿⠿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⡶⣿⣿⠇⠀⠀⠀⠀⢹⣶⣤⣴⣦⣤⣦⣴⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⣿⣿⣿⠟⣿⣼⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣿⣋⣁⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠀⠹⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⠟⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣷⡿⠀⠀⠀⠀⠀⣾⣿⢷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⠀⠈⠉⠚⠛⠛⠉⣸⣿⠿⣷⣶⣤⣄⣀⣀⣤⣴⣶⣿⣿⣿

⣶⣤⣤⡃⠀⠀⠀⠀⠀⠀⠀⢀⡘⠫⢭⣭⣶⣾⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⣧⠞⡀⠀⠀⠀⣾⣿⣿⣿⡈⠙⣿⣿⣿⣿⠟⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠋⠛⠀⠈⣻⣿⣿⠿⠛⢛⣻⣭⣿⣿⣷

⠉⠉⠉⠛⠿⣦⡔⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⠟⠒⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠭⢟⡡⢀⡀⠀⣿⣿⣿⣿⣏⡀⢈⣿⣿⣯⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣤⣠⣴⣾⠿⠛⣉⣤⢰⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣌⠙⢷⣦⣤⡀⣰⣶⣶⣶⣶⣾⡄⠀⣀⣀⣽⣿⣶⣶⡶⠿⠿⢿⣿⣶⣶⢴⣿⡿⠛⠁⠠⠔⠀⠀⣠⣼⣿⣿⣿⠿⠃⢸⣿⣟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⢻⣧⡀⠈⠉⢻⣿⣿⣿⣿⣿⣷⣾⣿⡿⠿⠛⣿⣿⠀⠀⠀⠀⢠⣯⣿⣿⡄⢠⣶⣶⡤⠤⠴⠒⣋⣡⣿⣿⢋⠀⠀⡠⢚⢿⣷⠘⢿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿

⠀⠀⣾⡄⠀⠀⠙⠿⣷⣶⣿⠛⠛⢿⣿⠿⠛⠉⠀⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⡃⠀⠻⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣇⣼⠁⠀⠀⢿⣷⠀⠻⣿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃

⠀⠀⠙⢿⣦⡀⠀⠀⠀⠛⣿⣿⣷⣶⣶⣶⡶⠶⠶⠾⠟⠙⢿⣆⠀⠀⣤⠞⢻⢽⣿⣿⠉⠙⣾⠇⠉⠉⠉⠁⣸⣿⡿⣸⣿⣿⣿⣤⣀⣤⣴⣾⣧⣤⣄⣀⠐⠛⠋⠉⠁⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿⠀⠀

⣷⠆⠲⣶⠿⢿⣿⣶⣶⠶⠟⠻⣿⡿⠋⠀⠀⠀⠀⠀⠠⣀⣼⡟⢀⡞⠀⠀⣿⣿⣿⣿⠒⠒⢶⢇⠀⠛⠿⢿⣿⣿⠿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠻⣿⣿⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣿⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⢃⣛⣤⣽⣿⣾⣿⣷⣿⣯⣜⡛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⣖⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣴⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⣿⠃⠀⠀⠀⠀⠀⠀⡟⠋⠛⣷⣦⣀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡆⠀⠀⠀⠀⠀⣾⠃⠐⠀⡘⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣢⣿⣿⣄⣀⣴⣤⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣸⣻⠿⠉⠉⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢀⣠⣶⠟⢾⣷⠀⠀⠀⠀⢻⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡿⠁⠀⢸⣿⣆⣀⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢽⡶⠿⠿⠛⠋⠈⠀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣆⠀⠀⠀⠀⣸⠘⢿⣿⣿⣶⣦⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠴⠛⠻⣿⡿⠛⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⣍⠈⢙⠄⠀⠀⠀⣿⡆⠀⠛⠻⢿⣿⣿⣿⣿⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣹⣷⡄⠀⢀⠏⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⢏⣿⣿⣿⣿⣿⣿⣿⡿⢛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣶⣾⣷⡿⠀⠀⠀⠀⠈⣷⣦⣦⣶⣤⣤⣤⣴⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠙⢿⣿⣿⡟⣿⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣟⣁⣤⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣾⠃⠀⠀⠀⠀⢰⣿⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⡀⠀⠉⠓⠛⠛⠋⢁⣿⡿⢿⣶⣦⣤⡀⣀⣠⣤⣶⣾⣿⣿

⣶⣤⣤⣜⠀⠀⠀⠀⠀⠀⠀⠀⣐⠻⢭⣭⣥⣶⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⢃⠀⠀⠀⣰⣿⣿⣿⣇⠙⢿⣿⣿⣾⡟⠋⢉⣉⣉⣉⠙⠀⠀⠀⠀⠘⠙⠃⠀⣙⣿⣿⡿⠟⠛⣻⣯⣽⣿⣿

⠉⠉⠉⠛⠻⢷⣴⠂⠀⠀⠀⠀⠙⠻⠾⢿⣿⣿⠒⠒⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡏⠽⣋⠄⠀⠀⢹⣿⣿⣿⣿⣃⠀⣻⣿⣿⣁⣀⣀⣀⣀⣀⠉⢀⣤⣤⣤⣀⣤⣶⡿⠟⢋⣡⠄⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡙⠳⣶⣤⣄⢀⣶⣶⣶⣶⣶⡇⠀⢀⣀⣨⣿⣷⣶⣶⡶⠿⠿⣿⣷⣶⡦⣾⣿⠟⠋⠀⠤⠀⠉⢠⣬⣿⣿⡿⡿⠟⠠⣿⣿⠟⣩⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠿⠋⠁⢀⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠸⣿⣄⠀⠉⠉⣿⣿⣿⣿⣿⣷⣶⣾⣿⠿⠿⢻⣿⡅⠀⠀⠀⠀⣼⣽⣿⡥⠄⣴⣶⣄⠤⠤⠖⢚⣁⣼⣿⡏⠁⠀⢀⠔⡻⣿⡄⢿⣿⣿⣿⣿⣿⠟⡁⠁⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⠀⣿⣿⣿⣿⣿⣿

⠀⠀⢸⣇⠀⠀⠉⠻⣿⣶⣾⡟⠻⢿⣿⡿⠿⠋⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⡇⠀⠸⠿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣠⡏⠀⠀⠺⣿⡄⠘⢿⡟⠛⠁⣼⣿⣿⣿⡿⡿⠿⠿⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟

⠀⠀⠘⢿⣷⣀⠀⠀⠀⠙⢻⣷⣶⣶⣦⣴⣦⡴⠶⠶⠿⠛⢻⣷⠀⠀⢠⡴⢛⡣⣿⣿⡏⠙⢳⡷⠈⠉⠉⠉⢡⣿⣿⢃⣿⣿⣿⣧⣆⣠⣤⣶⣷⣤⣄⣀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠜⠃⢀⣀⣼⣿⣿⣿⣿⡇⠀

⢰⡇⠲⣶⠿⢿⢿⣶⣶⡶⠾⠛⢿⣿⠟⠁⠀⠀⠀⠀⠀⣄⣸⣿⠀⣰⠃⠀⢸⣿⣿⣿⡗⠂⢲⣶⡀⠚⠿⠿⣿⣿⡿⢿⣅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⠛⢿⣿⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⡟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⣛⣠⣽⣿⣾⣿⣷⣿⣯⣼⣛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣽⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠀⠀⠀⠈⢿⣧⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡏⠀⠀⠀⠀⠀⠀⣸⠛⠙⢻⣶⣄⡀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢰⡟⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⣐⣾⣿⣧⣀⣠⣦⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡻⠿⠏⠉⠙⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⣤⡾⠣⣿⡆⠀⠀⠀⠘⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⠏⠀⠀⣿⣧⣀⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠯⣷⠾⠻⠟⠛⠁⠁⢀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡇⠻⣿⣿⣷⣴⣤⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠞⠛⢿⣿⠟⠛⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⢀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⢉⢩⡉⠉⠣⠀⠀⠀⢸⣥⠀⠘⠛⠿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣿⣦⠀⠀⡸⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣹⣿⣿⣿⣿⣿⣿⣿⠟⣃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣷⣦⣿⣶⠇⠀⠀⠀⠀⢻⣦⣤⣰⣦⣤⣤⣤⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠿⢿⣿⣿⢻⣷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢿⣿⣿⣋⣡⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⣷⡿⠀⠀⠀⠀⠠⣾⣿⣷⣶⣤⣀⣀⠀⠀⢀⣀⣀⣀⠀⠈⠉⠚⠛⠛⠉⣸⣿⠿⣷⣶⣤⣄⢀⣀⣤⣴⣾⣿⣿

⣤⣤⣤⣤⡂⠀⠀⠀⠀⠀⠀⠀⢄⡈⠻⣟⣭⣵⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠾⡀⠀⠀⢀⣾⣿⣿⣿⡈⠻⣿⣿⣷⣿⠛⠉⣁⣉⣉⡉⠃⠀⠀⠀⠀⠋⠛⠀⢁⣻⣿⣿⠟⠛⢛⣿⣽⣿⣿

⠉⠉⠉⠛⠻⢿⣆⡄⠀⠀⠀⠀⠘⠛⠶⢾⣿⣿⡷⠒⠲⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠩⠟⡁⠀⠀⠀⣿⣿⣿⣿⣟⡀⢘⣿⣿⣯⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣄⣠⣴⣾⠿⠛⣉⣤⢰⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣈⠻⢶⣤⣄⡀⢰⣶⣶⣶⣤⣶⡀⠀⢀⣀⣻⣷⣴⣶⣶⡾⠿⢿⣷⣶⣶⢤⣿⡿⠛⠁⠠⠄⠈⠉⣠⣽⣿⣿⢿⠿⠃⢸⣿⡻⢋⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠟⠉⠀⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⢿⣧⡀⠈⠛⢻⣿⣿⣿⣿⣿⣧⣶⣾⣿⠿⠿⣿⣭⠁⠀⠀⠀⢠⣭⣽⣿⡤⢤⣶⣦⡠⠤⠴⠖⣋⣡⣿⣿⠉⠀⠀⡠⢚⢿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠇⢸⣿⣿⣿⣿⣿

⠀⠀⠀⣾⡀⠀⠈⠙⢿⣶⣦⣾⠻⠿⣿⣿⡿⠟⠉⠁⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⠿⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣅⣼⠁⠀⠀⢿⣧⠀⠻⣿⠛⠋⢠⣾⣿⣿⣿⢿⠿⠿⠟⠋⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿

⠀⠀⠀⠫⣿⣄⡀⠀⠀⠈⠛⣻⣶⣶⣶⣤⣤⣤⡤⠶⠾⠟⠛⣿⡆⠀⠀⣠⠾⢛⢹⣿⣿⠉⠻⣶⠆⠉⠉⠉⠉⣼⣿⡟⣸⣿⣿⣿⣤⣀⣠⣴⣾⣧⣤⣄⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿⠀

⠐⢷⠲⣶⠛⢿⠿⣷⣶⣶⠶⠛⠻⣿⡿⠋⠀⠀⠀⠀⠀⢠⣀⣼⡏⢀⡞⠁⠀⣿⣷⣿⣿⠒⠒⣶⣆⠐⠻⠿⢷⣿⣿⠿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠻⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡯⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⢛⣀⣽⣯⣼⣿⣷⣿⣿⣼⣿⣛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠖⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠟⠉⠀⠀⠀⠈⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⡏⠀⠀⠀⠀⠀⠀⣿⠛⠙⢿⣶⣄⡀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⣰⡇⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣀⣀⣰⣾⣿⣧⣀⣰⣤⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⣿⠏⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⠀⢀⣤⡾⢳⣿⡄⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠏⠀⠀⣿⣧⣀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡿⣷⠿⠻⠟⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣾⣿⣿⣿⣦⡀⠀⠀⠀⢀⡇⠻⣿⣿⣦⣴⣤⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠾⠻⣿⣿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠋⠉⠉⢛⠉⠙⠣⠀⠀⠀⢸⣥⠀⠐⠿⡿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣿⣆⠀⠀⡹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣹⣿⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣴⣦⣬⣷⣶⠇⠀⠀⠀⠀⢻⣤⣤⣤⣄⣤⣤⣬⣵⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠿⢿⣿⣷⢻⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣠⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠘⠀⠉⠁⠈⡻⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢸⣷⡟⠀⠀⠀⠀⠠⣾⣿⣷⣶⣤⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠚⠛⠋⠁⣸⣿⠻⣷⣶⣤⣄⣀⣠⣤⣶⣾⣿

⣤⣤⣤⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⢄⠩⠟⣛⣫⣥⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠖⡀⠀⠀⢀⣾⣿⣿⣿⡈⠻⣿⣿⣷⣿⠛⠉⣉⣉⣉⡉⠃⠀⠀⠀⠀⠋⠛⠈⢁⣩⣿⡿⠟⠛⣛⣯⣽⣿

⡛⠋⠛⠛⠛⠿⢶⣄⠄⠀⠀⠀⠀⠘⠻⢶⣿⣿⣿⡿⠓⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠟⡡⠀⠀⠘⣿⣿⣿⣿⣏⡀⢘⣿⣿⣇⣀⣀⣀⣀⣀⣈⠀⣠⣤⣤⣄⣤⣴⣾⠿⠛⣉⡤⢰⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⣉⠳⣦⣤⣀⡀⢰⣶⣤⣤⣤⣶⡀⠀⠀⣀⣻⣷⣤⣶⣶⡶⠿⣿⣶⣶⣦⣴⣿⡿⠛⠀⠠⠄⠈⠉⣠⣽⣿⣿⢿⠿⠃⣾⣿⡿⢋⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠛⠉⢀⡠⠀⠀⣰⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⢀⠀⠀⢿⣇⠀⠙⠛⢳⣿⣿⣿⣿⣿⣥⣶⣾⣿⡿⠿⣿⣯⠉⠀⠀⠀⢨⣭⣿⣯⠤⢤⣶⣦⡠⠤⠴⠖⣋⣠⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠇⢸⣿⣿⣿⣿

⠀⠀⠀⠀⣾⡀⠀⠈⠛⢷⣶⣤⣾⠿⠿⣿⣿⡿⠟⠉⠁⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⠿⠟⠁⠀⠀⣸⣿⣿⣿⣿⣷⣅⣼⠁⠀⠐⢿⣧⠀⠻⣿⠛⠋⢠⣿⣿⣿⣿⠿⠿⠿⠟⠋⢛⢩⣤⣀⣸⣿⣿⣿⣿

⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠉⠻⢿⣶⣶⣦⣥⣤⣤⣤⡴⠶⠿⠛⣿⡆⠀⠀⣠⠾⢛⢿⣿⣿⠉⠛⣶⠆⠉⠉⠉⠉⣹⣿⡟⣸⣿⣿⣿⣴⣀⣠⣤⣾⣦⣤⣀⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿

⠐⠖⠾⣶⠋⢿⠿⢿⣶⣶⣦⠀⠛⠿⣿⣿⠛⠈⠀⠀⠀⠀⢄⣀⣼⡇⢀⡞⠁⠀⢾⣷⣿⣿⠒⠲⢶⣆⠐⠺⠾⢷⣿⣿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⠟⠻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⣿⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⢛⣀⣽⣯⣼⣿⣷⣿⣿⣾⣿⣛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠟⠉⠀⠀⠀⠈⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡏⠀⠀⠀⠀⠀⠀⣾⠛⠙⢿⣶⣄⡀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⣰⡏⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⢿⠏⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⠀⢀⣤⡾⢿⣿⡄⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠏⠀⠀⣿⣧⣀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡿⡶⠿⠻⠟⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⢀⡇⠿⣿⣿⣦⣴⣤⣿⣿⣿⢿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠾⠻⣿⣿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⢀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠋⠉⠙⢛⠉⠙⠣⠀⠀⠀⢸⣇⠀⠘⠿⡿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣿⣆⠀⠀⡙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣹⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣴⣦⣤⣷⣶⠇⠀⠀⠀⠀⢻⣤⣠⣤⣄⣤⣤⣬⣵⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠿⢿⣿⣷⢻⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣠⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠀⠉⠁⠈⡻⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢸⣷⡟⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠚⠛⠛⠁⣸⣿⠿⣷⣶⣤⣄⣀⣠⣤⣶⣾⣿

⣤⣤⣤⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⢄⠩⠟⣛⣫⣥⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠖⡀⠀⠀⢀⣾⣿⣿⣿⠈⠻⣿⣿⣷⣿⠛⠉⣉⣉⣉⡉⠃⠀⠀⠀⠀⠋⠛⠈⢉⣩⣿⡿⠟⠛⣛⣭⣽⣿

⡛⠛⠉⠛⠛⠿⢶⣄⠄⠀⠀⠀⠀⠘⠻⢶⣾⣿⣿⡿⠒⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⠟⡁⠀⠀⠘⣿⣿⣿⣿⣏⡀⢘⣿⣿⣇⣀⣀⣀⣀⣀⣈⠀⣠⣤⣤⣄⣤⣴⣾⠿⠛⣩⡤⢰⣿⣿⣿⣿⣿

⣿⠀⠀⠀⠀⠀⠀⣉⠳⣦⣤⣀⡀⢰⣶⣤⣤⣤⣶⡀⠀⠀⣀⣻⣷⣤⣶⣶⡾⠿⣿⣶⣶⣦⣼⣿⡿⠛⠀⠠⠄⠈⠉⣠⣽⣿⣿⢿⠿⠃⣾⣿⡿⢋⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠛⠉⢀⡠⠀⠀⣰⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⢀⠀⠀⢿⣇⠀⠙⠛⢳⣿⣿⣿⣿⣿⣧⣶⣾⣿⡿⠿⣿⣯⠉⠀⠀⠀⢨⣭⣿⣯⠤⢤⣶⣦⡤⠤⠤⠖⣋⣡⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠇⢸⣿⣿⣿⣿

⠀⠀⠀⠀⣼⡀⠀⠈⠛⢷⣶⣤⣾⠿⠿⣿⣿⡿⠟⠋⠁⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⢿⠟⠁⠀⠀⣸⣿⣿⣿⣿⣧⣆⣼⠁⠀⠐⢿⣧⠀⠻⣿⠛⠋⢠⣿⣿⣿⣿⠿⠿⠿⠟⠋⢛⢩⣤⣀⣸⣿⣿⣿⣿

⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠉⠻⢿⣶⣶⣦⣥⣤⣤⣤⠴⠶⠿⠛⣿⡆⠀⠀⣠⠾⢛⠿⣿⣿⠉⠓⣶⠆⠉⠉⠉⠉⣹⣿⡟⣸⣿⣿⣿⣴⣀⣠⣴⣾⣦⣤⣀⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿

⠐⠖⠾⣶⠉⢿⠿⢿⣶⣶⣦⠀⠛⠿⣿⣿⠛⠉⠀⠀⠀⠀⢄⣀⣼⡗⢀⡞⠁⠀⣼⣷⣿⣿⠐⠲⢶⣆⠐⠺⠾⢷⣿⣿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢸⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⠟⠻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡗⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠋⠛⠋⠀⠙⠛⠙⠘⠃⠛⢀⣹⣯⣼⣿⣷⣿⣿⣾⣿⣿⣃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⡇⠀⠀⠀⠀⠀⠀⡿⠉⠙⢿⣦⣄⡀⠀⢀⣤⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣼⡇⠈⠄⡈⢿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣰⣾⣿⣦⣀⣴⣤⣾⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠿⢿⠏⠛⠻⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⣠⡾⢿⣷⡀⠀⠀⠀⢹⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠟⠀⠀⣿⣇⡀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡽⡶⠿⠻⠛⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣶⣾⣿⣶⣦⠀⠀⠀⠀⠀⡇⢿⣿⣿⣦⣤⣠⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⠛⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⠛⠛⢛⠛⠛⠇⠀⠀⠀⢸⣁⠀⠹⠿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣙⣿⣆⠀⠀⡙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢩⣻⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣤⣦⣬⣷⣴⡇⠀⠀⠀⠀⢿⣤⣴⣤⣄⣤⣭⣩⣵⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠍⠿⢿⣿⣷⢿⣧⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣤⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠘⠁⠉⠉⠉⠻⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢸⣷⡏⠀⠀⠀⠀⠠⣾⣿⢷⣶⣤⣀⡀⠀⠀⢀⣀⣀⣀⠀⠈⠙⠚⠙⠋⠁⣸⣿⠻⣷⣶⣶⣤⣀⣤⣤⣶⣿

⢀⣠⣤⣄⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠽⢟⣛⣛⣥⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠖⡀⠀⠀⢠⣾⣿⣿⣿⠈⠻⣿⣿⣷⣿⠛⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠉⠛⠀⢉⣭⣿⡿⠟⠛⣻⣭⣽

⣟⡛⠛⠛⠛⠻⠷⣶⡀⡄⠀⠀⠀⠀⠘⠷⣶⣾⣿⣿⡿⠷⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠟⡡⠀⠀⠘⣿⣿⣿⣿⣏⡀⢘⣿⣿⣇⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣄⣤⣴⣾⠟⠋⣩⡤⣸⣿⣿⣿⣿

⣿⣿⡀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣀⠀⢰⣦⣤⣤⣤⣾⡀⠀⠀⢈⣻⣷⣤⣴⣶⣶⡾⣷⣶⣶⣦⣼⣿⡿⠛⠀⠠⠄⠈⠉⣠⣽⣿⣿⢻⠿⠇⣼⣿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⡠⠀⢀⣰⣿⣿⣿⣿⣿

⣿⠿⠁⠀⠀⠀⠀⠀⢿⣆⠈⠙⠛⢳⣿⣿⣿⣿⣿⣭⣴⣾⣿⡿⠿⣿⣯⠉⠀⠀⠀⢨⣭⣿⣯⠤⢤⣶⣤⡤⣤⠤⠖⣚⣡⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠇⢸⣿⣿⣿

⠀⠀⠀⠀⠀⣼⡀⠀⠈⠻⣷⣦⣤⣼⠿⠿⣿⣿⣿⠿⠋⠉⠀⢀⣼⣿⡏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⢿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣆⣼⠁⠀⠐⢿⣧⠀⠻⢿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠛⠋⢉⢩⣤⣄⣸⣿⣿⣿

⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠉⠻⢿⣶⣶⣬⣭⣤⣤⣤⡴⠶⠿⠻⣿⡆⠀⠀⣠⡾⢏⢻⣿⣿⠉⠰⣶⠆⠉⠉⠉⠉⣽⣿⡿⢹⣿⣿⣿⣤⣀⣠⣤⣾⣧⣤⣄⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡰⠛⠀⣄⣤⣿⣿⣿⣿

⠰⠖⠲⣾⠟⢶⠞⠻⢿⣶⣦⣀⠀⠛⠿⣿⣿⠟⠉⠀⠀⠀⠀⢀⣀⣸⡟⠀⡞⠁⠀⣻⣷⣿⣿⠒⠰⢶⣆⠐⠲⠶⢶⣿⣿⣿⣯⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢠⣿⡅⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠟⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⣙⣯⣼⣿⣷⣿⣿⣾⣿⣿⣇⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣾⡿⠀⠀⠀⠀⠀⠀⢸⠏⠉⠻⣷⣤⣀⠀⠀⣠⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢀⣿⠀⠁⢀⠹⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣀⣶⣿⣷⣄⣠⣦⣴⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠿⡿⠛⠛⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⢀⣤⠿⣴⣆⠀⠀⠀⠙⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣾⡿⠃⠀⢸⣿⡀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢿⠾⠟⠟⠛⠃⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⣰⠸⣿⣿⣧⣤⣄⣸⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⡴⠿⢿⣿⡿⠛⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠛⠛⠻⠛⠛⠻⡀⠀⠀⠀⣿⡀⠈⠿⢿⣿⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢻⣧⡀⠀⢈⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢏⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣴⣄⣹⣦⣾⠀⠀⠀⠀⠙⣧⣀⣄⣤⣈⣈⣉⣩⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻⢿⣿⣿⡾⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣛⣡⡴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠋⠉⠉⠉⠻⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⣿⣾⠃⠀⠀⠀⠀⢴⣿⣿⣶⣦⣄⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠓⠉⠙⠃⢀⣿⡟⠿⣶⣶⣦⣄⣠⣤⣶⣾

⠀⢀⣀⣀⣀⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣟⣛⣫⣵⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⢂⠀⠀⠀⣰⣿⣿⣿⡆⠙⢿⣿⣿⣾⡟⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠉⣉⣽⣿⠿⠛⣛⣭⣭

⣐⡛⠛⠛⠛⠻⠿⣶⣦⢀⡀⠀⠀⠀⠀⠳⢶⣶⣿⣿⣿⠯⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⢋⠀⠀⠀⢻⣿⣿⣿⣿⣅⠀⣻⣿⣿⣀⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣤⣤⣶⡿⠟⠋⣥⠄⣿⣿⣿⣿

⣿⣿⣧⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⣠⣤⣤⣬⣥⣇⠀⠀⠀⢙⣿⣦⣤⣴⣶⣶⣾⣶⣶⣴⣤⣾⣿⠟⠓⠀⠤⠀⠉⢁⣬⣿⣿⡿⡿⠿⠀⣿⣿⠟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠄⠀⢀⣾⣿⣿⣿⣿

⣿⣿⠟⠀⠀⠀⠀⠀⠸⣷⡀⠉⠹⠻⣾⣿⣿⣿⣿⣿⣭⣶⣾⣿⡿⢿⣿⡍⠉⠀⠀⠀⣹⣿⣿⡥⠤⣵⣶⣄⣤⣤⠴⢒⣋⣸⣿⡟⠁⠀⢀⠔⡻⣿⡄⠿⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⠀⠀⣀⣀⣠⣶⣿⡿⠁⣿⣿⣿

⠁⠀⠀⠀⠀⢀⣎⠀⠀⠙⢿⣶⣤⣤⡿⠿⢿⣿⣿⣿⠟⠉⠉⠀⢀⣾⣿⠃⠀⠀⠀⣴⣿⣿⣿⡿⠀⠸⣿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣯⣠⡏⠀⠀⠸⣿⡆⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠟⠛⠉⡉⢥⣤⣀⣿⣿⣿

⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠉⠙⠿⣧⣦⣤⣭⣡⣤⣀⣠⣤⣾⠟⢿⣧⠀⠀⢀⣤⠿⡟⢿⣿⡏⠓⢰⣶⠘⠉⠙⠉⢉⣿⣿⠇⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⡀⠘⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⠠⣠⣼⣿⣿⣿

⠀⠶⠶⣶⠿⢷⠄⠻⢿⣶⣶⣄⡀⠘⠻⢿⣿⡿⠋⠉⠉⠀⠀⠀⡀⢀⣿⠇⢠⠏⠀⠀⣿⣿⣿⡗⠀⠤⣶⡀⠒⠶⠶⣾⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⣸⣯⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⡿⠟⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡗⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⣙⣫⣼⣿⣷⣿⣿⣾⣿⣿⣇⡋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠖⣶⣶⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⠃⠀⠀⠀⠀⠀⢀⡟⠋⠙⣿⣦⣄⡀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⡄⠀⠀⠀⠀⠀⣼⠃⠈⠀⡈⣿⣿⣿⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣴⣾⣿⣦⣀⣴⣤⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠸⣿⣿⠛⠛⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⣠⡾⢻⣷⠀⠀⠀⠈⢻⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣿⠟⠀⠸⣿⣇⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⡼⡷⠿⠛⠛⠋⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⢠⠇⢿⣿⣿⣄⣤⣠⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⠟⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠚⠛⠛⠿⠛⠻⠆⠀⠀⠀⣼⣀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢙⣿⡄⠀⠀⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢝⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣤⣆⣘⣦⣤⡇⠀⠀⠀⠈⣿⣄⣠⣤⣀⣉⣉⣉⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠙⠿⣿⣿⣶⢿⣇⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⣿⣿⣟⣉⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⠉⠋⠉⠙⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢸⣷⡏⠀⠀⠀⠀⢠⣾⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠛⠛⠉⠀⣼⣿⠻⣶⣶⣶⣤⣀⣤⣴⣶

⠀⠀⣀⣀⣀⣂⣀⠇⠀⠀⠀⠀⠀⠀⠀⡉⠿⣿⣿⣛⣫⣴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣥⠖⡀⠀⠀⢠⣾⣿⣿⣧⠈⠻⣿⣿⣷⣿⠛⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠉⠛⠈⢁⣭⣿⡿⠟⢛⣫⣭

⣀⣻⠟⠛⠛⠛⠿⣶⣦⣄⡠⠀⠀⠀⠀⠸⢶⣤⣾⣿⣿⡯⠥⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠟⡠⠀⠀⠸⣿⣿⣿⣿⣇⡀⢹⣿⣿⣇⣀⣀⣀⣀⣀⣈⢀⣠⣤⣤⣤⣤⣶⡾⠟⠋⢩⡤⣸⣿⣿⣿

⣿⣿⣷⡀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⢠⣤⣤⣤⣩⣽⠁⠀⠀⠈⣿⣷⣤⣤⣴⣶⣶⣶⣶⣦⣤⣴⣿⡿⠛⠀⠠⠄⠈⠁⣠⣿⣿⣿⢻⠿⠃⣿⣿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢀⡠⠀⢀⣴⣿⣿⣿⣿

⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣆⠈⠙⠟⢲⣿⣿⣿⣿⣿⣭⣤⣶⣿⣿⢿⣿⡛⠉⠁⠀⠀⢉⣿⣿⣯⠨⢭⣶⣤⣤⣤⡤⠖⣚⣡⣿⣿⡃⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⡈⠀⠀⠀⠀⣀⣀⣠⣴⣿⡿⠏⢸⣿⣿

⡏⠀⠀⠀⠀⠀⣼⠀⠀⠘⠻⣷⣤⣄⡼⠿⣿⣿⣿⣿⡿⠙⠉⠁⠀⣼⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⢿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣅⣼⠁⠀⠘⢿⣧⠀⠿⣿⠛⠋⢠⣿⣿⣿⣿⠿⠿⠿⠛⠋⢉⠩⣤⣄⣸⣿⣿

⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠙⠿⣿⣤⣤⣭⣉⣀⣀⣠⡤⣴⡿⠿⣿⡄⠀⠀⣠⡼⢿⢿⣿⣿⠓⠲⣶⡆⠃⠉⠋⠉⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣤⣾⣦⣤⣀⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡰⠋⠀⣄⣤⣿⣿⣿

⠀⠶⠶⣶⢿⢷⠄⠹⠿⣷⣶⣄⣀⠀⠻⢿⣿⣿⠿⠉⠉⠁⠀⠀⢀⠀⣸⡇⠀⡼⠁⠀⣸⣷⣿⣿⠀⠠⢴⣆⠐⠲⠶⢶⣿⣿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢰⣿⡁⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡗⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⢙⣋⣼⣿⣷⣿⣿⣾⣿⣿⣧⣋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡆⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠀⠀⠀⠀⢿⣷⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡟⠀⠀⠀⠀⠀⠀⣸⠛⠉⢻⣷⣤⣀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢰⡟⠀⠂⢀⢹⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣠⣶⣿⣧⣀⣠⣦⣾⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⢿⢿⡿⠛⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⢀⣴⡟⣶⡄⠀⠀⠀⠙⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀

⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⣶⡿⠃⠀⢻⣿⡀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢯⢿⠾⠟⠟⠛⠁⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⣠⣶⣶⣶⣦⡀⠀⠀⠀⠀⡴⠸⣿⣿⣧⣠⣀⣸⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⡿⠻⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠛⠛⠿⠿⠛⠷⠀⠀⠀⠀⣇⠀⠨⢿⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢻⣧⠀⠀⢸⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣙⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣤⣀⣳⣤⣴⠀⠀⠀⠀⠹⣧⡀⣄⣌⣉⣉⣉⣉⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠻⢿⣿⣷⡾⣿⣐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⣿⣋⣡⡴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠋⠛⠛⠙⠻⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⣿⣾⠁⠀⠀⠀⠀⣴⣿⣷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠛⠛⠉⠁⢠⣿⡟⠿⣶⣶⣦⣄⣠⣤⣶

⠀⠀⠀⣀⣀⣐⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⠙⢿⡿⢿⣛⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣴⢂⠀⠀⠀⣴⣿⣿⣿⡀⠙⢿⣿⣿⣾⡟⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠁⣩⣽⣿⠿⠛⣛⣭

⣀⣰⡿⠿⠻⠿⠿⢷⣦⣤⣀⠀⠀⠀⠀⠀⠶⣦⣼⣿⣿⣿⠭⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠻⢋⠀⠀⠀⢻⣿⣿⣿⣿⣁⠈⣿⣿⣿⣀⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣤⣴⣶⡿⠛⠉⣥⢄⣿⣿⣿

⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⣤⣤⣨⣍⣩⡏⠀⠀⠀⢹⣿⣦⣤⣤⣶⣶⣶⣶⣶⣤⣤⣾⣿⠟⠃⠀⠤⠀⠉⢀⣼⣿⣿⡟⡿⠟⢸⣿⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠄⠀⣠⣾⣿⣿⣿

⣿⣿⣿⠟⠀⠀⠀⠀⠀⠸⣷⡀⠙⠻⠷⣴⣿⣿⣿⣿⣿⣩⣴⣶⣿⣿⢿⣟⡋⠉⠀⠀⠀⣹⣿⣿⡅⠍⣵⣦⣄⣤⣤⠤⠖⣋⣼⣿⡟⠀⠀⢀⠔⣻⣿⡄⢿⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⠀⢀⣀⣀⣤⣾⣿⡿⠁⣿⣿

⣿⠃⠀⠀⠀⠀⢀⡆⠀⠀⠛⢿⣦⣄⣠⡿⣿⣿⣿⣿⣿⠏⠛⠉⠁⢀⣾⣿⠁⠀⠀⠀⣤⣿⣿⣿⡇⠀⠹⣿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣯⣠⡏⠀⠀⠺⣿⡄⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠟⠛⠉⡉⢥⣤⣀⣿⣿

⠇⠈⢁⡀⠀⠀⠈⢿⣦⠀⠀⠀⠉⠻⣿⣧⣤⣤⣍⣉⣀⣀⣀⣤⣶⠿⢿⣧⠀⠀⢀⣤⠿⣿⢿⣿⡟⠒⢶⣶⠐⠈⠛⠉⢉⣿⣿⠇⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⠠⣤⣼⣿⣿

⠀⠖⡶⣶⠿⢷⠆⠸⠿⢿⣶⣤⣀⠀⠸⢿⣿⣿⡿⠏⠉⠉⠁⠀⠀⡀⢀⣿⠇⢠⠏⠀⢀⣿⣾⣿⡇⠀⠤⣶⡀⠒⠶⠶⣾⣿⣿⣿⣅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣸⣯⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡗⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⠙⢋⣘⣿⣧⣿⣿⣾⣿⣿⣷⣯⣙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⢰⣖⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡟⠉⠀⠀⠀⠈⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⢻⣷⣤⣀⠀⢀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣰⡏⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣰⣾⣿⣧⣄⣰⣦⣾⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠈⢿⣿⡿⠛⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣴⡟⣶⡄⠀⠀⠈⠻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣧⣽⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣶⡿⠋⠀⣿⣧⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢯⢷⠾⠟⠛⠉⠁⠀⢀⣼⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀

⣾⠁⠀⠀⢠⣤⣶⣤⣤⠀⠀⠀⠀⠀⡄⢰⣿⣿⣇⣀⡀⣹⣿⣿⣷⣿⡿⠗⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⠿⠻⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠀⠀⠰⠿⠿⠿⠿⠿⢧⠀⠀⠀⢀⣇⠀⠩⣿⣿⣿⣿⣿⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣦⠀⠀⢹⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣙⣿⣿⣿⣿⣿⣿⣿⠟⣁⡦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣀⣳⣄⣼⠀⠀⠀⠀⢻⣆⠀⣄⡉⢉⣉⣙⣋⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠿⣿⣿⣷⡶⣿⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⣿⣋⣤⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠟⠛⠛⠛⠿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⣯⣿⠁⠀⠀⠀⠀⣾⣿⣷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠛⠉⠉⠁⢠⣿⡟⢿⣶⣶⣦⣄⣤⣴

⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⠿⠿⣛⣡⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣯⡴⢂⠀⠀⠀⣼⣿⣿⣿⡀⠙⢿⣿⣿⣾⡟⠋⣉⣈⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⢀⣩⣽⣿⠟⠋⣉

⠀⠀⣰⠾⠿⠿⠿⠿⣷⣤⡄⡀⡀⠀⠀⠀⠀⢷⣤⣭⣿⣿⣿⠭⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡲⠋⠀⠀⠀⢿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣀⣀⣀⣀⣀⣀⡉⣀⣤⣤⣤⣤⣴⣾⠿⠛⠉⡤⢆⣿⣿

⣾⣿⣿⣿⣆⠀⠀⠀⠀⠈⠙⠿⣤⣀⠀⠀⠀⣤⣈⣉⣉⣩⡏⠀⠀⠀⠹⣷⣄⣤⣤⣴⣶⣶⣶⣦⣤⣤⣾⣿⠟⠃⠀⠤⠀⠉⢀⣸⣿⣿⡿⡿⠟⢸⣿⣟⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⣠⠄⠀⣠⣾⣿⣿

⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣷⠈⠙⠿⠷⣴⣿⣿⣿⣿⣿⣩⣤⣶⣿⣿⣿⣟⡛⠉⠉⠀⠈⣙⣿⣿⣁⠩⣥⣦⣀⣤⣤⠤⠖⣋⣼⣿⣏⡁⠀⢀⠔⣻⣿⡄⢿⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⢀⣀⣀⣀⣤⣾⣿⠟⠀⣿

⣿⣿⠋⠉⠀⠀⠀⠀⡆⠀⠀⠻⢷⣤⣄⣀⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⢀⣾⣿⠀⠀⠀⠀⣤⣿⣿⣿⡇⠀⠹⣿⠟⠀⠀⠀⣾⣿⣿⣿⣿⣧⣠⡏⠀⠀⠺⣿⡄⠘⢿⡟⠛⠁⣼⣿⣿⣿⠿⠿⠿⠟⠛⠉⡉⠥⣤⣄⣿

⣿⡏⠀⠁⠀⠀⠀⠘⣿⣆⠀⠀⠈⠙⠻⣿⣧⣤⣬⣙⣉⣁⣀⣀⣤⣴⡿⢿⣧⠀⠀⠀⣠⡿⣿⢿⣿⡟⠒⢲⣶⠐⠈⠛⠋⢉⣿⣿⠏⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⡀⠔⠁⠠⣤⣼⣿

⡿⠖⠳⣶⠯⢷⡶⠲⠺⠿⣷⣦⣄⣀⠀⠘⢿⣿⣿⣿⠏⠉⠉⠉⠀⠀⡀⢈⣿⠆⢠⠞⠁⠀⣿⣾⣿⡧⠀⠤⣶⡀⠲⠶⠶⣾⣿⣿⣿⣅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⢸⣯⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⠙⠋⣘⣿⣧⣽⣿⣾⣿⣿⣷⣯⣝⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⢰⡖⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⠀⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢷⣿⡿⠋⠀⠀⠀⠀⢻⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣾⣿⠁⠀⠀⠀⠀⠀⢸⡟⠉⠙⣷⣦⣄⡀⠀⣠⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⢀⣾⠀⠁⢀⠘⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣀⣀⣶⣿⣿⣤⣠⣶⣴⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠀⠀⢹⣿⣿⠟⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣷⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⣀⣾⢻⣧⠀⠀⠀⠙⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠟⣻⣬⡟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣾⠟⠁⢸⣿⡀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠾⡶⠿⠛⠋⠉⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⣶⡞⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⠄⣾⣿⣿⣀⣀⢈⣿⣿⣷⣶⣿⠿⠂⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

⠋⠁⠀⠀⠼⠿⠿⡿⠿⠿⡄⠀⠀⠀⣸⡀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣷⡀⠀⠈⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢉⣻⣿⣿⣿⣿⣿⣿⡿⢋⣱⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣄⠰⣄⣠⡆⠀⠀⠀⠘⣿⣀⢠⣈⠉⣉⣋⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⠻⢿⣿⣿⣶⢾⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣡⡤⣾⣿⣦⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⠛⠛⠛⠻⢿⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠙⠛⢸⣿⡏⠀⠀⠀⠀⢰⣾⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠋⠉⠉⠀⣼⣿⠻⢷⣶⣶⣤⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⠿⢿⣋⣵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣭⠖⠀⠀⠀⢠⣾⣿⣿⣇⠉⠻⣿⣿⣷⣿⠛⢉⣀⣉⣉⡉⠃⠀⠀⠀⠀⠁⠋⠀⣀⣭⣿⡿⠛⣉

⠀⠀⠀⠶⠿⠿⠿⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠸⣦⣬⣽⣿⣿⣿⠧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣓⠞⠠⠀⠀⠸⣿⣿⣿⣿⣇⠀⢹⣿⣿⣇⣀⣀⣀⣀⣀⣈⢁⣠⣤⣤⣤⣤⣶⡿⠟⠋⢡⠴⣸⣿

⣠⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⠳⣧⣀⡀⠀⠀⢀⣀⣉⣉⣉⣽⠁⠀⠀⠉⣿⣦⣠⣤⣤⣴⣶⣶⣦⣤⣤⣴⣾⣿⠛⠀⢨⠄⠈⠁⣀⣿⣿⣿⡿⠿⠃⣿⣿⡻⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⡤⠀⢀⣴⣿⢿

⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣶⡆⠉⠻⠿⢦⣾⣿⣿⣿⣿⣋⣥⣴⣶⣿⣿⣿⣛⠋⠉⠁⠀⢙⣛⣿⣏⠈⢉⣤⣄⣠⣤⡤⠴⢚⣡⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⢿⣿⣿⣿⣿⡿⢋⡈⠀⠀⢀⣀⣀⣀⣠⣴⣿⡿⠏⠘

⣿⣿⡿⠉⠁⠀⠀⠀⢠⠀⠀⠘⢿⣦⣄⣀⣸⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⣰⣿⡟⠀⠀⠀⢀⣼⣿⣿⣿⠀⠈⣿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣆⣼⠁⠀⠐⢿⣧⠀⠻⢿⠛⠋⢠⣿⣿⣿⡿⠿⠿⠟⠛⠉⢉⠩⠤⣤⣸

⣿⣿⠁⠈⠁⠀⠀⠀⢿⣧⡀⠀⠀⠉⠛⢿⣿⣤⣤⣙⣛⣉⣀⣀⣠⣤⣾⠿⣿⡄⠀⠀⢀⣼⢿⣿⣿⣿⠒⠲⣶⡆⠒⠚⠚⠉⣹⣿⡿⢹⣿⣿⣿⣤⣀⣠⣤⣾⣧⣤⣄⣀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⠠⠊⠀⢤⣤⣿

⣿⡟⠲⣶⠿⢷⠶⠶⠲⠿⢿⣶⣤⣀⠀⠀⠿⣿⣿⣿⡿⠛⠉⠉⠁⠀⣀⠀⢹⣿⠀⡴⠋⠀⢸⣷⣿⣿⠤⠠⢤⣆⠐⠶⠶⢶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⡅⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠃⠉⢿⣷⣤⣀⣀⣀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣼⡇⠈⠀⡄⢻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣰⣾⣿⣧⣄⣴⣦⣾⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠉⠀⠘⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡆⠀⠀⠀⠀⠀⠀

⠉⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣴⣟⣿⡅⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣧⣿⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⣤⣶⣿⠋⠈⣿⣇⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⢿⠾⠟⠛⠉⠁⠀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀

⣶⣶⠋⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣇⣀⡀⣹⣿⣿⣶⣾⡿⠇⠀⠀⠀⠀⠀⢀⣾⠿⣿⣿⡿⠿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⣀⣠⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠛⠋⠀⠀⢰⠿⠿⣿⡿⠿⣧⠀⠀⠀⢀⣿⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⣿⣦⠀⠀⢹⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡶⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⠂⢦⣀⣼⠀⠀⠀⠈⢿⣧⡀⣄⡉⢙⣙⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⡾⠻⠿⣿⣿⣷⡾⣿⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⢿⣿⣿⣋⣤⣴⣿⣷⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⡟⠿⠟⠻⢿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠛⠃⣿⣿⠁⠀⠀⠀⠀⣾⣿⣷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠛⠉⠉⠃⢠⣿⡟⢿⣿⣷⣶⣤⣤

⠀⠀⠀⠀⠀⠁⠀⠠⠀⢰⠁⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠿⣟⣩⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣯⣵⠂⠀⠀⠀⣴⣿⣿⣿⣟⠛⣿⣿⣿⣿⡟⠋⣉⣈⣉⣉⠙⠀⠀⠀⠀⠈⠙⠋⢀⣨⣿⣿⠟⠋

⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣤⣀⡀⡀⠀⠀⠀⠈⣷⣭⣽⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡳⠋⠄⠀⠀⣿⣿⣿⣿⣿⡄⠈⣿⣿⣿⣀⣀⣀⣀⣀⣀⡉⣀⣴⣶⣤⣤⣴⣾⠿⠛⠩⡤⢆⣿

⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠉⠛⢿⣄⡀⠀⠀⠀⣄⣈⣉⣙⣋⡏⠀⠀⠈⢻⣷⣄⣤⣤⣤⣶⣶⣶⣦⣤⣤⣶⣿⡿⠃⠀⣡⠀⠉⢀⣼⣿⣿⣿⡿⠟⢸⣿⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⣠⠄⠀⣠⣾⡿

⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣦⠉⠻⢿⣷⣴⣿⣿⣿⣿⣿⣫⣤⣶⣾⣿⣿⣿⡛⠋⠉⠉⠉⣻⣿⣿⣇⣍⣩⣦⣄⣤⣤⠤⠖⣋⣼⣿⣿⡃⠀⢀⠔⣻⣿⡄⢿⣿⣿⣿⣿⣿⠟⣁⠁⠀⣀⣀⣀⣀⣀⣤⣾⣿⠿⠁

⣿⣿⣿⠟⠉⠁⠀⠀⢀⣾⠁⠀⠻⣷⣤⣀⣀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢀⣿⣿⠃⠀⠀⠀⣠⣿⣿⣿⡏⠀⢹⣿⠟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣠⡏⠀⠀⠻⣿⡆⠸⢿⡟⠛⠁⣼⣿⣿⣿⠿⠿⠿⠟⠋⠉⡩⠥⢤⣤

⢸⣿⡟⠐⠋⠀⠀⠀⢸⣿⣄⠀⠀⠈⠙⠿⣿⣇⣬⣌⣛⣋⣁⣀⣀⣤⣴⡿⣿⣯⠀⠀⠀⣠⣿⣿⣿⣿⡟⠒⢶⣶⠘⠒⠛⠋⢉⣿⣿⠏⣿⣿⣿⣧⣄⣀⣤⣴⣿⣦⣤⣀⡀⠚⠛⣉⠁⠀⠀⠀⠀⠀⡠⠞⠁⠠⣤⣾

⣾⣿⠳⣿⢿⢿⢷⣶⠾⠿⠿⣷⣤⣄⡀⠀⢸⣿⣿⣿⣿⠟⠛⠛⠉⠉⢉⡀⠈⣿⡇⢠⡞⠁⢀⣿⣿⣿⡧⠤⢬⣴⡀⠲⠶⠶⣾⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⢿⣿⣶⣷⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣿⡿⠀⠀⠀⠀⠀⠀⣸⡟⠉⠻⣷⣦⣄⣀⣀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢠⣿⠀⠡⢠⠹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣆⣀⣀⣶⣿⣿⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠉⠁⠀⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣷⠀⠀⠀⠀⠀⠀

⠋⠉⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⠙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣼⡏⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣴⣾⠟⠁⢹⣿⡀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⡿⠟⠛⠋⠉⠀⢀⣤⣿⣿⡀⠀⠀⠀⠀⠀⠀

⣷⣶⡞⠁⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣀⡀⢸⣿⣿⣶⣶⣿⠿⠀⠀⠀⠀⠀⠀⣰⠿⢿⣿⡿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⠟⠛⠁⠀⠀⡾⠿⢿⣿⠿⢿⡀⠀⠀⠀⣼⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⢀⠊⢻⣧⡀⠀⢈⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡄⠰⣄⣠⡇⠀⠀⠀⠻⣿⣠⢀⣈⠉⣛⠛⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢲⠟⢿⢿⣿⣿⣶⢿⣄⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣟⣥⣴⣿⣿⣦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⠿⠿⠛⠿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠙⠃⢸⣽⡏⠀⠀⠀⠀⢰⣿⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠋⠉⠙⠀⣽⣿⢻⣿⣿⣶⣦⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⠿⢿⣋⣵⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣭⣆⠀⠀⠀⢠⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⠛⢉⣁⣉⣉⡉⠃⠀⠀⠀⠀⠉⠋⠁⣀⣽⣿⡿⠛

⠀⠀⠀⢀⣶⣿⣿⣿⣷⣿⣦⣄⣀⢀⠀⠀⠀⠀⢹⣦⣭⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣓⠞⡀⠀⠀⢸⣿⣿⣿⣿⣇⠀⣹⣿⣿⣇⣀⣀⣀⣀⣀⣈⢀⣤⣶⣦⣤⣤⣶⡿⠟⠋⠥⠶⣸

⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠉⠙⠿⣧⣀⠀⠀⠀⣀⣈⣉⣉⣛⣻⠁⠀⠀⠙⣿⣦⣀⣤⣤⣴⣶⣶⣤⣤⣤⣴⣿⣿⠗⠀⣈⠄⠉⠁⣠⣿⣿⣿⣿⠿⠀⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⡤⠀⢀⣼⣿

⢘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣶⡌⠛⠿⣷⣦⣾⣿⣿⣿⣿⣛⣤⣴⣶⣾⣿⣿⡟⠛⠉⠉⠈⢙⣿⣿⣏⣈⣩⣥⣄⣠⣤⡤⠴⣚⣩⣿⣿⣏⠀⠀⡠⢻⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⡈⠀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠋

⢸⣿⣿⡿⠛⠉⠀⠀⠀⢰⡍⠀⠸⢿⣦⣀⣀⣹⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⣸⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⠀⠘⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣇⣼⠁⠁⠘⢿⣧⠈⠿⣿⠛⠋⢠⣿⣿⣿⡿⠿⠿⠟⠛⠉⢉⠭⠤⣤

⠀⣿⣿⠃⠒⠁⠀⠀⠀⣿⣧⡀⠀⠀⠙⠻⣿⣿⣠⣁⣛⣛⣉⣀⣀⣀⣤⣾⢿⣿⡄⠀⠀⢀⣼⣿⣿⣿⣿⠓⠶⣶⡆⠓⠚⠛⠉⣽⣿⡿⢹⣿⣿⣿⣤⣀⣠⣤⣾⣷⣤⣄⣀⠐⠛⢋⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⢤⣴

⢸⣿⡿⣶⠿⢿⣏⣲⡶⠾⠿⣿⣦⣄⣀⠀⠀⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⡁⠀⣹⡷⠀⡴⠋⠀⣾⣿⣿⣿⠤⠤⣥⣆⠐⠶⠶⢶⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⡅⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀

⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠉⠀⠀⠀⠘⣿⣷⣾⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⢻⣷⣦⣀⣀⣀⣤⣾⣿⣿⠂⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣰⡟⠀⠃⢀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣄⣀⣰⣾⣿⣷⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠉⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀

⣿⠟⠉⠻⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣾⣿⡅⠀⠀⠈⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣷⣼⠇⠀⠀⠀⠀⠀

⣿⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⣾⠟⠁⢻⣷⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⢿⢿⠾⠟⠛⠋⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀

⣿⣷⣤⡖⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣯⢀⡀⢸⣿⣷⣶⣶⣿⠿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⡿⠿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠁⢠⠚⢿⣧⠀⠀⢙⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡜⢢⣀⣠⠃⠀⠀⠀⢿⣧⡀⣈⡙⠙⠛⠛⠛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⢿⣿⣿⣷⣶⣾⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣛⣥⣴⣿⣷⣆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⢿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠉⠙⠃⣿⣽⠏⠀⠀⠀⠀⣴⣿⣷⣶⣦⣄⣀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠛⠉⠉⠉⢠⣿⣿⢿⣿⣷⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⣛⣥⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣭⢆⠀⠀⠀⢰⣿⣿⣿⣏⠟⢿⣿⣿⣿⣿⠛⢉⣀⣉⣉⡉⠀⠀⠀⠀⠈⠉⠋⢁⣨⣽⣿⠿

⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣾⣄⣀⡀⢀⠀⠀⠀⠀⢷⣬⣿⣿⣿⣿⣟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣳⠞⡀⠀⠀⢹⣿⣿⣿⣿⣇⠀⣻⣿⣿⣅⣀⣀⣀⣀⣀⡉⢀⣤⣶⣦⣤⣴⣾⡿⠟⠋⠤⠶

⠀⠀⣠⣶⣾⣿⣦⠀⠀⠀⠈⠉⠛⢿⣇⡀⠀⠀⠀⣀⣉⣙⣛⢛⣛⠁⠀⠈⠻⣷⣄⣀⣤⣤⣤⣶⣦⣤⣤⣄⣴⣾⣿⠗⠀⣉⠄⠉⠀⣈⣿⣿⣿⣿⠿⠀⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⡤⠀⢀⣼

⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣶⡈⠻⢿⣶⣄⣿⣿⣿⣿⣿⣛⣠⣴⣶⣾⣿⣿⡟⠛⠉⠉⠉⢻⣿⣿⣏⣉⣩⣥⣄⣠⣠⣤⠴⢚⣹⣿⣿⡏⠀⠀⡠⢻⣿⣇⠹⣿⣿⣿⣿⣿⡿⢋⠁⠀⣀⣀⣀⣀⣀⣤⣶⣿⡿

⠀⢸⣿⣿⡿⠛⠋⠀⠀⠀⢠⠀⠀⠹⣷⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⣼⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⠀⠸⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣄⣾⠁⠁⠘⢿⣇⠈⠿⣿⠛⠋⣰⣿⣿⣿⡿⠿⠿⠟⠛⠉⢉⠥⠤

⣰⠀⣿⣿⠃⠒⠀⠀⠀⠀⣿⣦⠀⠀⠀⠙⠿⣿⣿⣉⣉⣛⠛⣋⠁⣀⣀⣤⣾⣿⣿⡀⠀⠀⢀⣼⣿⣿⣿⡿⠒⢶⣼⡄⠒⠒⠚⠋⣽⣿⡟⣹⣿⣿⣿⣤⣀⣠⣤⣿⣦⣤⣄⣀⠐⠛⢋⠁⠀⠀⠀⠀⠀⣀⠴⠋⠀⣤

⡿⢾⣿⣿⠿⢿⠏⢳⣶⡶⠿⢿⣷⣦⣀⡀⠀⠈⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠁⠀⣿⡇⠀⡴⠋⠁⣿⣿⣿⣿⠤⢤⣭⡄⠴⠶⣶⣶⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⡅⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡟⠉⠀⠀⠀⠈⣿⣶⣶⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⠻⣷⣦⣀⡀⣀⣠⣾⣿⣿⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣰⡏⠀⠂⠀⢹⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⣰⣾⣿⣧⣄⣰⣶⣾⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠉⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀

⣿⠋⠉⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡆⣮⡅⠀⠀⠈⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣧⣼⠇⠀⠀⠀⠀⠀

⣻⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣤⣤⣾⠟⠁⢻⣷⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣄⣀⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠨⠿⢷⠾⠟⠛⠋⠁⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⠀

⣿⣧⣤⡖⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢠⢠⣿⣿⣇⢀⡀⢸⣿⣷⣶⣶⣿⠿⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⡥⣶⣶⢶⣾⠟⢿⡟⠛⠸⠀⠀⠀⢡⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⡿⠿⠛⠀⠀⠀⣾⣿⣿⣿⢿⣧⠀⠀⠀⠀⣼⠀⠙⣿⣿⣿⣿⣿⣿⣿⣯⣿⠷⠶⠞⢛⣛⣏⡉⣽⣷⣶⣮⣿⣿⠟⢿⣿⣿⣿⢹⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⢮⢏⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠄⢢⡀⣠⠃⠀⠀⠀⢻⣇⠀⠈⣻⠙⣻⣿⢻⣿⣿⣿⡿⢿⣦⣿⡿⠙⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣋⣥⡴⣿⣷⣆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⠿⠿⠟⢿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠈⣻⣿⣧⠀⣿⣯⣿⡍⢻⣿⣿⡿⠻⣿⣿⠿⠿⣛⣙⣛⣴⣿⣷⣶⣶⣟⣛⠙⠀⠀⣀⣀⣀⣀⠀⠈⠑⠉⠉⠁⠀⣿⣿⠻⢿⣷⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣶⣶⠀⣶⣶⢛⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⣾⣿⣿⡟⣩⣿⣿⣷⣿⣿⣶⣾⣿⣶⣿⣾⡟⠛⢉⣀⣉⣉⡉⠀⠀⠀⠀⠈⠁⠋⠀⣠⣽⣿⠟

⠀⠀⠀⠀⠀⣴⣶⣿⣷⣶⣾⣄⣀⠀⣿⣿⣇⣿⣿⢽⣿⣿⣾⣿⣿⣟⣋⣤⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⡇⠀⣿⣿⣿⡗⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣅⣀⣀⣀⣀⣀⡉⢀⣤⣶⣤⣤⣤⣶⡿⠛⠉⠤⠖

⠀⠀⣠⣶⣾⣶⣤⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣸⣿⣿⣻⣿⣿⠉⠀⢸⣿⣷⣿⣿⣠⣿⣿⣶⣦⣤⣤⣄⣿⣿⡿⠗⣿⣿⡇⣿⣿⣇⣿⣿⡿⣿⣿⣿⣿⣿⠹⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢀⡤⠀⢀⣼

⠀⢰⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣶⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣠⣤⣾⣿⡿⣿⣿⡟⣿⣿⣁⣿⣿⣿⣏⣿⣿⣧⣄⣿⣿⡧⢿⣿⣿⣿⣿⡇⣿⣿⣸⣿⣿⣇⣙⣻⣿⣿⣿⣿⣛⣃⠀⠀⢀⣀⣀⣀⣀⣠⣶⣿⡿

⠀⠈⣿⣿⡿⠛⠋⠀⠀⠀⢠⠀⠀⠹⣿⣇⣘⠛⣛⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⣻⣿⡟⠃⠈⠛⢻⣿⣿⣿⣿⠛⠛⣻⡿⠛⠛⠃⢸⣿⣿⣿⣯⣷⣛⣿⠀⠛⠛⢿⣟⠛⠛⣛⠛⠛⢻⣿⣿⣿⠿⠿⠿⠟⠛⠉⢉⠡⠤

⠀⠀⣿⣿⠃⠒⠀⠀⠀⠀⢿⣆⠀⠀⠀⠙⠿⣿⣏⣉⣉⣛⠛⠉⠀⠀⣀⣠⣾⢿⣿⡀⠀⠀⢀⣼⠿⢿⣿⡟⠒⠲⣤⡀⠒⠒⠚⠋⣽⣿⡟⢹⣿⣿⣷⣤⣀⣠⣤⣾⣦⣤⣀⣀⠐⠛⠋⠁⠀⠀⠀⠀⠀⢀⠴⠋⠀⢤

⡇⢾⣿⣿⠿⢿⠏⠰⠶⠶⠞⠹⣷⣤⣀⡀⠀⠈⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⠁⠀⢿⡇⠀⡴⠋⠀⣾⣿⣿⣿⠤⢠⣭⡄⠰⠶⣶⣶⣿⣿⣷⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢀⣿⡅⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣷⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀

⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⠟⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⠟⠁⠀⠀⠀⠘⣿⣶⣶⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣽⡏⠀⠀⠀⠀⠀⠀⣼⠉⠉⢻⣷⣦⣀⣀⣀⣴⣿⣿⡿⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢇⠀⠀⠀⠀⠀⣰⡇⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣄⣀⣠⣾⣿⣷⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠙⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀

⣿⣿⠟⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢠⡿⣭⡁⠀⠀⠉⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣷⣼⠇⠀⠀⠀⠀

⠛⢳⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣀⣤⣾⠟⠁⢿⣷⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣀⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠨⠿⢷⠾⠟⠛⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀

⠀⣿⣦⣤⡴⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢠⢨⣿⣿⣇⠀⠀⢸⣿⣶⣶⣶⣿⡿⠀⠀⢀⣀⣠⣄⣴⣿⣿⣿⣿⡿⢿⣿⣿⣯⡥⣶⡶⢶⣾⠿⢿⡟⠛⠸⠀⠀⠀⠀⢠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀

⣿⣿⡿⠟⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⡞⠈⢙⣿⣿⣿⣷⣿⣿⣿⣯⣿⠷⠖⢛⣛⣏⡉⣽⣿⣷⣦⣻⣿⣿⣿⣾⣿⡟⣿⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⢌⢏⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⠀⠀⠀⠀

⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⢈⠂⠀⠀⠀⢻⡇⠀⢻⠙⣻⣿⢻⣿⣻⣿⡿⢿⣦⣿⡿⠙⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣿⣋⣥⠴⣿⣷⣆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠲⠿⡷⠾⢿⣿⠀⠀⠀⠀⠀⢻⣷⣿⣿⣾⣿⣿⣿⣿⣿⡇⠈⣻⣿⣧⠀⣿⣯⣿⡏⢻⣿⣿⡯⠻⣿⣿⣿⠿⣛⣙⣛⣤⣴⣿⣷⣶⣿⣟⣙⠀⠀⠀⣀⣀⣀⣀⠀⠈⠘⠉⠉⠁⠀⣿⣿⢻⢿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣶⠀⣶⣶⠙⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣿⣿⣷⣶⡝⣿⣶⣻⣾⡟⠋⢉⣀⣁⣉⡉⠀⠀⠀⠀⠀⠁⠉⢀⣠⣼⣿

⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣾⣅⣀⣿⣿⣇⣿⣿⢸⣿⣿⣹⣿⣿⣿⣿⣤⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⡆⠀⣿⣿⡇⣸⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣧⣿⣿⢿⣿⣅⣀⣀⣀⣀⣀⡈⢀⣤⣶⣦⣤⣴⣾⠿⠛⠉⠤

⣷⠀⠀⢀⣴⣶⣾⣄⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⣛⠁⢸⣿⡟⣿⣿⣀⣿⣿⣤⣴⣤⣤⣤⣿⣿⣷⡿⣿⣿⣏⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⢀⠄⠀⢀

⣿⠀⠀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣿⡟⢻⣿⣿⣼⣿⣿⣿⣿⣿⠛⣀⣼⣿⣿⣿⣿⡟⣿⣿⣏⣿⣿⣿⣿⣿⣿⣏⣤⣿⣿⣇⣿⣿⣟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣇⣘⣻⣿⣿⣿⣿⡛⢃⠀⠀⣀⣀⣀⣀⣀⣤⣶⣿

⡿⠀⠀⣿⣿⣿⠛⠋⠀⠀⠀⢀⠀⠀⠻⣿⣌⡛⠛⢸⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⣹⣿⡇⠈⠛⠛⢛⣿⣿⣿⣿⠛⠛⣿⡟⠛⠃⠈⢻⣿⣿⣿⣿⣛⣛⣼⠛⠛⠘⢿⣟⠛⠛⢛⠛⠛⢣⣿⣿⣿⠿⠿⠿⠛⠛⠉⢉⠡

⣿⢀⠀⣿⣿⠇⠐⠂⠀⠀⠀⢼⣆⠀⠀⠀⠛⠿⣿⣿⣉⣉⡛⠛⠋⠁⠀⣀⣠⣴⣿⣿⡀⠀⠀⢀⣼⡿⢿⣿⣿⠒⠶⣤⡄⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣤⣾⣦⣤⣀⣀⠀⠛⢋⠁⠀⠀⠀⠀⠀⢀⠴⠋⠀

⣿⡿⢲⣿⡿⢶⠖⠲⠲⠶⠶⠂⠻⣷⣤⣀⠀⠀⠈⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠁⠀⢻⡇⠀⡴⠋⠁⣸⣿⣿⣿⠄⠠⣭⡄⠠⠶⣶⢶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣿⡅⠀⠀⠀⠀⠀⢀⣠⣴⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀

⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣷⢾⣿⡀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⣿⠁⠀⠀⠀⠀⠀⢰⡏⠈⠙⢿⣶⣤⣀⣀⣠⣾⣿⣿⠇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⢀⣾⠀⠐⢀⠈⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣀⣀⣴⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⡟⣇⠀⠀⠀⠀

⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠛⠉⠉⢻⣿⣿⡿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀

⣰⣿⡿⠛⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣰⢏⣝⠀⠀⠈⠙⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⢹⣦⡿⠀⠀⠀⠀

⠛⠛⡇⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⣤⡾⠋⠸⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠽⠶⠿⠿⠛⠋⠉⠀⢀⣠⣼⣿⡇⠀⠀⠀⠀

⠀⢸⣷⣤⣤⠆⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡈⣽⣿⣿⠀⠀⠀⣿⣷⣶⣶⣶⣿⠇⠀⢀⣀⣠⣄⣤⣾⣿⣿⣿⡿⢿⣿⣿⣿⡥⣶⡶⢶⣾⠟⢿⡟⠛⠸⠀⠀⠀⠀⠀⢤⣄⣄⣀⣠⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀

⣿⣿⣿⠿⠟⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⡇⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠞⢛⣛⣏⡉⣽⣷⣾⣦⣻⣿⣿⣿⣾⣿⡻⢻⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠰⡙⣹⣿⣿⣿⣿⣿⣿⡿⠛⣡⡆⠀⠀⠀

⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣅⠀⡹⠀⠀⠀⠘⣷⡀⢾⠉⣻⣿⢻⣿⢛⣿⣿⢿⣦⣿⡿⠛⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⡿⣟⣭⡤⢾⣿⣾⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⠶⢿⣿⡟⠀⠀⠀⠀⠘⣿⣾⣾⣿⣿⣿⣿⣿⣿⡟⠈⣻⣿⣧⠀⣿⣯⣿⡉⢿⣿⣿⡗⠹⣿⢽⣿⣿⣛⣙⣛⣤⣤⣾⣿⣷⣿⣿⣙⣀⠀⠀⢀⣀⣀⣀⣀⠀⡉⠉⠉⠉⠀⢸⣿⡟⠻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣶⣶⠀⣶⣶⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡿⣩⣿⣿⣶⣾⣿⣾⣶⡌⣿⣿⣽⣿⣿⠟⠉⣁⣀⣀⣉⡁⠀⠀⠀⠀⠀⠈⠁⣀⣤⣾

⡆⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣮⣀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣿⣿⣧⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⢀⣿⣿⡷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣯⣀⣀⣀⣀⣀⣀⡁⣠⣶⣶⣦⣤⣶⡿⠟⠋⠁

⣼⡆⠀⠀⣠⣶⣾⣯⡀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⢛⡋⢸⣿⡟⣿⣿⣀⣿⣿⣤⣤⣦⣤⣤⣿⣿⣷⣿⣿⣿⣇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⡠⠆⠀

⣿⡟⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣾⣿⣿⣿⣿⣿⡟⢃⣸⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣟⣿⣿⣿⣏⣡⣿⣿⣇⣿⣿⣗⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣀⣛⣻⣿⣿⣿⣿⠛⣁⠀⢀⣀⣀⣀⣀⣠⣴⣾

⣿⡇⠀⢸⣿⣿⡟⠛⠃⠀⠀⠀⠰⠐⠛⢿⣾⣛⠛⠀⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠙⣻⣿⠈⠛⠛⠛⣻⣿⣿⣿⡟⠃⢻⣻⠟⠃⠈⠛⣿⣿⣿⣿⣛⣛⣠⡟⠛⠈⠻⣿⡛⠛⠛⡛⠛⠃⣼⣿⣿⡿⠿⠿⠟⠛⠋⠁⣉

⣿⡇⠀⢸⣿⡿⠀⠐⠀⠀⠀⠠⣷⡀⠀⠀⠘⠻⢿⣿⣏⣉⣙⠻⠛⠉⠀⠀⣀⣠⣾⣿⣏⠀⠀⠀⣀⣿⠿⣿⣿⡗⠲⣤⣤⠐⠒⠒⠛⢉⣿⣿⠏⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⣀⠘⠛⣉⠀⠀⠀⠀⠀⠀⡠⠞⠁

⣿⣿⠷⣾⣿⢷⠖⠲⠲⠶⡶⠀⠛⢿⣦⣄⡀⠀⠀⢩⣿⣿⣿⣿⡿⠛⠛⠋⠉⠉⠀⠈⣿⡆⢀⡞⠉⠀⣦⣾⣿⡧⠀⢬⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⢸⣿⠀⠀⠀⠀⠀⢀⣀⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀

⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⢿⣿⠟⠁⠀⠀⠀⠘⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣾⠃⠀⠀⠀⠀⠀⠀⡿⠁⠉⢿⣷⣦⣀⣀⣠⣴⣿⣿⡟⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⣸⡇⠈⠀⡄⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⢀⣠⣾⣿⣧⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀

⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠋⠉⠙⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀

⢀⣿⣿⠟⠛⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢠⡟⣽⡁⠀⠀⠙⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠻⠋⣷⣼⠇⠀⠀⠀

⠟⠛⣧⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣄⣀⣤⣾⠟⠙⣿⣇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠨⠦⠿⠾⠛⠛⠉⠁⠀⣀⣴⣿⣿⠀⠀⠀⠀

⠀⠀⣿⣤⣀⡤⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣩⣿⣿⡇⠀⠀⢻⣿⣶⣶⣶⣿⡏⠀⢀⣀⣠⣄⣤⣴⣿⣿⣿⡿⢿⣿⣿⣿⡥⣶⡶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⢠⣤⣠⣀⣀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀

⣿⣾⣿⣿⠿⠀⠀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⠀⣾⠈⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟⢛⢛⣏⡉⣽⣷⣾⣦⣻⣿⢿⣿⣾⣿⣻⢻⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⢎⣙⣿⣿⣿⣿⣿⣿⣿⠟⣡⡶⠀⠀⠀

⠻⠿⠁⠀⠀⠀⠀⠀⠁⠀⠈⢅⠀⢉⠂⠀⠀⠀⢿⡆⢾⡉⣻⣿⢻⣿⠿⣿⣿⣿⣦⣿⡿⠙⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⡿⢿⣫⣤⠴⣿⣷⣦⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⡶⠾⣿⣿⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋⣻⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡗⠻⣿⠟⣿⣿⣛⣙⣛⣤⣤⣴⣿⣷⣿⣿⣙⣀⠀⠀⢀⣀⣀⣀⣀⠀⢈⠊⠉⠉⠁⠀⣿⣿⠛⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⣶⣶⠀⣶⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣿⣯⣿⣿⣶⣶⣿⣾⣷⡄⣾⣿⣿⣿⣾⡟⠋⢉⣀⣀⣉⡉⠀⠀⠀⠀⠈⠀⠉⢀⣠⣴

⣷⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣼⣁⣿⣿⣇⣿⣿⢸⣿⣿⣹⣿⣿⣿⣿⣷⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣀⣀⣀⣀⣀⡈⢀⣴⣶⣶⣤⣴⣾⠿⠛⠉

⣠⣦⠀⠀⢀⣤⣶⣯⣍⠈⠉⠉⠉⠛⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⠛⡛⢹⣿⡏⣿⣿⡄⣿⣿⣤⣤⣤⣤⣤⣿⣿⣷⣶⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠠⠔⠀

⣿⣿⠀⠀⣾⣿⣿⣿⣿⠆⠀⠀⠀⠀⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠗⣸⣿⣿⣿⣿⡿⣿⣿⣋⣿⣿⢻⣿⣿⣿⣏⣉⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⢹⣿⣿⢛⣿⣇⣙⣛⣿⣿⣿⣿⠟⢁⡀⢀⣀⣀⣀⣀⣠⣤⣶

⣿⡏⠀⠀⣿⣿⣿⠛⠋⠀⠀⠀⢀⠒⠛⢻⣿⣟⡛⠀⢹⣿⣿⣿⣿⣿⣿⠛⠛⠛⠙⣻⣿⡏⠛⠛⠛⢋⣾⣿⣿⣿⠃⠸⣛⡟⠃⠈⠛⢻⣿⣿⣿⣟⣛⣀⡿⠛⠘⠛⢿⣟⠛⠛⠛⠛⠋⢠⣿⣿⣿⠿⠿⠿⠛⠛⠉⢉

⣿⣿⠀⠀⣿⣿⠇⠤⠀⠀⠀⠀⣿⣆⠀⠀⠈⠻⢿⣿⣿⣉⣉⠻⠟⠋⠁⠀⢀⣠⣴⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⡿⠒⢦⣬⡀⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣴⣾⣦⣤⣄⣀⠀⠛⣋⡁⠀⠀⠀⠀⠀⢀⠴⠋

⣿⣿⡿⣶⣿⣿⠶⠲⠶⠶⢶⠀⠀⢻⣷⣄⡀⠀⠀⠉⣿⣿⣿⣿⣿⠏⠛⠛⠉⠉⠁⠀⢻⡇⠀⡰⠋⠁⣶⣾⣿⣿⠠⢠⣭⡄⠠⠶⣶⣶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣿⡅⠀⠀⠀⠀⠀⣀⣠⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⠿⣿⣿⡇⠀⠀⠀

⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣦⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣿⡟⠀⠀⠀⠀⠀⠀⢸⠏⠉⠹⣿⣶⣤⣀⣀⣴⣾⣿⣿⠃⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢠⡿⠀⠁⢠⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣠⣼⣿⣷⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀

⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠛⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⠀⠀⠀

⠀⣸⣿⡿⠛⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⢫⡏⠀⠀⠈⠻⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⢽⣦⡟⠀⠀⠀

⡿⠛⠿⡅⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⣀⣀⣴⡾⠋⢹⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠽⠾⠿⠟⠛⠋⠉⠀⣀⣠⣾⣿⡇⠀⠀⠀

⠀⠀⢸⣧⣀⣠⠄⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡈⣽⣿⣿⠀⠀⠈⣿⣷⣶⣴⣾⣿⠇⢀⣀⣠⣄⣤⣤⣾⣿⣿⣿⢿⣿⣿⣿⣷⣶⡶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⣤⣄⣄⣀⣰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀

⣿⣶⣿⣿⡿⠇⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⠉⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⢛⣛⣏⡉⣽⣷⣶⣮⣻⣿⢿⣿⣾⣿⡈⣿⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠰⣹⣽⣿⣿⣿⣿⣿⣿⠟⢋⣴⠆⠀⠀

⠿⠿⠏⠀⠀⠀⠀⠀⠈⠉⢈⠩⡁⠈⡱⠀⠀⠀⠸⣶⢻⠉⣩⣿⢻⣿⠿⣿⣿⣿⣧⣿⡿⠙⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠙⠋⠛⠛⢿⢿⣿⣥⡴⢾⣿⣿⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⣷⣶⢿⣿⡇⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⣻⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡗⠺⣿⠟⢿⣿⣟⣙⣛⣤⣤⢴⣾⣿⣿⣿⣽⣀⡀⠀⠀⣀⣀⣀⣀⣀⢀⡈⠉⠉⠉⠀⢸⣿⡏⠻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⠀⣶⣶⠀⣽⣿⣿⣿⣿⣿⡿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣟⣿⣿⣿⣶⣦⣾⣶⣿⣷⣶⣿⣿⣿⣷⣿⠋⠉⣀⣠⣀⣉⡁⠀⠀⠀⠀⠀⠈⠁⣀⣤

⣶⡆⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⣤⣎⣿⣿⣇⣿⣿⢸⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣯⣀⣀⣀⣀⣀⣀⡁⣠⣶⣶⣶⣴⣶⡿⠟⠉

⣃⣱⡄⠀⠀⣠⣤⣾⣭⡉⠉⠉⠉⠙⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⠛⢛⢻⣿⡏⣿⣿⣦⣿⣿⣀⣤⣤⣤⣤⣿⣿⣧⣶⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣟⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠤⠂

⣿⣿⡟⠀⠰⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠛⣻⣿⣿⣏⣉⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⢹⣿⣿⢜⣻⣿⣈⣛⣿⣿⣿⣿⣿⠛⣄⣀⣀⣀⣀⣀⣠⣤⣴

⣿⣿⡇⠀⢸⣿⣿⡿⠟⠃⠀⠀⠀⠐⠛⠛⢿⣟⡛⠈⠙⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠋⣰⣿⣿⣿⡇⠀⢛⣻⠛⠈⠛⠛⣿⣿⣿⣿⣛⣤⣻⡟⠘⠛⠻⣿⡛⠛⠛⡛⠋⢁⣼⣿⣿⠿⠿⠻⠛⠛⠉⠁

⢿⣿⡆⠀⢸⣿⣿⠁⠄⠀⠀⠀⢰⣷⡀⠀⠀⠙⠿⣿⣿⡏⣉⠙⠿⠛⠋⠀⠀⣀⣠⣾⣿⣏⠀⠀⠀⣠⣿⣿⣿⣿⠗⠶⣤⣥⠐⠒⠒⠛⢉⣿⣿⠋⣿⣿⣿⣧⣄⣀⣤⣶⣿⣤⣤⣀⣀⠈⢋⣁⠀⠀⠀⠀⠀⠀⠠⠞

⠸⣿⣿⣶⢿⣿⡧⠴⠶⠶⠶⡀⠀⠹⣿⣦⣀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠀⠘⣿⠄⢀⡞⠉⢀⣿⣿⣿⡇⠀⣬⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡀⠀⠀⠀⠀⢀⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⣿⣿⡇⠀⠀

⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡟⠁⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡟⠀⠀⠀⠀⠀⠀⣸⠋⠉⠹⣿⣶⣤⣀⣠⣴⣿⣿⣿⠁⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢠⡯⠀⠁⠠⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣠⣼⣿⣷⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠟⠛⠛⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⠀⠀

⠀⠀⢸⣿⣿⠿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣬⢙⡋⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣻⣿⣿⠿⠟⠋⢽⣶⡟⠀⠀

⣶⡶⠿⢿⡁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣴⡾⠋⢻⣿⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠺⠾⠟⠛⠛⠉⠁⠀⣀⣤⣿⣿⡇⠀⠀

⡏⠀⠀⢸⣧⣀⣠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⠀⠀⠘⣿⣷⣦⣤⣾⣿⢀⣀⣠⣄⣤⣤⣴⣾⣿⣿⣿⣿⢿⣿⣿⣶⣶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⣤⣄⣄⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀

⣿⣿⣶⣾⣿⣿⠇⠀⠀⢠⣾⣿⣿⣿⣧⡀⠀⠀⠀⢰⠎⣛⣿⣿⣿⣷⣾⣿⣿⣿⣿⣟⣛⣟⡉⣽⣷⣶⣦⣻⣿⠟⣿⣿⣿⡀⢹⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠰⣙⣽⣿⣿⣿⣿⣿⣿⠟⢋⣴⠃⠀

⠻⠿⠿⠟⠁⠀⠀⠀⠀⠈⠉⢉⢩⡉⠉⡣⠀⠀⠀⠸⣿⠋⣩⣽⢻⣿⠿⣿⣿⣿⣿⣿⡿⠛⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣿⢿⣫⣥⡶⢾⣿⣿⣄

⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣦⣿⣾⠇⠀⠀⠀⠀⢹⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠝⠿⢿⣿⣟⣛⣤⣤⢤⢶⣾⣿⣿⣿⣤⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⡈⠉⠉⠁⠀⢸⣿⡏⠛

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣿⣯⣿⣿⣶⣦⢀⣶⣶⣿⣶⣶⠹⣿⣿⣷⣿⠋⠉⣀⡠⢄⣈⡁⠀⠀⠀⠀⠀⠈⠁⣠

⣤⣶⣆⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣿⣿⣷⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣇⣿⣿⡏⣿⣿⣿⣿⣿⡀⢈⣿⣿⣧⣠⣤⣀⣀⣀⣀⡀⣠⣶⣶⣶⣶⣾⡿⠟

⠻⣏⣹⡄⠀⠀⢀⣤⣼⣭⡉⠉⠉⠉⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⠛⠛⢻⣿⡏⣿⣿⣷⣿⣿⣀⣀⣤⣤⣤⣿⣿⣇⣀⣿⣿⡿⣿⣿⡇⣿⣿⣇⣿⣿⣿⣿⣿⠇⢸⣿⣿⠛⣭⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⠋⠁⠀⠤

⢼⣿⣿⡿⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⣿⡇⢻⣿⣿⢾⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⠋⠙⣿⣿⣟⡉⣿⣿⣇⣿⣿⣧⣿⣿⠏⣿⣿⢹⣿⣿⢀⣜⣻⣿⣀⣛⣻⣿⣿⣿⣿⠋⣄⣀⣀⣀⣀⣀⣠⣤

⠀⣻⣿⡇⠀⢸⣿⣿⡿⠿⠋⠀⠀⠀⠛⠓⠘⣿⣟⡀⠙⠛⣿⣿⣿⣿⣿⣟⣛⠻⠛⠛⠋⣿⣿⠛⠛⠋⠀⣰⣿⣿⣿⡇⠛⢛⣻⠟⠛⠛⠛⣿⣿⣿⣿⣴⣛⣻⡟⠛⠛⠻⣿⡟⠛⠛⡛⠋⠁⣼⣿⣿⠿⠿⠻⠛⠛⠉

⣾⣿⣿⡇⠀⢸⣿⣿⠁⠠⠀⠀⠀⠠⣦⡀⠀⠈⠙⠿⣿⣶⡏⠙⠻⠿⠟⠋⠀⠀⣀⣠⣾⣿⣏⠀⠀⠀⣀⣿⣿⣿⣿⠗⠲⣦⣥⠐⠒⠒⠛⢉⣿⣿⠃⣿⣿⣿⣧⣄⣀⣤⣶⣿⣦⣤⣀⣀⠈⢋⣁⠀⠀⠀⠀⠀⠀⠠

⠑⠾⣿⣿⡿⢾⣿⡷⠶⠶⠶⠀⠀⠀⠹⣿⣦⣀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠗⠛⠛⠉⠉⠁⠘⣿⠄⢀⡞⠉⠀⣷⣿⣿⡇⠀⣬⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⢿⣿⡟⠀⠀

⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⡿⠋⠀⠀⠀⠀⠹⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣿⠁⠀⠀⠀⠀⠀⢠⡏⠉⠉⢿⣷⣦⣄⣀⣤⣾⣿⣿⠏⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣾⠁⠈⠀⠄⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⣀⣤⣿⣿⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⢳⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣾⡇⠀

⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣝⣟⠁⠀⠈⠙⢿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⢿⣿⣿⣿⡿⠿⠛⠩⣶⣾⠃⠀

⣤⣶⡾⠿⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣠⣶⠟⠙⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠘⠶⠿⠛⠛⠋⠉⠀⢀⣠⣶⣿⣿⠀⠀

⣿⠉⠀⠀⣿⣀⣀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡃⠀⠀⢿⣿⣦⣤⣴⣿⣇⣀⣠⣄⣤⣤⡴⣶⣿⣿⣿⣿⠿⣿⣿⣷⣶⢶⣮⠟⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⣠⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀

⣿⣷⣶⣶⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⡏⢙⣻⣿⣷⣾⣶⣿⣿⣿⣿⣿⣛⣟⡉⣽⣷⣶⣦⣻⣿⠿⣿⣿⣿⡀⢹⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢎⣩⣿⣿⣿⣿⣿⣿⡿⠛⣡⡞⠀

⠛⢿⢿⡿⠋⠁⠀⠀⠀⠀⠉⠉⠙⣋⠉⠙⠄⠀⠀⠀⣿⡟⣩⣿⢻⡿⠿⣿⡿⣿⣿⣿⡿⠛⣿⣽⣷⣴⣿⣻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⢻⠿⣿⣭⡴⠖⣿⣿⣧

⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣥⣼⣷⣾⠀⠀⠀⠀⠸⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠟⠿⠿⣿⣽⣛⣤⣤⢤⠶⣶⣿⣿⣿⣦⣄⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠉⠉⠉⠀⠀⣿⣿⠙

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣟⣿⣿⣿⣶⣦⠀⣶⣶⣿⣷⣶⠙⢿⣷⣿⣾⡟⠉⢁⣀⠤⣄⣉⠀⠀⠀⠀⠀⠀⠉⣀

⣠⣴⣦⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣻⣿⣶⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⢀⠀⣹⣿⣿⣤⣤⣄⣀⣀⣀⣀⢀⣴⣶⣶⣶⣶⡿⠟

⠟⢿⡉⣦⠀⠀⠀⣠⣤⣿⡋⠉⠉⠉⣿⣿⣿⣿⣿⢸⣿⣿⢺⣿⣿⠛⠻⢿⣿⡏⣿⣿⠻⣿⣿⣀⣀⣀⣤⣤⣿⣿⣇⡀⣿⣿⡿⣿⣿⣏⣿⣿⣇⣿⣿⣿⣿⣿⠸⠀⣿⣿⡟⢫⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠠

⠤⣾⣿⣿⠇⠀⣼⣿⣿⣿⣿⡆⠀⠀⣿⡇⢻⣿⣿⢾⣿⣿⣸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠋⠉⣿⣿⣟⡏⣿⣿⣧⣿⣿⣇⣿⣿⠟⣿⣿⣿⣿⣿⢀⣀⣛⣿⣇⣘⣛⣿⣿⣿⣿⡟⢡⣀⣀⣀⣀⣀⣀⣤

⠀⠘⣿⣿⠀⠀⣻⣿⣿⡿⠟⠁⠀⠀⠛⠓⠈⢻⣿⣀⠙⠛⢻⣿⣿⣿⣿⣿⣛⡻⠟⠛⠋⢹⣿⡟⠛⠋⠀⢀⣻⣿⣿⣿⠛⠛⣻⡿⠛⠛⠛⢻⣿⣿⣿⣷⣛⡛⣼⠛⠛⠛⢿⣿⠛⠛⢻⠛⠉⢠⣿⣿⡿⠿⠟⠟⠛⠋

⣶⣾⣿⣿⠀⠀⣽⣿⡟⠀⠄⠀⠀⠀⣰⣆⠀⠀⠉⠻⣿⣶⣿⠙⠛⠿⠿⠛⠁⠀⠀⣀⣴⣿⣿⠁⠀⠀⠀⣸⣿⢿⣿⡿⠦⢤⣬⡄⠒⠒⠒⠋⣹⣿⡿⢹⣿⣿⣿⣤⣀⣠⣴⣶⣷⣤⣄⣀⡀⠙⣉⡀⠀⠀⠀⠀⠀⠀

⠘⠆⢿⣿⣿⢷⣿⣿⠷⠶⠶⠀⠀⠀⠘⢿⣶⣄⡀⠀⠀⠙⣻⣿⣿⣿⣶⠷⠾⠛⠛⠉⠉⠀⢻⣧⠀⣠⠟⠁⣶⣾⣿⣿⠀⢀⣩⡄⠠⠶⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣇⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠿⣿⣿⠂⠀

⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⡏⠀⠀⠀⠀⠀⠀⣼⠉⠈⠹⣿⣶⣤⣀⣠⣴⣿⣿⡿⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢧⠀⠀⠀⠀⠀⣰⡏⠀⠁⠠⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣠⣾⣿⣷⣤⣴⣷⣾⣿⣿⣿⣿⣿⣿⠟⡆⠀

⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⠀

⠀⠀⠀⢹⣿⣿⠿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣬⣻⡋⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⣿⣿⡿⣿⣻⣿⣿⠿⠛⠋⣽⣾⡟⠀

⣤⣴⣶⠿⢿⠁⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣤⡾⠋⢻⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣦⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠳⠿⠟⠛⠛⠉⠁⠀⣀⣴⣿⣿⡇⠀

⣿⡏⠁⠀⢸⣇⡀⣀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⠁⠀⠸⣿⣦⣤⣤⣾⣿⣀⣠⣄⣤⣤⡴⣶⣾⣿⣿⣿⠿⣿⣿⣿⣶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀

⣿⣷⣶⣦⣾⣿⣿⡏⠀⠀⢀⣶⣿⣿⣿⣦⠀⠀⠀⠀⢸⣈⣻⣿⣿⣶⣷⣾⣿⣿⣟⣿⣟⣟⡉⣽⣷⣶⣦⣻⣿⢟⣿⣿⣿⡀⢹⣿⣿⣿⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠰⣁⣽⣿⣿⣿⣿⣿⣿⠟⢉⣴⠃

⠻⠿⣿⣿⡟⠉⠁⠀⠀⠀⠘⠉⠙⢛⡉⠉⠣⠀⠀⠀⢾⣿⣩⣽⢻⡿⠿⣿⡿⢿⣿⣿⡿⠛⣿⣽⣷⣴⣿⣻⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⡿⢿⣯⣥⠶⢻⣿⣿

⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⣤⣿⣾⠇⠀⠀⠀⠸⣿⣾⣿⣾⣿⣷⣿⣷⣿⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⣇⠸⣿⠟⠿⠿⣻⣿⣟⣤⣤⢤⠶⢶⣿⣿⣿⣷⣄⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⡈⠁⠀⠁⠀⣸⢿⡏

⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣿⠁⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣹⣿⣿⣶⣦⠀⣶⣶⣿⣿⣶⠈⠻⣿⣿⣿⣿⠋⠉⣀⠤⠤⣀⡁⠀⠀⠀⠀⠀⠈⢀

⣀⣠⣴⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣬⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣛⣿⣷⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⡷⣿⣿⡇⣿⣿⣿⣿⣿⠘⡀⢈⣿⣿⣧⣤⣤⣀⣀⣀⣀⡀⣤⣶⣶⣶⣶⣾⠿

⡿⢻⡛⢱⡄⠀⠀⢀⣠⣬⣟⠉⠉⠉⣿⣿⣿⣿⣿⢸⣿⣿⢺⣿⣿⠛⠛⢻⣿⡏⣿⣿⠙⣿⣿⠀⣀⣀⣠⣤⣿⣿⣇⣀⣿⣿⣿⣿⣿⣇⣿⣿⡇⣿⣿⣿⣿⣿⠸⠇⢸⣿⣟⠋⣭⣿⣿⣿⣿⣿⣿⡿⡿⠟⠛⠋⠁⠀

⣤⢼⣿⣿⡿⠀⢠⣿⣿⣿⣿⣷⠀⠀⣿⡇⢻⣿⣿⠻⣿⣿⣼⣿⣿⣿⣿⣾⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⠋⠉⣿⣿⣿⣟⣿⣿⣧⣿⣿⣇⣿⣿⠗⣿⣿⣿⣿⣿⢀⣀⣈⣻⣿⣀⣛⣻⣿⣿⣿⣿⠋⣤⣀⣀⣀⣀⣠⣤

⠀⠀⢻⣿⡇⠀⢘⣿⣿⡿⠿⠏⠀⠀⠛⠓⠘⠛⣿⣄⠙⠛⠻⣿⣿⣿⣿⣿⣟⣻⠟⠛⠛⠉⣿⣿⠛⠋⠀⠀⣛⣿⣿⣿⡟⠛⢻⣿⠟⠛⠛⠋⣿⣿⣿⣿⣛⣛⣸⡟⠛⠛⠻⣿⡟⠛⠻⡟⠋⠀⣼⣿⣿⠿⠟⠛⠛⠛

⢲⣶⣿⣿⡇⠀⢸⣿⣿⢃⡀⠀⠀⠀⢠⣶⡀⠀⠈⠙⢿⣷⣾⡏⠛⠻⠿⠟⠋⠀⠀⢀⣠⣾⣿⣏⠀⠀⠀⢀⣿⣿⣿⣿⠗⠤⣤⣅⠐⠒⠒⠚⢉⣿⣿⠋⣿⣿⣿⣧⣄⣀⣤⣶⣾⣦⣤⣀⣀⠈⢋⣁⠀⠀⠀⠀⠀⠀

⠀⠿⠺⣿⣿⣷⢾⣿⡿⠶⠶⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠈⢛⣿⣿⣿⣷⡶⠶⠾⠛⠋⠉⠁⠘⣿⡄⢀⡴⠋⠠⣾⣼⣿⡇⠀⣈⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⢿⣿⡇⠀

⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠀⠀⠀⠀⢹⣿⢿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣷⡄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⣿⠀⠀⠀⠀⠀⠀⢸⡏⠁⠉⢿⣷⣦⣤⣠⣴⣾⣿⣿⠏

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡄⠀⠀⠀⠀⢀⣿⠀⠈⠀⠌⣿⣿⣿⣿⣿⣿⣿⡇⠀

⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣀⣼⣿⣿⣦⣤⣾⣶⣿⣿⣿⣿⣿⣿⡿⢳⠀

⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⡆

⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣨⢟⣟⠀⠀⠉⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢹⣷⣿⠀

⣠⣤⣴⡾⢿⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⣀⣠⣾⠟⠹⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠚⠾⠿⠛⠛⠉⠀⠀⢀⣤⣾⣿⣿⠀

⣿⣿⠉⠀⠀⣿⣀⢀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡃⠀⠀⣿⣷⣤⣤⣴⣿⣇⣠⣄⣤⣤⡴⣶⣾⣿⣿⣿⡿⣿⣿⣿⣷⣶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⣠⣤⣶⣿⣿⣿⣿⣿⣿⠀

⣿⣿⣶⣦⣴⣿⣿⣿⠁⠀⠀⣰⣾⣿⣿⣷⡄⠀⠀⠀⠀⣇⣙⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣟⡉⣽⣷⣶⣦⣻⣿⠟⣿⣿⣿⣄⢹⣿⣿⣿⣿⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢌⣼⣿⣿⣿⣿⣿⣿⡿⠋⣡⡞

⠛⠿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠋⠉⠛⡋⠉⠛⠄⠀⠀⢸⣿⣩⣭⢫⣿⠿⣿⡿⢿⣿⣿⡿⠛⣿⣿⣷⣴⣿⡻⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣛⠿⣿⣥⡴⠞⣿⣿

⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⢶⣤⣼⣶⡾⠀⠀⠀⠸⡟⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠟⠿⠿⣛⣿⣿⣥⣤⢤⠶⠶⣿⣿⣿⣷⣦⣄⣀⡀⠀⢀⣀⣠⣤⣀⣀⣀⠉⠀⠀⠀⠀⡿⣿

⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⣾⡇⣶⣶⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣧⣰⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣶⣿⣾⣷⠀⠙⢿⣿⣿⣿⡟⠉⠁⡤⠤⠤⣈⠀⠀⠀⠀⠀⠀⠁

⣄⣀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣙⣻⣥⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⢿⢃⠀⣹⣿⣿⣤⣤⣄⣀⣀⣠⣄⢠⣶⣶⣶⣶⣶⡿

⣿⠟⢟⢛⣧⠀⠀⠀⣀⣠⣿⡋⠉⠛⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⣿⠛⠛⢻⣿⡿⣿⣿⠙⣿⣿⡄⣀⣀⣀⣤⣿⣿⣇⣀⣿⣿⣷⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⠸⠿⠀⣿⣿⡟⢩⣽⣿⣿⣿⣿⣿⣿⢿⠿⠛⠛⠁⠀

⣯⣠⣾⣾⣿⡇⠀⣴⣿⣿⣿⣿⡄⠀⣿⡇⢻⣿⣿⠻⣿⣿⣼⣿⣿⣿⣾⣿⣿⡿⢿⣿⣧⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⠷⣿⣿⣿⣿⣿⠀⣀⣐⣙⣿⣇⣘⣛⣿⣿⣿⣿⠟⢡⣄⣀⣀⣀⣠⣤

⠁⠀⠘⣿⣿⠀⠀⣿⣿⣿⡿⠿⠁⠀⠛⠓⡘⠛⢻⣧⡙⠛⠛⢻⣿⣿⣿⣿⣿⣻⡟⠛⠛⠋⢻⣿⡟⠋⠀⠀⢛⣻⣿⣿⣿⠛⠻⣿⡿⠛⠛⠋⢸⣿⣿⣿⣟⣛⣐⣿⠛⠛⠛⠻⣿⠛⠻⠿⠙⠁⣠⣿⣿⡿⠿⠛⠛⠋

⠲⣶⣾⣿⣿⠀⠀⣿⣿⡟⣀⠀⠀⠀⠀⣼⣆⠀⠀⠉⠿⣷⣶⣯⠛⠛⠿⠿⠟⠃⠀⠀⣀⣴⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠢⢤⣬⡄⠒⠒⠒⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣴⣶⣷⣤⣤⣀⡀⠙⣉⡀⠀⠀⠀⠀⠀

⠀⠞⢷⣿⣿⣷⠆⣾⣿⠷⠶⠀⠄⠀⠀⠘⢿⣦⣀⠀⠀⠀⠙⣻⣿⣿⣿⣶⠶⠲⠞⠛⠉⠉⠈⢻⣧⠀⣠⠟⠁⣼⣷⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠛⠛⠻⢿⣿⡇

⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡿⣿⡟⠁⠀⠀⠀⠀⢻⣿⢿⣧⡀⠀⠀⠀⠀⠀⢀⣿⣷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣷⡟⠀⠀⠀⠀⠀⠀⢸⠏⡀⠙⢿⣷⣦⣤⣤⣴⣿⣿⡿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡵⡀⠀⠀⠀⠀⢠⣿⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⡆

⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣠⣼⣿⣿⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⡟⣷

⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿

⠀⠀⠀⠀⠉⣿⣿⣿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⢛⡛⠀⠀⠉⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡿⢿⣿⡿⣿⣻⣿⣿⡿⠟⠛⢹⣷⡿

⣀⣀⣤⣤⣶⣿⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⢀⣠⣶⠟⢸⣿⡄⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠿⠛⠉⠉⠀⠀⢀⣴⣾⣿⣷

⣿⣿⣿⠋⠀⠀⣷⡀⠀⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠃⠀⠀⣿⣷⣤⣤⣴⣿⣧⣄⣤⣤⡴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⡿

⢻⣿⣿⣶⣦⣴⣿⣿⣿⠁⠀⠀⣰⣶⣿⣷⣶⡀⠀⠀⠀⢀⣇⣛⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡉⣽⣷⣶⣦⣻⣿⠟⢿⣾⣿⣿⣽⣿⣿⣿⣿⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣨⣿⣿⣿⣿⣿⣿⠟⠋⣴

⡘⠻⠿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠛⠛⠛⡋⠉⠳⠀⠀⢸⠹⣿⣭⢩⣿⠿⣿⡿⢿⣿⣿⣿⡟⣿⣿⣷⣴⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣛⣿⣿⣥⡶⠞⣿

⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣤⣽⣶⡾⠀⠀⠸⡆⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⠁⣿⣯⣿⡉⢻⣿⣿⡇⠹⣿⠝⠿⠿⣻⣙⣿⣿⣥⢤⠶⠖⠛⣿⣿⣷⣶⣦⣄⣄⠀⠀⣀⣀⣤⣤⣀⣀⣀⠁⠀⠀⠀⢀⠿

⣷⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠙⣷⣶⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣷⣦⠀⣶⣶⣼⣶⣿⣿⡄⠙⢿⣿⣿⣿⡏⠉⠠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀

⠯⣀⢀⣠⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣷⣿⣿⢸⣿⣿⢸⣿⣿⣜⣻⣭⣿⣿⣿⣷⠖⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡏⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢁⠀⣹⣿⣿⣤⣤⣄⣀⣠⣤⣄⣠⣶⣶⣶⣶⣶

⣴⣿⡿⣟⠛⣄⠀⠀⠀⢀⣀⣟⡛⠛⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⣿⠙⠛⢻⣿⡿⣿⣿⠉⣿⣿⣦⣀⣀⣀⣀⣿⣿⣧⣄⣿⣿⣷⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠙⡿⠿⠀⣿⣿⡛⢩⣽⣿⣿⣿⣿⣿⣿⢿⠿⠛⠋⠁

⣿⣏⣀⣼⣽⣿⡆⠀⣼⣿⣿⣿⣿⡄⣿⡇⢻⣿⣿⣹⣿⣿⣼⣿⡿⣼⣶⣾⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⣧⣿⣿⢹⣿⣿⢀⣀⣀⣐⣙⣿⣇⣘⣻⣿⣿⣿⣿⠟⢡⣀⣀⣀⣤⣤

⣿⠁⠀⠘⣿⣿⠀⠀⣿⣿⣿⣿⠿⠁⠛⠃⠘⠛⠛⢻⣿⡛⠛⠛⣹⣿⣿⣿⣿⣿⣟⣛⠛⠛⠛⢻⣿⡏⠀⠀⠛⢛⣻⣿⣿⣿⠃⠸⣿⡿⠛⠋⠀⢻⣿⣿⣿⣛⣘⣛⣿⠛⠛⠛⠻⣿⠃⠻⠿⠉⠁⣠⣿⣿⠿⠿⠛⠛

⣿⠶⣶⣶⣿⣿⠀⠀⣿⣿⡟⢀⠀⠀⠀⠀⣼⡅⠀⠀⠙⠿⣷⣶⣿⠛⠛⠿⡿⠟⠃⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣸⡿⢿⣿⡿⠲⢤⣬⡀⠒⠒⠒⠋⣹⣿⡿⢹⣿⣿⣿⣤⣀⣤⣴⣶⣷⣤⣤⣀⣀⠉⣁⡀⠀⠀⠀⠀

⡿⠆⠺⣿⢿⣿⣷⠶⣿⣿⢷⠀⠀⠄⠀⢀⠙⢻⣦⣀⠀⠀⠀⠙⣻⣿⣿⣷⣶⠶⠶⠖⠛⠛⠋⠈⢻⡇⠀⣠⠞⠁⣴⣽⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡵⡀⠀⠀⠀⠀⣠⣿⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠉⣿⣿⣿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⢛⡛⠀⠀⠉⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⡿⣿⣻⣿⣿⡿⠟⠛⢹⣷⡿

⣀⣀⣤⣤⣶⣿⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⢀⣠⣶⠟⢺⣿⡄⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠿⠛⠉⠉⠀⠀⢀⣴⣾⣿⣷

⣿⣿⣿⠋⠀⠀⣷⡀⠀⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠃⠀⠀⣿⣷⣤⣤⣴⣿⣧⣄⣤⣤⡴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠟⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⣠⣴⣶⣿⣿⣿⣿⣿⡿

⢻⣿⣿⣶⣦⣴⣿⣿⣿⠁⠀⠀⣴⣶⣿⣿⣶⡀⠀⠀⠀⢀⣇⣛⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡉⣽⣷⣶⣦⣻⣿⠟⢿⣾⣿⣿⣹⣿⣿⣿⣿⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣬⣿⣿⣿⣿⣿⣿⠟⠋⣴

⡘⠻⠿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠛⠛⠛⡋⠉⠳⠀⠀⢺⠹⣿⣭⢩⣿⠿⣿⡿⢿⣿⣿⣿⡟⣿⣿⣷⣴⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣻⣿⣿⣥⡶⠞⣿

⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣽⣶⡾⠀⠀⠸⡆⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⠁⣿⣯⣿⡉⢻⣿⣿⡇⠹⣿⠝⠿⠿⣻⣙⣿⣿⣥⢤⠶⠖⠛⣿⣿⣷⣶⣦⣄⣄⡀⠀⣀⣀⣤⣤⣀⣀⣀⠉⠀⠀⠀⢀⠿

⣷⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠙⣷⣶⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣷⣦⠀⣶⣶⣼⣷⣿⣿⡄⠙⢿⣿⣿⣿⡟⠉⠀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀

⠿⣄⢀⣠⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣧⣿⣿⢸⣿⣿⢸⣿⣿⣘⣛⣭⣿⣿⣿⣷⠖⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡏⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢁⠀⣹⣿⣿⣤⣤⣄⣀⣠⣤⣄⣠⣶⣶⣶⣶⣶

⣴⣿⡿⣟⠛⣄⠀⠀⠀⢀⣠⣿⡛⠛⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⣿⠙⠓⢻⣿⡿⣿⣿⠉⣿⣿⣦⣀⣀⣀⣀⣿⣿⣧⣄⣿⣿⣷⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠙⡿⠿⠀⣿⣿⡛⢩⣽⣿⣿⣿⣿⣿⣿⢿⠿⠛⠋⠁

⣿⣏⣀⣼⣽⣿⡆⠀⣼⣿⣿⣿⣿⡄⣿⡇⢻⣿⣿⣹⣿⣿⣼⣿⡿⣿⣶⣾⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⣧⣿⣿⢹⣿⣿⢀⣀⣀⣐⣙⣿⣇⣘⣻⣿⣿⣿⣿⠟⢡⣄⣀⣀⣤⣤

⣿⠁⠀⠘⣿⣿⠀⠀⣿⣿⣿⣿⠿⠁⠛⠃⠘⠛⠛⢻⣿⡛⠛⠛⣹⣿⣿⣿⣿⣿⣞⣛⠛⠛⠛⢻⣿⡏⠀⠀⠛⢛⣻⣿⣿⣿⠃⠸⣿⡟⠛⠋⠀⢻⣿⣿⣿⣛⣘⣛⣿⠛⠛⠛⠻⣿⠃⠻⠿⠉⠁⣠⣿⣿⡿⠿⠛⠛

⣿⠶⣶⣶⣿⣿⠀⠀⣿⣿⡟⢀⠀⠀⠀⠀⢼⡄⠀⠀⠙⠿⣷⣶⣯⠛⠛⠿⠿⠟⠃⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣸⣿⢿⣿⡿⠲⢤⣬⡀⠒⠒⠒⠋⣹⣿⡿⢹⣿⣿⣿⣤⣀⣤⣴⣶⣷⣤⣤⣀⣀⠉⣁⡀⠀⠀⠀⠀

⡿⠆⠺⣿⢿⣿⣷⠶⣿⣿⢧⠀⠀⠄⠀⠀⠙⢿⣦⣀⠀⠀⠀⠙⣻⣿⣿⣷⣶⠶⠶⠖⠛⠛⠋⠈⢻⣇⠀⣠⠞⠁⣶⣽⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠘⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢠⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⡇⠀⠀⠀⠀⠀⠀⣼⠋⡀⠙⢿⣷⣦⣤⣤⣶⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣰⡟⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣀⣠⣾⣿⣿⣦⣴⣿⣾⣿⣿⣿⣿⣿⣿⡏

⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢘⢛⡟⠀⠈⠙⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⡿⠿⣿⣻⣿⣿⠿⠋⠋⢸⣷

⣀⣀⣀⣀⣤⣴⣿⡏⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⣀⣶⠟⢺⣿⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣴⠦⠾⣖⣛⡋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠞⠟⠛⠉⠁⠀⢀⣠⣴⣾⣿

⣿⣿⣿⣿⠋⠀⠀⣧⠀⠀⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⠃⠀⠘⣿⣧⣤⣤⣴⣿⣇⣤⣤⡴⣶⣶⣓⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿

⢈⣿⣿⣿⣤⣄⣤⣿⣿⣿⠁⠀⠀⣰⣶⣶⣶⣦⡀⠀⠀⠀⣀⣇⣻⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⣽⣷⣶⣦⣻⣿⠟⢿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣎⣼⣿⣿⣿⣿⣿⣿⠟⠉

⠆⠘⠻⣿⣿⣿⣿⠟⠉⠁⠀⠀⠘⠛⠛⠛⡛⠙⢣⠀⢸⠉⣹⣯⢩⣿⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣇⢸⡇⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣛⣟⣿⣵⠶⠛

⣀⠀⠀⢀⠃⠈⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣹⣦⣾⠀⠸⡆⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⡿⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣻⣻⣯⣿⢤⠶⠖⠛⠛⣿⣿⢷⣶⣦⣄⣄⡀⠀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀

⣿⣷⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣶⣿⠉⣿⣷⠀⣴⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣿⣧⠀⣶⣶⡄⣶⣶⣿⣿⡄⠙⢿⣿⣿⣿⡏⠉⠠⠤⠤⠤⣀⠀⠀⠀⠀⠀

⠿⢿⣁⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣻⣯⣿⣿⣿⣿⠷⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣷⣿⣿⣿⣿⣿⢀⠀⣻⣿⣿⣤⣤⣤⣤⣤⣤⣄⣠⣶⣿⣿⣶

⢀⣰⣿⡿⣟⠟⣄⠀⠀⠀⢀⣀⣿⠛⣿⣿⣿⣿⣿⣾⣿⣿⢻⣿⣿⠈⠙⢻⣿⡿⣿⣿⠉⣿⣿⢷⣦⣀⡀⣀⣿⣿⣧⣤⣿⣿⣇⣿⣿⡿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⡿⠿⠀⣿⣿⡛⣩⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉

⣿⣿⣏⣀⣼⣾⣿⡆⠀⣰⣿⣿⣿⣿⣿⡇⢻⣿⣿⠸⣿⣿⣾⣿⣿⠀⣶⣾⣿⣿⣿⣿⣇⣿⣿⣶⣿⣿⠿⠟⣿⣿⡏⢻⣿⣿⡏⣿⣿⣧⣿⣿⣇⣿⣿⢻⣿⣿⣟⣁⣀⣀⣔⣙⣿⣇⡙⢿⣿⣿⣿⣿⠟⣡⣄⣀⣠⣤

⣿⣟⠁⠀⠹⣿⣿⠁⠀⣻⣿⣿⣿⡿⠛⠃⠘⠛⠛⠀⢿⣿⡛⠛⠋⣿⣿⣿⣿⣿⣿⣛⣻⠿⠟⠛⢻⣿⡇⠀⠛⠛⢃⣾⣿⣿⣿⠈⠛⣿⡿⠋⠀⠛⢻⣿⣿⣿⣟⣛⣛⣿⠛⠛⠛⠻⣧⠀⠹⠿⠉⠁⣠⣿⣿⠿⠟⠛

⣿⣿⠶⣤⣴⣿⣿⠀⠀⣿⣿⡟⢀⡀⠀⠀⠀⢸⡄⠀⠈⠙⢿⣶⣦⣞⠛⠛⠿⡿⠟⠋⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠶⢤⣭⡀⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣤⣴⣶⣷⣤⣤⣀⣀⠉⣁⡀⠀⠀⠀

⣿⣿⠲⣿⠟⢿⣿⣶⠶⣿⣿⣃⠀⠤⠄⠀⠀⡙⣿⣦⡀⠀⠀⠈⠛⢿⣾⣿⣶⣶⠶⠶⠶⠛⠛⠋⠈⢻⡇⠀⣠⠞⠁⣶⣼⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠛⠻⣿

⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⡿⢿⡿⠀⠀⠀⠀⠀⠀⠀⢻

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⡿⠋⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣼⣿⠁⠀⠀⠀⠀⠀⢠⡟⢀⠈⠻⣿⣶⣦⣤⣴⣾⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⢀⣼⠇⠀⠀⠆⣹⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣠⣴⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡄⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡛⣻⠃⠀⠉⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⢿⣿⢿⢿⣿⣿⣿⡿⠛⠙⠁⣿

⡃⠀⠀⢀⣠⣤⣾⣿⠋⠀⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢀⣠⡾⠓⣿⡆⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣴⡦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⠻⠛⠋⠉⠁⠀⣀⣤⣾⣿

⣻⣿⣿⣿⡟⠋⠀⢸⡆⠀⠀⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⡟⠀⠀⢻⣿⣤⣤⣤⣾⣿⣤⣤⡴⣶⣶⡒⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣶⣾⣿⣿⣿⣿

⠀⣹⣿⣿⣧⣤⣀⣼⣿⣷⡏⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⣀⣸⣘⣿⣿⣷⣶⣶⣾⣿⣿⣟⣿⣿⣷⣶⣦⣻⣿⠟⢿⣿⣿⡚⢿⣿⣿⣷⣿⡿⣿⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣡⣿⣿⣿⣿⣿⣿⡿⠋

⠰⠀⠻⢿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠚⠛⠛⠟⠛⠛⠄⢺⠉⣩⣿⣭⣧⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣯⣿⣷⣾⣿⣿⣿⣿⡀⣿⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣻⣻⣯⣶⠞

⣄⡀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣈⣶⣴⡇⠸⡆⣾⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣛⣟⣾⣽⣿⠶⠖⠛⠛⢹⣿⣿⣶⣶⣤⣠⣀⠀⢀⣠⣤⡤⢤⣀⣀⡀⠀⠀⠀⠀

⣿⣿⣶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠉⣾⣿⠀⣴⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣾⣯⡄⣶⣶⡄⣶⣾⣿⣿⣧⠈⠻⣿⣿⣿⣿⠉⠁⠤⠤⠤⠤⡀⠀⠀⠀⠀

⠿⢿⣏⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣻⣮⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣿⣿⣿⡟⣿⣿⣧⣿⣿⣿⣿⣿⡏⡀⢈⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣴⣿⣿⣿

⠀⢀⣼⣿⢿⡿⢣⡀⠀⠀⠀⣀⣸⡿⣿⣿⣿⣿⣿⢾⣿⣿⢻⣿⣿⠈⠈⢻⣿⡿⣿⣿⠟⣿⣿⠳⣶⣄⡀⢀⣿⣿⣧⣤⣿⣿⣇⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⢸⣿⣟⠋⣼⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉

⣿⣿⣿⣇⣀⣷⣾⣷⠀⢀⣾⣿⣿⣿⣿⡇⢻⣿⣿⠸⣿⣿⣾⣿⣿⡀⢰⣾⣿⣿⣿⣿⡇⣿⣿⣤⣿⣿⣿⠿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣧⣿⣿⣇⣿⣿⢾⣿⣿⣿⣋⣀⣀⣀⣊⣻⣿⡀⠻⢿⣿⣿⣿⡿⠋⣤⣀⣠⣤

⢿⣿⡟⠉⠈⢻⣿⡟⠀⢸⣿⣿⣿⣿⠟⠃⠘⠛⠛⠀⠙⣿⣟⠛⠙⠛⣿⣿⣿⣿⣿⣟⣛⡿⠟⠛⠛⣿⣿⠀⠛⠛⠃⣰⣿⣿⣿⡏⠛⢟⣿⠏⠀⠛⠛⣿⣿⣿⣿⣛⣛⣻⡟⠛⠛⠛⢿⣆⠈⠛⠏⠉⢀⣼⣿⡿⠿⠛

⣿⣿⣿⣤⣤⣼⣿⡇⠀⠘⣿⣿⡏⢀⠀⠀⠀⢀⣼⠀⠀⠉⠻⣷⣶⣴⡟⠛⠻⣿⠿⠟⠁⠀⠀⣠⣾⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠤⣤⣥⠐⠒⠒⠚⢉⣿⣿⠋⣿⣿⣿⣧⣄⣠⣴⣶⣾⣶⣤⣤⣀⡈⢉⣠⠀⠀⠀

⣿⣿⡷⣾⠿⢿⣿⣿⡶⠶⣿⣿⢀⠁⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠉⠻⣷⣿⣷⣶⣶⠶⠶⠞⠛⠛⠉⠙⣿⡄⢀⡴⠋⠁⣧⣿⣿⡇⠀⣈⣥⠀⠤⢶⣶⣾⣿⣿⣾⣧⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠁⢸⣿⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠛⠛⢿

⠀⠀⣀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⠟⠛⠛⢿⡿⠿⣟⡃⠀⠀⠀⠀⠀⠀⢸

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⠟⠁⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣸

⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣾⡇⠀⠀⠀⠀⠀⠀⣾⠁⡀⠙⢿⣿⣦⣤⣤⣾⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣰⡏⠁⠀⠰⢈⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣤⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⣘⢛⡟⠀⠉⠙⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⡿⣿⣯⣿⣿⠻⠋⠋⢸

⢣⠀⠀⠀⣀⣠⣼⣿⡟⠁⠈⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⣠⣴⠟⢾⣷⠀⠀⠀⠀⣻⡗⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠞⠟⠛⠉⠁⠀⢀⣠⣴⣿

⠛⣿⣿⣿⣿⠟⠁⠉⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠃⠀⠸⣿⣦⣤⣤⣴⣿⣥⣤⡴⣶⣶⡒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣴⣶⣿⣿⣿⣿

⠀⢙⢿⣿⣿⣤⣄⣠⣿⣷⣾⠁⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⣀⣀⣗⣻⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣻⣿⠟⢿⣿⣿⡈⢿⣿⣿⣷⣾⡿⢿⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣼⣿⣿⣿⣿⣿⣿⠟

⠀⠄⠘⠿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠰⠟⠛⠿⠛⠛⢧⢺⠉⣩⣽⣯⣧⠘⣿⡿⣿⣿⣿⡿⣿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣯⣿⡷⣾⣿⣿⣿⣿⣇⢼⡇⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣛⣟⣫⣵⡶

⣤⡀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣀⣳⣤⣾⠸⡆⣾⣿⣿⣿⣷⣿⣧⣼⣿⣿⣿⣿⣿⣯⣿⡍⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣛⣿⣼⣯⣿⠶⠖⠛⠛⠙⣿⣿⣷⣶⣦⣤⣄⡀⠀⣀⣤⣤⠤⣄⣀⣀⠁⠀⠀⠀

⣿⣿⣧⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠋⣾⣿⡇⣴⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⡿⣶⣯⣵⣶⣶⡄⣶⣶⣿⣿⣿⡄⠙⢿⣿⣿⣿⠏⠉⠠⠤⠤⠤⣄⠀⠀⠀⠀

⠿⢿⣟⡁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣫⣤⣿⣿⣿⣿⣾⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣇⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣀⠀⣽⣿⣿⣤⣤⣤⣤⣤⣤⣄⣠⣾⣿⣿

⠀⠀⣠⣿⡿⡿⠿⡄⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⢾⣿⣿⢿⣿⣿⠈⠀⢻⣿⡿⣿⣿⡿⣿⣿⠓⣶⣦⡀⠀⣿⣿⣧⣤⣿⣿⣇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣿⣿⡛⣠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋

⣿⣿⣿⣟⠀⣹⣶⣿⡆⠀⣰⣿⣿⣿⣿⡇⢻⣿⣿⠸⣿⣿⣿⣿⣿⣀⠀⣾⣿⡿⣿⣿⡧⣿⣿⣤⣿⣿⣿⠿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⢼⣿⣿⣿⣟⣁⣀⣀⣔⣙⣿⣇⠙⠿⣿⣿⣿⣿⠟⢡⣄⣠⣤

⠻⣿⣿⠋⠉⠹⣿⣿⠁⠀⣿⣿⣿⣿⣿⠃⠈⠛⠛⡀⠙⢿⣟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣓⣿⡿⠟⠛⢻⣿⡇⠛⠛⠃⢀⣿⣿⣿⣿⠛⠻⣿⡿⠀⠛⠛⢸⣿⣿⣿⣛⣛⣛⣿⠛⠛⠛⠻⣧⡀⠙⠿⠉⠁⣰⣿⣿⠿⠟

⣾⣿⣿⣧⣤⣤⣿⣿⠀⠀⣿⣿⣿⠁⢀⠀⠀⠀⣼⡇⠀⠈⠛⢿⣶⣤⣿⠛⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⢿⣿⡿⠦⢤⣭⡀⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣤⣶⣶⣷⣦⣤⣀⣀⠉⣁⡀⠀⠀

⣿⣿⣿⣾⠿⢿⢿⣿⣶⠶⣿⣿⠇⣉⣀⣀⠀⠀⣹⣿⣦⡀⠀⠀⠈⠛⣿⣾⣷⣶⣶⣶⠶⠶⠞⠛⠋⠉⢿⣇⠀⣠⠞⠉⣸⣽⣿⣿⡀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣿⣷⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠙⢻

⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⣿⠿⢟⣛⠀⠀⠀⠀⠀⠀⠀

⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡟⣿⡟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀

⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣷⣿⠀⠀⠀⠀⠀⠀⢰⡇⢀⠈⠻⣿⣷⣦⣤⣶⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⠀⠀⠀⠀⢀⣿⠀⠀⠀⠆⣻⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣼⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠇⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⡻⡻⠃⠈⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⢿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁

⠻⠄⠀⠀⢀⣀⣠⣿⣿⠋⠀⠙⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢀⣤⡿⠳⣿⡆⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣦⡾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠉⠀⢀⣀⣤⣿

⠛⢿⣿⣿⣿⡿⠋⠉⢹⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡏⠀⠀⢿⣷⣤⣤⣤⣾⣯⣤⡴⣶⣶⡒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣴⣤⣤⣾⣿⣿⣿⣿

⠀⠘⠻⣿⣿⣧⣤⣀⣼⣿⣶⡏⠀⠀⢀⣴⣶⣶⣦⡄⠀⠀⣀⣀⣘⣸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣻⣿⠟⢿⣾⣿⡀⢻⣿⣿⣷⣾⣿⠻⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⣿⣿⣿⣿⣿⣿⡿

⠀⠠⠀⠿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠾⠛⠛⠿⠛⠻⣾⠉⣩⣭⣿⣷⠈⣿⡿⢿⣿⣿⣿⢿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣯⣿⣷⢾⣿⣿⣿⣵⣿⡠⣿⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⣛⣧⣶

⣦⣄⠈⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣘⣦⣴⡽⡆⣾⣿⣾⣿⣿⣿⣷⣬⣿⣿⣷⣿⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠟⠿⠿⣛⣛⣻⣧⣿⣽⠷⠖⠛⠛⠙⢲⣿⣿⣶⣶⣤⣤⣀⠀⣀⣠⣤⡤⠤⢄⣠⡀⠀⠀⠀

⣿⣿⣿⣴⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠛⣿⣿⢿⣴⣷⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣰⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣾⣩⣶⣶⡄⣶⣶⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠉⠀⠤⠤⠤⠤⡀⠀⠀⠀

⠿⠿⣿⣋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⣼⣿⣿⢸⣿⣿⣘⣋⣤⣿⣿⣿⣿⣾⣿⣿⠙⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣗⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⣀⣴⣿⣿

⠀⠀⠀⣼⣿⣿⠿⢧⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⣿⣿⢾⣿⣿⠉⠀⢸⣿⡿⣿⣿⡿⣿⣿⠛⣲⣶⣄⠀⣿⣿⣇⣤⣿⣿⣇⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣹⣿⣿⣻⠟⠃⢸⣿⣟⠃⣼⣿⣿⣿⣿⣿⣿⡿⠿⠛

⣿⣿⣿⣿⡏⢈⣷⣾⣷⠀⢀⣾⣿⣿⣿⣧⢻⣿⣿⠸⣿⣿⣻⣿⣿⣄⡀⣸⣿⡿⣿⣿⡿⣿⣿⣤⣿⣿⣿⡿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣟⣿⣿⣇⣿⣿⢼⣿⣿⣿⣿⣋⣀⣀⣠⣊⣻⣿⡄⠛⢿⣿⣿⣿⡿⢋⣤⣠⣤

⠘⢿⣿⡟⠉⠉⢿⣿⡟⠀⢸⣿⣿⣿⣿⡟⠈⠛⠛⢀⠙⠻⣿⡛⠉⠛⢻⣿⣿⣿⣿⣿⣗⣿⣿⠿⠛⠋⣿⣿⠛⠛⠃⠀⢻⣿⣿⣿⡟⠛⢟⣿⠇⠛⠛⠀⣿⣿⣿⣟⣛⣛⣻⡟⠛⠛⠛⢿⣆⠈⠛⠏⠉⢀⣾⣿⠿⠟

⣰⣿⣿⣿⣤⣤⣼⣿⡇⠀⠸⣿⣿⡏⠀⡀⠀⠀⢀⣧⠀⠀⠙⠻⣷⣦⣼⡟⠻⢻⣿⡿⠟⠁⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠤⣤⣅⠐⠒⠒⠋⢉⣿⣿⠃⣿⣿⣿⣧⣄⣠⣴⣶⣾⣶⣶⣤⣄⡈⢉⣤⠀⠀

⣿⣿⣿⣿⠟⢿⠏⣿⣿⣾⠶⣿⣿⠉⣁⣀⡀⠀⢈⣿⣷⣄⠀⠀⠀⠙⠻⣷⣶⣶⣶⣶⡶⠶⠾⠛⠛⠉⠙⣿⡄⢀⡴⠋⢁⣦⣿⣿⣇⡀⣈⣥⠀⠤⢶⡶⣾⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⠁⢸⣿⣆⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠙

⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣛⡃⠀⠀⠀⠀⠀⠀

⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡟⣿⠟⠁⠀⠀⠀⠀⢹⣿⢻⣿⣄⡀⠀⠀⠀⠀

⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⡟⠀⠀⠀⠀⠀⠀⣸⠇⢀⠈⠻⣿⣷⣶⣴⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡄⠀⠀⠀⠀⣠⣿⠀⠀⠀⠂⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠜⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣤⣼⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠇⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣻⠻⠉⠉⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠿⣿⣿⣯⣿⣿⠟⠛⠉

⢻⠿⠀⠀⠀⠀⣀⣠⣿⣿⠋⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢀⣴⡟⢻⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠀⢀⣠⣤

⣿⠾⣿⣷⣾⣿⡿⠋⠉⢻⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⡏⠀⠀⣿⣧⣤⣤⣤⣾⣧⡴⣶⣶⡓⢛⣿⣽⣿⣿⣿⣿⢿⣿⣿⣿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡴⣦⣶⣿⣿⣿⣿

⠁⠀⠜⢻⣿⣿⣇⣀⣀⣼⣷⣶⡞⠀⠀⢀⣤⣶⣶⣦⡀⠀⣀⣀⣀⣬⣽⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⠟⢿⣾⣿⡁⢹⣿⣿⣷⣾⡿⢹⢻⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣧⣿⣿⣿⣿⣿⣿

⠀⠀⠠⠁⠿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠾⠿⠻⠿⠛⢿⡉⣩⣭⢩⣿⡠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣻⣿⣾⣿⣏⣿⣧⢿⣿⣿⣿⣷⡴⣿⡸⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢟⡛⢵

⣀⣦⡄⠈⠀⠀⠨⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣄⣘⣦⣼⡇⣾⣿⣾⣿⣿⣿⣗⣾⣿⣿⣧⣶⣿⣿⣿⡍⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣛⣛⣿⣧⣿⣿⠷⠛⠛⠙⠀⢴⣿⣿⣶⣶⣤⣤⣀⠀⣀⣤⣤⠤⠤⠤⢤⡀⠀⠀

⣿⣿⣿⣷⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⣶⣶⠛⣾⣿⠛⣿⣷⣿⣿⡿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⣿⣷⣶⡄⣶⣶⢰⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠁⠀⠤⠤⠤⠤⠀⠀⠀

⠿⠿⢿⣿⡟⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⣷⣿⣿⠸⣿⣿⣿⣿⣤⡀⢨⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣶⣿

⡀⠀⠀⠀⣽⣷⣿⡿⢷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠉⠀⢸⣿⡟⣿⣿⡿⣿⣿⠋⣑⣲⣦⣄⣿⣿⣇⣀⣿⣿⣇⣿⣿⣧⣿⣿⡷⣿⣿⣿⣿⣿⣀⣽⣿⣿⠿⠟⠃⢸⣿⣟⠃⣼⣿⣿⣿⣿⣿⣿⡿⠿

⣿⣿⣶⣿⣿⡏⢈⣷⣾⣷⠀⢀⣴⣿⣿⣿⣿⣿⣿⠸⣿⣿⣹⣿⣿⣤⣀⣸⣿⡿⣿⣿⣷⣿⣿⣀⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⣸⣿⣿⢁⣿⣿⣃⣀⣀⣠⣊⡻⣿⡄⠛⢿⣿⣿⣿⡿⢋⣤⣤

⠀⠘⣿⣿⡟⠉⠙⢿⣿⡟⠀⢸⣿⣿⣿⣿⡟⠛⠛⠀⢙⠛⠻⣿⡁⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⠛⠃⠀⠛⣻⣿⣿⣿⡟⠛⢿⣿⠛⠛⠀⠛⣿⣿⣿⣿⣛⣛⣻⡟⠛⠃⠙⢿⣆⠀⠛⠏⠁⢀⣾⣿⠿

⣤⣠⣾⣿⣷⣤⣀⣼⣿⡇⠀⠸⣿⣿⡏⠁⠀⠀⠀⢠⣟⠀⠀⠙⠻⣷⣦⣼⡿⠿⢿⣿⡿⠟⠀⠀⠀⣀⣾⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠤⣤⣥⠐⠒⠒⠋⢩⣿⣿⠃⣿⣿⣿⣧⣄⣠⣴⣶⣾⣶⣶⣤⣤⡈⢉⣤⠀

⢰⣿⣿⣿⡿⢿⠿⠻⣿⣷⣾⢀⣿⣿⠉⣉⣀⡀⠀⠈⣿⣧⣄⠀⠀⠈⠙⢿⣷⣶⣶⣶⣶⣶⠶⠶⠛⠛⠉⠹⣿⡄⢀⡴⠋⢡⣾⣿⣿⣇⡀⣈⣥⠀⠤⢶⡶⣾⣿⣿⣿⣧⢸⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣯⠁⢸⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

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

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

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

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

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⡿⠛⠙⠛⢿⣿⣛⣛⠀⠀⠀⠀⠀⠀

⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⢻⡿⠋⠀⠀⠀⠀⠈⣿⡟⢿⣧⣀⠀⠀⠀⠀

⣴⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⣿⠁⠀⠀⠀⠀⠀⢀⡿⠀⡀⠙⣿⣿⣶⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⢀⣼⡇⠀⠀⡐⢸⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣠⣴⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣻⢿⠏⠉⠉⠛⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⢿⣿⣿⣽⣿⠿⠛⠋

⣛⡿⢇⠀⠀⠀⠀⣀⣼⣿⡟⠉⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⣠⣾⠟⣿⣧⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠈⠀⠀⣀⣤

⣿⡿⠿⣷⣶⣿⣿⠟⠉⠉⣇⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠁⠀⢸⣿⣦⣤⣤⣴⣿⡶⣶⣶⡓⢛⣟⢉⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣦⢶⣴⣾⣿⣿⣿

⡟⠁⠀⠛⢿⣿⣿⣀⡀⣀⣿⣶⣶⠃⠀⠀⣠⣴⣶⣦⣄⠀⣀⣀⣀⣠⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⠟⢿⣾⣿⡋⢹⣿⣿⣷⣾⡿⠈⣿⣿⡆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠰⠿⠿⠿⠟⢻⢏⣩⣭⢩⣿⣧⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣻⣿⣾⣿⣏⣿⡧⣼⣿⣿⣿⣿⣦⢾⣇⣿⡇⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⣟⠿

⣀⢠⣤⠈⠀⠀⠉⠝⠙⠋⠀⠀⠀⠀⠀⢀⢀⣠⣀⣳⣼⣮⣾⣿⣾⣿⢿⣿⣷⣸⣿⣿⣧⣴⣿⣿⣿⡏⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣿⣿⢼⣿⡿⠛⠛⠙⠀⠀⣾⣿⡷⣶⣦⣤⣤⣀⢀⣠⣤⡤⠤⠤⠤⣤⠀⠀

⣿⣿⣿⣿⣦⣤⡴⠀⠀⠀⠀⠀⠀⠀⣶⣶⡙⣶⣿⠙⣿⣿⣿⣿⡿⣿⡿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⢸⣿⣶⡄⣶⣶⠀⣼⣿⣿⣿⡄⠉⢿⣿⣿⣿⠏⠀⠠⠤⠶⠤⠤⠀⠀

⠾⠿⠿⣿⣿⠃⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣷⣿⣿⠀⢿⣿⣿⣿⣷⣄⠀⡽⣿⣿⣦⣤⣤⣤⣤⣤⣤⣰⣾

⣀⡀⠀⠀⢈⣿⣶⣿⡿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠉⠀⢸⣿⡟⣿⣿⡿⣿⣿⠋⣉⣒⣶⣦⣿⣿⣇⣀⣿⣿⣧⣿⣿⡇⣿⣿⡿⣿⣿⣿⣿⣿⢀⣬⣿⣿⣟⠿⠛⠀⣿⣯⡟⢠⣿⣿⣿⣿⣿⣿⣿⠻

⣿⣿⣷⣶⣿⣿⠁⢹⣦⣿⡆⠀⢠⣾⣿⣿⣿⣿⣿⠸⣿⣿⣸⣿⣿⣤⣄⣸⣿⡿⣿⣿⣷⣿⣿⣄⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡿⣿⣿⣏⣿⣿⣧⣿⣿⣸⣿⣿⢋⣹⣿⣟⣁⣀⣀⣔⡙⢿⣧⡘⠻⣿⣿⣿⣿⠟⣡⣦

⠉⠀⢻⣿⣿⠟⠉⠹⣿⣿⠇⠀⣿⣿⣿⣿⣿⠛⠛⠀⠙⣛⠛⢿⣇⠈⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡟⠃⠀⠛⢛⣿⣿⣿⣿⠛⠻⣿⡟⠛⠀⠛⢻⣿⣿⣿⣟⣛⣛⣿⠛⠃⠈⠻⢷⡄⠘⠻⠉⠁⣠⣿⡿

⣤⣄⣰⣿⣿⣧⣄⣠⣿⣿⠀⠀⢹⣿⣿⠁⠁⠀⠀⠀⣸⡇⠀⠈⠛⢿⣶⣤⣿⠿⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠦⢤⣬⡄⠒⠒⠚⠉⢹⣿⡿⢸⣿⣿⣿⣶⣀⣤⣶⣾⣿⣶⣶⣤⣄⠉⢡⣤

⠀⣾⣿⣿⣿⢿⠿⠿⢿⣿⣷⡆⢸⣿⡏⠉⣁⣀⡀⠀⢹⣿⣦⡀⠀⠀⠉⠻⣿⣶⣶⣶⣶⣶⣶⠶⠞⠛⠛⠉⢻⣧⠀⢠⠞⠉⢼⣾⣿⣿⣀⢀⣩⡄⠠⠴⣶⢶⣿⣿⣷⣿⣌⢿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⡍⠀⢸⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⠟⠉⠉⢻⣿⣟⣛⡃⠀⠀⠀⠀⠀

⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⡿⣿⣄⡀⠀⠀⠀

⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⡇⠀⠀⠀⠀⠀⠀⣼⠃⠄⠈⢻⣿⣷⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⣰⣿⠀⠀⢀⢀⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣄⣤⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠁⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠿⠉⠉⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⠿⠟⠋

⣙⣿⣿⡀⠀⠀⠀⢀⣠⣿⡿⠋⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⢀⣴⡿⢸⣿⡀⠀⠀⠀⢹⡷⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣾⣶⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⢀⣠

⣿⣿⢿⣿⣶⣾⣿⡿⠋⠉⣻⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡿⣾⣿⠏⠀⠀⣿⣧⣤⣄⣤⣾⡷⣶⣶⡓⢛⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣴⣶⣶⣿⣿⣿

⣼⠋⠀⠜⣿⣿⣿⣅⣀⢀⣿⣷⣶⡞⠀⠀⢀⣤⣴⣶⣤⡀⣀⣀⣀⣀⣦⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⠟⢿⣾⣿⡊⢹⣿⣿⣿⣾⡿⠈⢹⣿⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿

⡇⠀⠀⢄⠁⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠾⠿⠿⠿⢿⠿⣩⣭⢩⣶⣷⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡧⣼⣿⣿⣿⣿⣶⣶⣿⣿⡟⠀⢳⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⢝⡟

⣃⣀⣄⡀⠁⠀⠈⠹⠋⠛⠁⠀⠀⠀⠀⠀⣀⣀⣄⣱⣾⣶⣿⣿⣾⣿⢿⣿⣧⣎⣿⣿⣧⣤⣿⣿⣿⡏⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣿⣿⢷⣿⣿⠛⠛⠙⠀⠀⣾⣿⣿⢶⣶⣤⣤⣄⣀⣠⣤⣤⠤⠤⠤⠤⡄⠀

⢻⣿⣿⣿⣷⣤⣤⠇⠀⠀⠀⠀⠀⠀⣶⣶⢸⣶⣾⠋⣿⣿⣿⣿⡿⣿⡿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣿⣷⣆⣶⣶⠀⢰⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠁⠀⠤⠒⠒⠤⠄⠀

⠶⢿⡿⣿⣿⠟⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣏⣿⣿⣸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣤⡀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣶

⣄⡀⠀⠀⠀⣹⣷⣾⡿⢇⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠊⠀⢸⣿⡟⣿⣿⡿⣿⣿⠟⣊⣓⡶⣦⣿⣿⣇⣀⣿⣿⣧⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣿⣿⣿⠿⠟⠃⢸⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⠿

⣿⣿⣷⣶⣾⣿⡏⢈⣷⣾⣧⠀⢀⣴⣿⣿⣿⣿⣿⠸⣿⣿⣸⣿⡿⣦⣄⣸⣿⡿⣿⣿⣷⣿⣿⣄⣿⣿⣥⣿⣿⣿⡿⠟⣿⣿⡿⣿⣿⣟⣿⣿⣧⣿⣿⣸⣿⣿⢚⣁⣿⣿⣋⣀⣀⣠⣊⠻⣿⣄⠻⢿⣿⣿⣿⡿⢃⣶

⠈⠁⠘⣿⣿⡿⠋⠙⢿⣿⡟⠀⢸⣿⣿⣿⣿⡟⠛⠀⠙⢛⡛⠻⣷⡀⠙⠛⢛⣿⣿⣿⣿⣿⣟⣿⣿⠿⠟⠛⣿⣿⠃⠀⠛⠛⣻⣿⣿⣿⡟⠋⢿⣿⠛⠀⠛⠛⣿⣿⣿⣟⣛⣛⣻⡟⠋⠀⠙⠿⣆⠈⠛⠏⠉⢀⣾⣿

⣤⣤⣠⣾⣿⣿⣀⣀⣸⣿⡇⠀⢸⣿⣿⡏⠉⠀⠀⠀⢀⣿⠀⠀⠙⢿⣶⣦⣼⡿⠿⢿⣿⡿⠟⠁⠀⠀⣠⣾⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠦⣬⣅⠐⠒⠒⠋⢉⣿⣿⠃⣿⣿⣿⣷⣆⣠⣴⣶⣿⣷⣶⣦⣤⡀⠉⣤

⠉⢷⣿⣿⣿⣿⠟⢿⠿⣿⣷⣬⠀⣿⣿⠁⣉⣀⡀⠀⠘⣿⣧⣀⠀⠀⠈⠙⢿⣷⣶⣶⣶⣶⣶⡶⠾⠛⠛⠋⠹⣿⡄⠀⡴⠋⢱⣶⣿⣿⣇⠀⣬⣥⠀⠴⢶⠶⣾⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⣿⣿⣛⣛⠀⠀⠀⠀⠀

⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⡿⢿⣦⣀⡀⠀⠀

⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⠀⠀⠀⠀⠀⠀⢠⡏⠠⠀⠙⣿⣿⣶⣶

⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣀⣾⡇⠀⢀⡂⣸⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣴⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡟⠁⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿⠿⠏⠉⠉⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⣿⣿⣛⣿⣿⡿⠿⠛

⢙⣻⣿⡇⠀⠀⠀⠀⣀⣼⣿⠟⠉⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⣠⣾⠓⣿⣇⠀⠀⠀⠈⣿⠆⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣾⣶⣟⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⣀

⢸⣿⡾⣿⣶⣶⣾⣿⠟⠋⢛⡆⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⡿⠁⠀⢸⣿⣤⣄⣤⣼⣿⣶⣶⡓⢛⣟⠉⣽⣿⣿⣿⣿⣿⢿⣿⣿⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⢶⣶⣾⣿⣿

⢠⡟⠁⠈⠻⣿⣿⣧⣀⡀⢸⣿⣦⣶⠃⠀⠀⣠⣤⣴⣤⣄⣀⣀⣀⣀⣼⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⢿⣾⣿⡀⢹⣿⣿⣿⣿⡿⠀⢹⣿⣿⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⣾⣿⣿⣿⣿

⣿⠀⠀⠀⡈⠸⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠰⠿⠿⠿⢿⠿⣯⣭⢩⣦⢸⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡇⢼⣿⣿⣿⣿⣷⣶⢾⣿⣿⠃⢷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣿

⣿⣀⣠⣀⠀⠀⠀⠉⠟⠛⠋⠀⠀⠀⠀⠀⢀⢀⣠⡈⣾⣦⣾⣿⣾⣿⢿⣿⣧⣸⣿⣿⣧⣤⣿⣿⣿⡟⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣿⣿⠿⢾⣿⡟⠛⠙⠀⠀⠠⣿⣿⡷⢶⣶⣤⣤⣀⣀⣤⣤⠴⠦⠤⠤⠤⠀

⠹⣿⣿⣿⣷⣆⣤⡴⠀⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠛⣿⣿⣿⣿⡿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣾⣿⡴⣶⣶⠀⠀⣾⣿⣿⣿⡄⠉⢿⣿⣿⣿⠏⠀⠀⠒⠒⠒⠤⠀

⠶⠾⣿⣿⣿⣿⠋⠀⠀⡀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣇⣿⣿⣷⣿⣿⠀⠀⢿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣶⣶⣦⣤⣤⣶⣦⣴

⣄⣀⠀⠀⠈⢉⣷⣶⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡌⠀⢸⣿⡇⣿⣿⡔⣿⣿⡿⣒⣙⡲⢶⣿⣿⡇⢀⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠉⢀⣬⣿⣿⡟⠿⠛⠀⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⡿

⣿⣿⣿⣶⣶⣿⣿⠁⢹⣤⣿⡄⠀⣠⣿⣿⣿⣿⣿⠸⣿⣿⣸⣿⡿⢶⣤⣼⣿⡿⣿⣿⣷⣿⣿⣧⣿⣿⣥⣼⣿⣿⡿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣯⣿⣿⣸⣿⣿⢖⣋⣸⣿⣟⣁⣀⣀⡔⡹⠿⣧⡘⠻⣿⣿⣿⡿⠏⣰

⠀⠉⠁⢻⣿⣿⠟⠋⠻⣿⣿⠇⠀⣟⣻⣿⣿⣿⠛⠀⠙⠛⣻⠛⢿⣆⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡇⠀⠛⠛⢃⣿⣿⣿⣿⠋⠹⣻⡟⠀⠛⠛⢸⣟⣿⣿⣛⣛⣛⣿⠃⠀⠈⠻⠷⡄⠘⠛⠁⠀⣰⣿

⣀⣤⣄⢴⣿⣿⣆⣀⣀⣿⣿⠀⠀⣻⣿⣿⠋⠁⠀⠀⠀⣸⡇⠀⠈⠛⣷⣦⣤⣿⠿⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠦⢤⣬⡄⠒⠒⠚⠉⣹⣿⡟⣸⣿⣿⣿⣶⣤⣴⣶⣿⣿⣷⣶⣤⣤⠀⢡

⠉⠗⣿⣿⣿⣿⠟⠻⡿⢿⣿⣧⡆⢸⣿⡏⢈⣁⣀⠀⠀⢻⣿⣄⠀⠀⠀⠉⠻⣿⣶⣶⣶⣦⣶⡶⠶⠞⠛⠛⠉⢻⣧⠀⢠⠞⠉⣴⣾⣿⣿⣀⢀⣭⡄⠠⠶⡶⢶⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡅⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⠟⠉⠉⠙⣿⣟⣛⣭⠀⠀⠀⠀

⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣿⠽⠿⣦⣄⡀⠀

⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠠⠀⠙⣿⣿⣷

⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣠⣿⡀⠀⢀⣃⣸⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⢈⣿⢿⠏⠉⠙⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠹⣿⣿⣿⣯⣿⡿⠟

⠙⢛⡻⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠋⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⣠⡾⠇⣿⡆⠀⠀⠀⠈⣿⠂⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣾⣶⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠁⠀⠀⢀

⠀⢸⣿⡿⣾⣶⣶⣶⣿⡿⠋⢻⡆⠀⠀⠀⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⣶⣿⡿⠁⢀⣻⣿⣤⣤⣤⣾⣿⣶⡓⢛⣟⠉⣭⣵⣿⣿⣿⣿⠿⢿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⢶⣶⣾⣿

⠀⢰⡟⠁⢈⠿⣿⣿⣯⣀⠀⢸⣷⣤⡴⠂⠀⠀⣀⣤⣤⣤⣄⣀⣀⣀⣤⣴⠼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣿⣿⣿⠀⢸⣿⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣾⣿⣿⣿

⢀⣾⠀⠀⠀⡘⢹⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⢸⠿⠿⣿⠿⣿⣯⢩⡦⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡇⢘⣿⣿⣿⣿⣿⣷⣶⣿⣆⣿⢷⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽

⢸⣿⢀⣠⣀⠀⠂⠈⠉⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣸⣦⣾⣿⣾⣿⢷⣿⣿⣬⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣴⣾⠿⠿⢾⣿⡟⠙⠀⠀⠀⢰⣿⣿⡿⢿⣶⣤⣤⣀⣀⣤⣴⠶⠲⠦⠤⠤

⠀⠻⣿⣿⣿⣷⣆⣀⣰⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠻⣿⣿⣿⣿⡿⣿⡿⠿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣾⣯⣶⣶⠀⠀⢀⣾⣿⣿⣿⡄⠈⢻⣿⣿⣿⠃⠀⠐⠒⠒⠒⠤

⠒⣶⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣋⢤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣯⣄⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶

⣦⣄⣀⠀⠀⠈⢉⣳⣶⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣉⡄⢸⣿⡇⣿⣿⠴⣿⣿⣷⣿⣚⠚⠲⣿⣿⡇⠀⣿⣿⣧⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⠈⠉⢠⣬⣿⣿⡿⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣷⣶⣶⣾⣿⠋⢹⣤⣿⡄⠀⣿⣿⣿⣿⣿⡸⣿⣿⣸⣿⡿⠻⢦⣼⣿⡿⢿⣿⣷⣿⣿⣶⣿⣿⣁⣠⣿⣿⣿⡿⣿⣿⡏⢿⣿⣿⣿⣿⣟⣿⣿⣸⣿⣿⢤⣖⣋⣸⣿⣏⣁⣀⣀⡜⡉⠿⣷⡈⠻⢿⣿⣿⡿⠟

⠀⠈⠉⠁⢻⣿⣿⠟⠒⠻⣿⣿⠇⠀⣛⣻⣿⣿⣿⠇⠙⠛⠛⣛⠁⢿⣄⠛⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡇⠛⠛⠃⢈⣿⣿⣿⣿⠀⠛⣻⡟⠛⠛⠐⢻⣿⣿⣿⣛⣛⣛⣿⠀⠀⠈⠛⠿⡄⠈⠛⠁⠀⣰

⣀⣀⣠⡄⣠⣿⣿⣆⣀⣀⣿⣿⠀⠀⢿⣿⣿⠋⠉⠀⠀⠀⣸⡇⠀⠘⠻⣷⣦⣤⣿⠿⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠖⢦⣬⡀⠒⠒⠛⠉⣹⣿⡟⣸⣿⣿⣿⣶⣤⣴⣶⣿⣿⣷⣶⣤⣤⠀

⠙⠟⠻⣿⣿⣿⣿⠻⠿⡿⢿⣿⣇⡆⢸⣿⡏⠐⢉⣀⠀⠀⢻⣿⣄⠀⠀⠀⠉⠻⣿⣶⣶⣶⣤⣤⠶⠶⠞⠛⠛⠉⢿⣧⠀⢠⠞⠉⣼⣼⣿⣿⡀⢠⣭⣄⠐⠶⠶⢶⣿⣿⡿⣿⣄⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⣿⣟⣛⣭⠀⠀⠀⠀

⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣿⠿⠿⣦⣄⡀⠀

⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠙⣿⣿⣷

⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⣠⣿⡇⠀⢀⣃⣸⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⢈⣿⢿⠏⠉⠙⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣿⣻⣯⣿⡿⠿

⠙⢛⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠋⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣠⡾⠇⣿⡆⠀⠀⠀⠈⣿⠆⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣾⣶⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⢀

⠀⢸⣿⡿⣾⣶⣶⣶⣿⡿⠋⢻⡆⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣶⣿⡟⠁⢀⣻⣿⣤⣤⣤⣾⣿⣶⡓⢛⣟⠉⣭⣵⣿⣿⣿⣿⠿⢿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⢶⣶⣾⣿

⠀⢸⡟⠁⢈⠿⣿⣿⣯⣀⠀⢸⣷⣤⡴⠂⠀⠀⣀⣤⣤⣤⣄⣀⣀⣀⣤⣼⠼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣿⣿⣿⠀⢸⣿⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣾⣿⣿⣿

⢸⣿⣀⣠⣀⠀⠂⠈⠉⡟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⣹⣦⣾⣿⣾⣿⢷⣿⣿⣬⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣴⣿⢿⠿⢾⣿⡟⠙⠀⠀⠀⢰⣿⣿⣿⢿⣶⣤⣤⣀⣀⣤⣴⠶⠲⠦⠤⠤

⠀⠻⣿⣿⣿⣷⣆⣀⣰⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠻⣿⣿⣿⣿⡿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣾⣯⣶⣶⠀⠀⢀⣾⣿⣿⣿⣄⠉⢻⣿⣿⣿⠃⠀⠐⠒⠒⠒⠢

⠒⣶⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣋⢤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣤⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶

⣦⣄⣀⠀⠀⠈⢉⣳⣶⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣉⡀⢸⣿⡇⣿⣿⡴⣿⣿⣷⣿⣚⡚⠲⣿⣿⡇⠀⣿⣿⣧⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⠈⠉⢡⣼⣿⣿⡿⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣷⣶⣶⣾⣿⠋⢻⣦⣿⡄⠀⣿⣿⣿⣿⣿⡸⣿⣿⣸⣿⡿⠻⢦⣼⣿⡿⢿⣿⣷⣿⣿⣶⣿⣿⣁⣠⣿⣿⣿⡿⣿⣿⡏⢿⣿⣿⣿⣿⣟⣿⣿⣸⣿⣿⢤⣖⣋⣸⣿⣏⣁⣀⣀⡜⡩⠿⣷⡘⠻⣿⣿⣿⡿⠟

⠀⠈⠉⠉⢿⣿⣿⠟⠒⠻⣿⣿⠇⠀⣛⣻⣿⣿⣿⠇⠙⠛⠛⣛⠁⢿⣄⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡇⠛⠛⠃⢈⣿⣿⣿⣿⠀⠛⣻⡟⠛⠛⠘⢻⣟⣿⣿⣛⣛⣛⣿⠀⠀⠈⠛⠿⡄⠘⠛⠁⠀⣰

⣀⣀⣠⡄⣤⣿⣿⣆⣀⣀⣿⣿⠀⠀⣿⣿⣿⠋⠉⠀⠀⠀⣸⡇⠀⠈⠻⣷⣦⣤⣿⠿⠿⣿⣿⠿⠋⠁⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠶⢦⣬⡀⠒⠒⠛⠉⣹⣿⡟⣸⣿⣿⣿⣶⣤⣴⣾⣿⣿⣷⣶⣤⣤⠀

⠙⠟⠻⣿⣿⣿⣿⠻⠿⡿⢿⣿⣇⡆⢸⣿⡟⠒⣉⣀⠀⠀⢻⣿⣄⠀⠀⠀⠉⠻⣿⣶⣶⣶⣦⣦⣶⠶⠞⠛⠛⠉⢿⣧⠀⢠⠞⠉⣽⣽⣿⣿⣄⢠⣭⣄⠐⠶⠶⢶⣿⣿⣿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⣿⣟⣫⣭⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⡟⣿⠏⠀⠀⠀⠀⠀⠘⡿⠿⠿⣦⣄⡀

⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⣸⡇⠠⠀⠙⣿⣿

⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣠⣿⡀⠀⢀⣃⣼⣿

⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣾⣿⣿⣿⣷⣿⣿⣿⣿

⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿

⠘⣿⣿⣿⣿⡟⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠀⠀⢘⣿⢿⠏⠉⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣻⣿⣾⠿

⠀⠙⠻⢿⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠛⠻⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⣠⡾⠧⣿⡆⠀⠀⠀⠘⣿⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⢀

⠀⠀⢸⣿⣿⣷⣦⣤⣶⣾⡿⠛⢻⡄⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢶⣶⣾⡿⢁⣀⣿⣷⣤⣤⣴⣾⣿⡗⢛⣟⠉⣭⡥⣶⣿⣿⣿⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣷⣶⣾

⠂⠀⢸⡿⠃⠙⢿⣿⣿⣏⠀⠀⢸⣷⣤⡴⠂⠀⠀⣀⣤⣤⣤⣀⣀⣀⣤⣤⢼⠾⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣷⣿⣿⣇⢸⣿⢙⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿

⠀⢀⣾⠁⠀⠀⠘⢹⣿⣿⣿⣷⣿⣿⠿⠃⠀⠀⢸⡿⢿⣿⣿⣿⣯⡦⠀⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⡇⢘⣿⣽⣿⣿⣾⣿⣿⣿⣿⣄⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣿⠀⣀⢀⠑⠀⠉⠛⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⣸⡖⣾⣿⣾⣿⢷⣿⡟⢿⣿⣿⣧⣤⣿⣯⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣤⣴⠿⠿⠿⢻⣿⡟⠀⠀⠀⠀⢰⣿⣿⣿⢿⣶⣴⣦⣀⣀⣤⡶⠶⠒⠖⠤

⠒⠊⢻⣿⣿⣿⣶⣄⣀⣰⠀⠀⠀⠀⣶⣶⠀⣶⣶⣟⣿⣿⣿⣿⡿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣶⣼⣿⣶⠀⠀⠀⢀⣿⣿⣿⣿⣄⠈⢻⣿⣿⣿⠃⠀⠐⠒⠒⠒

⠀⠰⣦⣽⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣿⣿⣇⣿⣿⢻⣿⣿⢸⣿⣿⣘⣋⢤⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣇⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⢁⠀⠀⠀⢿⣿⣿⣿⣿⣤⠀⣿⣿⣿⢶⣶⣶⣶⣶⣶

⣶⣤⣀⡀⠈⠀⠉⠙⣶⣴⣾⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣭⢀⣸⣿⡇⣿⣿⠽⣿⣿⣿⣷⣿⡒⠓⣿⣿⣇⠀⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⡠⠈⠉⢡⣼⣿⣿⡿⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿⣿

⠻⣿⣿⣿⣷⣦⣤⣾⣿⠋⢻⣥⣷⡄⣿⣿⣿⣿⣿⣾⣿⣿⣸⣿⡿⠉⠻⣾⣿⣿⣿⣿⣷⣿⣿⣦⣿⣿⠁⣀⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡏⣿⣿⣽⣿⣿⣠⣴⣒⣋⣸⣿⣟⣁⡀⢀⠜⡨⠿⣷⡈⠛⣿⣿⣿⡿

⠀⠀⠉⠉⠋⢻⣿⣿⡿⠒⢺⣿⣿⡇⠛⣛⣿⣿⣿⣿⠟⠛⠛⠛⢁⠀⣿⣟⠛⠻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⡟⠛⠃⠈⢛⣿⣿⣿⣿⠛⠛⣿⡟⠛⠘⠛⢻⣟⣿⣿⣛⣛⣣⣾⠀⠀⠀⠙⠿⡄⠘⠛⠁⠀

⠀⢀⣀⣀⡀⢨⣿⣿⣆⣀⣀⣿⣿⠀⠀⢿⣿⣿⠛⠉⠀⠀⠀⣰⡇⠀⠘⠿⣷⣦⣤⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠶⢦⣬⡄⠒⠒⠛⠉⣽⣿⡟⣸⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣶⣦⣤

⠛⠟⠻⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣧⡆⢸⣿⡟⠒⠊⠁⠀⠀⢹⣷⣄⠀⠀⠈⠉⠻⣿⣶⣶⣶⣤⣤⣤⡶⠾⠛⠛⠉⢻⣧⠀⢠⠞⠉⣾⣽⣿⣿⣄⢠⣭⣄⠠⠶⠶⢶⣿⣿⡿⣿⣄⢿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠋⠈⠉⢻⣿⣫⣭⡄⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢿⢹⡟⠁⠀⠀⠀⠀⠀⣿⠿⠿⢿⣦⣀

⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⢀⡿⠀⠄⠈⢻⣿

⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⣠⣼⣇⠀⠀⣈⣠⣿

⠀⢰⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢹⣿⣿⣿⣿⠛⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⢻⡿⡟⠉⠉⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⡿

⠀⠘⠛⠿⣿⣿⠀⠀⠀⠀⠀⢀⣿⡿⠛⠛⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣴⡿⢼⣧⠀⠀⠀⠀⣻⡗⠀⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⣿⣟⣿⣦⣤⣴⣶⣿⠟⠛⣧⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣶⣿⢋⣀⣸⣿⣦⣤⣴⣶⣿⡟⢛⣿⠉⣭⡥⣶⣾⣿⣿⣿⢿⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠾⣾⣿

⠐⠀⠀⣽⠟⠀⡻⣿⣿⣿⡁⠀⠀⣿⣦⣤⡖⠀⠀⢀⣠⣤⣤⣄⣀⣀⣤⣤⠴⡷⢿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣷⣾⡿⣿⣼⣿⠈⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿

⠀⠀⢰⡏⠀⠀⠈⠊⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⣿⣿⣿⣿⣿⢯⣦⠀⣶⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⡇⢘⣿⢽⣿⠿⣷⣿⣿⣿⡾⣧⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⡇⠀⡀⠈⠂⠈⠙⢻⠻⠿⠃⠀⠀⠀⠀⠀⠀⢸⡆⣾⣿⣾⣿⢷⣿⡇⢻⣿⣿⣧⣄⣿⣯⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣤⣤⠶⠿⠿⠛⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⡿⣿⣶⣶⣤⣀⣤⣴⠶⠒⠒⠒

⠒⠒⠛⢿⣿⣿⣷⣦⣀⣀⡆⠀⠀⠀⣶⣶⠀⣶⣶⢸⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⣄⣿⣷⢂⠀⠀⠀⣸⣿⣿⣿⣧⡀⠙⣿⣿⣿⡟⠀⠀⠒⠚⠒

⠀⠀⢶⣬⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣯⡀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠏⡀⠀⠀⠸⣿⣿⣿⣿⣦⡄⢸⣿⣿⣷⢶⣶⣶⣶⣶

⣷⣦⣄⡀⠈⠉⠉⠙⢳⣦⣴⣿⣧⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣭⡄⣸⣿⡇⣿⣿⠘⣿⣿⣿⣿⣾⡗⠚⣿⣿⣧⡄⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⠨⠄⠈⢁⣤⣽⣿⣿⠿⠛⠃⢸⣿⣯⠁⣾⣿⣿⣿⣿

⠻⢿⣿⣿⣿⣶⣤⣴⣿⡿⠉⣏⣽⣦⣿⣿⣻⣿⣿⣿⣿⣿⣸⣿⡟⠉⠛⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⠅⠀⣿⣿⣿⣿⣿⣿⡟⢿⣿⣟⣿⣿⣟⣿⣿⣽⣿⣿⣠⣤⣖⣊⣁⣿⣿⣋⡀⠀⣠⠃⠝⢿⣦⠙⢻⣿⣿⣿

⠀⠀⠈⠙⠛⠙⣿⣿⣿⠗⠒⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⠛⠛⠛⠁⡀⢸⣿⡛⠛⠟⢛⣿⣿⣿⣿⣿⣿⣾⣿⠻⠛⠛⣿⣿⠛⠃⠈⠛⣻⣿⣿⣿⡟⠛⢿⣿⠛⠘⠛⠛⣿⣻⣿⣿⣛⣳⣴⡇⠀⠀⠈⠻⢷⠀⠙⠋⠀

⠀⠀⢀⣀⣀⠀⣽⣿⣷⣀⡀⢸⣿⣏⠀⠸⣿⣿⡿⠋⠁⠀⠀⢀⣾⠀⠀⠛⢿⣶⣤⣼⡿⠿⢿⣿⣿⠿⠉⠀⠀⢀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⡗⠶⣤⣥⠐⠒⠛⠉⢉⣿⣿⢇⣿⣿⣿⣷⣶⣤⣶⣿⣿⣿⣿⣶⣶

⠙⠟⠻⣿⢿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣠⠀⣿⣿⠓⠒⠉⠀⠀⠘⣿⣧⡀⠀⠀⠉⠙⢿⣷⣶⣶⣦⣤⣤⣴⠶⠛⠛⠋⠙⣿⡄⠀⡴⠋⠁⣿⣾⣿⣧⡠⢬⣥⡀⠲⠶⠶⢾⣿⣿⠿⣷⡜⣿⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠁⠉⠙⣿⣯⣭⣧⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⡏⣿⠋⠀⠀⠀⠀⠀⢸⡿⠟⠿⣷⣤

⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠀⠀⠀⠀⠀⠀⣸⠇⠠⠀⠙⣿

⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⣀⣴⣿⡀⠀⣠⣅⣼

⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠸⣿⣿⣿⣿⡿⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠘⣿⢿⠋⠉⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿

⠀⠀⠛⠻⢿⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣠⡾⢷⣿⡄⠀⠀⠀⢸⣿⠂⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠁⠀⠀

⠀⠀⠂⢸⣿⣿⣷⣤⣤⣴⣶⡿⠛⢿⡀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣿⣿⣁⣠⣿⣷⣤⣴⣶⣾⡟⢛⣿⠉⣿⡥⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠷⣷⣿

⠀⠂⠀⢈⡿⠋⠙⣿⣿⣿⣏⠀⠀⢸⣧⣤⡴⠂⠀⠀⣀⣤⣤⣄⣀⣀⣤⣤⠴⢾⠾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠿⣿⣾⣿⡀⢹⣿⣿⣷⣾⡿⢿⣿⣿⠀⢙⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿

⠄⠀⢀⣾⠁⠀⠈⠺⣻⣿⣿⣿⣷⣿⣿⠿⠇⠀⠀⣸⣿⣿⣿⣿⢿⣧⠀⣶⡿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⡇⢘⣿⢹⣿⣿⢶⣿⣿⣿⡶⢿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⣿⠠⢀⠀⠁⠄⠙⠛⡿⠿⠟⠀⠀⠀⠀⠀⠀⠸⣦⣾⣿⣾⣿⢷⣿⡇⠙⣿⣿⣷⣤⣿⣯⣿⣯⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣤⣤⠴⠾⠿⠛⢻⣿⡏⠀⠀⠀⠀⢰⣿⣿⣿⢿⣷⣴⣦⣄⣠⣴⡶⠖⠒⠒

⠐⠦⠘⠿⣿⣾⣿⣶⡄⣀⣰⠀⠀⠀⣶⣶⠀⣶⣶⠘⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣶⡄⣾⣷⠖⡀⠀⠀⢀⣿⣿⣿⣿⣄⠈⢻⣿⣿⣿⠃⠀⠐⠚⠛

⠀⠀⠠⣤⣽⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⡿⣿⣿⠞⣿⣿⣟⣿⣿⣿⣅⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣷⣿⣿⡺⢁⠀⠀⠀⢿⣿⣿⣿⣷⣤⠀⣿⣿⣿⠶⣶⣶⣶⣶

⣿⣶⣤⣁⠀⠉⠉⠉⠛⢶⣤⣾⣷⡀⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣭⣤⢸⣿⡇⣿⣿⠀⣿⣿⣿⣿⣷⡿⠒⣿⣿⣷⣄⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⠀⠤⠈⠉⣠⣼⣿⣿⡟⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿

⠛⠿⣿⣿⣿⣶⣤⣤⣾⣿⠏⢻⣥⣷⣿⣟⢻⣿⣿⣿⣿⣿⣸⣿⡿⠈⠙⣿⣿⣿⣿⣿⡇⣿⣿⣶⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣿⣿⣿⣿⣹⣿⣿⢠⣤⣴⣒⣉⣸⣿⣟⣁⠀⢀⠞⡨⢻⣷⡌⠛⢿⣿⣿

⠀⠀⠀⠉⠛⠛⢻⣿⣿⡿⠖⢾⣿⣿⡟⠛⣟⣻⣿⣿⣿⡟⠛⠛⠁⢀⠀⣿⣟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣶⣿⡿⠟⠛⢻⣿⡟⠃⠈⠛⢛⣿⣿⣿⣿⠛⠸⣻⡟⠘⠛⠛⢻⣟⣿⣿⣟⣻⣦⣾⠀⠀⠀⠙⠻⡆⠈⠙⠁

⠀⠀⠀⢀⣀⡐⢨⣿⣿⣆⡀⠀⣿⣿⠀⠀⢿⣿⣿⠟⠉⠀⠀⠀⣸⡇⠀⠘⠻⣷⣦⣤⣿⠿⠿⣿⣿⡿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⠒⢦⣤⡄⠃⠛⠋⠉⣹⣿⡿⣸⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⣶

⠛⠟⠿⣿⠿⢿⣿⣿⣿⡿⠿⣿⢿⣿⣇⡄⢸⣿⡟⠒⠊⠁⠀⠀⢻⣷⣄⠀⠀⠈⠉⠻⣿⣴⣶⣶⣤⣤⣤⡶⠾⠛⠛⠉⢻⣧⠀⢠⠞⠉⢼⣿⣿⣿⣤⠤⣭⣄⠰⠶⠶⠶⣿⣿⡿⢿⣦⢻⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠈⠉⢿⣿⣭⣽⡀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⣿⡟⠁⠀⠀⠀⠀⠈⣿⠿⠻⣷⣦

⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⢠⡿⠀⠄⠈⢻

⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢀⣠⣾⣇⠀⢀⣌⣼

⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢿⣿⣿⣿⣿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⣿⡿⡟⠉⠙⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣿⣿⣿⣿⢿

⡇⠀⠘⠻⠿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠛⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⢀⣴⠿⣿⣧⠀⠀⠀⠈⣿⡆⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠉⠀⠀

⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣶⣾⠟⠻⣇⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⣾⣿⣏⣠⣼⣿⣤⣴⣶⣶⣿⢛⣿⠉⣽⡥⣶⣶⣿⣿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⢻⣾

⠀⠰⠀⠀⣿⠟⠋⢿⣿⣿⣿⡁⠀⠀⣿⣤⣤⠖⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⠴⠶⡿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡂⢹⣿⣿⣿⣾⡿⠿⣿⣿⠀⠈⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿

⠠⠀⠀⣰⡏⠀⠀⠑⢿⣿⣿⣿⣿⣾⣿⡿⠿⠀⠀⢀⣿⣿⣿⣿⢿⣧⠀⣶⡿⢿⣷⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡇⢘⣿⢹⣿⡽⡾⣾⣿⣿⣶⠾⣷⣸⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⡇⠀⡀⠈⠠⠈⠛⢻⠿⠿⠃⠀⠀⠀⠀⠀⠸⣄⣾⣿⣾⣿⢷⣿⡇⠈⣿⣿⣧⣦⣿⣯⣿⣯⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣭⣤⠴⠶⠿⠛⠛⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⡿⣿⣶⣶⣤⣀⣤⡶⠶⠒⠒

⠐⠢⠄⠻⣿⣿⣿⣷⣤⢀⣀⡇⠀⠀⣶⣶⠀⣶⣶⠀⣽⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣿⣵⢂⠀⠀⠀⣼⣿⣿⣿⣧⡄⠙⣿⣿⣿⡟⠀⠐⠒⠛

⡀⠀⠀⢤⣬⣿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣟⣋⣤⣿⣿⣿⣷⠚⣿⣿⣟⣿⣿⣷⣯⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣲⠏⡀⠀⠀⠸⣿⣿⣿⣿⣦⡄⣼⣿⣿⡷⢶⣶⣶⣶

⣿⣷⣤⣈⠁⠉⠉⠉⠛⠳⣤⣴⣾⣆⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣯⣤⣸⣿⡇⣿⣿⠀⣿⣿⣷⣾⣿⣾⠗⣿⣿⣷⣦⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⠀⠠⠄⠉⢁⣤⣿⣿⣿⠿⠛⠁⢸⣿⣯⢡⣾⣿⣿⣿

⠙⠻⣿⣿⣿⣷⣦⣤⣴⣿⡟⠙⣯⣽⣿⣿⢻⣿⣿⣿⣿⣿⣸⣿⡿⠈⠉⣻⣿⣿⣿⣿⡇⣿⣿⣦⣿⣿⣿⠄⣿⣿⣧⣿⣿⣿⡿⢿⣿⣏⣿⣿⣿⣿⣿⢹⣿⣿⢠⣤⣤⣖⣋⣀⣿⣿⣃⡀⠀⡰⢁⠹⣿⣦⠙⢻⣿⣿

⠀⠀⠀⠉⠛⠛⠻⣿⣿⣿⠷⠲⣿⣿⣿⠛⢸⣛⣿⣿⣿⡿⠛⠛⠁⠀⠀⢻⣟⡋⠛⠛⢓⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⢛⣿⣿⠃⠈⠛⠛⣻⣿⣿⣿⡟⠈⢛⡿⠛⠛⠛⢛⣿⣻⣿⣟⣻⣷⣴⡇⠀⠀⠈⠻⢧⠀⠉⠋

⠀⠀⠀⠀⢀⣀⢂⣹⣿⣷⡀⠀⢸⣿⡇⠀⢸⣿⣿⡿⠛⠁⠀⠀⢀⣾⠁⠀⠻⢷⣦⣤⣼⡿⠿⢿⣿⣿⠟⠉⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠗⠶⣤⣥⠐⠘⠛⠉⢉⣿⣿⢃⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣷

⠛⠟⠿⣿⠿⢿⣿⣿⣿⣿⠿⢿⡿⣿⣷⣰⠀⣿⣿⠓⠒⠁⠀⠀⠘⣿⣦⡀⠀⠀⠉⠹⢿⣧⣶⣶⣬⣤⣤⣴⠶⠟⠛⠋⠹⣿⡄⢀⡴⠋⢹⣿⣿⣿⣧⡤⢬⣥⡀⠲⠶⠶⣾⣿⣿⠿⣷⡜⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⢿⣯⣭⣽⡀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⠟⠛⣷

⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⢰⡏⠐⠄⠈

⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⢤⣿⣇⡀⢠⣬

⠀⠀⠀⣸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿

⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿

⣧⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠈⣿⣿⠏⠉⠙⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠛⣿⣿⣭⣿

⣿⡆⠀⠸⠿⣿⣿⣿⠀⠀⠀⠀⠀⢨⣿⡿⠟⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⢀⣾⠏⣿⣆⠀⠀⠀⠈⣿⢆⣀⣠⣤⣤⣤⠴⢶⣾⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡉⠁⠀

⣿⠀⠀⠀⠀⣶⣿⣿⣤⣤⣤⣶⣶⠿⠿⡇⠀⠀⠀⢻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⣿⣣⣄⣽⣿⣴⣶⣶⣿⣿⣿⠉⣿⡥⣶⣶⣶⣾⣿⣿⡿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⢻

⠏⠀⠰⠀⠀⣿⠟⠝⢿⣿⣿⣿⠁⠀⠀⣿⣄⣠⠔⠀⠀⢀⣀⣤⣄⣀⣤⣤⠴⠶⢾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡂⢹⣿⣿⣷⣿⡿⠜⢿⣿⡀⠈⡏⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿

⠀⠀⠀⠀⣰⡏⠀⠀⠁⢿⣿⣿⣿⣷⣾⣿⣿⠿⠀⠀⢺⣿⣿⣿⣿⣿⣦⣶⡿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠥⡼⡾⣾⣿⣿⣶⢿⣧⣺⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠀⠀⠰⣿⡇⠄⠀⠑⠬⠉⠛⢿⠿⠿⠃⠀⠀⠀⠀⢸⡆⣾⣿⣾⣿⣿⣿⡇⠈⣻⣿⣧⣆⣿⣯⣿⣯⣿⣿⣿⣿⢸⣿⠝⠿⠿⣛⣙⣛⣴⣬⢤⠶⠿⠛⠛⠙⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣶⣶⣤⣠⣴⡶⠾⠛

⠀⠐⠤⠄⠻⣿⣿⣿⣷⣤⠀⠀⡅⠀⣶⣶⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⣯⡵⢂⠀⠀⠀⣼⣿⣿⣿⣧⡁⠙⣿⣿⣿⡏⠀⠀⠚

⣀⠀⠀⠀⢤⣽⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣏⣤⣿⣿⣿⣷⠒⣿⣿⡿⣿⣿⣧⣶⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣟⡻⢋⠀⠀⠀⠹⣿⣿⣿⣿⣷⡄⣼⣿⣿⡷⢾⣿⣶

⣿⣿⣶⣤⣈⠉⠉⠉⠉⠛⠳⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣧⣼⣿⣇⣿⣿⠀⣿⣿⡷⣶⣾⣿⣿⣿⣿⡗⢶⣿⣿⡇⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⠓⠀⠠⠄⠈⢁⣤⣿⣿⣿⠻⠋⠁⢸⣿⣿⠡⣿⣿⣿

⠉⠙⠿⣿⣿⣿⣷⣤⣤⣤⣿⡿⠛⣿⣿⣿⢻⣿⣿⣾⣿⣿⣸⣿⡿⠀⠈⣹⣿⡿⣿⣿⡇⣿⣿⣦⣿⣿⣷⣾⣿⣿⣇⣤⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⢹⣿⣿⣄⣠⣤⣤⣖⣋⣠⣿⣿⣏⡀⠀⡰⠁⠙⣿⣧⠙⢻⣿

⡄⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⠷⠴⣿⣿⣿⠘⢛⣻⣿⣿⣿⣿⠛⠁⠀⠀⠛⢻⣧⠙⠛⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠟⢛⣿⣷⠈⠛⠛⠛⣻⣿⣿⣿⡆⠛⢛⡿⠛⠛⠛⢛⣿⣻⣿⣿⣿⣷⣼⡇⠀⠀⠈⠛⣷⡀⠉

⠀⠀⠀⠀⠀⠀⢀⠂⣹⣿⣧⠀⠀⢸⣿⡇⠀⢸⣿⣿⡿⠛⠁⠀⠀⢀⣾⠁⠀⠻⢷⣦⣤⣼⡿⠿⢿⣿⣿⠟⠉⠀⠀⣀⣾⣿⡏⠀⠀⠀⢐⣿⣿⣿⣿⠗⠶⣦⣦⠘⠉⠛⠉⢡⣿⣿⢇⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿

⠛⠟⠿⣿⠿⢿⠿⣿⣿⣿⣿⠿⣿⡿⣿⣷⣰⠈⣿⣿⠓⠒⠃⠀⠀⠸⣿⣦⡀⠀⠀⠉⠻⢿⣧⣶⣶⣬⣤⣤⣶⠶⠟⠛⠋⠹⣿⡄⠀⡴⠋⢹⣿⣿⣿⣧⠤⢬⣥⡀⠒⠶⠶⣿⣿⣿⠿⣷⡜⣿⣿⡿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠈⠹⣿⣽⣷⣆

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⢿⣿⡿⠁⠀⠀⠀⠀⠀⢹⡟⠛⠻

⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀

⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⢠⣼⣿⣀⢀⣤

⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿

⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣿⣿

⣿⡆⠀⢸⣿⣿⣿⣿⡿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⢹⡿⠿⠉⠉⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣯⣽

⣿⣷⠀⠈⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⣹⣿⡿⠛⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⣠⡿⢼⣷⡀⠀⠀⠀⢹⣧⣀⣠⣤⣤⣤⠴⠶⣾⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠈⠀

⣿⡏⠀⠀⠀⢰⣾⣿⣧⣄⣤⣤⣶⣾⠿⢿⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣾⣿⣄⣬⣿⣷⣶⣶⣶⣿⣿⠉⣿⡥⣶⣶⢶⣾⣿⣿⣿⠿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡟

⠻⠁⠀⠄⠀⢸⣿⠯⠹⣿⣿⣿⡏⠁⠀⢸⣧⣀⡤⠂⠀⠀⣀⣠⣤⣀⣤⣤⠴⠶⠖⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡂⢹⣿⣿⣷⣾⡿⠠⢻⣿⣆⠈⡇⢹⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺

⠀⠀⠀⠀⠀⣾⠁⠀⠘⠸⣿⣿⣿⣿⣶⣿⣿⡿⠇⠀⢺⣹⣿⣿⣿⣿⣷⣶⡿⢿⣦⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠡⢴⢗⢿⣿⣿⣷⣿⢿⣔⣿⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠠⠂⠀⠀⢸⣿⠀⠀⠈⠢⠌⠛⠻⡿⠿⠟⠀⠀⠀⠀⠸⡇⣾⣿⣾⣿⣷⣿⡇⠈⣻⣿⣿⣴⣿⣯⣿⣯⣿⣿⣿⣿⢿⣿⠝⠿⠿⣛⣙⣛⣤⣦⢥⠶⠖⠛⠛⠛⢻⣾⠇⠀⠀⠀⠀⢸⣿⣿⣿⠿⣷⣶⣶⣤⣤⣶⠿⠛

⠀⠀⠢⠤⠜⢿⣷⣿⣿⣤⡄⠀⢨⠀⣶⣶⠀⣶⣶⠀⣴⣿⣿⣿⡿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⣸⣭⠖⡀⠀⠀⢠⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⠃⠀⠀

⣄⡀⠀⠀⢠⣤⣿⣿⣿⣿⣿⡟⠉⠀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣻⣤⣿⣿⣿⣷⠒⣿⣿⡿⣿⣿⣯⣴⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣿⣛⠿⣁⢀⡀⠀⢿⣿⣿⣿⣿⣦⠀⣿⣿⣿⠿⣿⣿

⣿⣿⣷⣦⣄⠉⠉⠉⠉⠛⠻⢦⣠⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣇⣿⣿⠀⣿⣿⠿⣶⣶⣾⣿⣿⣿⡗⠲⣿⣿⡇⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⠟⠂⠀⠤⠀⠀⣠⣼⣿⣿⡿⠟⠉⠀⣿⣿⡏⢸⣿⣿

⠉⠉⠻⢿⣿⣿⣿⣦⣤⣤⣼⣿⠟⢻⣿⣿⣻⣿⣿⣼⣿⣿⣾⣿⡿⠀⠀⣹⣿⡿⣿⣿⣇⣿⣿⣦⣿⣿⣧⣶⣿⣿⣇⣠⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣻⣿⣿⣤⣀⣤⣤⣴⣚⣁⣼⣿⣿⣀⠀⢀⠎⠘⢻⣿⣌⠙⢿

⣄⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⡿⠤⢾⣿⣿⡟⠛⣛⣿⣿⣿⣿⡟⠁⠀⠀⠛⠛⣷⡜⠛⠻⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⠛⢻⣿⡎⠛⠛⠛⢋⣿⣿⣿⣿⠛⠛⣿⠟⠛⠛⠛⣻⣟⣿⣿⢿⣿⣦⣿⠀⠀⠀⠉⣛⣆⡈

⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣇⠀⠀⣿⣿⠃⠀⣿⣿⣿⠟⠋⠀⠀⠀⣰⡏⠀⠘⠿⣶⣤⣄⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣰⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⠒⢶⣶⡄⠋⠙⠉⠉⣸⣿⣿⣰⡿⣿⣿⣷⣦⣶⣿⣿⣿⣿

⠙⠟⠿⣷⠿⢿⠿⢿⣾⣿⣿⡿⢿⣿⢿⣿⣇⣄⢸⣿⡿⠐⠒⠁⠀⠀⢿⣷⣄⠀⠀⠈⠙⠿⣿⣴⣶⣦⣥⣤⣤⡶⠾⠻⠛⠉⢻⣧⠀⢠⠞⠉⢸⣿⣿⣿⡤⠤⣭⣆⠐⠲⠶⠿⣿⣿⡿⢿⣦⢻⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⢿⣯⣽⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠹⣿⣿⠋⠀⠀⠀⠀⠀⢈⡿⠛⠛

⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⣸⡇⠐⠀

⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⣴⣿⣇⣀⣠

⠀⠀⠀⠀⣰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣿⣿⣿⣿⣿⣿

⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿

⣿⣧⠀⠀⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠈⣿⣿⠏⠉⠙⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣯

⣿⣿⡄⠀⠻⠿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠟⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢠⣾⠯⣿⡆⠀⠀⠀⠘⣿⣀⣠⣤⣤⣤⠴⠶⢾⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠁

⣿⣿⠀⠀⠀⠀⣶⣿⣿⣄⣀⣤⣴⣶⠿⠿⡇⠀⠀⠈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣶⣿⣇⣤⣿⣿⣶⣶⣶⣿⣿⠉⣿⡥⣶⣶⢶⣾⣿⣿⣿⡿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻

⠻⠏⠀⠠⠀⠀⣿⡿⠝⣿⣿⣿⣿⠉⠀⠀⣿⣀⣠⠔⠀⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢻⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡂⢹⣿⣿⣷⣾⡿⢀⢼⣿⣧⡈⡇⠈⡏⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠇⠀⢀⠀⠀⢰⡏⠀⠀⠣⢿⣿⣿⣷⣶⣾⣿⣿⠿⠀⢸⢹⣿⣿⣿⣿⣿⣶⡿⢿⣦⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠁⠤⡾⡺⣿⣿⣿⣷⠿⣧⣺⡇⠀⠀⠀⠀⢀⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠤⠤⠀⠀⠠⣿⡇⠀⠀⠑⠌⠙⠻⢿⠿⠿⠋⠀⠀⠀⠸⡎⣾⣿⣾⣿⣷⣿⡇⠈⣻⣿⣿⣦⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⠝⠿⠿⣛⣙⣛⣤⣴⢴⠶⠖⠛⠛⠛⠙⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣶⣶⣦⣤⣴⠾⠟

⠀⠀⠀⠤⠤⢿⣷⣾⣷⣦⣄⠀⠀⡅⣶⣶⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⢰⣯⡴⢀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠙⢿⣿⣿⡏⠀⠀

⣤⣀⠀⠀⠀⣤⣹⣿⣿⣿⣿⡿⠛⠁⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣋⣧⣿⡿⣿⣷⠒⣿⣿⡿⣿⣿⣿⣥⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣿⣟⡻⢋⠀⣀⠀⠹⣿⣿⣿⣿⣷⡄⣼⣿⣿⡿⠿⣿

⣿⣿⣿⣦⣄⡘⠉⠉⠋⠙⠛⢧⣄⣴⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⠿⣶⣶⣾⣿⣿⣿⡗⠒⣿⣿⡇⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⡿⠓⠀⠠⠄⠀⢀⣤⣿⣿⣿⠿⠋⠁⢹⣿⣿⠡⣿⣿

⠉⠉⠙⠿⣿⣿⣿⣶⣤⣤⣤⣿⡿⠛⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡟⠀⠀⣹⣿⡿⣿⣿⣇⣿⣿⣦⣿⣿⣧⣴⣿⣿⣇⣀⣿⣿⣿⣿⣿⣟⣿⣿⠿⣿⣿⣿⣿⣿⣤⣄⣠⣤⣴⣒⣋⣠⣿⣿⣇⡀⠀⡴⠁⠛⣻⣧⡈⠻

⢄⣀⠀⠀⠈⠙⠛⠛⠻⣿⣿⣿⡧⠴⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⠁⠀⠀⠛⠛⢻⣞⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⠛⠛⠛⠋⣸⣿⣿⣿⡛⠛⢿⡿⠛⠛⠛⢛⣿⣻⣿⣿⣿⣷⣼⡇⠀⠀⠈⢙⣳⣀

⣀⠀⠀⠀⠀⠀⠀⠀⠂⣻⣿⣯⠀⠀⢸⣿⡏⠀⢸⣿⣿⡿⠛⠁⠀⠀⢀⣾⠁⠀⠻⢷⣦⣤⣸⡿⠿⢿⣿⣿⠟⠉⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠗⠲⣶⣦⠘⠉⠋⠉⢀⣿⣿⢃⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿

⠙⠟⠷⣷⠿⢿⠿⠿⣷⣿⣿⣿⠿⣿⡿⣿⣷⣠⠈⣿⣿⠃⠖⠂⠀⠀⠸⣿⣦⡀⠀⠀⠉⠻⢿⣧⣶⣶⣬⣤⣤⣴⡶⠟⠟⠋⠹⣿⡄⠀⡴⠋⢰⣿⣿⣿⡧⠤⢬⣴⡀⠒⠶⠾⣿⣿⣿⠿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠹⣿⣽⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⣻⡟⠁⠀⠀⠀⠀⠀⣿⠟⠛

⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⢠⡿⠀⠂

⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⣤⣾⣧⣀⢀

⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣾⣿⣿⣿⣿⣿

⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⣿⣿⣿

⣿⣿⡄⠀⢸⣿⣿⣿⣿⡿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⢻⢿⡟⠉⠙⠻⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⢻⣿⣯

⣿⣿⡇⠀⠘⠿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⣴⡿⣿⣧⠀⠀⠀⠀⣻⣇⣠⣤⣤⣤⠴⠶⠾⣶⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠈

⣿⣿⡇⠀⠀⠀⢰⣿⣿⣦⣀⣀⣤⣶⡾⠿⣯⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣶⣶⣿⣏⣤⣼⣿⣶⣶⣖⣿⣿⡏⣿⡥⣶⣶⢶⣾⣿⣿⣿⣿⠿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟

⡟⠿⠁⠀⡄⠀⢸⣿⠯⢿⣿⣿⣿⡏⠀⠀⢸⣆⣀⡤⠀⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢛⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⡃⢹⣿⣿⣷⣾⡿⠀⣸⣿⣿⣌⡇⠀⣹⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⠀⠀⡀⠀⠀⣾⠁⠀⠑⠽⣿⣿⣿⣶⣶⣿⣿⡿⠇⢺⠉⣿⣿⣿⣿⣿⣿⡿⢿⣦⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠁⠠⢴⢿⣿⣿⣿⣷⡾⣿⣴⡿⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠥⠤⠄⠀⠀⣼⣿⢠⠀⠈⠢⠉⠻⠿⡿⠿⠟⠁⠀⠀⠸⡆⣿⣿⣾⣿⣷⣿⡇⠈⣻⣿⣿⣷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠝⠿⠿⣛⣙⣛⣤⣤⢶⠶⠖⠛⠛⠛⠃⢿⣾⠃⠀⠀⠀⠀⣸⣿⣿⣿⢿⣷⣶⣶⣤⣤⡶⠿

⠀⠀⠀⠠⣄⠸⣿⣷⣿⣶⣤⡀⠀⢸⣶⣶⠀⣶⣶⠀⣴⣷⣿⣿⣿⣿⡿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⠀⣿⣥⢆⡀⠀⠀⢰⣿⣿⣿⣿⡤⠈⠻⣿⣿⣿⠁⠀

⣤⣄⠀⠀⠀⢠⣈⣿⣿⣿⣿⣿⠟⠋⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⣼⣿⣿⣿⣷⠒⣿⣿⣟⣿⣿⣟⣯⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢸⣿⡛⠟⡠⢀⡀⠈⢿⣿⣿⣿⣯⣆⢰⣿⣿⣿⠻⣿

⣿⣿⣿⣶⣤⣀⠋⠉⠛⠙⠛⠻⣄⣠⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣇⣿⣿⠀⣿⣿⠚⣶⣶⣾⣿⣿⣿⡗⠒⣿⣿⣇⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⣿⠟⠂⠠⠤⠀⠀⣠⢼⣿⣿⡿⠏⠉⠈⣿⣿⡇⢼⣿

⠉⠉⠙⠿⣿⣿⣿⣶⣤⣄⣀⣴⣿⠟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠀⠀⣸⣿⡿⢿⣿⣇⣿⣿⣀⣿⣿⣧⣤⣿⣿⡇⣀⣿⣿⣿⣿⣿⣟⣿⣿⠟⣿⣿⣿⣿⣿⣡⣤⣀⣤⣤⣖⣊⣁⣼⣿⣟⣅⠀⢠⠎⠜⢛⣿⣄⠙

⠀⣀⡀⠀⠀⠉⠛⠿⠟⣿⣿⣿⣿⠤⢿⣻⣿⡟⠛⣿⣿⣿⣿⣿⠅⠀⠀⠛⠛⠃⣿⡛⠛⠿⠟⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⠛⣻⣿⡟⠛⠛⠋⢠⣿⣿⣿⡟⠛⠙⣻⠟⠛⠛⠛⣻⣟⣿⣿⣿⣿⣦⣿⠀⠀⠀⠉⣛⣆

⣀⠀⠀⠀⠀⠀⠀⠀⠐⢘⣿⣿⡅⠀⠈⣿⣿⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⣰⡍⠀⠹⢿⣦⣤⣀⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣰⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡟⠒⢶⣴⡀⠋⠉⠉⠁⣼⣿⡟⣸⡿⣿⣿⣿⣶⣶⣿⣿⣿

⠙⠟⠷⣶⠿⢶⠿⠿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣆⡄⢸⣿⡿⠰⠒⠀⠀⠀⢿⣷⡀⠀⠀⠉⠛⠿⣿⣴⣶⣭⣥⣤⣴⣶⠾⠛⠛⠉⢿⣇⠀⣠⠞⠁⣾⣾⣿⣿⡤⠤⣥⣆⠐⠲⠶⢿⣿⣿⡿⢿⣦⢻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣿⣿⡿⠋⠀⠀⠀⢹⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣻⣻⡏⠀⠀⠀⠀⠀⠀⣿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⢠⡟⠀

⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⢠⣴⣿⣷⣄

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⣿⣿⣿⣿

⣦⣄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢿⣿⣿⣿

⣿⣿⣷⡀⠀⢹⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⣿⢿⡟⠉⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⢻⣿

⣿⣿⣿⡇⠀⠸⢷⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣴⡿⣿⣧⠀⠀⠀⢈⣿⣷⣤⣤⣤⠴⠶⠾⣖⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⣿⣿⣿⡇⠀⠠⠀⣸⣿⣿⣆⣀⣀⣤⣴⣾⠿⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣶⣿⣯⣤⡼⣿⣶⣖⣛⣿⣿⣿⡧⣶⣶⢶⣾⢿⣿⣿⣿⣿⠿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡟⣿⠁⠀⡄⠀⢸⣿⢿⢿⣿⣿⣿⡏⠀⠀⢸⣄⣀⡤⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢛⣛⣟⣿⣿⣿⣶⣦⣻⣿⣿⣿⣿⣿⡋⢹⣿⣿⣷⣾⡿⠊⢸⣿⠻⣿⣇⠀⠀⡹⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⣿⠀⠀⡀⠀⠀⣾⠁⠀⠙⠿⣿⣿⣷⣶⣶⣿⣿⣿⢿⠉⣩⣿⣿⣿⣿⣿⣿⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⢹⣿⠁⠀⠠⡼⣿⡿⣿⣿⣷⡾⣷⣼⡟⠀⠀⠀⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀

⡾⠥⠤⠄⠀⠀⣼⣿⢠⠀⠘⠀⠙⠻⠿⣿⣿⠟⠉⠀⠸⡆⣾⣿⣾⣿⢿⣿⣧⠋⣻⣿⣯⢻⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⡟⠿⠿⣛⣙⣛⣤⣤⢤⠷⠗⠛⠛⠙⠛⠃⣿⣾⠁⠀⠀⠀⠀⣸⣿⣿⣟⠿⣿⣾⣶⣤⣴⡾

⠁⠀⠀⠀⠤⣀⠸⣿⣶⣿⣶⣄⡀⠀⣶⣶⠀⣶⣶⠀⣴⣷⣿⣿⣿⣿⡿⢿⣿⣷⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⠀⠀⣿⣴⢇⡀⠀⠀⢰⣿⣿⣿⣿⡤⠈⠻⣿⣿⣿⠁

⣶⣤⣀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⡿⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⣤⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⣟⣛⣿⣿⣿⡉⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣷⣿⣿⠀⣸⣿⠛⢟⡠⢀⣀⠈⢿⣿⣿⣿⣿⣦⢰⣿⣿⣿⠟

⢿⣿⣿⣿⣶⣄⡀⠛⠛⠛⠛⠛⠯⣤⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⣿⣶⣾⣿⣇⣿⣿⡀⣿⣿⠁⣐⣷⣶⣾⣿⣿⡗⠒⣿⣿⣷⣿⣿⡇⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⠟⠂⠠⠔⠀⠀⣴⢾⣿⣿⡿⠋⠉⠈⢿⣿⡆⢸

⠀⠙⠛⠛⠿⣿⣿⣷⣶⣤⣀⣀⣴⣿⣿⣿⢻⣿⣿⠸⣿⣿⣾⣿⣿⠀⠀⣸⣿⡿⢿⣿⣧⣿⣿⣀⣿⣿⣧⣤⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⢈⣡⣦⣀⣤⣤⣖⣋⣥⣾⣿⣿⣤⠀⢠⠎⠐⠛⣿⣆

⠀⠀⣀⡀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡄⠀⠛⠛⠃⠘⣿⡋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠛⣿⣿⡟⠛⠋⠀⢛⣿⣿⣿⡟⠘⠛⣻⠟⠛⠛⢛⣻⣿⣿⣿⢿⣿⣧⣿⠀⠀⠀⢈⣛

⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣿⣿⡅⠀⠈⣿⣿⠀⢀⣿⣿⣿⠟⠛⠀⠀⠀⣰⡏⠀⠹⠿⣶⣤⣀⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣟⠒⢶⣶⡄⠋⠉⠉⠁⣼⣿⣿⣸⡿⣿⣿⣿⣷⣾⣿⣿

⠉⠟⠻⣶⠿⢶⠶⠾⠿⢷⣾⣿⣿⡿⣿⣾⣿⣿⣆⡄⢹⣿⡿⠤⠒⠀⠀⠀⢿⣷⣄⠀⠀⠉⠛⠿⣿⣴⣶⣬⣥⣤⣴⣶⠾⠛⠛⠉⢿⣧⠀⣠⠟⠁⣾⣿⣿⣿⠤⠤⣴⣆⡐⠚⠿⢿⣿⣿⡿⠿⣧⢹⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣿⣿⡿⠋⠀⠀⠀⢹⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⣽⡏⠀⠀⠀⠀⠀⠀⣿⠛

⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⢠⣴⣿⣷⣄

⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⣿⣿⣿⣿

⣦⣄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢻⣿⣿⣿

⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⣻⢿⡟⠉⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⢻⣿

⣿⣿⣿⡇⠀⠸⢿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣴⡿⣿⣧⠀⠀⠀⢈⣿⣷⣤⣤⣤⠴⠶⠾⣖⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢

⣿⣿⣿⡇⠀⠠⠀⢼⣿⣿⣆⣀⣀⣤⣴⣾⢿⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣶⣿⣯⣤⡼⣿⣶⣖⣛⣿⣿⣿⡧⣶⣶⢶⣾⢿⣿⣿⣿⣿⠿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡟⣿⠁⠀⡄⠀⢸⣿⢿⣿⣿⣿⣿⡏⠁⠀⢸⣄⣀⡤⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢛⣛⣟⣿⣿⣿⣶⣦⣻⣿⣿⣿⣿⣿⡋⢹⣿⣿⣷⣾⡿⠊⢸⣿⠻⣿⣇⠀⠀⡹⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠙⣿⠀⠀⡀⠀⢀⣾⠁⠀⠘⠿⣿⣿⣷⣶⣶⣿⣿⣿⢿⠉⣩⣿⣿⣿⣿⣿⣿⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⢹⣿⠁⠀⠠⣼⣿⡿⣿⣿⣷⡾⣷⣼⡟⠀⠀⠀⠀⢀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀

⡾⠥⠤⠄⠀⠀⣼⣿⢠⠀⠘⠀⠙⠻⠿⣿⣿⠟⠉⠀⠸⡆⣾⣿⣾⣿⢿⣿⣧⠋⣻⣿⣯⢻⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⡟⠿⠿⣛⣙⣛⣤⣤⢤⠷⠗⠛⠛⠙⠛⠃⢿⣾⠁⠀⠀⠀⠀⣸⣿⣿⣟⠿⣿⣾⣶⣤⣴⡾

⠁⠀⠀⠀⠤⣀⠸⣿⣶⣿⣶⣄⡐⠀⣶⣶⠀⣶⣶⠀⣴⣷⣿⣿⣿⣿⡿⢿⣿⣷⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⠀⠀⣿⣴⢇⡀⠀⠀⢰⣿⣿⣿⣿⡤⠈⠻⣿⣿⣿⠁

⣶⣤⣀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⡿⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⣤⣿⣿⣿⣷⠒⣿⣿⠛⣿⣿⣟⣛⣿⣿⣿⡉⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣷⣿⣿⠀⣸⣿⠛⢟⡠⢀⣀⠈⢿⣿⣿⣿⣷⣦⢰⣿⣿⣿⠟

⢿⣿⣿⣿⣶⣄⡀⠛⠛⠛⠛⠛⠯⣤⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⣿⣶⣾⣿⣇⣿⣿⡀⣿⣿⠁⣐⣷⣶⣿⣿⣿⡗⠒⣿⣿⣧⣿⣿⡇⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⠟⠂⠠⠔⠀⠀⣴⢾⣿⣿⡿⠋⠉⠈⢿⣿⡆⢼

⠀⠉⠛⠛⠿⣿⣿⣷⣶⣤⣀⣀⣴⣿⣿⣿⢿⣿⣿⠸⣿⣿⣾⣿⣿⠀⠀⣸⣿⡿⢿⣿⣧⣿⣿⣀⣿⣿⣧⣤⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⢈⣡⣦⣀⣤⣤⣖⣋⣥⣾⣿⣿⣤⠀⢠⠎⠐⠙⣿⣆

⠀⠀⣀⡀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠠⣿⣿⣿⣿⣿⡄⠀⠛⠛⠃⠘⣿⡋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠛⣿⣿⡟⠛⠋⠀⢛⣿⣿⣿⡟⠘⠛⣻⠟⠛⠛⢛⣻⣿⣿⣿⢿⣿⣷⣿⠀⠀⠀⢈⣛

⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣿⣿⡅⠀⠈⣿⣿⠀⠀⣿⣿⣿⠟⠛⠀⠀⠀⣰⡏⠀⠹⠿⣶⣤⣀⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣟⠒⢶⣶⡄⠋⠉⠉⠁⣼⣿⣿⣸⡿⣿⣿⣿⣷⣾⣿⣿

⠉⠟⠻⣶⠿⢶⠶⠶⠿⢷⣾⣿⣿⡿⣿⣾⣿⣿⣆⣌⢸⣿⡿⠤⠒⠀⠀⠀⢿⣷⣄⠀⠀⠉⠛⠿⣿⣴⣶⣬⣥⣤⣴⣶⠾⠛⠛⠉⢿⣧⠀⣠⠟⠁⣾⣿⣿⣿⡤⠤⣴⣆⡐⠚⠿⢿⣿⣿⡿⠿⣷⢹⣿⣿⣻⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 2781

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/irc-log-260523/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/irc-log-260523/

Gemini_version_available_♊︎

✐ IRC_Proceedings:_Friday,_May_26,_2023⠀✐

Posted in IRC_Logs at 2:06 am by Needs Sunlight

Also available via the Gemini protocol at:

* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-260523.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-260523.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-social-260523.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-260523.gmi

Over HTTP:

                                  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_

                                     #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5

                                  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_

                                #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5

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

                                      #techrights_log_as_text                                                                                   #boycottnovell_log_as_text

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

                                 #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text

                      Enter_the_IRC_channels_now

=> =============================================================================

§ IPFS Mirrors⠀➾

CID Description Object type

                                             IRC log for

Qmf3Ey2afxYusRQPgHcYn54SY3RySaL1z49BFyKH6xxQsv #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #boycottnovell

QmSEdTzpBG847PCMzfFiaEwrEtV4V6n1TUT82EGerdjfiZ (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

                                             IRC log for

                                             #boycottnovell-

Qmc673N3qocgnALqt6wWL9L2onWe5hDN3c3eQg3n3jhF4t social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #boycottnovell-

QmeXYx9cXMZ153JhxpyEMJqb96aj1dyz2kngTmrAcD19ud social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             (full IRC log

                                             as plain/ASCII

                                             text)

                                             IRC log for

QmcCxrrVumz6u7g3G2GBrePq8pU1qhutngqV641AVQeJsF #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #techbytes

QmZpDMgRgVQMrT2eEbv6ijjF9rdstDcKHDiGXpeyAmEEee (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

                                             IRC log for

QmX5i9soierb1iQKYtLzoDNxy4dMrX9y3NEzKT5DdB9oxP #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

                                             as HTML)

                                             IRC log for

                                             #techrights

QmZz6ob1zdcu6v3HNwzKSQZ4aUTxVZMFgqdTHp77sGWogu (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈

§ Bulletin for Yesterday⠀➾

Local_copy | CID (IPFS): QmX2VFCGCawxbCCUo2h1FKvHmTmxLRFAdDLmVDjFaZoLpw

                ䷩ 𝚕𝚒𝚗𝚎 2908

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/social-control-networks-need-to-be-purged/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/social-control-networks-need-to-be-purged/

Gemini_version_available_♊︎

✐ Social_Control_Media_Needs_to_be_Purged_and_We_Need_to_Convince_Others_to

Quit_It_Too_(to_Protect_Ourselves_as_Individuals_and_as_a_Society)⠀✐

Posted in Deception, Free/Libre_Software at 7:57 am by Dr. Roy Schestowitz

Video_download_link | md5sum 58fe869dbe56783f7f1ce90f27458ef6

Collective Risk From Social Control Networks

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/social-control-media-harms-everybody.webm

Summary: With the Tux Machines anniversary (19_years) just days away we

seriously consider abandoning all social control media accounts of that site,

including Mastodon and Diaspora; social control networks do far more harm than

good and they’ve gotten a lot worse over time

AMONG the potential topics for today we’ve included the impact of social

control media ‘by peer’, e.g. within families (dinner table, sleep) or inside

workplaces. I’ve meanwhile noticed, as stated in the above video, that

Mastodon’s largest instance does not like GNU/Linux sites. It does_not_like

GNU/Linux_users,_either. Tux Machines (username tuxmachines) has been delisted

and demoted; it’s not visible, even if it’s still there, and nothing gets

imported into the account.

“Tux Machines (username tuxmachines) has been delisted and demoted; it’s not

visible, even if it’s still there, and nothing gets imported into the

account.”For now I’ve decided not to even ‘fix’ the tuxmachines social control

media accounts. It’s just not worth the trouble and as early as next week Tux

Machines might quit social control media altogether. It’s a total catastrophe

and nobody deserves to have to deal with such crap.

The video above focuses on this_new_article_from_YLE. It talks about how

children’s use of crap_like_Fentanylware/TikTok_harms_health; those are topics

that we did not cover or barely covered before.

To make society better off and more secured/protected from harm — both domestic

and foreign — we need to convince peers/family/friends to abandon social

control media, including federated/Free software/decentralised derivatives/

copycats of the same behavioural machines. “Free (as in Freedom) platforms

would not drive “engagement” nor aim for other aspects of addiction and harm,”

an associate noted. █

                ䷩ 𝚕𝚒𝚗𝚎 2973

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/some-privacy-still-feasible/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/some-privacy-still-feasible/

Gemini_version_available_♊︎

✐ Anonymously_Travelling:_Still_Feasible?⠀✐

Posted in Free/Libre_Software at 6:57 am by Dr. Roy Schestowitz

Video_download_link | md5sum 6f335d84226615033fae0b1049d476d8

Anonymous Travel as a Right

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/travel-dignity.webm

Summary: The short story is that in the UK it’s still possible to travel

anonymously by bus, tram, and train (even with shades, hat and mask/s on), but

how long for? Or how much longer have we got before this too gets banned under

the false guise of “protecting us” (or “smart”/”modern”)?

THE element of “curious Roy” has long motivated and led me to “testing” all

sorts of stores and businesses, sometimes even government departments. I did

assessments and surveys, then published the outcomes in my personal site. Back

in the days there were media/societal watchdogs that did this routinely and

reported their latest-found outcomes.

“Surveillance states mostly punish law-abiding people.”The other day I decided

to check the experience of travelling by train anonymously. In a nutshell, it’s

still possible to purchase train tickets and travel anonymously. It’s also

possible to do this with an actual human and the queue was short even at 8:

30AM. Yes, actual humans are available! And they talk back at you with advice

and stuff…

Of course not every train station still has humans available. In some countries

the regime and the corporations (graft) try to herd people into “smart” “apps”

and other such nonsense. Those should not be needed. More of that is covered in

the video above, including why in a free society anonymous travel is still very

important. In some parts of the world it’s already impossible to travel

privately in a car, unless it’s a stolen car. Does this prevent crime? Hardly.

Many criminals already exercise special caution and steal cars, from which

crimes get committed. Surveillance states mostly punish law-abiding people. █

                ䷩ 𝚕𝚒𝚗𝚎 3032

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/stuttgarter-zeitung-epo/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/stuttgarter-zeitung-epo/

Gemini_version_available_♊︎

✐ German_Media_About_Industry_Patent_Quality_Charter_(IPQC)_and_the_European

Patent_Office_(EPO)⠀✐

Posted in Europe, Law, Patents at 5:16 am by Dr. Roy Schestowitz

More translations (with more languages) available in the site of the EPO‘s

union, SUEPO

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

Siemens is one of the largest applicants at the European Patent Office.

                       Source: Matthias Balk/dpa

Summary: SUEPO has just released 3 translations of new articles in German; this

is the first of the three (“Industrie_kritisiert_Europäisches_Patentamt”)

THE following was translated by staff of the EPO. The staff wants to general

public to know this:

 § Industry criticises European Patent Office⠀➾

 An initiative of several large companies is concerned about the

 quality of patent examinations at the European Patent Office. There,

 speed comes before accuracy, they say. The office sees things

 differently.

 The European Patent Office (EPO) has come in for criticism from

 industry. An initiative of now 21 companies is concerned about the

 quality of patent examination. “We have the impression that the EPO

 is primarily concerned with processing as many patents as possible,”

 says Beat Weibel, head of patents at Siemens, who initiated the

 Industry Patent Quality Charter (IPQC), in an interview with the

 Deutsche Presse-Agentur. Examiners, he says, are exposed to ever-

 increasing production pressure and are therefore no longer in a

 position to examine thoroughly enough. “While in our case we see that

 the amount of work required for a patent application on average is

 always bigger, things have to move faster and faster at the EPO,”

 explains Weibel. “That worries us because the quality of the

 examination suffers as a result. He does not receive exact figures

 from the EPO on the time budget of the examiners, he says. “But if

 you look at the number of examiners and the number of examinations

 patents, the result is roughly a halving over the past ten years.”

 Jörg Thomaier, head of patents at Bayer, which is also a member of

 the IPQC, shares Weibel’s

 concerns.

 “The EPO used to be known for taking a long time to test. In recent

 years, we have the impression that more attention is paid to speed

 and that examinations are no longer as thorough,” he says. “Things

 are faster now, but the revocation rate in the patent appeal process

 has gone up.”

 Such a revocation is extremely unfavourable for the patent

 applicants. “Patents are extremely important for a company like

 Bayer,” Thomaier emphasises. “It’s not so much the quantity that

 matters, but that I can enforce them – if necessary – and that they

 don’t fall over at the first gust of wind of a review.” The Swiss

 company Roche, which has also joined the IPQC, says: “As an industry,

 we depend on reliable patents. That is the basis for investing in our

 research.”

 Siemens is one of the largest applicants at the European Patent

 Office. Last year, the Munich-based company was number six among

 applicants at the EPO, and number two among European companies –

 behind Ericsson. The Swedes are also members of the IPQC.

 “We would like the auditors to have more time to do their job,

 because the Patents are becoming more and more complex,” says

 Gabriele Mohsler, Vice President Patent Development there. “In

 individual cases, we have also seen that the searches were not

 sufficiently thorough.”

 Overall, however, her assessment is not quite as critical:

 “Basically, I think the quality at the EPO is good. But we don’t want

 it to drop and in some areas it could be higher,” says Mohsler.

 Thomaier from Bayer also says: “In a global comparison, the quality

 of the EPO is not bad. But it is a long way from what it once was:

 the clear gold standard. And that’s where we as an industry want to

 get back to.” A key solution in his eyes: more staff.

 “More applications also require more examiners,” he emphasises. “At

 the moment, we have the

 impression that the capacity is not sufficient.

 The EPO, on the other hand, emphasises on request that the quality of

 patent searches “always has top priority”. Many countries regard its

 work “as a global benchmark for patent quality”. This is also

 reflected in surveys by “leading intellectual property journals”, in

 which the EPO “consistently ranks first among patent professionals”.

 Some of the figures used by the IPQC, however, are inaccurate.

 In addition, the Patent Office points out that it has its own working

 group on quality in its Standing Consultative Committee with 74

 members from 40 countries. Last October, it also published a new

 Quality Charter, “in which our commitment to high quality and

 excellence at every stage of the patent granting process is set out”.

There are two more English translations that we wish to reproduce for plain

text and Gem(ini)Text. Then comes a new video. █

⠈⠻⢷⣦⡀⠐⠤⠀⠐⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣷⠀⣠⣾⠿⠋⠑⣇⡀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢀⣠⣾⣿⠟⠋⣠⣴⣿

⠀⠀⠀⠉⠻⢷⡄⠈⠒⠀⠙⠻⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⠿⠋⣿⡄⣀⣴⢿⠋⠀⠀⠛⣤⣶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢁⣠⣾⣿⣿⣿

⣦⣀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢸⣿⣿⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⠀⣹⣿⡟⠃⠀⢸⣀⣴⣾⣿⣿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿

⠈⠙⠧⣤⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢀⡀⣿⠛⠁⠀⡇⣠⣴⣿⣿⣿⠿⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⠁⠃⣤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⠈⠁⢸⠀⢰⣾⣿⣿⡿⠟⡏⠀⠀⠀⠍⠠⠀⠀⠀⠀⠀⢠⡀⠆⢀⠀⠀⠀⢀⠀⠀⣠⣾⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠳⠶⠶⠶⠶⠶⠶⣿⣾⣶⣤⣤⣤⣤⣤⣽⣟⠀⠀⢸⣿⣿⣿⢿⣿⢿⣿⣿⣿⢻⠀⢴⣸⣿⣿⠿⣏⠁⠀⢀⣧⠶⠀⠀⢠⠀⠀⠀⣤⡀⡄⢨⣟⣼⠇⠀⠀⠀⢉⣠⣾⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠉⠩⠍⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣴⡿⢻⡍⠀⢀⣿⠴⠈⠉⢱⠀⣄⣤⣤⣞⡄⠟⠻⣤⠛⡻⡻⠋⠀⠀⢀⣴⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣤⣤⡄⠀⢸⣧⣤⣤⣈⣽⣉⡉⣉⢙⢹⠀⠀⠘⡇⠀⠈⢹⠀⣠⣤⣼⣿⣿⣿⣿⡯⣣⢿⣿⠋⠀⠀⠀⠀⢀⣴⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣦⡖⠁⠀⠀⠀⠀⠛⢿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⡇⠀⣤⣾⣾⣿⣿⣿⣿⣿⣿⡇⠂⠋⠀⠀⠀⠀⠀⣠⣶⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣅⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢰⢾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠐⢂⣀⡇⠰⣿⣿⣿⣿⣿⡿⡟⠛⠉⠀⠀⣀⠀⠀⠋⣠⣾⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢐⣴⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⣿⣷⣼⣿⠿⡟⠋⠱⢐⠃⡤⠔⠀⠀⠀⢀⣴⡿⠛⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡴⠋⠁⠈⠀⠀⠆⠀⠀⠀⠀⠀⡄⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣹⣼⡿⠿⣏⠉⠀⢀⡇⠤⠽⠋⢡⢀⣘⡁⢀⣴⠿⠋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢹⠀⠀⠀⣇⣀⣤⣶⣾⣿⣿⠟⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⢀⡀⠀⢀⣸⢀⣴⣾⣿⣿⣿⣿⣿⡫⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢐⣿⣏⠹⣿⣿⣿⣿⠟⠏⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⡿⠦⠙⠉⠉⠁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣾⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣭⣽⣿⠛⠛⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡾⠂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⢛⣛⣛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣧⠀⠄⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠆⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠄⠀⠀⢠⣄⣀⣀⠀⣤⣀⣤⣄⣤⣤⣤⣤⣄⠀⠀⣀⣤⣜⣧⣤⢰⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠿⠷⠾⠿⠿⠿⠾⠀⠀⢻⣿⣿⣿⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠶⠂⠠⠀⠰⠶⠆⢰⠶⠶⠆⢶⣾⣿⡿⣿⣿⣿⡦⠀⠈⢿⣿⣿⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠻⠛⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠛⠛⠛⢛⣛⠛⢛⣛⣛⢛⣛⣛⣛⣛⣋⣛⣛⣛⣁⠀⢀⣠⡦⣤⡤⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣤⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⠄⠴⠶⠶⠾⠿⠿⠶⠿⠿⠷⠿⢿⣿⡿⣿⣟⢀⠀⢼⡧⠤⠤⢸⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⡿⢫⣿⡿⢿⡿⠿⠿⠛⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⡀⠀⠀⠀⠒⠒⠒⠒⠒⠿⠟⠺⠟⢓⡚⢻⣗⡛⣻⣛⡃⠘⣇⣄⣀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⠷⠀⠀⠀⠀⠀⠈⠉⠉⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⡯⡇⠀⣿⣿⣿⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⡿⠇⠀⣿⣿⣿⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⣴⠄⠀⡀⠀⠀⠀⠒⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡅⠀⠙⢛⠋⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡴⢦⢰⣯⣼⡅⣭⢠⡶⠆⣾⣻⡆⠀⢺⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿

⡄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡿⡇⢀⣄⣌⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣇⢸⠇⡇⢸⡆⢻⠸⣧⣤⢿⣭⡅⠀⠈⠻⣶⡶⠈⠻⠿⠿⠇⠘⠛⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⡟⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢁⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰

⠀⣼⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡻⡇⣯⣷⢸⣍⠀⠀⣿⠻⣆⢹⡟⢰⣟⣻⣎⢿⣆⣾⡇⣼⣟⣿⣦⠻

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠛⠃⠛⠶⠰⠾⠂⠀⠹⣴⠟⠸⣇⠈⢿⣭⣭⠈⢿⣿⠃⢹⣿⣙⣛⡀

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠉⠛⠛⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

                ䷩ 𝚕𝚒𝚗𝚎 3202

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/stuttgarter-zeitung-thomas-magenheim-on-epo/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/stuttgarter-zeitung-thomas-magenheim-on-epo/

Gemini_version_available_♊︎

✐ EPO_Applicants_Complain_That_Patent_Quality_Sank_and_EPO_Management_Isn’t

Listening_(Nor_Caring)⠀✐

Posted in Deception, Europe, Patents at 5:36 am by Dr. Roy Schestowitz

More translations (with more languages) available in the site of the EPO‘s

union, SUEPO

Summary: SUEPO has just released 3 translations of new articles in German (here

is the_first_of_the_batch); the following is the second of the three (“Kritik

am_Europäischen_Patentamt_–_Patente_ohne_Wert?”)

THIS is an article from yesterday, composed by Thomas Magenheim, who

understands_these_matters. The following is at least partly machine-generated:

 § Criticism of the European Patent Office Patents without value?⠀➾

 26.05.2023 – 00:00 hrs

 Photo: imago/STL

 To increase its revenues, the European Patent Office grants

 questionable patents, say critics. Transparency International sees

 structures that favour corruption.

 Thomas Magenheim

 The example described by the Munich patent attorney makes it clear

 what is at stake. A pharmaceutical company developed a pill against

 infertility, had it protected at the European Patent Office (EPO) and

 invested in its marketing. Then a rival entered the market with an

 alleged plagiarism. The patent holder went to court and lost. The

 alleged imitator was able to show a US patent that Epa examiners had

 overlooked. This rendered their property right worthless. “In extreme

 cases, this can cause millions in damages,” explains the patent

 attorney, who wishes to remain anonymous. He works for one of the

 largest patent law firms in Europe. Patenting for several countries

 alone consumes a six-figure sum and many times that amount is

 invested in production in reliance on the patent. There is a system

 of meagre returns, the expert complains. Examiners are encouraged to

 grant more and more patents because this maximises the office’s

 income. Quality research falls by the wayside.

 Michael Heisel hangs the grievances even higher. “We see structural

 problems at the Epa that facilitate corruption,” says the Bavarian

 head of the anti-corruption organisation Transparency International.

 An element of this, he says, is the Epa Board of Directors, in which

 39 European countries are represented and which is supposed to

 control the management of the office. But this is called into

 question by a conflict of interests, warns Heisel. On the one hand,

 the office takes over the patent examination for many countries. On

 the other hand, the states receive a share of the Office’s income for

 granted patents. “The supervisory authorityThe administrative board

 is not independent of the person being controlled, and that can’t

 work,” Heisel criticises. Epa service instructions support this view.

 “Productivity has to improve, very soon, . …because productivity is

 the only thing that guarantees that our payroll will be paid on 26.

 of each month,” writes an Epa director. The clarity of a patent is

 not a priority, the inventive step is not to be examined in depth, it

 continues. It is to be examined quickly, decided positively and

 recognised a lot, it means.

 ⚓  Siemens is also among the critics⠀⇛

 This practice is also a thorn in the side of Siemens patent chief

 Beat Weibel. His company is the largest German patent applicant and

 initiator of an industry initiative with the abbreviation IPQC. 20

 major international corporations such as Siemens, Bayer or Nokia, but

 also smaller companies, have united because they fear for effective

 patent protection. “We have nothing in our hands if patent examiners

 can’t find the state of the art and can only do incomplete research

 due to internal time pressure,” complains Weibel. Siemens, too, has

 had similar experiences with Epa patents. Representatives of IPQC and

 Office 2023 have met twice to discuss and resolve problems. But that

 already fails in terms of awareness. “The Management of the office

 has denied quality deficiencies,” regrets the Siemensian. The

 Critics, meanwhile, remain silent. “We ask for your understanding

 that Epa does not wish to comment on this,” a spokesperson explains

 succinctly when asked.

 The data speak a clear language. For example, Siemens has documented

 an increase in the time spent on patent applications by one third in

 the past decade. At the same time, according to internal Epa

 statistics, the time available to examiners per patent search has

 almost halved, i.e. the opposite development has taken place. As a

 result, those who challenge patents are becoming more successful.

 From 2015 to 2021, the revocation rate climbed from 41 to 46 per

 cent, according to Siemens. For 2022, a study by the Chair of

 Intellectual Property at the University of Osnabrück has determined a

 revocation rate of almost 50 per cent at the Epa Board of Appeal.

 Another almost 40 per cent of contested patents were marginally to

 substantially restricted. It is striking that not even one in ten

 revocations is based on documents that could not be found in the Epa

 patent database, the study authors write. This means that in nine out

 of ten contested cases, the patent should not have been granted in

 the first place if a precise search had been carried out.

 ⚓  Internal complaints have gone unheard⠀⇛

 “We need reliable patents, and for that examiners need enough time

 and experience,” emphasises a patent expert from the pharmaceutical

 company Roche in Switzerland. He too is a member of the IPQC. Epa –

 Staff representatives support the accusations from industry and

 research. To the outside world, the office management claims that

 everything is fine and plays down quality deficiencies or ignores

 them altogether, they explain. Only four out of five exiting auditors

 are replaced, despite an increase in work. Internal complaints that

 this is at the expense of the quality of research have gone unheard.

 “The Office must provide more examiners and more examination time,”

 the Munich patent attorney also demands. A few years ago, several

 large patent law firms sent a fire letter to the Office. which

 criticised the declining quality of patents. This has been negated on

 the part of the office. “Nothing happened,” regrets the expert. Like

 Transparency International, he sees the Epa Board of Directors as

 problematic.

 ⚓  Aiming for patent fees⠀⇛

 “There are states for which this is a significant source of income,”

 says Weibel, criticising the control body’s actions and its focus on

 patent fees. Patent trolls have also recognised this and are taking

 advantage of it. These are applicants who apply for superficial

 patents, which are granted if the examination is poor, explains

 Heisel. These patents then block competitors. “China in particular

 applies for a large number of patents, and if they are not carefully

 examined, German companies can lose innovation opportunities.

 [sic] take,” warns Heisel. This is another reason why the IPQC

 remains persistent. “We will not give up,” promises Weibel in the

 fight for patent quality.

 ⚓  European Patent Office⠀⇛

 Organisation

 The European Patent Office (EPO), with its headquarters in Munich, is

 a supranational organisation, not an EU organisation, which is only

 subject to very limited state jurisdiction in the German country

 where it has its headquarters. The management of the Office, under

 President Antonio Campinos, is controlled by the Epa Administrative

 Council. It is made up of representatives of the 39 European states

 that are members of the European Union.

 Patent Convention have acceded to. These representatives are usually

 the heads of the national patent offices. For Germany, there is a

 Secretary of State for Justice.

 Patents

 In particular, patent applications from China have been on the rise

 at the European Patent Office for years. In 2022, the increase on

 this basis was a good 15 percent to more than 19,000 requests for

 protection by Chinese inventors. By comparison, applications from the

 USA grew by only three percent to a good 48,000 requests, while those

 from Germany fell by almost five percent to 24,684 inventions.

 However, these figures say nothing about their quality.

EPO managers redefined quality as speed of granting. That’s not quality at all.

Remember that the EPO hired people from Transparency International (noted

above). That helped silence them about EPO corruption for a while. █

                ䷩ 𝚕𝚒𝚗𝚎 3398

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/suepo-and-epo-articles/#comments

Gemini version at gemini://gemini.techrights.org/2023/05/27/suepo-and-epo-articles/

Gemini_version_available_♊︎

✐ With_EUIPO_in_Focus,_and_Even_an_EU_Kangaroo_Tribunal,EPO_Corruption(and

Cross-Pollination_With_This_EU_Agency)_Becomes_a_Major_Liability/Risk_to_the

EU⠀✐

Posted in Europe, Patents at 6:25 am by Dr. Roy Schestowitz

Video_download_link | md5sum 17b91cbac42af9980f77f07a77c03d7d

EPO Under Scrutiny, But Will EU Listen?

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/epo-backlash-2023.webm

Summary: With the UPC days away (an illegal and unconstitutional kangaroo court

system, tied to the European Union in spite of critical deficiencies) it’s

curious to see EPO scandals of corruption spilling over to the European Union

already

THE EU is about to get contaminated with the EPO cancer (EPO staff compares the

administration to a cancer). Will that doom the union? Well, it certainly won’t

help.

“To get promoted in these institutions one must be profoundly corrupt or

participate in profound corruption.”In past years we covered EUIPO corruption

that had come from (or via) the EPO. Does the EU really want to go on with

this? Will_EUIPO_replace_the_EPO? The European Commission does not seem to

understand what it’s doing; it’s a puppet on strings for corporate lobbyists —

even actors working on behalf of foreign countries.

SUEPO has just taken note of the following article, which was put behind a

paywall except this_part:

 We provide a rundown of Managing IP’s news and analysis coverage from

 the week, and review what’s been happening elsewhere in IP

 French govt complained to EPO over EUIPO election conduct

 French finance minister Bruno Le Maire wrote to António Campinos,

 president of the EPO, to complain over the timing of an event that

 will be held in Lisbon one week before the EUIPO leadership vote,

 Managing revealed this week.

 Le Maire, minister for the economy and finance since 2017, suggested

 the event could be seen as interfering with the process to select a

 new EUIPO executive director.

 Managing IP can also reveal that the incumbent executive director,

 Christian Archambeau, hinted at interference “from Munich” in the

 decision to remove him last November.

We previously saw more coverage related to this; that too was behind a paywall,

so only the patent microcosm can see it. Remember that António Campinos is in

fact French and he’s only using the Portuguese government to forge his

political career of corruption, coercion, and suppression. António Campinos is

using EPO budget to bribe governments and officials, mimicking exactly what

Benoît_Battistelli did before him (same modus operandi). António was born to a

well-known father (already dead while António was a teenager) who fought to

bury people like his son, António. As for Archambeau, he’s just another_EPO

opportunist who is still reviled by some EPO longtimers. To get promoted in

these institutions one must be profoundly corrupt or participate in profound

corruption.

More in the video above… █

                ䷩ 𝚕𝚒𝚗𝚎 3490

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

Gemini_version_available_♊︎

✐ Links_27/05/2023:_Plans_Made_for_GNU’s_40th_Anniversary⠀✐

Posted in News_Roundup at 11:33 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Applications

      o Instructionals/Technical

      o Games

      o Desktop_Environments/WMs

            # K_Desktop_Environment/KDE_SC/Qt

* Distributions_and_Operating_Systems

      o Fedora_Family_/_IBM

      o Canonical/Ubuntu_Family

      o Devices/Embedded

      o Open_Hardware/Modding

      o Mobile_Systems/Mobile_Applications

* Free,_Libre,_and_Open_Source_Software

      o Education

      o Programming/Development

            # Python

* Leftovers

      o Education

      o Health/Nutrition/Agriculture

      o Proprietary

      o Security

            # Privacy/Surveillance

      o Defence/Aggression

      o Transparency/Investigative_Reporting

      o Environment

            # Wildlife/Nature

      o AstroTurf/Lobbying/Politics

      o Censorship/Free_Speech

      o Freedom_of_Information_/_Freedom_of_the_Press

      o Civil_Rights/Policing

      o Digital_Restrictions_(DRM)

      o Monopolies

            # Trademarks

            # Copyrights

* Gemini*_and_Gopher

      o Personal

      o Technical

            # Internet/Gemini

* § GNU/Linux⠀➾

      o § Applications⠀➾

            # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to

              Apple_Activity_Monitor⠀⇛

                   Activity Monitor displays a variety of resources in

                   use on a system in real time. These include

                   processes, disk activity, memory usage, and more to

                   provide a sort of dashboard.

                   Activity Monitor is proprietary software and not

                   available for Linux. We recommend the best free and

                   open source alternatives.

            # ⚓ DebugPoint ☛ Top_10_Debian-Based_Linux_Distributions_for

              Everyone⠀⇛

                   Debian is a Linux operating system that has been

                   around for a long time and is known for its

                   universal compatibility. It is well known for long-

                   term support, stability, security, and critical

                   business use cases.

                   The Debian stable version is one of the sought-

                   after Linux distributions because its support spans

                   multiple years. This helps if you are running older

                   versions of applications or packages which are

                   critical.

                   We review ten Debian-based Linux distributions,

                   which you may want to try out for all use cases.

            # ⚓ TecMint ☛ 10_Most_Popular_Download_Managers_for_Linux_in

              2023⠀⇛

                   Download managers on Windows are one of the most

                   needed tools that are missed by every newcomer to

                   the Linux world, programs like Internet Download

                   Manager Download Accelerator Plus and Free Download

                   Manager are very wanted, but these tools are not

                   available under Linux or Unix-like systems.

                   No, to worry, you will find several alternate

                   download managers for Linux that can help you

                   manage and accelerate your file downloads on a

                   Linux desktop.

      o § Instructionals/Technical⠀➾

            # ⚓ Ubuntubuzz ☛ What_To_Do_After_Installing_elementary_OS_7⠀⇛

            # ⚓ OSTechNix ☛ 15_Essential_Linux_Commands_Every_Beginner

              Should_Know⠀⇛

            # ⚓ Herman Õunapuu ☛ I_held_a_talk_about_my_self-hosting

              adventure!⠀⇛

                   The talk took place on May 25th 2023 at k-space, a

                   hackerspace in Tallinn, Estonia.

            # ⚓ Adriaan Roselli ☛ Brief_Note_on_Popovers_with_Dialogs⠀⇛

                   The fake page is meant to mimic the stress of

                   filling out a complex multi-step form while working

                   against the clock. As the user hits a toggle-tip to

                   get more information on a field, a dialog appears

                   telling the user they will be logged out unless

                   they hit the button.

            # ⚓ University of Toronto ☛ In_practice,_Grafana_has_not_been

              great_at_backward_compatibility⠀⇛

                   We started our Prometheus and Grafana based metrics

                   setup in late 2018. Although many of our Grafana

                   dashboards weren’t created immediately, the

                   majority of them were probably built by the middle

                   of 2019. Based on release history, we probably

                   started somewhere around v6.4.0 and had many

                   dashboards done by the time v7.0.0 came out. We’re

                   currently frozen on v8.3.11, having tried v8.4.0

                   and rejected it and all subsequent versions. The

                   reason for this is fairly straightforward; from

                   v8.4.0 onward, Grafana broke too many of our

                   dashboards. The breakage didn’t start in 8.4, to be

                   honest. For us, things started to degrade from the

                   change between the 7.x series and 8.0, but 8.4 was

                   the breaking point where too much was off or not

                   working.

            # ⚓ Jim Nielsen ☛ Link_Preload_as_Image⠀⇛

                   I’ve been playing with these fancy new view

                   transitions and my experience thus far is that they

                   work ok on localhost, but as soon as I push code to

                   a preview branch on a remote server, the image

                   loads between transitions are janky because of

                   image loading.

            # ⚓ How_to_install_the_AWS_CLI_on_Linux_using_PIP_of_Python⠀⇛

                   The AWS Command Line Interface (CLI) is a free tool

                   provided by the Amazon web service, a cloud

                   computing platform. It allows users to interact and

                   manage the various AWS services directly from their

                   system’s command terminal. Well, if you are a

                   Ubuntu Linux user then can install AWS CLI directly

                   using the APT package manager, however, for other

                   distro users who want to get the latest AWSL CLI

                   version but using the PIP, this article is for

                   them. PIP is a popular package manager developed to

                   install libraries and other dependencies for a

                   Python project.

            # ⚓ Network World ☛ Resizing_images_on_the_Linux_command_line_|

              Network_World⠀⇛

                   The convert command from the ImageMagick suite of

                   tools provides ways to make all sorts of changes to

                   image files. Among these is an option to change the

                   resolution of images. The syntax is simple, and the

                   command runs extremely quickly. It can also convert

                   a image from one format to another (e.g., jpg to

                   png) as well as blur, crop, despeckle, dither, flip

                   and join images and more.

                   Although the commands and scripts in this post

                   mostly focus on jpg files, the convert command also

                   works with a large variety of other image files,

                   including png, bmp, svg, tiff, gif and such.

            # ⚓ Beebom ☛ 10+_Ways_to_Use_the_find_Command_in_Linux_|

              Beebom⠀⇛

                   Have you ever found yourself frantically searching

                   for an important file, only to realize that you

                   wasted many hours trying to look in every directory

                   but the file is nowhere to be found? Well, this is

                   a common problem that most Linux users face,

                   especially new users with a huge number of

                   disorganized files and directories. In this

                   article, we explain how you can search for files

                   and directories in different ways using the find

                   command in Linux.

      o § Games⠀➾

            # ⚓ GamingOnLinux ☛ Warhammer_40,000:_Gladius_–_Relics_of_War

              is_free_to_keep_until_June_1st⠀⇛

                   Get your 4x Warhammer strategy gaming on, as

                   Warhammer 40,000: Gladius – Relics of War from

                   Proxy Studios and Slitherine Ltd is free to claim

                   and keep until June 1st. It has Native Linux

                   support and is Steam Deck Playable.

            # ⚓ GamingOnLinux ☛ Highly_rated_colour-changing_puzzle

              adventure_‘Hue’_free_to_keep_until_June_8th⠀⇛

                   Need a free game? You’re in luck as Hue from

                   Fiddlesticks Games and Curve Games is currently

                   free to keep on Steam until June 8th. Released

                   originally back in 2016, it has a Native Linux

                   version available and is rated Steam Deck Playable.

            # ⚓ GamingOnLinux ☛ Many_years_later_Neverwinter_Nights:

              Enhanced_Edition_is_still_getting_better⠀⇛

                   Originally released in 2002 and then later as

                   Neverwinter Nights: Enhanced Edition from Beamdog,

                   many years on it’s still getting major upgrades

                   including a new Toon shader and loading speed

                   improvements.

            # ⚓ GamingOnLinux ☛ Nintendo_hits_Valve_with_DMCA_against_the

              Dolphin_emulator_release⠀⇛

                   Back in March the plan was announced for the Wii

                   and GameCube emulator Dolphin to release on Steam,

                   along with some useful Steam features but now that

                   seems unlikely to happen.

            # ⚓ GamingOnLinux ☛ Stone_Age_farming_life-sim_Roots_of_Pacha

              has_returned_to_Steam⠀⇛

                   After a messy situation with their publisher, Soda

                   Den has now split from Crytivo and Roots of Pacha

                   has returned for sale on Steam.

            # ⚓ GamingOnLinux ☛ Valve_upgrades_Proton_Experimental_with_a

              number_of_bug_fixes⠀⇛

                   Today there’s a new build of Proton Experimental

                   available for Steam Deck and desktop Linux gamers,

                   with it Valve has given us a bunch of bug fixes.

                   With there now being many different Proton versions

                   it can get a bit confusing, so head on over to

                   my beginner’s guide on Steam Play and Proton for

                   more info.

      o § Desktop Environments/WMs⠀➾

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

                  # ⚓ Nate Graham ☛ This_week_in_KDE:_Night_color_on

                    Wayland_with_NVIDIA⠀⇛

                         This week probably the biggest news is that

                         in Plasma 6, the Night Color feature will

                         work as expected on Wayland when you’re using

                         an NVIDIA GPU! Because NVIDIA’s drivers don’t

                         support the necessary Gamma LUT features to

                         make it work in an optimal way as on Intel

                         and AMD GPUs, we had to use a slightly

                         different approach that isn’t quite as

                         efficient. But hopefully that’s better than

                         not having the feature work at all, and if

                         you care about the increased resource usage,

                         you’re welcome to not use the feature.

* § Distributions and Operating Systems⠀➾

      o § Fedora Family / IBM⠀➾

            # ⚓ HPC Wire ☛ CIQ_Extends_Enterprise-Grade_Support_for_Rocky

              Linux_9.2_and_8.8⠀⇛

                   CIQ, the company supporting enterprises with the

                   next generation of software infrastructure built

                   atop the Rocky Linux enterprise Linux distribution,

                   announced today that it has certified its suite of

                   software products on recently released Rocky Linux

                   9.2 and Rocky Linux 8.8. Certified CIQ products

                   include Warewulf and Apptainer as well as the newly

                   launched Fuzzball and images available in the

                   Mountain repo as a service offering. CIQ also

                   announced enterprise grade professional support on

                   both of the new versions of Rocky Linux.

                   [...]

                   Additionally, CIQ is announcing long term support

                   (LTS) for Rocky 9.2 which will include support for

                   the Federal Information Processing Standards

                   (FIPS). The addition of LTS brings support to CIQ

                   customers for Rocky Linux 9.2 for an additional 18

                   months, providing support beyond the community

                   edition for customers who need assurance that a

                   trusted partner will be there to support them for a

                   guaranteed time frame.

      o § Canonical/Ubuntu Family⠀➾

            # ⚓ Ubuntu ☛ Ubuntu_Summit_2023⠀⇛

                   After the success of last year’s Ubuntu Summit in

                   Prague, the organizers at Canonical set a goal to

                   make this year’s Summit bigger, better and bolder.

                   With this goal in mind, we are all extremely

                   excited to announce that this year’s Ubuntu Summit

                   will be hosted in the beautiful city of Riga,

                   Latvia!

                   The Ubuntu Summit is more than just a conference;

                   it’s an annual celebration of the most compelling

                   and groundbreaking innovations from the open source

                   ecosystem. Produced and hosted by Canonical, the

                   publishers of Ubuntu, the Summit offers a unique

                   opportunity to experience first-hand the cutting-

                   edge innovations and pioneering technologies that

                   are transforming our world.

            # ⚓ Ubuntu ☛ Time_to_prepare_for_Ubuntu_18.04_LTS_end_of

              standard_support_on_31_May_2023_–_Options_for_Google_Cloud

              users⠀⇛

                   In accordance with the information shared in our

                   latest blog post, it is important to note that

                   Ubuntu 18.04 LTS, codenamed ‘Bionic Beaver,’ is

                   approaching the end of its standard five-year

                   maintenance period on 31 May 2023. Consequently,

                   unless you hold an Ubuntu Pro subscription, updates

                   for Ubuntu 18.04 LTS servers will cease to be

                   available.

                   By subscribing to Ubuntu Pro, you can ensure that

                   your Ubuntu 18.04 LTS deployment remains fully

                   supported until 2028. This extended support period

                   provides you with continued assistance and

                   maintenance for your workloads running on Google

                   Compute Engine (GCE).

      o § Devices/Embedded⠀➾

            # ⚓ ZimaBoard_832_Single_Board_Server_Review_for_All_Creators⠀⇛

                   The ZimaBoard 832 Single Board Server is a compact

                   and powerful solution that caters to a wide range

                   of server applications. In this comprehensive

                   review, we will explore its design, features, and

                   capabilities, highlighting its potential as a

                   versatile and efficient server platform.

                   [...]

                   Once the hardware setup is complete, the next step

                   is to install the operating system (OS) on the

                   ZimaBoard 832. The board supports a range of OS

                   options, including Linux distributions such as

                   Ubuntu, Debian, or Fedora.

            # ⚓ Linux Gizmos ☛ Debix_Model_B_SBC_targets_industrial

              embedded_applications⠀⇛

                   The Debix Model B is a single board computer

                   integrating the NXP i.MX8M Plus processor with 2.3

                   TOPs NPU and with extended operating temperature

                   range. The new embedded device comes in a Raspberry

                   Pi form-factor and offers similar peripherals.

      o § Open Hardware/Modding⠀➾

            # ⚓ Arduino ☛ Analyze_the_ambient_sound_around_you_with_this

              Arduino_setup⠀⇛

                   Like the visualizer of the equalizer on an old

                   stereo receiver, this displays the levels of

                   several frequency bands within the audio it

                   monitors. In this case, that audio is the sound

                   around the device collected by an onboard

                   microphone. It shows the levels for seven different

                   frequencies: 63Hz, 160Hz, 400Hz, 1kHz, 2.5kHz,

                   6.3kHz, and 16kHz. Most devices like this use LEDs

                   to show the levels, but this shows them on a OLED

                   screen instead and that allows for more

                   flexibility.

            # ⚓ Olimex ☛ New_Open_Source_Hardware_design_is_verified:

              ESP32-SBC-FabGL_single_board_computer_based_on_FabGL_library

              with_PS2_keyboard,_mouse_and_VGA_display_with_many_retro

              computer_emulators⠀⇛

                   This is how the idea for ESP32-SBC-FabGL was born.

                   I wanted to create a board that could be used as a

                   graphics/sound/IO co-processor for other retro

                   computers based on different processors.

      o § Mobile Systems/Mobile Applications⠀➾

            # ⚓ India Today ☛ New_virus_targets_Android_phone,_steals_call

              records,_passwords_and_other_sensitive_data_of_users_–_India

              Today⠀⇛

            # ⚓ The Register UK ☛ Predator_may_have_more_spyware

              capabilities_than_we_know_•_The_Register⠀⇛

            # ⚓ SlashGear ☛ Android_TV’s_Live_Tab:_What_It_Is_And_How_To

              Use_It⠀⇛

            # ⚓ 9to5Google ☛ Google_gives_tips_for_how_to_buy_Android_TV

              box_without_malware⠀⇛

            # ⚓ The Sun ☛ Billions_of_Android_phone_owners_must_beware

              ‘masquerade’_call_that_steals_your_money_–_sinister_sign

              you’re_a_victim_|_The_US_Sun⠀⇛

            # ⚓ Make Use Of ☛ Is_GM_Ditching_Android_Auto_and_Apple_CarPlay

              a_Sign_of_Things_to_Come?⠀⇛

            # ⚓ Phone Arena ☛ Inexpensive_tool_can_be_used_to_easily_break

              into_Android_phones_–_PhoneArena⠀⇛

            # ⚓ Android Authority ☛ How_to_turn_off_your_Android_phone_–

              Android_Authority⠀⇛

            # ⚓ Lifewire ☛ How_to_Add_Apps_to_Android_Auto⠀⇛

            # ⚓ XDA ☛ Android_14_Beta_2.1_arrives_with_a_whole_bunch_of

              stability_improvements⠀⇛

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

      o ⚓ The Register UK ☛ Why_you_might_want_an_email_client_in_the_era

        of_webmail⠀⇛

             A rather nice feature for Linux and BSD users is that now

             you can use the middle-click function, which pastes

             whatever text is currently selected, to create a new tab.

             Google Chrome has done this for years, so it’s welcome to

             see it come to Firefox. It works for URLs and for plain

             text — if what you’re pasting doesn’t look like a web

             address, then Firefox will search for it.

      o § Education⠀➾

            # ⚓ GNU ☛ GNU_40th_Anniversary⠀⇛

                   Join us to celebrate the GNU Project’s freedom-

                   spreading accomplishments with presentations in

                   English about various GNU packages, hacking on free

                   software and making new releases! The 40th

                   anniversary hacker meeting is open to all who want

                   to celebrate, work on, or learn about free

                   software. We are putting together an appropriate

                   schedule, if you have something to contribute,

                   please contact <gnu40@gnu.org> with an informal

                   proposal. We hope to put together a diverse

                   selection of presentations, discussions and

                   announcements all day long.

      o § Programming/Development⠀➾

            # ⚓ Daniel Lemire ☛ Expected_performance_of_a_Bloom_filter⠀⇛

                   A Bloom filter is a standard data structure in

                   computer science to approximate a set. Basically,

                   you start with a large array of bits, all

                   initialized at zero. Each time you want to add an

                   element to the set, you compute k different hash

                   values and you set the bits at the k corresponding

                   locations to one.

            # ⚓ Daniel Pocock ☛ JSON_CEE_structured_logging_for_WebRTC,_SIP

              and_XMPP⠀⇛

                   I’ve recently added JSON CEE structured logging to

                   reSIProcate and submitted pull requests for

                   identical functionality in some related projects.

                   The use case for structured logging is quite

                   compelling in the RTC world, which includes WebRTC,

                   SIP and XMPP software. In the early days, we would

                   do everything with a single process like Asterisk

                   and we would only have to deal with a single log

                   file. Today, especially with WebRTC, we often have

                   multiple processes involved in a single phone call

                   or video meeting. When something goes wrong, we

                   need to be able to look at the logs from all of

                   these processes. Structured logging provides a

                   convenient way to combine and analyze the log

                   files.

            # ⚓ Earthly ☛ CI/CD_Security:_Challenges_and_Best_Practices⠀⇛

                   This article will delve into the challenges and

                   risks associated with CI/CD security, best

                   practices for securing the pipeline, code, and

                   infrastructure, and an overview of the tools and

                   technologies available to organizations to ensure

                   their CI/CD process is secure. By the end of this

                   article, you will have a better understanding of

                   the importance of CI/CD security, and the steps

                   necessary to mitigate the risks associated with it.

            # ⚓ PR Newswire ☛ The_Linux_Foundation_Announces_WasmCon_Event

              Focused_on_WebAssembly_Technologies⠀⇛

            # § Python⠀➾

                  # ⚓ Earthly ☛ Querying_Relational_Databases_With

                    SQLAlchemy_in_Python⠀⇛

                         If you are interested in working with

                         relational databases in Python, then you need

                         to know what SQLAlchemy is. It is a Python

                         library that provides a high-level, SQL

                         abstraction layer for relational databases.

                         With SQLAlchemy, you can interact with

                         databases using Python objects and methods,

                         rather than writing raw SQL queries. In this

                         tutorial, you will learn how to get started

                         with SQLAlchemy and also learn how to

                         interact with and query an SQLite relational

                         database with the SQLAlchemy library.

* § Leftovers⠀➾

      o ⚓ Telex (Hungary) ☛ ‘Life_shouldn’t_be_taken_too_seriously,_you

        must_be_able_to_smile_about_it’⠀⇛

             It is very rare for an athlete to become an Olympic

             champion without first having won an individual gold

             medal at a European or World Championship, or even at a

             Hungarian championship. Valéria Gyenge won a gold medal

             at the most successful Olympics for Hungary, the 1952

             Helsinki Olympics without having been a national champion

             before. Her victory was a surprise even though she had

             won the 400 freestyle at a smaller event a month before

             the Olympics, having set a good time. The Hungarian

             swimmers were at their best then, and the team was by far

             the strongest ever, with four of the five gold medals

             going to Hungary.

      o ⚓ The Nation ☛ When_Tina_Turner_Rocked_Out_for_George_McGovern⠀⇛

             Tina Turner, a native of Tennessee who lived much of her

             life in Europe, only rarely waded into American politics.

             The “Queen of Rock and Roll,” who died Wednesday at age

             83, quietly supported Barack Obama for the presidency in

             2008, with the encouragement of Oprah Winfrey and some

             inspiration from Caroline Kennedy. But Turner’s one high-

             profile political performance came decades earlier, as

             part of a remarkable show of women’s solidarity with the

             anti–Vietnam War campaign of 1972 Democratic presidential

             nominee George McGovern.

      o ⚓ Scheerpost ☛ What’s_Your_Sign⠀⇛

      o § Education⠀➾

            # ⚓ BIA Net ☛ Erdoğan_makes_fun_of_intellectuals_his_government

              included_in_the_Peace_Process⠀⇛

                   Erdoğan used the term “entel-dantel” to name these

                   people who were included in the process to

                   strengthen public support for it..

                   While “entel” is short for “entellektüel,”

                   (intellectual in Turkish), dantel means lace. The

                   term is used to mock those who are either well-

                   educated or who write or express their opinions in

                   different ways, especially on political or social

                   issues and problems.

            # ⚓ Democracy Now ☛ “Education_Leads_to_Liberation”:_Nikole

              Hannah-Jones_on_The_1619_Project_&_Teaching_Black_History⠀⇛

                   As attacks on the teaching of Black history

                   escalate in Florida and other states, we hear from

                   The New York Times journalist Nikole Hannah-Jones,

                   who won a Pulitzer Prize for her work on “The 1619

                   Project.” She spoke on May 19 at the Malcolm X and

                   Dr. Betty Shabazz Memorial and Educational Center,

                   which is housed in the former Audubon Ballroom in

                   New York where Malcolm X was assassinated in 1965,

                   and talked about the impact Malcolm X’s writing had

                   on her life, as well as the importance of teaching

                   the full history of the United States. “What we

                   commonly call history is actually memory, and that

                   memory in the United States has been shaped too

                   often by white men in power who want us to remember

                   the history of a country that never existed,” she

                   said.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ YLE ☛ Telia_prohibits_employees’_TikTok_use_on_company

              devices⠀⇛

                   The new rules will go into effect at the end of

                   this month, affecting its operations in Finland and

                   six other countries in which it operates.

                   The Swedish company based its decision on data

                   security concerns related to the social media

                   platform that have been raised by authorities,

                   according to the firm’s quality and security

                   management chief in Finland, Kalle Kaasalainen.

            # ⚓ New York Times ☛ The_Surgeon_General’s_Social_Media_Warning

              and_A.I.’s_Existential_Risks⠀⇛

                   The U.S. surgeon general, Dr. Vivek Murthy, says

                   social media poses a “profound risk of harm” to

                   young people. Why do some in the tech industry

                   disagree?

            # ⚓ Variability_≠_“We_don’t_know”_how_COVID_vaccines_work⠀⇛

                   It’s been a while since I’ve written about a basic

                   science paper misinterpreted and/or misused by

                   antivaxxers. It’s also been a while since I’ve

                   encountered an antivax influencer or blogger with

                   whom I was unfamiliar when first seeing their

                   blather. So when I came across a post by someone

                   going by the ‘nym of Joomi entitled, New study

                   shows how little we know about how mRNA vaccines

                   “work”—along with a blurb claiming that “Vastly

                   different levels of spike protein depending on cell

                   type”—I knew I had my topic for today. I have no

                   idea who “Joomi” is other than this description

                   from the Substack Let’s Be Clear:

      o § Proprietary⠀➾

            # ⚓ Ars Technica ☛ Green_hills_forever:_Windows_XP_activation

              algorithm_cracked_after_21_years⠀⇛

                   On the blog of tinyapps.org (first spotted by The

                   Register), which provides micro-scale, minimalist

                   utilities for constrained Windows installations, a

                   blog post appropriately titled “Windows XP

                   Activation: GAME OVER” runs down the semi-recent

                   history of folks looking to activate Windows XP

                   more than 20 years after it debuted, nine years

                   after its end of life, and, crucially, some years

                   after Microsoft turned off its online activation

                   servers (or maybe they just swapped certificates).

            # ⚓ The Register UK ☛ Microsoft_has_made_Azure_Linux_generally

              available._Repeat,_Azure_Linux [Ed: The Register pushing

              Microsoft agenda; this isn't support of GNU/Linux but an

              attack on it]⠀⇛

            # ⚓ Dev Class ☛ Azure_Linux_released_at_Build_–_where_Microsoft

              revealed_why_it_did_not_fork_Fedora [Ed: Microsoft mole Tim

              Anderson moved from The Register to this other site, in which

              he continues to actively attack and tarnish the Linux brand

              for Microsoft]⠀⇛

            # § Windows TCO⠀➾

                  # ⚓ Security Week ☛ Organizations_Worldwide_Targeted_in

                    Rapidly_Evolving_Buhti_Ransomware_Operation⠀⇛

                         In a recent attack, the Buhti operators used

                         a minimally modified version of the LockBit

                         3.0 (LockBit Black) ransomware to target

                         Windows machines. The builder for LockBit

                         leaked online in September 2022.

      o § Security⠀➾

            # ⚓ Bleeping Computer ☛ New_Buhti_ransomware_gang_uses_leaked

              Windows,_Linux_encryptors [Ed: Ransomware is about 95%

              Windows; when Microsoft puts back doors in Windows, it blames

              "China"; when it's something like WordPress extensions,

              Microsoft media blames "Linux". The pinnacle of one's nerve

              is attributing holes in proprietary software of VMware to

              "Linux". Defective software can be installed on any system,

              but that's like saying cars are unsafe because you can drive

              them down a cliff.]⠀⇛

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

                   Security updates have been issued by Debian

                   (sniproxy), Fedora (c-ares), Oracle (apr-util,

                   curl, emacs, git, go-toolset and golang, go-

                   toolset:ol8, gssntlmssp, libreswan, mysql:8.0,

                   thunderbird, and webkit2gtk3), Red Hat (go-toolset-

                   1.19 and go-toolset-1.19-golang and go-toolset:

                   rhel8), Slackware (ntfs), SUSE (rmt-server), and

                   Ubuntu (linux-raspi, linux-raspi-5.4 and python-

                   django).

            # ⚓ ABC ☛ Patients_told_to_contact_NT_Health_following_privacy

              breach_of_identifiable_medical_records⠀⇛

                   Northern Territory Health says the onus is on

                   individuals to check if the privacy of their

                   medical records has been breached by the

                   government.

            # ⚓ Data Breaches ☛ NT_Health_throws_breach_notification

              obligations_out_the_window;_says_patients_should_call_them_to

              find_out_if_they_were_affected?!⠀⇛

                   According to Northern Territory Health’s website,

                   the Australian government agency manages the

                   Northern Territory public health system, operating

                   across five service delivery regions, six

                   hospitals, 74 health clinics, and seven corporate

                   offices.

            # ⚓ Data Breaches ☛ Tennessee_Orthopaedic_Clinics_notifies_HHS

              of_breach;_has_yet_to_notify_patients⠀⇛

                   An undated message on the Tennessee Orthopaedic

                   Clinics website states that TOC recently responded

                   to a security incident. They don’t say when they

                   discovered it, but their investigation determined

                   “that an unauthorized party accessed some of our

                   systems between March 20, 2023, and March 24, 2023,

                   and may have accessed or acquired certain files.”

            # ⚓ Data Breaches ☛ Two_ransomware_groups_claimed_to_have

              attacked_Albany_ENT_&_Allergy_Services_and_leaked_data,_but

              AENT_doesn’t_mention_that_at_all_in_their_notification?

              ⠀⇛

                   On April 28, DataBreaches reported that two

                   different ransomware groups claimed to have

                   attacked Albany ENT & Allergy Services, P.C. in

                   Albany, New York. This week, Albany ENT & Allergy

                   Services notified regulators and 224,486 affected

                   employees and patients about a breach. Their

                   notification is stunning, however, for its lack of

                   certain details.

            # ⚓ NYSDFS_Fines_Lender_and_Mortgage_Servicer_$4.25M_for

              Cybersecurity_Failures_Including_Vendor_Management⠀⇛

                   Yesterday, New York’s Department of Financial

                   Services (“DFS”) announced another enforcement

                   action under the state’s Cybersecurity Requirements

                   for Financial Services Companies, 23 N.Y.C.R.R.

                   Part 500 (“Reg 500”). According to the press

                   release, OneMain Financial Group LLC (“OneMain”)

                   will pay a $4.25 million penalty to New York State

                   for alleged violations of Reg 500.

            # ⚓ Security Week ☛ Google_Cloud_Users_Can_Now_Automate_TLS

              Certificate_Lifecycle⠀⇛

                   Google makes ACME API available to all Google Cloud

                   users to allow them to automatically acquire and

                   renew TLS certificates for free.

            # ⚓ Krebs On Security ☛ Phishing_Domains_Tanked_After_Meta_Sued

              Freenom⠀⇛

                   The number of phishing websites tied to domain name

                   registrar Freenom dropped precipitously in the

                   months surrounding a recent lawsuit from social

                   networking giant Meta, which alleged the free

                   domain name provider has a long history of ignoring

                   abuse complaints about phishing websites while

                   monetizing traffic to those abusive domains.

            # ⚓ Security Week ☛ Zyxel_Firewalls_Hacked_by_Mirai_Botnet⠀⇛

                   A Mirai botnet has been exploiting a recently

                   patched vulnerability tracked as CVE-2023-28771 to

                   hack many Zyxel firewalls.

            # ⚓ Ubuntu ☛ How_to_secure_your_MLOps_tooling?⠀⇛

                   Production-grade AI initiatives are not an easy

                   task. Organisations need to go through different

                   stages to prepare data, develop the model and

                   deploy it. Reproducibility and portability are

                   essential for such projects. This is where machine

                   learning operations (MLOps) can help.

            # § Privacy/Surveillance⠀➾

                  # ⚓ The Register UK ☛ Subpoenaed_PyPI_says_bye-bye_to_as

                    much_IP_address_data_as_it_can⠀⇛

                         But now that the code repository has

                         disclosed receiving three subpoenas for data

                         on five users earlier this year, the Python

                         community package registry wants developers

                         to understand that it’s working to minimize

                         the user data that it stores.

                  # ⚓ Techdirt ☛ Leaked_Document_Shows_Spain_Is_Fully_On

                    Board_With_The_EU_Commission’s_Plan_To_Criminalize

                    Encryption⠀⇛

                         For a few years now, the EU Commission has

                         been pushing legislation that would

                         undermine, if not actually criminalize, end-

                         to-end encryption. It’s “for the children,”

                         as they say. To prevent the distribution of

                         CSAM (child sexual abuse material), the EU

                         wants to mandate client-side scanning by tech

                         companies — a move that would necessitate the

                         removal of one end of the end-to-end

                         encryption these companies offer to their

                         users.

      o § Defence/Aggression⠀➾

            # ⚓ Scheerpost ☛ ‘There_Is_No_Safe_Place_in_Gaza’:_Palestinians

              Speak_Out_During_Israeli_Assault⠀⇛

                   In a vicious five-day assault, Israeli occupying

                   forces killed 33 Palestinians in Gaza.

            # ⚓ Scheerpost ☛ How_a_Small_Activist_Sailing_Ship_Successfully

              Challenged_the_Nuclear_Arms_Race⠀⇛

                   The 1958 voyage of the Golden Rule offers important

                   strategic lessons on how to confront an

                   overwhelming evil and win.

            # ⚓ Democracy Now ☛ Seditious_Conspiracy:_Oath_Keepers_Founder

              Stewart_Rhodes_Gets_18_Years_in_Prison_for_Jan._6⠀⇛

                   Stewart Rhodes, founder of the far-right Oath

                   Keepers group, has been sentenced to 18 years in

                   prison for his role in the attack on the U.S.

                   Capitol. It is the longest sentence handed down so

                   far to any participant in the January 6

                   insurrection, when thousands of Trump supporters

                   stormed the halls of Congress to stop the

                   certification of Joe Biden’s 2020 presidential

                   victory. One of Rhodes’s associates, Kelly Meggs,

                   who led the Florida chapter of the Oath Keepers,

                   was sentenced Thursday to 12 years in prison. A

                   jury had convicted both men of seditious conspiracy

                   in November. The sentences are a “substantial win

                   for democracy,” says Kristen Doerer, who reports on

                   right-wing extremism and followed the case.

            # ⚓ The Nation ☛ What_We_Can_Learn_From_the_Surge_of_Far-Right

              Violence_in_India⠀⇛

                   Are you worried about the rising political power of

                   violent white nationalists in America? Well, you’ve

                   got plenty of company, including US national

                   security and counterterrorism officials. And we’re

                   worried, too—worried enough, in fact, to feel that

                   it’s time to take a look at the experience of

                   India, where Hindu supremacist dogma has

                   increasingly been enforced through violent means.

                   While there are striking parallels between both

                   countries, India appears to have ventured further

                   down the road of far-right violence. Its experience

                   could potentially offer Americans some valuable, if

                   grim, lessons.

            # § War in Ukraine⠀➾

                  # ⚓ Scheerpost ☛ Ukraine:_Why_Negotiations_Are_the_Only

                    Rational_Option_in_the_Face_of_Climate_Chaos_and

                    Nuclear_Dangers⠀⇛

                         The Pentagon Leaks have shown that, from the

                         U.S. military’s perspective, the

                         confrontation between Russia and Ukraine has

                         reached a stalemate. Neither side can win in

                         the foreseeable future, according to the

                         assessment.

                  # ⚓ Meduza ☛ Medvedev_says_‘conflict_in_Ukraine’_could_be

                    ‘going_on_for_decades’_—_Meduza⠀⇛

                         During an official visit to Vietnam on

                         Friday, Russian Security Council Deputy Chair

                         (and former President) Dmitry Medvedev told

                         journalists that the “military conflict” in

                         Ukraine will be “long-lasting.”

                  # ⚓ Meduza ☛ Russia_carries_out_deadly_missile_strike_on

                    Dnipro_medical_center_—_Meduza⠀⇛

                         A Russian missile has struck a medical center

                         in Dnipro, killing at least one person and

                         injuring at least 15, according to Ukrainian

                         President Volodymyr Zelensky.

                  # ⚓ Meduza ☛ ‘I_prayed_I_wouldn’t_be_next’_The_secretive

                    prisons_where_Russia_hides_and_tortures_Ukrainian

                    civilians⠀⇛

                         Over the last 14 months, Russia has abducted

                         thousands of Ukrainian civilians, from

                         volunteers and journalists to former soldiers

                         and officials, and locked them in Russian

                         prisons. The victims don’t have POW status,

                         they’re not allowed to see their lawyers or

                         loved ones, and most of them are impossible

                         to communicate with from outside. Those who

                         have managed to get out often still don’t

                         know the official reasons for their

                         incarceration or their release. In Simferopol

                         alone, more than 100 civilian hostages (as

                         they’re called by human rights advocates) are

                         currently in captivity. Meduza special

                         correspondent Lilia Yapparova spoke with

                         Ukrainians who have been released from the

                         facilities, as well as with their relatives

                         and lawyers, to find out how this clandestine

                         prison system works.

                  # ⚓ Latvia ☛ Police_car_convoy_heads_from_Latvia_to

                    Ukraine_Friday⠀⇛

                         On Friday, May 26, a convoy with technical

                         aid was sent by the Latvian State Police to

                         soldiers in Ukraine. In cooperation with the

                         Ministry of Defense and the Entrepreneurs for

                         Peace Fund, a 12-vehicle convoy has been

                         launched today, but there are more cars in

                         the aid package, as well as unmanned

                         aircraft, generators, mobile power stations

                         and uniforms.

                  # ⚓ Meduza ☛ The_second_drone_war_How_Ukraine_and_Russia

                    are_trying_to_use_drones_to_their_advantage_—_Meduza⠀⇛

                  # ⚓ Meduza ☛ Russian_intelligence_ship_returns_to

                    Sevastopol_following_naval_drone_attack_—_Meduza⠀⇛

                         The Russian intelligence ship Ivan Khurs,

                         part of Russia’s Black Sea Fleet, has

                         returned to Sevastopol. Video footage of the

                         ship circulated on Telegram, and Russian news

                         outlet Kommersant confirmed that the Ivan

                         Khurs had returned to Sevastopol Bay.

                  # ⚓ Meduza ☛ Georgian_President_Salome_Zourabichvili

                    criticizes_government_for_appeasing_Russia_and_drifting

                    away_from_Europe_—_Meduza⠀⇛

                         In her Independence Day address, Georgian

                         President Salome Zourabichvili criticized the

                         government for its policies with regard to

                         Russia and Russian immigrants.

                  # ⚓ Latvia ☛ Baltic_states_and_Germany_pledge_long-term

                    support_for_Ukraine⠀⇛

                         The Prime Ministers of the Baltic

                         states gathered in Tallinn, Estonia May 26 to

                         meet with German Chancellor Olaf Scholz.

                  # ⚓ Latvia ☛ LTRK_President:_Latvians_should_help

                    Ukrainians_into_the_European_market⠀⇛

                         The revival of Ukraine’s economy will also be

                         an opportunity for Latvian entrepreneurs, who

                         should help Ukrainians to break into the

                         European market, Aigars Rostovskis, president

                         of the Latvian Chamber of Commerce and

                         Industry, said in an interview to Latvian

                         Television on May 26.

                  # ⚓ AntiWar ☛ Trying_To_Build_Peace_One_BRICS_at_a_Time⠀⇛

                         In the early days of the war in Ukraine,

                         Ukrainian President Volodymyr Zelensky was

                         open to negotiating a peace. The United

                         States was not.

                  # ⚓ The Strategist ☛ Putin_may_lose_it_all_by_going_all-

                    in_for_Ukraine⠀⇛

                         Russia’s continued isolation from the G7, and

                         the expansion of sanctions against Moscow,

                         have made the severe consequences of

                         President Vladimir Putin’s invasion of

                         Ukraine clearer than ever.

                  # ⚓ France24 ☛ Deadly_Russian_strike_on_hospital,_Kremlin

                    talks_with_China_and_Brazil⠀⇛

                         A hospital in the eastern Ukrainian city of

                         Dnipro was hit Friday morning in a Russian

                         missile attack, regional governor Serhiy

                         Lysak said. This comes as Russia held

                         separate talks with China and Brazil on the

                         war in Ukraine. Follow our blog to see how

                         the day’s events unfolded. All times are

                         Paris time (GMT+2).

                  # ⚓ France24 ☛ In_Ukraine’s_Avdiivka,_divided_loyalties

                    after_nearly_a_year_of_Russian_assault⠀⇛

                         Russian forces have for months been

                         concentrating their offensive on eastern

                         Ukraine with the aim of capturing the Donetsk

                         region. Avdiivka, a town located on the

                         outskirts of the occupied regional capital,

                         is one of the most dangerous places on the

                         front line. It has resisted Russian assaults

                         for nearly a year of continuous siege, and

                         Russian aircraft and missiles have been

                         ravaging what remains of the town for weeks.

                         FRANCE 24 reporters Catherine Norris Trent,

                         Johan Bodin and Dymitro Kovalchuk went in to

                         speak with the people there.

                  # ⚓ Hong Kong Free Press ☛ EU_urges_China_to_push_Russia

                    to_withdraw_from_Ukraine⠀⇛

                         The European Union told China’s envoy on

                         Thursday that it expects Beijing to help push

                         Russia to stop the bloodshed in Ukraine and

                         withdraw from the country. Senior EU foreign

                         policy official Enrique Mora met China’s Li

                         Hui in Brussels on the latest leg of

                         Beijing’s special representative for Eurasian

                         affairs’ European tour. Li has received

                         coordinated […]

                  # ⚓ Meduza ☛ Peskov_confirms_plans_to_move_Andrey

                    Rublev’s_fragile_‘Holy_Trinity’_icon_to_cathedral,

                    despite_conservators’_fears_—_Meduza⠀⇛

                         The Kremlin Press Secretary Dmitry Peskov

                         says that plans for transporting Andrey

                         Rublev’s “Holy Trinity” icon from the

                         Tretyakov Gallery to Moscow’s Christ the

                         Savior cathedral have been finalized and

                         approved by stakeholders.

                  # ⚓ LRT ☛ Lithuania_presents_next_military_aid_package

                    for_Ukraine⠀⇛

                         Lithuania’s next military assistance package

                         for Ukraine will include drone jamming

                         equipment, ammunition, military rations and

                         other support, Defence Minister Arvydas

                         Anušauskas has said.

                  # ⚓ RFERL ☛ Russian_Arms_Maker_Kalashnikov_Boosts_Output

                    Of_Kamikaze_Drones⠀⇛

                         Russian arms producer Kalashnikov, maker of

                         the world’s most widely used assault rifle,

                         said on May 26 it was launching a new

                         division for the production of kamikaze

                         drones — one of the key weapons used in the

                         Ukraine war.

                  # ⚓ RFERL ☛ German_Chancellor_Warns_Putin_Against_Frozen

                    Conflict_In_Ukraine⠀⇛

                         German Chancellor Olaf Scholz warned

                         President Vladimir Putin against creating a

                         frozen conflict along the borders of the

                         Ukrainian territories seized by Russia, in

                         remarks published on May 26 in the Koelner

                         Stadt-Anzeiger newspaper.

                  # ⚓ RFERL ☛ Blinken_To_Travel_To_Sweden,_Norway,_Finland,

                    As_Stockholm_Reiterates_NATO_Aspirations⠀⇛

                         U.S. Secretary of State Antony Blinken is set

                         to visit to Sweden, Norway, and Finland from

                         May 29 to June 2 as Washington seeks to

                         deepen transatlantic cooperation amid

                         Russia’s ongoing invasion of Ukraine.

                  # ⚓ RFERL ☛ EU’s_Former_Top_Diplomat_Concedes_Ukraine

                    Oversights,_Saying_‘Hindsight_Is_Always_Difficult’⠀⇛

                         The European Union’s former high

                         representative for foreign affairs and

                         security policy, Catherine Ashton, has

                         defended the bloc’s initial response after

                         Russia occupied Crimea in 2014, but

                         acknowledged “we did not know then what we

                         know now.”

                  # ⚓ RFERL ☛ Protesters_Condemn_Screening_Of_Russian

                    Azovstal_‘Propaganda’_In_Bulgaria⠀⇛

                         Dozens of people protested the screening at a

                         Russian cultural center in Sofia on May 25 of

                         a Russian film casting the capture last year

                         of the Azovstal steel plant in southern

                         Ukraine as a “liberation” from “neo-Nazis.”

                  # ⚓ teleSUR ☛ Moscow_Rejects_Sullivan’s_Remarks_About

                    Strikes_on_Russia⠀⇛

                         “We have not placed limitations on Ukraine

                         being able to strike on its territory within

                         its internationally recognized borders,” U.S.

                         Security Adviser said.

                  # ⚓ The Atlantic ☛ The_Russian_Red_Line_Washington_Won’t

                    Cross—Yet⠀⇛

                         Ukraine wants long-range missiles in order to

                         regain Crimea and end the war. Why won’t

                         Washington supply them?

                  # ⚓ YLE ☛ Migri_opening_17_new_reception_centres⠀⇛

                         Most reception system clients have come to

                         Finland from Ukraine, according to the

                         Finnish Immigration Service.

                  # ⚓ New York Times ☛ Russian_Missile_Strike_Hits

                    Ukrainian_Hospital⠀⇛

                         A Russian missile killed at least two people

                         and wounded dozens more at a hospital, while

                         apparent Ukrainian strikes hit occupied

                         cities in the south.

                  # ⚓ New York Times ☛ For_Ukraine_Military,_Far-Right

                    Russian_Volunteers_Make_for_Worrisome_Allies⠀⇛

                         Some fighters who led an incursion into

                         Russian territory this week have neo-Nazi

                         ties. “I worry that something like this could

                         backfire on Ukraine because these are not

                         ambiguous people.”

                  # ⚓ New York Times ☛ Anti-Kremlin_Group_Involved_in

                    Border_Raid_Is_Led_by_a_Neo-Nazi⠀⇛

                         The leader of the Russian Volunteer Corps,

                         one of the two insurgent groups responsible

                         for an armed incursion into Russia this week,

                         is a far-right extremist, German officials

                         and humanitarian groups say.

                  # ⚓ New York Times ☛ Ukraine_NATO_Bid_Mirrors_West

                    Germany’s_During_Cold_War⠀⇛

                         West Germany joined NATO in 1955, choosing

                         security over immediate territorial

                         integrity. Some suggest the same path could

                         be the best guarantee for Ukraine.

                  # ⚓ New York Times ☛ Russian_Public_Appears_to_Be_Souring

                    on_War_Casualties,_Analysis_Shows⠀⇛

                         Support for the war in Ukraine remains high

                         but could potentially turn if concern over

                         the high numbers of casualties persists,

                         according to FilterLabs AI.

                  # ⚓ Reason ☛ Eli_Lake:_Trump,_Russiagate,_and_the_End_of

                    FBI_Credibility⠀⇛

                         The Durham report is a “black eye” for the

                         FBI, leading Democrats, and the media, says

                         Lake.

                  # ⚓ New York Times ☛ The_Counteroffensive_Is_Coming⠀⇛

                         We preview what is next in the war in

                         Ukraine.

                  # ⚓ Defence Web ☛ Arms-to-Russia_row_raises_doubt_about

                    South_Africa’s_compliance,_which_could_face_tougher

                    scrutiny⠀⇛

                         The recent furore over accusations by the US

                         ambassador to South Africa, Reuben Brigety,

                         that South Africa was supplying arms to

                         Russia despite its declared policy of non-

                         alignment, has sparked a debate on whether

                         the country’s arms control is lax, non-

                         compliant and lacks oversight.

                  # ⚓ LRT ☛ Russia_moves_ahead_with_deployment_of_tactical

                    nuclear_weapons_in_Belarus⠀⇛

                         Russia moved ahead on Thursday with a plan to

                         deploy tactical nuclear weapons in Belarus,

                         whose leader said the warheads were already

                         on the move, in the Kremlin’s first

                         deployment of such bombs outside Russia since

                         the 1991 fall of the Soviet Union.

                  # ⚓ LRT ☛ Lithuanian_language_commission_sceptical_about

                    renaming_Kaliningrad⠀⇛

                         The State Commission of the Lithuanian

                         Language (VLKK) has rejected a proposal by

                         several MPs to stop calling the Russian

                         exclave wedged between Lithuania and Poland

                         ‘Kaliningrad’.

                  # ⚓ LRT ☛ Lithuania_hosts_9th_Vilnius_Russia_Forum⠀⇛

                         The Lithuanian capital is hosting the 9th

                         Vilnius Russia Forum on Friday.

                  # ⚓ RFA ☛ Malaysia’s_Mahathir_says_Russia_may_take

                    nuclear_option⠀⇛

                         The former prime minister also told Asia not

                         to take sides in U.S.-China disputes

                  # ⚓ RFERL ☛ Kazakhstan_Says_It_Has_No_Plans_To_Join_Any

                    Union_States⠀⇛

                         Kazakh presidential spokesman Ruslan

                         Zheldybai told journalists on May 26 that the

                         energy-rich Central Asian country has no

                         plans to join any union states, adding that

                         the integration process within the Russian-

                         led Eurasian Economic Union should only be in

                         the sphere of economics.

                  # ⚓ The Atlantic ☛ What_Happens_if_Russia_Stashes_Nukes

                    in_Belarus⠀⇛

                         And some news about that Kremlin drone strike

                  # ⚓ YLE ☛ No_reply_from_Russia_about_freezing_Finnish

                    embassy,_consulate_accounts⠀⇛

                         The bank accounts of the Finnish Embassy in

                         Moscow and the Consulate General’s office in

                         St Petersburg were frozen at the end of last

                         month.

                  # ⚓ New York Times ☛ Evan_Gershkovich_Appeals_Russia’s

                    Extension_of_His_Detention⠀⇛

                         Already jailed for two months on charges for

                         which Russia has provided no evidence, Mr.

                         Gershkovich has been ordered to remain in

                         prison for three more.

                  # ⚓ Meduza ☛ RIA_Novosti_source_threatens_‘consequences’

                    for_journalist_Evan_Gershkovich_if_WSJ_continues_to

                    publish_‘disinformation’_about_Russia_—_Meduza⠀⇛

                         Russia’s state news agency, RIA Novosti,

                         published a message from an “informed source

                         in Moscow,” warning The Wall Street Journal

                         (WSJ) of “consequences” for Evan Gershkovich,

                         a WSJ journalist who was arrested in Russia

                         in March 2023.

                  # ⚓ New York Times ☛ U.S._Condemns_Deal_Allowing_Russia

                    to_Deploy_Nuclear_Weapons_in_Belarus⠀⇛

      o § Transparency/Investigative Reporting⠀➾

            # ⚓ Techdirt ☛ Twitter_Demands_Academics_Who_Won’t_Pay_$42k/

              Month_Delete_Any_Twitter_Data_They_Currently_Have⠀⇛

                   Elon Musk has insisted that “transparency is the

                   key to trust” in rebuilding Twitter in his image.

                   He says it all the time. But, of course, under

                   Musk, Twitter has been significantly less

                   transparent, choosing to skip its transparency

                   reports, and generally close itself off. But one of

                   the key methods for transparency on Twitter has

                   long been its willingness to allow academic

                   researchers to access its API and do research

                   around Twitter and its users.

            # ⚓ The Dissenter ☛ Kissinger_Vs._‘The_Most_Dangerous_Man_In

              America’⠀⇛

      o § Environment⠀➾

            # ⚓ The Nation ☛ Warning_Signs_Are_Everywhere⠀⇛

            # ⚓ ANF News ☛ Ecologists_call_on_people_not_to_vote_for_those

              who_destroy_nature_and_history⠀⇛

                   Ecocide is one of the most disastrous acts

                   perpetrated by the AKP government during its 22-

                   year rule. The AKP government has deliberately

                   plundered the nature of Kurdistan, not only through

                   construction, but also through dams and power

                   plants.

            # § Wildlife/Nature⠀➾

                  # ⚓ The Nation ☛ Should_We_Bring_Species_Back_From

                    Extinction?⠀⇛

                         If you had a chance to save a species from

                         extinction, would you take it? I would—and I

am.

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ FAIR ☛ Montana_TikTok_Ban_a_Sign_of_Intensified_Cold_War

              With_China⠀⇛

                   Republicans see this as momentum to push other

                   state bans. Lawmakers of both major parties are

                   pushing legislation that “would block all

                   transactions from any social media company in or

                   under the influence of a ‘country of concern,’ like

                   China and Russia,” a move that would ban TikTok in

                   the US (USA Today, 12/13/22). Such a sweeping ban

                   is popular among voters, especially among

                   Republicans (Pew, 3/31/23; Wall Street Journal, 4/

                   24/23).

            # ⚓ Common Dreams ☛ Show_Don’t_Tell:_Josh_Hawley’s_Manly,

              Rancid,_Ludicrous_Log_of_Suet⠀⇛

                   Improbably – is there enough irony left in the

                   world to contain it? – “spineless chicken man,”

                   “sniveling li’l bitch,” liar, coward and “coifed,

                   soft, seditionist” Josh Hawley, famed for his “wee

                   scamper of fear” from Jan. 6 rioters he abetted,

                   has written a book about…manhood. Predictably, it’s

                   been shredded by the former Marine and Democrat

                   seeking his Senate seat and most of the known world

                   for banalities like, “Every man is called to be a

                   warrior.” Most cogent review: “As if.”

            # ⚓ Insight Hungary ☛ EU_Commissioner:_Long_way_to_go_for

              Hungary_to_receive_EU_funds⠀⇛

                   EU Budget Commissioner Johannes Hahn says there is

                   no specific deadline for the ongoing procedure

                   against Hungary, Euronews reports. It is also

                   possible that the closure of the case will slip

                   into the next Commission’s tasks in 2024. “There

                   are still major issues to be resolved, so we are

                   nowhere near the finish line,” said Hahn during a

                   hearing at the European Parliament. The Austrian

                   politician called the setting up the Integrity

                   Authority a step forward but said the Hungarian

                   government had not yet met the conditions.

                   He also denied that the Commission was blocking the

                   deal. The Commission is interested in a solution

                   that serves the interests of Hungarian citizens, he

                   added. Hahn also said that since the rule of law

                   procedure has no time limit, the process could be

                   completed after the next European Commission is in

                   place. He suggested that it might be worth changing

                   the rules of the procedure in the future.

            # ⚓ Telex (Hungary) ☛ Three_upcoming_national_elections_could

              bring_about_Orbán’s_veto_coalition_and_a_turnaround_in

              Europe,_think_tank_expects⠀⇛

                   Nézőpont Institute, the government-affiliated think

                   tank, isn’t expecting any major changes at the 2024

                   EP elections. Speaking at an event organised by the

                   institute on Thursday at the headquarters of

                   Polgári Magyarországért Alapítvány (Foundation for

                   a Civic Hungary, the party foundation of Fidesz) on

                   Stefánia út, Ágoston Sámuel Mráz said that

                   according to their latest analysis, Fidesz could

                   win as big a victory on 9 June 2024 as it did at

                   the last EP elections or five years before.

            # ⚓ The Nation ☛ Biden_Must_Remake_His_Candidacy⠀⇛

                   Joe Biden’s reelection campaign isn’t going well.

                   Since announcing his bid for a second term in

                   April, the president’s poll numbers have remained

                   dismal. RealClearPolitics’ average of recent polls

                   gives him a 41.4 percent approval rating among

                   likely voters, while 53.8 percent disapprove. And

                   it won’t necessarily get better when Biden is in a

                   two-person race against a MAGA Republican. The

                   overall RCP average of recent polls currently has

                   Biden trailing former president Donald Trump by 1.4

                   points, while a mid-May Harvard CAPS/Harris survey

                   put the incumbent down by seven points against the

                   indicted Republican. An early May ABC News/

                   Washington Post poll had Florida Governor Ron

                   DeSantis leading Biden by five points.1

            # ⚓ The Nation ☛ Fox’s_Lies_Are_the_Folklore_of_Racial

              Capitalism⠀⇛

                   It’s been a rough couple of weeks for the handful

                   of indefatigable optimists who took a Susan

                   Collins–like posture on the prospects that Fox News

                   might have learned some newsgathering lessons from

                   its $787.5 million settlement with Dominion News

                   over the election lies it aired in the wake of the

                   2020 presidential balloting. Yes, Fox cut ties with

                   white nationalist hate merchant Tucker Carlson,

                   purportedly over a private text communication in

                   which he remained a bit too true to the bit even

                   for the jaded and Caligulan Fox executive class.

                   But there’s been no broader institutional reckoning

                   with the network’s flagrant mendacity—indeed,

                   without missing a beat, the network that has aired

                   endless variations on the War on Christmas and a

                   steady stream of James O’Keefe–grade election-

                   season agitprop has resumed fabulizing about

                   virtually every facet of public life in the United

                   States.

            # § Misinformation/Disinformation/Propaganda⠀➾

                  # ⚓ Deutsche Welle ☛ EU:_Twitter_leaves_voluntary_pact_on

                    fighting_disinformation⠀⇛

                         Twitter has withdrawn from a voluntary

                         European Union agreement to stamp out

                         disinformation online, a top EU official said

                         late Friday.

                         “Twitter leaves EU voluntary Code of Practice

                         against disinformation. But obligations

                         remain,” EU Internal Market Commissioner

                         Thierry Breton wrote on Twitter.

                  # ⚓ The Revelator ☛ The_Perils_of_Capitalism_and

                    Disinformation:_4_Critical_New_Books⠀⇛

                  # ⚓ DeSmog ☛ Revealed:_1_in_3_GB_News_Hosts_Spread

                    Climate_Denial_On_Air_in_2022⠀⇛

                         A majority of GB News hosts attacked climate

                         action on the channel in 2022, while one in

                         three spread climate science denial, a DeSmog

                         analysis can reveal.

                         Opponents of green policies have seized on

                         the energy crisis sparked by Russia’s

                         invasion of Ukraine to denounce the UK’s net

                         zero target and push for new,

                         environmentally-damaging fossil fuel

                         extraction.

      o § Censorship/Free Speech⠀➾

            # ⚓ RFA ☛ Tiananmen_Mothers_calls_on_China’s_Xi_to_‘take

              responsibility’_for_1989_massacre⠀⇛

                   Tiananmen Mothers, a group representing victims of

                   the June 4 massacre that ended weeks of pro-

                   democracy protests in 1989 has called on Chinese

                   leader Xi Jinping to take responsibility for the

                   actions of the government ahead of this year’s 34th

                   anniversary.

            # ⚓ Techdirt ☛ The_Supreme_Court_May_Not_Have_Read_Our_Brief

              About_The_First_Amendment_And_Copyright,_But_You_Can⠀⇛

                   Technically we’ve posted this analysis before, when

                   we posted our entire amicus brief submitted to the

                   Supreme Court in the Andy Warhol Foundation v.

                   Goldsmith case, along with a summary of what we had

                   written in it. But that summary also included other

                   arguments, and a very condensed version of this

                   one, that the First Amendment requires copyright

                   law to be interpreted in a way that doesn’t harm

                   future free expression. It is an idea important

                   enough to be worth more attention – especially

                   given that it seems the Supreme Court itself

                   overlooked it.

            # ⚓ Meduza ☛ Alexey_Navalny’s_new_felony_trial_scheduled_to

              begin_May_31._Prosecution_may_seek_30-year_sentence_for

              jailed_politician.⠀⇛

                   The first hearing in a new criminal case against

                   the imprisoned Russian politician Alexey Navalny

                   has been scheduled for May 31, according to

                   Navalny’s social media accounts.

            # ⚓ Meduza ☛ Russian_journalist_hit_with_misdemeanor_charges

              for_sharing_Meduza’s_reporting⠀⇛

                   The St. Petersburg authorities have opened a

                   misdemeanor case against journalist Valery Nechay,

                   the former head of the radio station Echo of St.

                   Petersburg, for participating in the activities of

                   an “undesirable” organization, according to the

                   human rights organization First Department.

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

            # ⚓ RFA ☛ Burmese_journalist_sentenced_to_10_years_in_jail_by

              military_junta_court⠀⇛

                   A Burmese journalist was sentenced on Friday to 10

                   years in prison with hard labor for violating

                   Myanmar’s counterterrorism law, in addition to a

                   three-year sentence she received in December 2022

                   for defamation, an attorney working on her case

                   said.

            # ⚓ ANF News ☛ Journalist_who_exposed_rape_to_stand_trial_while

              alleged_rapists_walk_free⠀⇛

                   Journalist Oktay Candemir covered the rape case in

                   Bêgirî (Muradiye) district last January. He

                   described how the “girl, studying at Muradiye

                   Nizamettin Aktaş High School, was made to use drugs

                   since 2019, and then was systematically sexually

                   assaulted. She was suspended from school on the

                   grounds that she was a drug addict. The people who

                   took pictures of Y., including police and officers,

                   raped Y. for years, using the pictures to blackmail

                   her.”

      o § Civil Rights/Policing⠀➾

            # ⚓ Amnesty International ☛ Afghanistan:_The_Taliban’s_war_on

              women:_The_crime_against_humanity_of_gender_persecution_in

              Afghanistan⠀⇛

                   After the Taliban seized control of Kabul in August

                   2021, the human rights situation of women and girls

                   in Afghanistan deteriorated severely, despite the

                   Taliban’s initial promise to respect women’s and

                   girls’ rights. The Taliban have been increasingly

                   introducing new restrictions with the apparent aim

                   of completely erasing women’s and girls’ presence

                   from public arenas. Taliban policies have been

                   further oppressing women and girls in almost all

                   aspects of their lives. The widespread and

                   systematic subjugation of girls and women in

                   Afghanistan is a flagrant violation of their human

                   rights and fundamental freedoms.

            # ⚓ [Repeat] New York Times ☛ Minnesota_Governor_Vetoes_Gig

              Worker_Pay_Bill⠀⇛

                   Gov. Tim Walz of Minnesota on Thursday vetoed a

                   bill that would have guaranteed a minimum wage and

                   other protections for Uber and Lyft drivers.

            # ⚓ EFF ☛ EFF_at_RightsCon_2023⠀⇛

                   RightsCon provides an opportunity for human rights

                   experts, technologists, government representatives,

                   and activists to discuss pressing human rights

                   challenges and their potential solutions.

                   We’re excited that many EFFers are heading to Costa

                   Rica and will be actively participating in this

                   year’s event – both online and in person. Several

                   members will be leading sessions and contributing

                   as speakers, as well as being available for

                   networking.

            # ⚓ Pro Publica ☛ How_We_Reached_Dairy_Farm_Workers_to_Write

              About_Them⠀⇛

                   Spanish-speaking dairy farm workers in Wisconsin,

                   many of them undocumented immigrants, are not

                   regular readers of our website. Most have never

                   heard of ProPublica, let alone formed a trusting

                   relationship with us. Some have low levels of

                   literacy and poor internet connections because the

                   farms they work on are remote. Connecting with

                   them, both to conduct our reporting and to share

                   our findings, is a challenge.

                   For months, Melissa Sanchez and Maryam Jameel have

                   been reporting on conditions at these farms. But

                   one of their earliest missions was crucial. They

                   needed to find out how the workers got their news

                   and make sure ProPublica’s reporting reached them

                   and their communities. The reporters’ process

                   underscores one of our central beliefs at

                   ProPublica: Publishing a story about injustice

                   isn’t enough if we don’t reach the people who are

                   directly affected.

            # ⚓ Pro Publica ☛ Colorado_Limits_Court_Use_of_Family

              Reunification_Camps⠀⇛

                   A bill signed into law this week in Colorado

                   prohibits family courts from ordering children to

                   participate in reunification programs that isolate

                   them from a trusted caregiver. Many of these

                   programs purport to offer treatments for parental

                   alienation, a psychological disorder that has been

                   rejected by mainstream scientific circles but

                   continues to influence custody decisions.

                   The new law, which takes effect immediately, also

                   requires experts who advise the court on custody

                   cases to have training in working with victims of

                   domestic violence and child abuse.

            # ⚓ Democracy Now ☛ Spike_Lee_on_“Malcolm_X”_&_How_Hollywood

              Almost_Prevented_Landmark_Film_from_Being_Made⠀⇛

                   May 19 marked what would have been the 98th

                   birthday of Malcolm X. The director Spike Lee gave

                   the keynote address at an event marking the day at

                   the Malcolm X and Dr. Betty Shabazz Memorial and

                   Educational Center, which is housed in the former

                   Audubon Ballroom in New York where Malcolm X was

                   assassinated in 1965. Lee discussed the challenges

                   of making his acclaimed 1992 biopic of Malcolm

                   starring Denzel Washington, and how he overcame

                   funding shortfalls and studio indifference to get

                   the film made. “We knew that we had to keep going,”

                   Lee said.

            # ⚓ Democracy Now ☛ Memorial_Day_Massacre:_Chicago_Cops_Killed

              10_During_1937_Steel_Strike,_Then_the_Media_Covered_It_Up⠀⇛

                   We look at the largely forgotten 1937 Memorial Day

                   Massacre, when police in Chicago shot at and gassed

                   a peaceful gathering of striking steelworkers and

                   their supporters, killing 10 people, most of them

                   shot in the back. It was a time like today, when

                   unions were growing stronger. The workers were on

                   strike against Republic Steel, and the police

                   attacked them with weapons supplied by the company.

                   The tragic story is told in a new PBS documentary.

                   “The mass media, right up to The New York Times,

                   was supporting the police story that they had no

                   choice but to open fire on this mob,” says Greg

                   Mitchell, who directed the new PBS documentary,

                   Memorial Day Massacre: Workers Die, Film Buried,

                   and edited a companion book that is the first oral

                   history on the tragedy. The film can be viewed at

                   PBS.org and was produced by Lyn Goldfarb.

            # ⚓ The Nation ☛ What_the_Brutal_Death_of_Gabriella_Gonzalez

              Tells_Us_About_Domestic_Violence_Post-Roe⠀⇛

                   In early May, Texas resident Gabriella Gonzalez

                   traveled to Colorado for abortion care. The journey

                   out of state is a familiar one for Texans, who have

                   lived under a draconian six-week abortion ban since

                   2021, long before the US Supreme Court overturned

                   Roe v. Wade last year, and a criminal “trigger law”

                   that imposes up to life in prison for providers,

                   since August. Like so many Texans, the 26-year-old

                   mother of three was forced out of her home state

                   for health care. Upon her return, Harold Thompson,

                   her 22-year-old ex-boyfriend who is believed to

                   have impregnated her and who did not approve of her

                   abortion—sought revenge. During an argument at a

                   gas station in Dallas the morning after she

                   returned, Thompson placed Gonzalez in a choke hold

                   and then fatally shot her once in the head and

                   several times thereafter.

            # ⚓ The Nation ☛ Unions_Are_Stepping_Up_to_Find_a_Solution_to

              California’s_Housing_Crisis⠀⇛

                   Today, Friday, May 26, unions in Los Angeles are

                   pushing some big new ideas into the public sphere.

                   Negotiators with UNITE HERE Local 11, the radical

                   trade union that represents thousands of

                   hospitality workers in restaurants, hotels, sports

                   arenas, and airports around the region, are

                   advancing a set of proposals for an updated

                   contract with 100 employers, replacing those

                   contracts that are expiring at the end of June.

            # ⚓ The Nation ☛ Fascism_by_Default⠀⇛

      o § Digital Restrictions (DRM)⠀➾

            # ⚓ Techdirt ☛ Hugely_Profitable_And_Consolidated_Streaming

              Platforms_Suddenly_Too_Cheap_To_Pay_Residuals_And_Writers,_Or

              Keep_Niche_Shows_Online⠀⇛

                   We’ve noted repeatedly that as the streaming sector

                   grows and consolidates, it’s revealing many of the

                   same problems we saw inherent in traditional,

                   shitty, cable TV. As in the need to provide Wall

                   Street improved quarterly returns at any cost has

                   them doing the sort of things common in the

                   traditional cable sector they used to criticize and

                   disrupt (see Netflix’s password sharing cash grab).

      o § Monopolies⠀➾

            # § Trademarks⠀➾

                  # ⚓ Techdirt ☛ Monster_Energy_Opposes_A_Fitness_Trainer’s

                    Trademark_Because_Of_Course_It_Did⠀⇛

                         Ah, Monster Energy. For regular readers of

                         Techdirt, the name of the company alone is

                         enough to get your eyes rolling harder than a

                         teenager at a rave. Posts on the company’s

                         trademark bullying ways are so legion that I

                         dare not even begin listing them; if you’re

                         unfamiliar with them, click the link and be

                         sure you have a pillow on your desk or you’re

                         going to suffer a concussion.

            # § Copyrights⠀➾

                  # ⚓ Walled Culture ☛ Top_EU_court_to_issue_definitive

                    ruling_on_whether_copyright_is_more_important_than

                    privacy⠀⇛

                         This is an important case, because it will

                         clarify whether copyright infringement can be

                         considered a “serious crime” that trumps

                         privacy concerns and allows general online

                         surveillance of the public despite the

                         region’s privacy laws. In bringing the case,

                         La Quadrature du Net naturally hopes that

                         data protection laws will not be trampled

                         upon so easily, and that the EU’s top court

                         will affirm copyright’s relative lack of

                         importance in the grand scheme of things, but

                         nothing is certain. Euractiv writes: [...]

                  # ⚓ Torrent Freak ☛ 2.5_Billion_Visits:_ACE_Targets

                    9anime_Among_Several_Pirate_Anime_Sites⠀⇛

                         Despite offering only one type of content,

                         9anime is one of the most-visited sites in

                         the world, period. Since that amounts to over

                         2.5 billion visits per year, it was no

                         surprise to see anti-piracy coalition ACE

                         back in court this week hoping to obtain

                         information on the site’s operators. Other

                         anime piracy sites are under the spotlight

                         too, including some that appear to have no

                         traffic at all.

                  # ⚓ Torrent Freak ☛ Court_Orders_Instagram_to_Expose

                    Pirates,_Boot_Their_Accounts,_and_Purge_URLs⠀⇛

                         The High Court in Bombay, India, has ordered

                         Instagram to share the personal details of

                         copyright-infringing users with a media

                         company. Through a broad dynamic injunction,

                         the social media giant is further required to

                         terminate associated accounts and purge

                         infringing URLs they shared from its

                         platform.

                  # ⚓ Techdirt ☛ Studies_Suggest_That_Rather_Than_Killing

                    Jobs,_AI_Could_Revive_The_Middle_Class⠀⇛

                         We’ve certainly been talking a lot about the

                         “AI Doomers” who insist that AI is all too

                         likely to destroy humanity. However, even

                         people who aren’t fully on board with the

                         existential threat of AI do often say that,

                         at the very least, it’s going to destroy jobs

                         for most people, potentially creating huge

                         problems. For years now, people have been

                         arguing for universal basic income, in large

                         part, because they think that automation and

                         AI will take away everyone’s jobs. I mean, it

                         was a core plank of Andrew Yang’s silly run

                         for President.

* § Gemini* and Gopher⠀➾

      o § Personal⠀➾

            # ⚓ 🔤SpellBinding:_AHLMNOR_Wordo:_TIDED⠀⇛

            # ⚓ PMBOK_Guide_7,_Underneath_the_Surface_(book)⠀⇛

                   I’ve written a new book on PMBOK 7 (the well-known

                   project management standard). I aimed to go

                   underneath the surface and explain what it really

                   means. It’s about appreciating its true value

                   without dogmatism.

      o § Technical⠀➾

            # ⚓ May_CLI_additions⠀⇛

                   I added a commandline cheatsheet for mutt (my mail

                   client) and updated the one for amforai (gemini

                   space browser).

                   The mutt cheatsheet is not a full step-by-step

                   tutorial, they aren’t meant to be. I’ve done my

                   best to give a structured outline of what I

                   tweaked.

            # § Internet/Gemini⠀➾

                  # ⚓ From_my_bubble_about_Bubble⠀⇛

                         There is much buzz about [Skyjake's project

                         called Bubble] on the Geminispace. There was

                         a long thread on Cosmos, which I can’t locate

                         now. A good start of discussion is

                         Bacardi55′s second gemlog article. So there

                         are many points of view, as usual in today’s

                         world.

                         It’s something like the plot of /Silo/ (a TV

                         series, according to Wikipedia: based on the

                         /Wool/ series of novels by author Hugh

                         Howey). /Silo/ is about the last ten thousand

                         people living in the underground concrete

                         bunker formed in a silo-shaped hole. They

                         live according to the rules called the Pact,

                         which origin is unclear. One of the Pact

                         regulations forbade the installation of

                         elevators. So they walk up and down the

                         stairs. There are hundreds of floors, so such

                         travels last all day.

                  # ⚓ From_my_bubble_about_Bubble⠀⇛

=> =============================================================================

Gemini_(Primer) links can be opened using Gemini_software. It’s like the

World Wide Web but a lot lighter.

                ䷩ 𝚕𝚒𝚗𝚎 5678

Gemini_version_available_♊︎

✐ Links_27/05/2023:_Goodbyes_to_Tina_Turner⠀✐

Posted in News_Roundup at 3:36 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Games

* Distributions_and_Operating_Systems

      o Fedora_Family_/_IBM

      o Open_Hardware/Modding

* Free,_Libre,_and_Open_Source_Software

      o Programming/Development

* Leftovers

      o Education

      o Hardware

      o Health/Nutrition/Agriculture

      o Security

            # Integrity/Availability/Authenticity

            # Privacy/Surveillance

      o Defence/Aggression

      o Transparency/Investigative_Reporting

      o Environment

            # Energy/Transportation

            # Wildlife/Nature

            # Overpopulation

      o Finance

      o AstroTurf/Lobbying/Politics

      o Censorship/Free_Speech

      o Freedom_of_Information_/_Freedom_of_the_Press

      o Civil_Rights/Policing

      o Internet_Policy/Net_Neutrality

      o Monopolies

            # Patents

            # Trademarks

            # Copyrights

* Gemini*_and_Gopher

      o Personal

      o Technical

            # Internet/Gemini

            # Programming

* § GNU/Linux⠀➾

      o § Games⠀➾

            # ⚓ Godot Engine ☛ Dev_snapshot:_Godot_4.1_dev_3⠀⇛

                   The end of May means the approach of the feature

                   freeze for Godot 4.1, and this dev snapshot aims to

                   give you as many new features to test as possible.

* § Distributions and Operating Systems⠀➾

      o § Fedora Family / IBM⠀➾

            # ⚓ Packit_Team:_Handling_of_Release_field_in

              propose_downstream_job⠀⇛

                   Handling of Release field in propose_downstream job

                   # We have recently made some fixes to the process

                   of handling the Release field regarding the

                   %autorelease macro, so let’s take that opportunity

                   to explain how it works.

                   You can maintain the Release field manually, you

                   can use a dummy value or you can take advantage of

                   the %autorelease macro.

                   Maintaining Release manually # You can maintain the

                   Release field manually as you would do downstream,

                   for example you could bump the value every time you

                   make changes to the spec file and reset it to 1

                   when you release a new version.

      o § Open Hardware/Modding⠀➾

            # ⚓ Arduino ☛ This_cheap_robot_arm_can_follow_recorded

              movements⠀⇛

                   There are many ways to control a robot arm, with

                   the simplest being a sequential list of rotation

                   commands for the motors. But that method is very

                   inefficient when the robot needs to do anything

                   complex in the real world.

            # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Updates_1980′s_Omnibot_with

              AI_and_Machine_Learning⠀⇛

                   Matt from Viam Robotics has upgraded an old 1980s

                   Omnibot with a Raspberry Pi to give it new modern

                   features.

            # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Brings_Ghostly_Betta_Fish_to

              Life⠀⇛

                   N4MI0 is using a Raspberry Pi to power a Pepper’s

                   Ghost effect betta fish project that looks like a

                   fish in a bowl.

            # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Helps_Research_Team_Monitor

              Glaciers_in_Peru⠀⇛

                   This research team is using Raspberry Pis to

                   monitor glacier calving in Peru and Iceland using

                   cameras to make 3D renders of glaciers.

            # ⚓ Tom’s Hardware ☛ Milk-V_Offers_a_Trio_of_RISC-V_Raspberry

              Pi_Alternatives⠀⇛

                   With models starting from $9, Milk-V is offering an

                   enticing trio of Raspberry Pi alternatives — all of

                   which are powered by a RISC-V CPU

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

      o § Programming/Development⠀➾

            # ⚓ Rlang ☛ What_is_the_sink()_function?_Capturing_Output_to

              External_Files⠀⇛

                   The sink() function in R is used to divert R output

                   to an external connection. This can be useful for a

                   variety of purposes, such as exporting data to a

                   file, logging R output, or debugging R code.

            # ⚓ Rlang ☛ R_Programming_and_Pharmaceutical_Data_Analysis_

              (Packages_for_Clinical_Trial_Data)⠀⇛

                   In the clinical trials reporting industry, there is

                   an incorrect assumption that SAS software is ideal

                   as regulatory agencies “require” it. Regulatory

                   agencies generally do not mandate the use of

                   specific software for clinical trials reporting.

                   They primarily focus on the accuracy, integrity,

                   and compliance of the reported data.

* § Leftovers⠀➾

      o ⚓ RTE ☛ Cruinniú_na_nÓg_2023_is_back_–_Supported_by_RTÉ⠀⇛

             WATCH our promo here. Cruinniú na nÓg takes place on

             Saturday 10th June, and this year more than 500 free

             creative events are planned for thousands of young people

             throughout the country, including Forest Bathing in

             Castlefreke, Celestial Mechanics at the Dunsink

             Observatory, a recreation of Clones Town in ceramics,

             Hula hooping in Waterford…

      o ⚓ New York Times ☛ Rolf_Harris,_Disgraced_British_Entertainer,_Dies

        at_93⠀⇛

             His career as a musician and a painter over six decades

             ended abruptly when he was convicted of sexually abusing

             teenage girls.

      o ⚓ The Atlantic ☛ Push_Notifications_Are_Out_of_Control⠀⇛

             There must be better ways of opting out.

      o § Education⠀➾

            # ⚓ Helsinki Times ☛ Massive_education_budget_cuts_proposed_in

              government_negotiations_–_Could_lead_to_closure_of_over_100

              educational_institutions⠀⇛

                   According to information made public, government

                   negotiators are considering a drastic 50 percent

                   cut in funding for adult education based on a

                   proposal by the Ministry of Finance. Such a

                   decision would have severe consequences for

                   employment, continuous learning, public well-being,

                   and regional equality. A joint statement from 14

                   organizations warns that numerous educational

                   institutions would be forced to shut down as a

                   result of these budget cuts.

      o § Hardware⠀➾

            # ⚓ CNX Software ☛ Ultrawide_8.8-inch_HDMI_and_USB_information

              display_is_offered_with_optional_touchscreen_support⠀⇛

                   Last year, I wrote about the Turing Smart Screen

                   low-cost 3.5-inch display based on a WCH CH552T 8-

                   bit E8051 core microcontroller that connects to a

                   PC or other device through a USB Type-C cable in

                   order to display system or other information using

                   AIDA64 software or an open-source Python software.

            # ⚓ CNX Software ☛ FireBeetle_2_ESP32-S3_camera_board_ships

              16MB_flash,_8MB_PSRAM,_PCB_or_external_antenna⠀⇛

                   DFRobot “FireBeetle 2 ESP32-S3” is a 2MP camera

                   board with ESP32-S3N16R8 dual-core WiFi and

                   Bluetooth microcontroller fitted with 16MB flash

                   and 8MB PSRAM, and offered in two versions: a more

                   compact variant with a PCB antenna, and one with an

                   external antenna offering a better signal quality.

            # ⚓ CNX Software ☛ SONOFF_TX_Ultimate_Review_–_A_smart_touch

              wall_switch_with_innovative_features⠀⇛

                   SONOFF has been producing a wide range of new

                   products over the years, and since the beginning of

                   the year, the company introduced various new

                   products and features including the iHost Smart

                   Home Hub local hub which no longer requires cloud

                   connectivity. The one we are going to review is the

                   Ultimate Smart Touch Wall Switch (also known as the

                   SONOFF TX Ultimate).

            # ⚓ CNX Software ☛ AMD_Ryzen_and_Athlon_7020-C_processors_to

              power_Chromebooks_with_up_to_19.5_hours_of_battery_life⠀⇛

                   AMD has just unveiled the Ryzen and Athlon 7020-

                   C series processor family designed for Chromebooks,

                   with up to four “Zen 2” cores clocked at up to 4.3

                   GHz, AMD RDNA 2 graphics, and promises of high

                   power efficiency with Chromebook based on the

                   entry-level Athlon Silver 7120C processor lasting

                   up to an estimated 19.5 hours on a charge.

            # ⚓ CNX Software ☛ Zotac_PI430AJ_Pico_mini_PC_features_Airjet

              solid-state_active_cooling_chips⠀⇛

                   ZOTAC PI430AJ Pico is the first mini PC equipped

                   with (two) Airjet solid-state active cooling chips

                   introduced at CES 2023, doing without the metal

                   case required by typical fanless systems, and

                   instead relying on a plastic case. The PI430AJ Pico

                   is powered by a recent 7W Intel Core i3-N300 octa-

                   core Alder Lake-N processor coupled with up to 16GB

                   LPDDR5 RAM and an M.2 NVMe SSD up to 1TB capacity.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ The Atlantic ☛ Think_About_Your_Death_and_Live_Better⠀⇛

                   Contemplating your mortality might sound morbid,

                   but it’s actually a key to happiness.

            # ⚓ The Atlantic ☛ Tina_Turner’s_Cosmic_Life⠀⇛

                   The late singer stretched human expression to its

                   fraying limits—and then her story became a

                   folktale.

            # ⚓ TwinCities Pioneer Press ☛ DEA’s_failure_to_punish

              distributor_blamed_in_opioid_crisis_raises_revolving_door

              questions⠀⇛

                   It has allowed one distributor to keep shipping

                   painkillers despite a judge’s recommendation to

                   strip its license.

            # ⚓ Science Alert ☛ 1st_Plastics_Pollution_Weather_Forecast

              Predicts_88_Pounds_of_Microplastic_Over_Paris⠀⇛

                   Hope your umbrella’s sturdy.

            # ⚓ teleSUR ☛ +300_Unprotected_Level_Crossings_to_Be_Secured_in

              Sri_Lanka⠀⇛

                   “…the modifications to secure the level crossings

                   will be completed in two months…”

      o § Security⠀➾

            # § Integrity/Availability/Authenticity⠀➾

                  # ⚓ Vice Media Group ☛ Captcha_Is_Asking_Users_to

                    Identify_Objects_That_Don’t_Exist⠀⇛

                         Discord’s captcha asked users to identify a

                         ‘Yoko,’ a snail-like object that does not

                         exist and was created by AI.

            # § Privacy/Surveillance⠀➾

                  # ⚓ Bruce Schneier ☛ Indiana,_Iowa,_and_Tennessee_Pass

                    Comprehensive_Privacy_Laws⠀⇛

                         It’s been a big month for US data privacy.

                         Indiana, Iowa, and Tennessee all passed state

                         privacy laws, bringing the total number of

                         states with a privacy law up_to_eight. No

                         private right of action in any of those,

                         which means it’s up to the states to enforce

                         the laws.

      o § Defence/Aggression⠀➾

            # ⚓ The Strategist ☛ Israel_at_75⠀⇛

                   Religion and miracles often go hand in hand, so it

                   should come as little surprise that Israel, which

                   just marked its 75th birthday, is something of a

                   miracle.

            # ⚓ The Strategist ☛ Parliamentary_scrutiny_is_essential_for

              effective_national_defence⠀⇛

                   Our dangerous times are driving an unprecedented

                   tempo of strategy writing in Canberra.

            # ⚓ New York Times ☛ A_Year_in_Uvalde⠀⇛

                   How grief has warped the lives of the Uvalde

                   shooting victims’ families and friends.

            # ⚓ New York Times ☛ USS_Mannert_L._Abele,_Navy_Ship_Sunk_in

              World_War_II,_Is_Found⠀⇛

                   The U.S.S. Mannert L. Abele was broken in half by

                   two kamikaze attacks and sank in 4,500 feet of

                   water, killing 84 sailors.

            # ⚓ New York Times ☛ Biden_to_Nominate_Gen._Charles_Q._Brown_to

              Be_Joint_Chiefs_Chairman⠀⇛

                   If confirmed by the Senate, the Air Force chief of

                   staff would become the senior military adviser to

                   the president.

            # ⚓ New York Times ☛ Nashville_Parents_Can_Have_Say_in_Case

              Over_Shooter’s_Writings,_Judge_Rules⠀⇛

                   A group of about 100 families will now have the

                   chance to argue in court against releasing the

                   writings of the assailant who killed six people at

                   a Christian school.

            # ⚓ New York Times ☛ A_Look_at_the_Fight_for_Gun_Control_Since

              the_Uvalde_Shooting⠀⇛

                   After the Supreme Court ruled last year that people

                   could carry guns outside their homes, legal

                   challenges and legislative debates have been

                   playing out across the country.

            # ⚓ CS Monitor ☛ One_year_after_Uvalde,_three_activists_share

              their_stories⠀⇛

                   The crucible of grief after school shootings has

                   spurred some people to push for change. One year

                   after Uvalde, three activists share their stories.

            # ⚓ YLE ☛ Finland_joins_Nato’s_Brunssum_HQ_in_the_Netherlands⠀⇛

                   As Nato is in a period of transition and

                   reorganisation, Finland’s time at the Netherlands’

                   headquarters may be temporary.

            # ⚓ RFERL ☛ In_Belgrade,_U.S._Senator_Urges_Quick

              Implementation_Of_Serbia-Kosovo_Agreement⠀⇛

                   U.S. Senator Chris Murphy told reporters during a

                   visit to Belgrade on May 25 that Serbia and Kosovo

                   should quickly implement an EU-brokered agreement

                   to normalize ties, calling it a step forward that

                   both sides should be proud of.

            # ⚓ teleSUR ☛ Putin_Calls_for_Enhanced_Eurasian_Union-LATAM

              Cooperation⠀⇛

                   “Our association is constantly asserting itself as

                   one of the independent and self-sufficient centers

                   of the emerging multipolar world,” he stressed.

            # ⚓ Latvia ☛ Stoltenberg:_“NATO_can_count_on_Latvia._And_Latvia

              can_count_on_NATO”⠀⇛

                   NATO Secretary General Jens Stoltenberg welcomed

                   Latvian Prime Minister Krišjānis Kariņš to NATO

                   Headquarters in Brussels on May 24, thanking

                   him for Latvia’s contributions to the Alliance,

                   including leadership on defense spending, and

                   deployments to maritime operations and missions in

                   Kosovo and Iraq.

            # ⚓ teleSUR ☛ Armenia_And_Azerbaijan_Move_To_Normalize

              Bilateral_Relations⠀⇛

                   Nagorno-Karabakh, an Armenian-populated enclave

                   within Azerbaijan, has been a source of conflict in

                   recent years.

            # ⚓ The Atlantic ☛ A_Chinese_American_Show_That_Doesn’t_Bother

              to_Explain_Itself⠀⇛

                   Disney+’s American Born Chinese, based on the best-

                   selling graphic novel, offers a confident take on

                   the second-generation experience.

            # ⚓ LRT ☛ Lack_of_training_facilities_‘showstopper‘_for

              Baltics,_says_German_general⠀⇛

                   The lack of military training facilities is a

                   “showstopper” for the Baltic states’ better

                   interoperability with allies, Harald Gante,

                   Commander of Germany’s Field Army, has said.

            # ⚓ teleSUR ☛ A_Fugitive_Wanted_for_Rwandan_Genocide_is

              Arrested⠀⇛

                   In 1994, Fulgence Kayishema, together with other

                   co-perpetrators, murdered over 2,000 men, women,

                   elderly and children refugees in Kivumu commune.

            # ⚓ JURIST ☛ DRC_files_ICC_complaint_against_Rwanda_over

              alleged_theft_of_natural_resources⠀⇛

                   Democratic Republic of the Congo (DRC) Minister of

                   Justice Rose Mutombo filed an International

                   Criminal Court (ICC) complaint against Rwanda on

                   Tuesday over Rwanda’s alleged involvement in the

                   theft of natural resources in the DRC.

            # ⚓ Vice Media Group ☛ A_New_Uber_Clone_With_Armed_Drivers_Is

              the_App_for_a_Violent_and_Paranoid_America⠀⇛

                   “What I’m creating is a necessary evil,” the app’s

                   founder claims while operating in a city with

                   falling crime rates.

            # ⚓ RFERL ☛ Bodies_Of_Migrants_Who_Died_In_Bulgaria_Returned_To

              Afghanistan,_Taliban_Says⠀⇛

                   Afghanistan’s Taliban-controlled Foreign Ministry

                   says the bodies of 18 Afghan migrants who died of

                   suffocation while attempting to cross into Bulgaria

                   have been transferred to Kabul.

            # ⚓ teleSUR ☛ Over_1_Mln_Are_Internally_Displaced_in_Somalia_in

              Four_Months⠀⇛

                   Currently, 3.8 million people are now displaced in

                   Somalia, exacerbating a dire humanitarian situation

                   where some 6.7 million people are struggling to

                   meet their food needs.

      o § Transparency/Investigative Reporting⠀➾

            # ⚓ Lumen_Researcher_Interview_Series:_Professor_Jon_Penney⠀⇛

                   the Lumen teamn chats with Professor Jon Penney

                   about how Lumen has been part of his work.

      o § Environment⠀➾

            # ⚓ New York Times ☛ Mawar_Becomes_a_Super_Typhoon_After

              Lashing_Guam:_Latest_Storm_Updates⠀⇛

                   Island residents experienced howling winds and

                   periods of intense rainfall, which left most of

                   Guam without power. Officials had yet to assess the

                   damage, but typhoon warnings remained in effect.

            # ⚓ teleSUR ☛ UN:_8.5_Mln_USD_for_Cyclone_Victims_in

              Madagascar⠀⇛

                   “We launched humanitarian projects to support

                   335,000 people in the most vulnerable areas”

            # ⚓ teleSUR ☛ Italy:_Massive_Emergency_Aid_Package_Approved,

              Flood-Hit_Region⠀⇛

                   “…it has an estimated value in excess of 2 billion

                   euros…”

            # ⚓ Federal News Network ☛ Guam_‘very_blessed’_with_no_early

              reports_of_major_damage_in_the_messy_aftermath_of_Typhoon

              Mawar⠀⇛

                   Residents of Guam are cleaning up after Typhoon

                   Mawar tore through the remote U.S. Pacific

                   territory and ripped roofs off homes, flipped

                   vehicles and shredded trees. Officials say there

                   were minor injuries reported but no fatalities. The

                   typhoon is the strongest to hit the territory of

                   roughly 150,000 people since 2002. It briefly made

                   landfall Wednesday night as a Category 4 storm. The

                   island’s international airport flooded and the

                   swirling typhoon churned up a storm surge and waves

                   that crashed through coastal reefs and flooded

                   homes. A police sergeant says Guam has been “very

                   blessed” without any deaths or major damage.

            # § Energy/Transportation⠀➾

                  # ⚓ New York Times ☛ France_Bans_Short_Domestic_Flights,

                    But_Not_Much_Changes⠀⇛

                         A decree formalizing the measure, which was

                         passed in 2021, is riddled with exceptions.

                         Critics call its effect symbolic, at best.

                  # ⚓ YLE ☛ Finland’s_average_electricity_price_slips_into

                    negative_territory⠀⇛

                         The oversupply of virtually emissions-free

                         electricity is mainly due to spring flooding,

                         which is super-charging hydropower

                         production.

                  # ⚓ Vice Media Group ☛ Scientists_Working_to_Generate

                    Electricity_From_Thin_Air_Make_Breakthrough⠀⇛

                         Scientists making the “Air-gen” device have

                         discovered that any material can be used to

                         generate electricity from the air.

                  # ⚓ Federal News Network ☛ California_unlikely_to_run

                    short_of_electricity_this_summer_thanks_to_storms,_new

                    power_sources⠀⇛

                         California regulators say the state is

                         unlikely to run short of electricity this

                         summer, thanks to new power sources and a wet

                         winter that filled reservoirs to restart

                         hydroelectric power plants shuttered during

                         the drought. Officials say more than 8,000

                         megawatts of new wind, solar and battery

                         power will come online by September. One

                         megawatt of electricity is enough to power

                         about 750 homes. California normally has more

                         than enough electricity to power the homes

                         and businesses of its more than 39 million

                         people. But the electrical grid has trouble

                         when it gets really hot and everyone turns on

                         their air conditioners at the same time.

                         California ran short of power in 2020. That

                         caused brief blackouts for hundreds of

                         thousands of households.

            # § Wildlife/Nature⠀➾

                  # ⚓ IDA ☛ IDSW_2023_Wrap-Up!⠀⇛

                         We at DarkSky International want to express

                         our sincerest thank you and congratulations

                         to dark sky advocates around the world for

                         making International Dark Sky Week 2023 a

                         resounding success!/blockquote>

                  # ⚓ New York Times ☛ Orcas_Have_Sunk_3_Boats_in_Southern

                    Europe,_Scientists_Say⠀⇛

                         A small group of orcas is ramming into

                         sailboats in waters off the Iberian

                         Peninsula. Researchers say they do not know

                         what is driving the unusual behavior toward

                         boats.

                  # ⚓ YLE ☛ Helsinki_zoo_opens_wildlife_emergency_help

                    line⠀⇛

                         Helsinki’s Korkeasaari Zoo has opened an

                         emergency number to provide advice to people

                         who find wild animals in urgent need of help.

                  # ⚓ Science Alert ☛ Study_Confirms_That_You_Can_Really

                    Communicate_With_Your_Cat_By_Doing_This⠀⇛

                         It really works.

                  # ⚓ Latvia ☛ Orphan_bear_to_move_to_France⠀⇛

                         On Thursday, May 25, the bear cub which was

                         delivered to the Rīga National Zoo in April

                         after being found alone next to a highway is

                         heading to her new home at the La Taniere zoo

                         in France, the Nature Conservation Agency

                         said.

            # § Overpopulation⠀➾

                  # ⚓ The Straits Times ☛ 1_out_of_10_paediatric_clinics_in

                    Seoul_shut_since_2017_amid_low_fertility_and_profits⠀⇛

                         While clinics face ultra-low birth rates, the

                         government has also frozen doctor appointment

                         fees.

      o § Finance⠀➾

            # ⚓ CNBC ☛ Tech_layoffs_ravage_the_teams_that_fight_online

              misinformation_and_hate_speech⠀⇛

                   Meta, Amazon, Alphabet and Twitter have all

                   drastically reduced the size of their teams focused

                   on internet trust and safety as well as ethics as

                   the companies focus on cost cuts.

            # ⚓ Atlantic Council ☛ There_is_no_alternative_to_US

              Treasuries⠀⇛

                   In the wake of a US default, investors searching

                   for safe assets may have no viable alternative to

                   US Treasuries.

            # ⚓ Axios ☛ The_gender_confidence_gap_in_investing⠀⇛

                   Note: Among non-retirees with self-directed

                   retirement savings. Data: Federal_Reserve; Chart:

                   Axios Visuals

Men are far more comfortable investing their own retirement money than women, a

new Fed survey shows.

⚓ CS Monitor ☛ How_much_would_debt_default_damage_US?_History_offers_clues.⠀⇛

 In U.S. debt limit talks, even going to the brink of default can harm

 investor confidence. Yet the nation has survived past cases of mini

 default.

⚓ The Atlantic ☛ The_Case_for_Debt-Ceiling_Optimism⠀⇛

 All of the public feuding is good, actually.

⚓ teleSUR ☛ Fitch_Places_US_AAA_Rating_on_Negative_Watch⠀⇛

 Despite reaching the US$31.4 trillion debt limit in January,

 discussions between the White House and congressional leaders only

 began on May 9.

⚓ teleSUR ☛ Eurasian_Economic_Union-BRICS_Turnover_Increases_by_60_Pct⠀⇛

 Policymakers from various countries meet in Moscow to discuss the

 issue of Eurasian integration in a multipolar world.

⚓ Latvia ☛ Latvia’s_unemployment_rate_slightly_above_EU_average_in_Q1⠀⇛

 Results of the Labour Force Survey (LFS) published on May 25 by the

 Central Statistical Bureau of Latvia (CSB) show that in Q1 2023

 Latvian unemployment rate constituted 6.4 %. Over the quarter it fell

 by 0.3 percentage points and over the year by 0.9 percentage points.

⚓ YLE ☛ European_Commission_says_Finland’s_debt_is_exceptional,_proposes_4_ways

to_cut_it⠀⇛

 PM-apparent Petteri Orpo (NCP) said that the latest EU comparison

 confirms the urgency of major fiscal reforms. Finland was the only EU

 state where the debt ratio of public finances rose last year.

⚓ Helsinki Times ☛ Limited_impact_of_tax_credit_for_household_expenses_on

shadow_economy_among_businesses⠀⇛

 A recent study conducted by the Grey Economy Information Unit of the

 Finnish Tax Administration has found that the tax credit for

 household expenses has a limited impact on reducing shadow economy

 activities among businesses. While there is a lower risk of engaging

 in shadow economy practices for companies that provide services

 eligible for the tax credit, the overall average risks of shadow

 economy activity do not differ significantly between sectors eligible

 for the credit and other sectors.

⚓ Michael West Media ☛ Greens_seek_to_release_list_of_names_in_PwC_tax_leak⠀⇛

 The Greens have sought to publicly release a list of names of PwC

 employees allegedly involved in the tax advice scandal. But the

 finance committee on Friday decided instead to refer the tabling of

 the document to Senate Clerk Richard Pye after concerns were raised

 it could jeopardise an Australian Federal Police investigation.

⚓ The Atlantic ☛ Why_the_GOP_Wants_to_Rob_Gen_Z_to_Pay_the_Boomers⠀⇛

 The budget clash, in many ways, represents the fiscal equivalent to

 the battle over cultural issues raging through Republican-controlled

 states.

⚓ The Atlantic ☛ Colorado’s_Ingenious_Idea_for_Solving_the_Housing_Crisis⠀⇛

 And why local governments hate it

⚓ Vice Media Group ☛ Tenants_Shut_Down_Brooklyn_Bridge_to_Protest_Predatory

Landlords⠀⇛

 Over a thousand tenants holding signs like “Cap the Rent” and “The

 Rent is Too Damn High” marched in one of NYC’s biggest tenant

 protests in years.

⚓ Quartz ☛ Gautam_Adani_has_scraped_his_way_back_into_the_world’s_top

billionaires’_list⠀⇛

 Gautam Adani has found his way back into the world’s top 20

 billionaires list as his conglomerate makes a stellar recovery after

 bleeding for weeks on the stock exchange.

⚓ Quartz ☛ Airbnb_is_encouraging_neighbors_to_complain_about_parties_at_its

rentals⠀⇛

 Summer revelers be warned—Airbnb is embarking on an anti-party

 crackdown.

§ AstroTurf/Lobbying/Politics⠀➾

* ⚓ Anger_most_dominant_emotion_prior_to_May_14′s_dual_election,_survey

  reveals⠀⇛

       A new report by Politus Analytics shows relatively similar

       emotional trends among Erdoğan and Kılıçdaroğlu supporters,

       with the February 6 earthquakes evoking large spikes in various

       emotions in both constituencies.

* ⚓ teleSUR ☛ Early_Voting_Ends_at_Turkish_Diplomatic_Missions_Abroad⠀⇛

       In the first round, Recep Tayyip Erdogan had earned 49.52

       percent of the vote while Kemal Kilicdaroglu received 44.88

       percent.

* ⚓ New York Times ☛ They_Cuddled_a_Kiwi._New_Zealand_Said,_‘Stop_That.’⠀⇛

       Video of the national bird being handled by Miami zoo visitors

       caused an outcry in New Zealand. Even the prime minister

       weighed in.

* ⚓ New York Times ☛ Why_the_‘Rules’_of_Politics_Don’t_Always_Stymie

  Outsiders_to_the_System⠀⇛

       For decades, many voters grew accustomed to a certain set of

       norms that seemed to govern political systems like rules. But

       elite groups have lost the power they once had to enforce those

       norms, or decided to change their own behavior.

* ⚓ New York Times ☛ Netanyahu_Budget_May_Risk_His_Economic_Legacy_in

  Israel⠀⇛

       Israel’s prime minister has long advocated a small state, free

       markets and benefit cuts. But his new budget is heavy on

       subsidies for the ultra-Orthodox community, whose political

       support he needs.

* ⚓ New York Times ☛ For_Senator_Feinstein,_There’s_No_Time_Like_the

  Present_to_Resign⠀⇛

       The country shouldn’t discriminate against older workers, and

       older workers shouldn’t insist on staying in jobs they can no

       longer really carry out.

* ⚓ The Straits Times ☛ Opposition_parties_to_boycott_new_Parliament

  inauguration_by_India’s_Modi⠀⇛

       Mr Modi has chosen to dedicate the building without the Indian

       President’s participation.

* ⚓ The Straits Times ☛ De-risking,_taken_too_far,_will_lead_to_fragmented

  and_decoupled_world_economy:_Lawrence_Wong⠀⇛

       The DPM was taking on the latest language that had emerged at

       the recently concluded Group of Seven summit.

* ⚓ The Straits Times ☛ Bangladesh_says_will_take_steps_to_address

  election-meddling_after_visa_threat_from_US⠀⇛

       The country is set to hold elections in January amid large

       protests.

* ⚓ LRT ☛ Lithuanian_president_could_call_snap_elections_in_case_of_no-

  confidence_in_cabinet_–_PM⠀⇛

       Lithuanian President Gitanas Nausėda could call an early

       general election if the parliament passed a motion of no

       confidence in the government, Prime Minister Ingrida Šimonytė

       said on Thursday.

* ⚓ The Atlantic ☛ DeSantis’s_Campaign_of_Trolling⠀⇛

       The Florida governor seems to understand that in today’s GOP

       primary, serious people need not apply.

* § Misinformation/Disinformation/Propaganda⠀➾

      o ⚓ ‘Shamelessness’⠀⇛

             The attitude that Erdoğan and his closest companions have

             in the face of the “fabricated video” scandal, that the

             state is addressing the public with lies and with

             falsifications, risks a total attack on society’s sense

             of reality. The near and serious threat is this.

      o ⚓ Marcy Wheeler ☛ ABC_Reports_that_Sources_Familiar_Say_2_+_2_=_5⠀⇛

             Trump milked grievance on his social media platform

             yesterday in advance of being indicted. ABC did him the

             favor of claiming he was doing something else.

§ Censorship/Free Speech⠀➾

* ⚓ Musicians_detained_on_‘terror’_charges_for_participating_in_Green_Left

  Party_events⠀⇛

       The musicians had participated in the opening events for the

       party’s election campaign offices in İzmir.

* ⚓ CS Monitor ☛ Picking_books_for_public_schools⠀⇛

       The push to restrict or place controversial books in public

       schools has prompted many local communities to seek greater

       empathy and civic engagement.

* ⚓ New Yorker ☛ The_Discovery_of_a_Forgotten_and_Banned_Nuremberg_Film⠀⇛

       “Filmmakers for the Prosecution” tells the story of how two

       scions of Hollywood contributed crucial evidence and made a

       documentary that was suppressed by the U.S. Army.

* ⚓ The Atlantic ☛ The_Israeli_Minister_Who_Is_Defending_Elon_Musk⠀⇛

       Amichai Chikli championed the billionaire when his tweets were

       criticized for anti-Semitic overtones. I asked Chikli why.

* ⚓ New Yorker ☛ Here_at_the_War-Poison_Factory,_We_Want_to_Run_a

  Progressive_Workplace⠀⇛

       Please, sleep easy knowing that you’re making war poison for a

       company that cares.

* ⚓ The Atlantic ☛ You_Hurt_My_Feelings_Is_a_Hilarious_Anxiety_Spiral⠀⇛

       The film traces a betrayal that’s trivial, comical, and also

       completely devastating.

§ Freedom of Information / Freedom of the Press⠀➾

* ⚓ Victory_Party_members_obstruct_Kurdistan24_journalists_covering

  Kılıçdaroğlu-Özdağ_presser⠀⇛

       The party members did not allow the K24 microphone on the

       lectern during the press conference of the two leaders.

§ Civil Rights/Policing⠀➾

* ⚓ Gezi_prisoners_granted_human_rights_award_in_İstanbul⠀⇛

       In the name of the eight prisoners, their family members

       received the award named after Sevinç Özgüner, a socialist

       politician assassinated in 1980.

* ⚓ What_Kılıçdaroğlu-Özdağ_deal_implies_about_removal_of_elected_mayors_in

  Kurdish_cities⠀⇛

       The government has replaced all but a few of the HDP mayors in

       Kurdish-majority regions since the 2019 local election. The

       Kılıçdaroğlu-Özdağ protocol pledges to maintain this practice,

       but exclusively for individuals with “proven connections to

       terrorism.”

* ⚓ Kılıçdaroğlu_pledges_to_expel_refugees_‘without_being_racist’_in_Hatay

  visit⠀⇛

       Ahead of the crucial presidential runoff on May 28, the main

       opposition leader repeated his claims to send all refugees back

       to their own county.

* ⚓ Crackdown_on_Kurdish-linked_groups_continues_as_18_detained_in_house

  raids⠀⇛

       Green Left Party and HDP members are among the detained in the

       raids that took place early in the morning.

* ⚓ New York Times ☛ 95-Year-Old_Australian_Woman_Dies_Days_After_Police

  Used_a_Taser_on_Her⠀⇛

       Hours before Clare Nowland died, the police announced charges

       against the officer who used the stun gun on her in the care

       facility where she lived.

* ⚓ The Straits Times ☛ Family_pays_tribute_to_Australian_woman,_95,_who

  died_after_police_taser⠀⇛

       Ms Nowland’s family said she died “surrounded by the love and

       support of her family”.

* ⚓ JURIST ☛ Bolivia_Catholic_Church_leaders_admit_failure_to_protect

  victims_of_sexual_abuse⠀⇛

       Bolivian Roman Catholic Church leaders Wednesday admitted that

       the Church had been “deaf” to the persistent sexual abuse which

       has occurred within its schools as outrage over recent reports

       of child sexual abuse by priests continues to grow.

* ⚓ LRT ☛ Vilnius_priest_accused_of_sexual_relations_with_minor_–_media⠀⇛

       The chancellor of the Vilnius Archdiocese has been convicted of

       the acquisition and possession of pornographic material. He was

       also accused of having sexual relations with a minor, but the

       investigation was later dropped, the Delfi news website

       reported.

* ⚓ RFA ☛ Court_in_Myanmar’s_Mandalay_imprisons_3_monks_for_funding

  terrorism⠀⇛

       They were accused of supporting People’s Defense Force members

       sheltering in a monastery.

* ⚓ teleSUR ☛ Major_Raid_on_Last_Generation_Members_by_German_Police⠀⇛

       “…preliminary proceedings initiated against seven individuals…”

* ⚓ JURIST ☛ New_UK_student_visa_reform_restricts_international_students’

  ability_to_bring_family_with_them⠀⇛

       The UK Home Office announced new reforms on Tuesday regarding

       international students and their ability to bring their

       families with them into the country. The move is seen as an

       attempt to control the UK’s rising immigration numbers. In

       2022, alone, the UK reportedly issued half a million student

       visas to international students.

* ⚓ LRT ☛ Opposition_party’s_no-confidence_initiative_against_Lithuanian

  cabinet_falls_through⠀⇛

       The Lithuanian Farmers and Greens Union’s initiative for a vote

       of no-confidence in the government has failed to get the

       backing of other opposition MPs.

* ⚓ The Atlantic ☛ The_Problem_With_How_the_Census_Classifies_White

  People⠀⇛

       Being an unspecified “white” person has allowed many Americans

       to blend in. In this era of identity-driven polarization, we

       should acknowledge all the ways we are different.

* ⚓ Federal News Network ☛ Texas_lawmakers_issue_20_articles_of_impeachment

  against_state_Attorney_General_Ken_Paxton⠀⇛

       Texas lawmakers have issued 20 articles of impeachment against

       state Attorney General Ken Paxton, ranging from bribery to

       abuse of public trust as state Republicans surged toward a

       swift and sudden vote that could remove him from office. The

       charges were released Thursday night, hours after a Republican-

       led House investigative committee recommended impeaching the

       state’s top lawyer. The House could vote on the recommendation

       as soon as Friday. If it impeaches Paxton, he would be forced

       to leave office immediately.

* ⚓ The Straits Times ☛ Cathay_CEO_says_Hong_Kong’s_image_damaged_by_cabin

  crew_discrimination_incident⠀⇛

       A passenger had recorded flight attendants joking about a

       Mandarin-speaking customer’s English-language ability.

* ⚓ RFERL ☛ Belarusian_Educator,_Family,_Friends_Handed_Parole-Like

  Sentences_Over_2020_Protests⠀⇛

       A court in Minsk on May 25 handed parole-like sentences to

       noted Belarusian educator Yauhen Livyant, his wife Yulia,

       daughters Halina and Hanna, son-in-law Mikita Drozd, and his

       associates Alyaksey Ivanov and Alyaksandra Ensayn (aka

       Vilchytskaya).

* ⚓ RFERL ☛ Iranian_Bill_Before_Parliament_Increases_Penalties_For_Defiance

  Of_Hijab⠀⇛

       A bill containing Iran’s Chastity and Hijab law has been

       presented to parliament, legislation that many see as a

       continuation of the government’s oppression of women and human

       rights.

* ⚓ Vice Media Group ☛ Drivers_Sue_Amazon_Over_‘Inhumane’_Conditions,

  Having_to_Pee_in_Bottles⠀⇛

       A proposed class action in Colorado alleges that Amazon broke

       state wage and anti-discrimination laws by not letting drivers

       take breaks to use the bathroom.

§ Internet Policy/Net Neutrality⠀➾

* ⚓ APNIC ☛ [Podcast]_A_look_back_at_notable_root_zone_changes⠀⇛

       How the DNS root zone has changed over the years and what’s

       coming next.

§ Monopolies⠀➾

* § Patents⠀➾

      o ⚓ This_week_on_MIP:_France_v_EPO_spat,_Med-El_loss⠀⇛

             We provide a rundown of Managing IP’s news and analysis

             coverage from the week, and review what’s been happening

             elsewhere in IP

             French govt complained to EPO over EUIPO election conduct

             French finance minister Bruno Le Maire wrote to António

             Campinos, president of the EPO, to complain over the

             timing of an event that will be held in Lisbon one week

             before the EUIPO leadership vote, Managing revealed this

             week.

             Le Maire, minister for the economy and finance since

             2017, suggested the event could be seen as interfering

             with the process to select a new EUIPO executive

             director.

             Managing IP can also reveal that the incumbent executive

             director, Christian Archambeau, hinted at interference

             “from Munich” in the decision to remove him last

             November.

* § Trademarks⠀➾

      o ⚓ TTAB Blog ☛ Sustaining_Tumblr’s_Opposition,_TTAB_Finds_“TUMBLOG”

        Generic_for_…._Guess_What?⠀⇛

             In a rare opposition based on genericness, the Board

             sustained Tumblr’s challenge to an application to

             register TUMBLOG for “[p]roviding customized on-line web

             pages and data feeds featuring user-defined information,

             which includes blog posts, new media content, other on-

             line content, and on-line web links to other websites,”

             deeming the proposed mark to be generic for the recited

             services. The Board, without explanation, applied a

             “preponderance of the evidence” standard, ignoring CAFC

             case law requiring “clear evidence” of genericness.

             Tumblr, Inc. v. Mark David-Dale Kindy, Opposition No.

             91252639 (May 19, 2023) [not precedential] (Opinion by

             Judge Jonathan Hudis).

* § Copyrights⠀➾

      o ⚓ New York Times ☛ Tina_Turner,_Magnetic_Singer_of_Explosive_Power,

        Is_Dead_at_83⠀⇛

             Hailed in the 1960s for her dynamic performances with her

             first husband, Ike, she became a sensation as a recording

             artist, often echoing her personal struggles in her

             songs.

      o ⚓ CS Monitor ☛ ‘Simply_the_Best’:_Icon_Tina_Turner_defined_survivor

        in_epic_career⠀⇛

             Beloved entertainer Tina Turner lived a storied life of

             strength, overcoming horrific abuse and a stalled solo

             career to become one of the most popular singers of her

             era.

      o ⚓ Marcy Wheeler ☛ RIP_Riverboat_Queen⠀⇛

             As you may have heard, Tina turner has passed at the age

             of 83. It is pretty hard to describe how incredible, and

             important, she was over so many decades.

§ Gemini* and Gopher⠀➾

* § Personal⠀➾

      o ⚓ Vegetation_map_of_Bicuar_National_Park_–_Teixeira_1968⠀⇛

             I’ve been searching around for a long time for a copy of

             a vegetation map of Bicuar National Park, Angola,

             produced in 1968 by J. B. Teixeira. A number of

             contemporary publications looking at the ecology of

             Bicuar reference this map, but I realised I have never

             seen it. To my knowledge, it remains the only vegetation

             map of Bicuar National Park. I would like to see if I can

             geo-reference this map and overlay it on a new vegetation

             map we are producing, to see how they line up.

* § Technical⠀➾

      o ⚓ Games_Showcase:_Half-Life_Alyx⠀⇛

             What happens when one of the most influential game

             developers of all time writes a love letter to Virtual

             Reality?

      o § Internet/Gemini⠀➾

            # ⚓ An_email_about_estimating_productivity⠀⇛

                   In our lab group we use a lot of repeat inventory

                   tree growth data, from plots in forests, savannas,

                   and woodlands, to understand rates of biomass

                   dynamics and land-atmosphere carbon exchange.

      o § Programming⠀➾

            # ⚓ R_functions_to_download_data_from_KoboToolbox⠀⇛

                   I have created a couple of R functions to download

                   data from a KoboToolbox[1] server, using their API.

                   The functions sometimes fail with a 502 bad gateway

                   error, so it might be worth wrapping them in a try

                   () statement to get them to fail nicely.

            # ⚓ Pair_Reviewing⠀⇛

                   The world of programming offers countless paths to

                   learning, from online tutorials and forums to

                   extensive documentation. But one rich avenue for

                   learning and development often goes unheralded:

                   pair reviewing. By pairing up to review code,

                   developers can sharpen their skills, learn from

                   their peers, and contribute to a culture of

                   continuous learning.

                   [...]

                   Pair reviewing not only fosters individual growth

                   but also strengthens the team as a unit. The

                   process encourages open communication, mutual

                   respect, and shared ownership of code. It nurtures

                   a sense of camaraderie and mutual respect within

                   the team, contributing to an overall healthier,

                   more productive work environment.

                   The shared learning experience also helps equalize

                   knowledge across the team, reducing the risk

                   associated with knowledge silos or ‘bus factors’.

                   As each developer has the opportunity to both learn

                   and teach, the team becomes more balanced and

                   resilient. As the renowned software engineer Grady

                   Booch once said, “The function of good software is

                   to make the complex appear to be simple.” Through

                   pair reviewing, developers not only work towards

                   creating good, simplifying software but also engage

                   in the enriching process of continuous learning and

                   knowledge exchange.

=> =============================================================================

Gemini_(Primer) links can be opened using Gemini_software. It’s like the

World Wide Web but a lot lighter.

                ䷩ 𝚕𝚒𝚗𝚎 7117

Gemini_version_available_♊︎

✐ Links_28/05/2023:_New_Wine_and_More⠀✐

Posted in News_Roundup at 8:48 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Instructionals/Technical

      o WINE_or_Emulation

      o Desktop_Environments/WMs

            # GNOME_Desktop/GTK

* Distributions_and_Operating_Systems

      o SUSE/OpenSUSE

      o Slackware_Family

      o Fedora_Family_/_IBM

      o Canonical/Ubuntu_Family

      o Mobile_Systems/Mobile_Applications

* Free,_Libre,_and_Open_Source_Software

      o Productivity_Software/LibreOffice/Calligra

      o Programming/Development

            # Python

* Leftovers

      o Science

      o Hardware

      o Health/Nutrition/Agriculture

      o Security

            # Privacy/Surveillance

      o Defence/Aggression

      o Environment

            # Energy/Transportation

            # Wildlife/Nature

      o Finance

      o AstroTurf/Lobbying/Politics

      o Censorship/Free_Speech

      o Civil_Rights/Policing

      o Internet_Policy/Net_Neutrality

      o Monopolies

            # Patents

            # Trademarks

* Gemini*_and_Gopher

      o Personal

      o Politics

      o Technical

            # Internet/Gemini

* § GNU/Linux⠀➾

      o § Instructionals/Technical⠀➾

            # ⚓ TecAdmin ☛ Setting_Up_Permissions_in_Home_Directory_on

              Linux⠀⇛

                   One of the fundamental aspects of system security

                   and user privacy in any Linux or Unix-based

                   operating system (OS) is the proper management of

                   permissions. In these systems, a home directory is

                   the default location for a user’s personal files,

                   documents, and configuration settings.

            # ⚓ TecAdmin ☛ Configuring_Apache_Userdir_on_Ubuntu_and_Debian:

              A_Simplified_Guide⠀⇛

                   Apache is a versatile, open-source HTTP server for

                   modern operating systems including UNIX and

                   Windows. It provides a secure, efficient, and

                   extensible server that provides HTTP services in

                   sync with the current HTTP standards.

            # ⚓ TecAdmin ☛ How_to_Install_Apache_CouchDB_on_Ubuntu_&

              Debian⠀⇛

                   Apache CouchDB is a database management system that

                   seamlessly takes the data to the edge and then back

                   again. It’s known for its ease of replication and

                   setup. If you want to install Apache CouchDB on

                   your Ubuntu or Debian system, you’re at the right

                   place.

            # ⚓ Ubuntu Handbook ☛ How_to_Install_Python_3.12_(Beta_so_far)

              in_Ubuntu_22.04_|_20.04_|_23.04⠀⇛

                   For developers who want to prepare their project

                   for the latest Python releases, here’s how to

                   install Python 3.12 in all current Ubuntu releases.

                   Python 3.12 now is in Beta development stage.

            # ⚓ Make Tech Easier ☛ How_to_Concatenate_Files_in_Linux⠀⇛

                   Being able to combine various files together into

                   one can be very helpful. You can arrange and sort

                   out your desktop and combine several related

                   documents into one. In Linux, there are several

                   ways to concatenate files together.

            # ⚓ Adam_Young:_Opening_the_perf_file_descriptor⠀⇛

                   A couple months back I recorded this line on my

                   blog as part of investigating perf:

            # ⚓ TecAdmin ☛ What_is_the_“/etc/profile.d/”_Directory’s_Role

              in_Linux⠀⇛

                   In the vast landscape of the Linux operating

                   system, understanding the intricacies of various

                   system directories is key to effective system

                   administration. The Linux directory structure holds

                   a set of directories, each with a unique purpose,

                   and among these is the “/etc/profile.d/” directory.

            # ⚓ TecAdmin ☛ How_to_Add_a_Directory_to_Your_$PATH_Variable_in

              Linux⠀⇛

                   The $PATH variable in Linux is an environment

                   variable that determines where the shell looks for

                   executable files. By adding directories to this

                   variable, you make it easier to run your scripts

                   from anywhere without having to specify the full

                   path to the script’s location.

            # ⚓ Policy_Power:_Using_Network_Policies_Effectively_in

              Kubernetes⠀⇛

                   Introduction With the increasing adoption of

                   containerization technology, Kubernetes has become

                   one of the most popular platforms for running and

                   managing containers.

            # ⚓ Xe’s Blog ☛ Syncing_my_emulator_saves_with_Syncthing⠀⇛

                   One of the most common upsells in gaming is “cloud

                   saves”, or some encrypted storage space with your

                   console/platform manufacturer to store the save

                   files that games make. Normally Steam, PlayStation,

                   Xbox, Nintendo, and probably EA offer this as a

                   service to customers because it makes for a much

                   better customer experience as the customer migrates

                   between machines. Recently I started playing Dead

                   Space 2 on Steam again on a lark and I got to open

                   my old Dead Space 2 save from college. It’s magic

                   when it works.

                   [...]

                   I own these two games on cartridge and I have

                   dumped my copy of them from cartridge using a

                   hackable Switch.

      o § WINE or Emulation⠀➾

            # ⚓ WINE Project (Official) ☛ WineHQ_–_Wine_Announcement_–_The

              Wine_development_release_8.9_is_now_available.⠀⇛

                   The Wine development release 8.9 is now available.

                   What's new in this release:

                     - Mono engine updated to version 8.0.0.

                     - Completion of PE conversion in the PostScript

                   driver.

                     - Doppler shift support in DirectSound.

                     - GdiPlus performance improvements.

                     - Various bug fixes.

                   The source is available at:

                   https://dl.winehq.org/wine/source/8.x/wine-

                   8.9.tar.xz

                   Binary packages for various distributions will be

                   available from:

                   https://www.winehq.org/download

                   You will find documentation on https://

                   www.winehq.org/documentation

                   You can also get the current source directly from

                   the git

                   repository. Check https://www.winehq.org/git for

                   details.

                   Wine is available thanks to the work of many

                   people. See the file

                   AUTHORS in the distribution for the complete list.

      o § Desktop Environments/WMs⠀➾

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ This Week in GNOME ☛ Felix_Häcker:_#97_GNOME_Latam

                    2023⠀⇛

                         Update on what happened across the GNOME

                         project in the week from May 19 to May 26.

* § Distributions and Operating Systems⠀➾

      o ⚓ Barry Kauler ☛ Little_Flapi,_Appi_and_pupX_fixes⠀⇛

             Caramel reported a problem, sometimes Flapi (the Flatpak

             Installer) did not detect when an app is already

             installed.

             I found that the OpenShot AppImage can now be updated.

             Previously Appi installed version 3.0.0 and the next

             release didn’t work. However, the latest, 3.1.1 does

             work.

      o § SUSE/OpenSUSE⠀➾

            # ⚓ William ☛ William_Brown:_Starting_with_Rage_on_OpenSUSE⠀⇛

                   Rage is a rust implementation of Age, a modern,

                   simple and secure file encryption tool. It is

                   easier to use than other tools like GPG, and being

                   written in a memory safe language it avoids many of

                   the exploits that may occur in C based tools.

                   § Installing Rage

                   You can install rage on leap or tumbleweed from

                   zypper

      o § Slackware Family⠀➾

            # ⚓ Eric Hameleers ☛ Chromium_114_Early_Release_on_Slackware⠀⇛

                   An “early release” of Chromium 114 source code was

                   published a few days ago, the release notes are on

                   the developer blog. Since Chromium 110, Google

                   rolls out new major releases to a small sub-set of

                   its users to monitor any potential breakage and

                   apply fixes before the majority of users get

                   upgraded. The formal release of Chromium will be on

                   May 30th, but I decided to go along with the early

                   release this time, and offer this version to

                   Slackware users already this weekend, to celebrate

                   the Pentecost.

                   Looking at the new stuff in Chromium 114, there’s

                   two things you might want to play with, since they

                   are already contained in the browser and mostly

                   usable in Chromium 114, but not yet enabled by

                   default.

      o § Fedora Family / IBM⠀➾

            # ⚓ Remi Collet ☛ Remi_Collet:_PHP_version_8.1.20RC1_and

              8.2.7RC1⠀⇛

                   Release Candidate versions are available in testing

                   repository for Fedora and Enterprise Linux (RHEL /

                   CentOS / Alma / Rocky and other clones) to allow

                   more people to test them. They are available as

                   Software Collections, for a parallel installation,

                   perfect solution for such tests, and also as base

                   packages.

                   RPM of PHP version 8.2.7RC1 are available

            # ⚓ Red Hat Official ☛ Save_the_date_for_Red_Hat_Summit_2024⠀⇛

                   As we close out the last day of this year’s Red Hat

                   Summit, it’s time to mark your calendar for next

                   year’s event. We’re headed to the Mile High City –

                   Denver, CO – for Red Hat Summit and AnsibleFest

                   2024! Join us at the Colorado Convention Center,

                   May 6-9, 2024, as we bring together thousands of

                   customers, partners and technology industry leaders

                   and open source community members from around the

                   world for another high-energy week of innovation,

                   education and collaboration.

            # ⚓ CRN ☛ Red_Hat_CEO_Keynote:_5_Boldest_Remarks_On_AI,_New

              Products⠀⇛

                   Red Hat CEO Matt Hicks kicked off Red Hat Summit

                   2023 on Tuesday in Boston by explaining his

                   company’s artificial intelligence, open-source

                   vision and new products to thousands in attendance.

                   “We’re in one of those [game-changing] moments

                   right now. It’s the moment of AI,” said Hicks

                   during his keynote at the Boston Convention Center

                   today. “AI has moved from the obscurity of academia

                   to the ubiquity of ChatGPT. But it’s also moved

                   from the power of few, to the power of many.”

                   Several of Red Hat’s key product launches include

                   generative AI for Ansible, an enterprise-grade open

                   developer hub and new services in the Red Hat

                   Trusted Software Supply Chain suite.

            # ⚓ TechCrunch ☛ Red_Hat_brings_generative_AI_to_IT_automation

              with_Ansible_Lightspeed⠀⇛

                   Red Hat is holding its annual customer summit in

                   Boston this week, and today it announced a couple

                   of enhancements to Ansible, its open source IT

                   automation tool, including the new AI-fueled

                   Lightspeed.

                   Automation at its core is about distilling complex

                   processes into a playbook or recipe of actions. The

                   next step is building low-code and no-code

                   workflows. The recent rise of generative AI could

                   strip that process down even more to simply

                   describing the process and letting the tool do the

                   rest, creating a set of steps and providing the

                   necessary code and tools to move it through a work

                   process without much further human intervention

                   required (at least in theory).

      o § Canonical/Ubuntu Family⠀➾

            # ⚓ FOSSLinux ☛ The_20_Best_Themes_for_Ubuntu_[2023_Edition]⠀⇛

                   In the world of Linux, customization is king. One

                   of the easiest ways to give your Ubuntu system a

                   personal touch is by changing its theme. From sleek

                   and modern to quirky and colorful, there’s a theme

                   to match every taste. As we step into 2023, a whole

                   new lineup of eye-catching and feature-rich themes

                   are available to add a touch of flair to your

                   Ubuntu desktop.

      o § Mobile Systems/Mobile Applications⠀➾

            # ⚓ Notebook Check ☛ T30_Pro,_Doogee’s_third_Android_tablet,

              set_to_arrive_next_month_–_NotebookCheck.net_News⠀⇛

            # ⚓ TechRadar ☛ Google’s_Pixel_8_Pro_needs_to_beat_this_Android

              phone_to_win_me_back_|_TechRadar⠀⇛

            # ⚓ SlashGear ☛ How_Use_Your_Android_Phone_As_A_Webcam_For_Your

              Computer⠀⇛

            # ⚓ Giz China ☛ How_to_Block_YouTube_Ads_on_Android_TV_–

              Gizchina.com⠀⇛

            # ⚓ SlashGear ☛ 14_Coolest_Android_Phones_You_Can’t_Buy_In_The

              United_States⠀⇛

            # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this

              week_–_Android_Apps_Weekly⠀⇛

            # ⚓ SlashGear ☛ 5_Of_The_Best_Money-Saving_Apps_You_Can_Use_On

              Android⠀⇛

            # ⚓ Tom’s Guide ☛ Android_AI_text_suggestions_are_here_—_but

              there’s_a_catch_|_Tom’s_Guide⠀⇛

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

      o § Productivity Software/LibreOffice/Calligra⠀➾

            # ⚓ LibreOffice_Community_at_Events_in_Italy,_Spring_2023⠀⇛

                   Emiliano Vavassori, Deputy Chairperson in The

                   Document Foundation’s Board of Directors, give us

                   an update on recent events in Italy: Linux Arena at

                   Fiera del Radioamatore — Pordenone, April 23rd and

                   24th As in every spring, the Pordenone Linux Users

                   Group (PNlug) organizes an internal event inside

                   the local ham radio/electronics fair, «Fiera del

                   Radioamatore»…

      o § Programming/Development⠀➾

            # ⚓ Qt ☛ May_26th,_2023:_Qt_5.15_Standard_Support_for_Legacy

              License_Holders_Ends_Today⠀⇛

                   Standard support for the last release of the Qt 5

                   series ends for term and perpetual license holders

                   today. Customers distributing applications and

                   embedded devices using Qt 5 series software should

                   evaluate how to access technical support and

                   maintenance releases which may include security and

                   major bug fixes.

            # § Python⠀➾

                  # ⚓ TecAdmin ☛ Understanding_Python’s_Underscore_(___):_A

                    Comprehensive_Guide⠀⇛

                         Python, as a flexible and intuitive language,

                         introduces many constructs that enable the

                         ease of coding. One such construct is the

                         underscore ( _ ), a special character with

                         multiple uses, ranging from variable naming

                         to interpreter purposes, and more. For novice

                         programmers, underscores might appear

                         confusing, but understanding their purpose

                         can significantly enhance your [...]

                  # ⚓ Linux Hint ☛ Seaborn_Theme⠀⇛

                         In Python, the “sns.set_theme()” method can

                         be used along with the “style” parameter and

                         its value to customize the seaborn theme.

                  # ⚓ Linux Hint ☛ Seaborn_Legend_Location⠀⇛

                         To set the seaborn legend location in Python,

                         the “plt.legend()” method can be used along

                         with the “loc= ‘value’” parameter.

                  # ⚓ Linux Hint ☛ Remove_Substring_from_String_in_Python⠀⇛

                         To remove the substring from a string, the

                         “replace()”, “for” loop with “replace()”,

                         “translate()”, and the “Index” methods are

                         used in Python.

* § Leftovers⠀➾

      o ⚓ Valhalla’s_Things:_Correspondence_Book⠀⇛

             I write letters. The kind that are written on paper with

             a dip pen 1 and ink, stamped and sent through the post,

             spend a few days or weeks maturing like good wine in a

             depot somewhere2, and then get delivered to the

             recipient.

             Some of them (mostly cards) are to people who will

             receive them and thank me via xmpp (that sounds odd, but

             actually works out nicely), but others are proper letters

             with long texts that I exchange with penpals.

             Most of those are fountain pen frea^Wenthusiasts, so I

             usually use a different ink each time, and try to vary

             the paper, and I need to keep track of what I’ve used.

      o ⚓ Valhalla’s_Things:_Late_Victorian_Combinations⠀⇛

             Some time ago, on an early Friday afternoon our internet

             connection died. After a reasonable time had passed we

             called the customer service, they told us that they would

             look into it and then call us back.

             On Friday evening we had not heard from them, and I was

             starting to get worried. At the time in the evening when

             I would have been relaxing online I grabbed the first

             Victorian sewing-related book I found on my hard disk and

             started to read it.

      o § Science⠀➾

            # ⚓ New York Times ☛ Brain_Implants_Allow_Paralyzed_Man_to_Walk

              Using_His_Thoughts⠀⇛

                   In a new study, researchers describe a device that

                   connects the intentions of a paralyzed patient to

                   his physical movements.

            # ⚓ Science Alert ☛ A_New_Type_of_Brain_Cell_Found_in_Mice_May

              Trigger_Overactive_Appetites⠀⇛

                   It’s been overlooked until now.

            # ⚓ Science Alert ☛ Earth-Like_World_Covered_in_Raging

              Volcanoes_May_Have_Been_Found⠀⇛

                   Hell on Earth?

            # ⚓ Science Alert ☛ Up_to_30%_of_Published_Neuroscience_Papers

              May_Be_Faked_–_And_That’s_Before_ChatGPT⠀⇛

                   Something is seriously wrong here.

            # ⚓ Science Alert ☛ For_The_First_Time,_Scientists_Have

              Detected_a_Cyclone_on_The_North_Pole_of_Uranus⠀⇛

                   “It isn’t just a plain blue ball of gas.”

            # ⚓ Science Alert ☛ Reactivated_Genes_From_Stone_Age_Dental

              Plaque_Reveal_Lost_Mouth_Microbes⠀⇛

                   Welcome back!

      o § Hardware⠀➾

            # ⚓ Hackaday ☛ Nice_Try,_But_It’s_Not_Aperture_Synthesis⠀⇛

                   Some of the world’s largest radio telescopes are

                   not in fact as physically large as they claim to

                   be, but instead are a group of telescopes spread

                   over a wide area whose outputs are combined to

                   produce a virtual telescope equal in size to the

                   maximum distance between the constituents of the

                   array. Can this be done on the cheap with an array

                   of satellite dishes? It’s possible, but as

                   [saveitforparts] found out when combining a set of

                   Tailgater portable dishes, not simply by linking

                   together the outputs from a bunch of LNBs.

            # ⚓ The Straits Times ☛ Washington_and_Tokyo_vow_closer_chip

              cooperation⠀⇛

                   The move comes as both the US and Japan reduce

                   exposure to China.

            # ⚓ Hackaday ☛ Nokia_N-Gage_QD_Becomes_Universal_Bluetooth

              Gamepad⠀⇛

                   The Nokia N-Gage might not have put up much of a

                   fight against Nintendo’s handheld dynasty, but you

                   can’t say it didn’t have some pretty impressive

                   technology for the time. [BeardoGuy] happens to

                   have a perfectly functional N-Gage QD, which he

                   turned into a universal Bluetooth gamepad.

            # ⚓ Hackaday ☛ Learning_3D_Printing_Best_Practices_From_A_Pro⠀⇛

                   It might seem like 3D printing is a thoroughly

                   modern technology, but the fact is, it’s been used

                   in the industry for decades. The only thing that’s

                   really new is that the printers have become cheap

                   and small enough for folks like us to buy one and

                   plop it on our workbench. So why not take advantage

                   of all that knowledge accumulated by those who’ve

                   been working in the 3D printing field, more

                   accurately referred to as additive manufacturing,

                   since before MakerBot stopped making wooden

                   printers?

            # ⚓ Hackaday ☛ Restoring_Dot_Matrix_Printer_Cartridges_For

              2023⠀⇛

                   The noise of a dot matrix printer is probably as

                   synonymous with 1980s computing as the modem

                   handshake would become with the desktop experience

                   a decade or more later. But unlike the computers

                   that would have driven it, a dot matrix printer can

                   still be a very useful device here in 2023. And why

                   not? They’re cheap to operate and can produce

                   surprisingly good quality when paired with suitable

                   drivers. There is a snag though; while cartridges

                   for popular models can still be found, there are

                   plenty whose consumables are long gone. [Drygol]

                   had an Apple ImageWriter II with exactly that

                   problem, and after finding all his cartridges were

                   non-functional, took a look at how to bring them

                   back.

            # ⚓ Ruben Schade ☛ A_new_old-stock_floppy_drive⠀⇛

                   This will be a quick post in my Am386 board

                   adventures today, but I received my new old stock

                   Panasonic 3.5-inch high density floppy drive today

                   this week, and it’s beautiful!

                   [...]

                   I’ve had Mitsumi, Sony, Mitsubishi, and Samsung

                   3.5-inch drives growing up, but this is my first

                   Panasonic that isn’t a 5.25-inch unit. One little

                   Easter Egg that doesn’t come up well on camera is

                   that the eject button is glossly! Maybe they

                   figured the matt beige plastic doesn’t stand up to

                   the rigours of regular pressing, so they buffed it

                   to a shine to make it look deliberate.

            # ⚓ Ruben Schade ☛ A_cool_Adaptec_AHA-1542CP_ISA_SCSI_card⠀⇛

                   All the parts I ordered months ago for my impromptu

                   Am386 build have stared arriving at once. Hot on

                   the heels of the Panasonic floppy drive last week,

                   we have another awesome new-old stock device, this

                   time a classic 16-bit ISA SCSI controller.

                   View_all_posts_in_the_Am386_series

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ Hackaday ☛ Generating_Hydrogen_Peroxide_For_Disinfecting

              Water_Using_A_Solar-Driven_Catalyst⠀⇛

                   Ensuring that water is safe to use and consume can

                   be a real chore, especially for those who live in

                   impoverished areas without access to safe drinking

                   water. Here is where researchers at Stanford

                   University hope that their recently developed low-

                   cost catalyst can make a difference. This catalyst

                   comes in the form of nano-sized particles

                   (nanoflakes) consisting out aluminium oxide,

                   molybdenum sulfide, copper and iron oxide. When

                   exposed to sunlight,  the catalyst performs like a

                   photon-sensitive semiconductor/metal junction (Cu-

                   MoS2), with the dislodged electrons going on to

                   react with the surrounding water, resulting in the

                   formation of hydrogen peroxide (H2O2) and hydroxy

                   radicals.

            # ⚓ The Straits Times ☛ Vietnam_to_cut_annual_rice_exports_by

              44%_to_4_million_tonnes_by_2030⠀⇛

                   The move is aimed at boosting exports of high-

                   quality rice, ensuring domestic food security,

                   protecting the environment and adapting to climate

                   change.

            # ⚓ Science Alert ☛ Exertion_Headaches_Can_Make_Exercise_a_Real

              Pain._Here’s_What_to_Do_About_Them⠀⇛

                   Mitigate the pain for your gain.

            # ⚓ Science Alert ☛ Fungal_Infections_Could_Obliterate_Our_Food

              Supply,_Scientists_Warn⠀⇛

                   The future is blight.

            # ⚓ uni Stanford ☛ ‘The_difference_water_can_make’:_Matt_Damon

              and_Gary_White_discuss_clean_water_access⠀⇛

                   Matt Damon and Gary White, co-founders of

                   WaterEquity and Water.org, spoke with students

                   about the economic and equity implications of water

                   scarcity around the world. The event was hosted by

                   the course SUSTAIN 345: Global Leaders and

                   Innovators in Human and Planetary Health:

                   Sustainable Societies Lab.

            # ⚓ Helsinki Times ☛ The_unrestricted_sale_of_nicotine_pouches

              poses_a_significant_threat_to_the_health_of_young_people_in

              particular⠀⇛

                   The sale of nicotine pouches was deregulated at the

                   beginning of April. Nicotine pouches, which fall

                   under the scope of the Medicines Act, are now

                   subject to tobacco and chemical regulations.

                   Nicotine pouches with high nicotine concentrations

                   are harmful to health, and young people are

                   particularly at risk. Nicotine pouches should be

                   subjected to stricter regulations promptly.

            # ⚓ Mexico News Daily ☛ Seized_psychiatric_medications_released

              by_health_regulator⠀⇛

                   Regulators have released medication seized from

                   manufacturer Psicofarma, to address a shortage of

                   mental health drugs in the country.

            # ⚓ Axios ☛ Sorry,_stevia:_Artificial_sweeteners_get_more_bad

              PR⠀⇛

                   The World Health Organization isn’t sweet on non-

                   sugar sweeteners, the_agency_announced.

                   Driving the news: It advised against using sugar

                   substitutes like Splenda, stevia and Sweet’n Low

                   for weight loss — and warned about potential long-

                   term health risks of too much intake.

      o § Security⠀➾

            # § Privacy/Surveillance⠀➾

                  # ⚓ Reason ☛ European_Union_Fines_Meta_$1.3_Billion

                    Because_of_NSA_Spying_Programs⠀⇛

                         The record penalty seems to be based less on

                         the Facebook parent company’s lax data

                         practices than the U.S. intelligence

                         community’s data-collection programs.

                  # ⚓ Quartz ☛ Tesla_could_face_a_$3.3_billion_fine_over_a

                    massive_data_leak⠀⇛

                         A whistleblower leaked a massive trove of

                         data about the electric carmaker Tesla to the

                         German publication Handelsblatt.

      o § Defence/Aggression⠀➾

            # ⚓ New York Times ☛ Sedition_Sentence_for_Oath_Keepers’

              Stewart_Rhodes_Marks_Moment_of_Accountability⠀⇛

                   The 18 years in prison given to Stewart Rhodes for

                   a rarely charged crime underscored the lengths to

                   which the Justice Department and the courts have

                   gone in addressing the assault on the Capitol.

            # ⚓ France24 ☛ Suspect_arrested_in_Japan_gun_and_knife_attack

              that_killed_four⠀⇛

                   Japanese police on Friday detained a man who had

                   holed up in a building after allegedly killing four

                   people, including two police officers, in a gun and

                   knife attack.

            # ⚓ France24 ☛ Over_a_dozen_‘innocent’_Westerners_still

              detained_in_Iran⠀⇛

                   Over a dozen Western passport-holders are detained

                   in Iran, even after the release on Friday of

                   Belgian aid worker Olivier Vandecasteele in an

                   exchange deal between Belgium and Iran brokered by

                   Oman.

            # ⚓ Reason ☛ A_Georgia_Woman_Died_After_Falling_Out_of_a_Moving

              Patrol_Car._Now,_Her_Family_Is_Suing_the_Cops_Responsible.⠀⇛

                   Brianna Grier was having a mental health crisis.

                   She needed an ambulance. She got two cops instead.

            # ⚓ Hong Kong Free Press ☛ Caught_in_the_crossfire:_Chinese

              diaspora_bears_brunt_of_Canada-Beijing_tensions⠀⇛

                   The Chinese diaspora has been caught in the

                   crossfire of Ottawa’s row with Beijing over its

                   alleged meddling in Canada’s affairs — facing both

                   intimidation from Chinese operatives and rising

                   stigmatization.

            # ⚓ France24 ☛ Saudi_and_US_report_improved_ceasefire

              conditions_in_Sudan⠀⇛

                   Saudi Arabia and the United States said Friday the

                   warring sides in Sudan’s conflict are adhering

                   better to a new, weeklong cease-fire following days

                   of sporadic fighting.

            # ⚓ France24 ☛ Investigation:_The_deadly_attacks_on_Syrian

              truffle_hunters_by_the_Islamic_State_group⠀⇛

                   The Bedouin communities living in the unforgiving

                   Badia, or the Syrian desert, are facing a surge in

                   armed attacks. The violence reaches a peak each

                   year between February and April: the truffle

                   season. As tribes go out to hunt truffles, they

                   risk being ambushed by sleeper cells of the Islamic

                   State group, which has taken refuge in the Badia

                   since 2019. This exclusive investigation from

                   FRANCE 24′s Observers team exposes the horrific

                   abuses being carried out deep in the desert.

            # ⚓ Latvia ☛ Latvia’s_healthcare_provision_for_children_has

              huge_room_for_improvement⠀⇛

                   Eurostat data published May 26 shows Latvia with

                   some of the least comprehensive healthcare

                   provision for children in the European Union.

            # ⚓ Latvia ☛ One_in_four_ticks_found_to_carry_Lyme_this_year_in

              Latvia⠀⇛

                   More than 20% of the ticks analyzed in all Latvian

                   laboratories have been tested positive for Lyme

                   borrelia this year. Borrelia can cause Lyme disease

                   against which there are no vaccines. The other

                   dangerous tick-borne illness – encephalitis – has

                   only been found in a few ticks, Latvian Television

                   reported on May 26.

            # ⚓ New York Times ☛ Passenger_Arrested_on_Suspicion_of_Forcing

              Open_Plane_Door_Mid-Flight⠀⇛

                   A man was arrested on suspicion of unlocking an

                   emergency exit on an Asiana Airlines flight in

                   South Korea when it was about 700 feet off the

                   ground.

            # ⚓ The Straits Times ☛ North_Korea_spent_the_pandemic_building

              a_huge_border_wall⠀⇛

                   It has enabled the regime to tighten the flow of

                   information and goods into the country and keep

                   foreign elements out.

            # ⚓ teleSUR ☛ Rwandan_Genocide_Fugitive_Appears_In_South

              African_Court⠀⇛

                   Fulgence Kayishema was arrested two days ago in

                   South Africa after more than two decades on the

                   run.

            # ⚓ JURIST ☛ UN_tribunal_arrests_man_wanted_for_Rwanda_genocide

              since_1994⠀⇛

                   A special tribunal established by the UN, known as

                   the International Residual Mechanism for Criminal

                   Tribunals (IRMCT), announced Thursday that fugitive

                   Fulgence Kayishema has been arrested in Paarl,

                   South Africa after 22 years on the run. Kayishema,

                   a police officer accused of orchestrating the

                   killing of more than 2,000 Tutsi refugees at Nyange

                   Catholic Church…

            # ⚓ France24 ☛ Rwanda_genocide_fugitive_Kayishema_appears_in

              South_Africa_court⠀⇛

                   Fulgence Kayishema, one of the last fugitives

                   sought over the 1994 Rwanda genocide, appeared

                   before a court in the South African city of Cape

                   Town on Friday, two days after being arrested

                   following 22 years on the run.

            # ⚓ Defence Web ☛ Measures_in_place_to_address_SANDF_sexual

              exploitation_–_Cabinet⠀⇛

                   South Africa’s Cabinet has commended a set of

                   measures that have been put in place to address the

                   incidents of sexual exploitation and abuse (SEA)

                   within peace keeping missions the South African

                   National Defence Force (SANDF) takes part in.

            # ⚓ DOD_sends_new_cyber_strategy_to_Congress,_releases

              unclassified_fact_sheet⠀⇛

                   The highly anticipated strategy is the first since

                   2018 and follows the release of the National

                   Cybersecurity Strategy in March.

            # ⚓ Defence Web ☛ Rwandan_fugitive_wanted_for_genocide_nabbed

              in_SA⠀⇛

                   A Rwandan fugitive, wanted in connection with the

                   1994 Rwandan genocide, has been arrested in Paarl

                   in the Western Cape by a South African Operational

                   Task Team (OTT).

            # ⚓ LRT ☛ ‘Historic_opportunity.’_Lithuania’s_airports_prepare

              for_challenges_during_Vilnius_NATO_summit⠀⇛

                   As Vilnius looks to host the NATO summit in July,

                   preparations are underway at Lithuania’s airports,

                   with aircraft service companies looking for extra

                   staff and airports coordinating security

                   procedures.

            # ⚓ Defence Web ☛ Top_UN_award_for_Ghanaian_female

              peacekeeper⠀⇛

                   Ghana’s position as the largest contributor of

                   female military personnel to United Nations (UN)

                   peacekeeping efforts received another boost when

                   Captain Cecilia Erzuah was named the world body’s

                   Military Gender Advocate of the Year.

      o § Environment⠀➾

            # ⚓ France24 ☛ Paris_to_ban_single-use_plastic_from_the_2024

              Olympic_Games⠀⇛

                   Paris Mayor Anne Hidalgo said on Friday the city

                   planned to ban single-use plastic when it holds the

                   2024 Olympic Games as part of efforts to tackle a

                   global plastic pollution crisis.

            # ⚓ Mexico News Daily ☛ New_plastic_recycling_collection_center

              opens_in_Tijuana⠀⇛

                   The center looks to increase Mexico’s recycling by

                   processing PET bottles from both Mexico and the

                   United States.

            # ⚓ CS Monitor ☛ Women_in_Guyana_plant_mangroves_to_battle

              rising_seas⠀⇛

                   Indigenous women use drones, scientific data, and

                   the replanting of mangroves to slow the progression

                   of rising seas in the South American nation of

                   Guyana.

            # ⚓ Mexico News Daily ☛ Drone_video_footage_shows_smoking

              Popocatépetl_crater⠀⇛

                   Footage obtained by the Mexican Navy shows the

                   first images of the crater, which has been

                   experiencing increased activity for two weeks.

            # ⚓ CS Monitor ☛ ‘Uncharted_territory’:_How_Asia_is_coping_with

              extreme_heat⠀⇛

                   When it comes to beating rising heats, there’s no

                   one-size-fits-all solution. Across Asia,

                   communities are adapting to extreme temperatures,

                   showcasing both human resilience and the far-

                   reaching costs of climate change.

            # § Energy/Transportation⠀➾

                  # ⚓ Hackaday ☛ Fly_Like_You_Drive_With_This_Flying_RC

                    Drift_Car⠀⇛

                         So it’s 2023, and you really feel like we

                         should have flying cars by now, right? Well,

                         as long as you ignore the problem of scale

                         presented by [Nick Rehm]’s flying RC drift

                         car, we pretty much do.

                  # ⚓ Ruben Schade ☛ Evolving_use_patterns_of_the_NYC

                    subway⠀⇛

                         The pandemic subway is a different system

                         than what cities have known in the past. The

                         same numbers of people aren’t flooding into

                         central business districts every weekday, but

                         ridership for many agencies has surged on

                         afternoons and weekends.

                  # ⚓ New York Times ☛ Gasoline_Prices,_a_Source_of_Pain

                    Last_Year,_Have_Come_Way_Down⠀⇛

                         Reasons include a stronger supply of oil and

                         weaker-than-expected demand, energy experts

                         say. Some people are saving hundreds of

                         dollars on fuel.

                  # ⚓ RFA ☛ Global_solar_investment_set_to_surpass_oil

                    spending,_report_says⠀⇛

                         China leads the way, according to the

                         International Energy Agency.

                  # ⚓ Science Alert ☛ Scientists_Find_a_Way_to_Harvest

                    Clean_Energy_From_Nothing_But_Air⠀⇛

                         “The air contains an enormous amount of

                         electricity.”

            # § Wildlife/Nature⠀➾

                  # ⚓ Science Alert ☛ Research_Reveals_The_Creepy_Way

                    Greedy_Gulls_Decide_What_to_Eat⠀⇛

                         Mine. Mine. Mine. Mine. Mine.

                  # ⚓ Axios ☛ Drones_go_out_on_shark_patrol⠀⇛

                         Lifeguards and beachgoers are getting a new

                         ally this summer in the fight to prevent

                         potentially dangerous shark encounters:

                         drones.

                         Why it matters: While actual shark-on-human

                         attacks are vanishingly rare, a spate of

                         sightings near shore has been raising alarms

                         from Massachusetts to Hawaii recently.

      o § Finance⠀➾

            # ⚓ RFERL ☛ Georgian_Billionaire_Wins_$926_Million_From_Credit

              Suisse_After_Fraud⠀⇛

                   Credit Suisse was ordered to pay $926 million to

                   Georgia’s former prime minister on May 26 for

                   losing part of his fortune, in a Singapore court

                   ruling that represents one of the biggest legal

                   awards made against the bank.

            # ⚓ YLE ☛ Specialty_shops_closing_in_Finnish_city_centres⠀⇛

                   The most successful shops in recent years sell

                   sporting goods, hardware, home electronics and

                   eyeglasses while the least successful offer books,

                   watches, jewellery and clothes.

            # ⚓ New Yorker ☛ Affirmations_for_the_Landlord_Facing

              Adversity⠀⇛

                   I am a landlord, not a charity. Eviction is a

                   healthy boundary-setting practice.

            # ⚓ Helsinki Times ☛ Expensive_food_often_leads_to_unhealthy

              choices_according_to_survey⠀⇛

                   Rising food prices have had an impact on consumer

                   behavior, resulting in new choices being made in

                   grocery stores. Vaasan has examined changes in

                   purchasing habits over the past year, and the

                   results reveal a concerning trend. An increasing

                   number of Finns are forced to carefully consider

                   their food purchases, which, for some, leads to

                   unhealthy choices. However, by choosing nutritious

                   alternatives, consumers can get the best value for

                   their money.

            # ⚓ The Straits Times ☛ Economic_development_in_Asia_still

              faces_many_challenges,_says_China’s_commerce_minister⠀⇛

                   China, as a major developing country, is willing to

                   make due contributions, Mr Wang said.

            # ⚓ Quartz ☛ Biden_and_Republicans_are_$70_billion_away_from

              settling_their_debt_ceiling_squabbles⠀⇛

                   US debt ceiling talks appear to have overcome an

                   impasse and are now close to finding a resolution.

            # ⚓ Axios ☛ U.S._economy_hotter_than_policymakers_would_like⠀⇛

                   Economic data released on Friday show a pickup in

                   consumer spending, alongside persistent inflation,

                   which suggests the Federal Reserve might not yet be

                   done with its rate-hiking campaign.

                   Why it matters: Demand across the economy is still

                   hotter than policymakers would like.

                   ===================================================

            # ⚓ Quartz ☛ New_York_City_is_withholding_new_deposits_at_five

              banks_accused_of_inaction_on_discrimination⠀⇛

                   >New York City is taking its business away from

                   banks that lack anti-discrimination plans.

            # ⚓ RFA ☛ US_debt_deal_nears,_but_Asia_will_look_on_warily⠀⇛

                   Lawmakers say they’re near a deal to pay America’s

                   debts, but the fight to get there has aired much

                   dirty laundry.

            # ⚓ YLE ☛ Statistics_Finland:_Wages_not_rising_in_line_with

              inflation⠀⇛

                   Real earnings dropped by nearly five percent

                   compared to early 2022.

            # ⚓ Vice Media Group ☛ Minnesota_Governor_Vetoes_Minimum_Pay

              for_Ridehail_Drivers_After_Uber_Threatens_to_Leave⠀⇛

                   The bill would have set minimum payouts for drivers

                   indexed to inflation.

            # ⚓ Axios ☛ U.S._will_run_out_of_money_on_June_5:_Yellen⠀⇛

                   Treasury Secretary Janet_Yellen has given Congress

                   a more precise date — June 5 — for when the U.S.

                   government will hit the debt ceiling and run out of

                   money to pay its bills.

            # ⚓ New York Times ☛ Will_Lawmakers_Sacrifice_Our_Health_and

              Safety_to_Get_a_Debt_Ceiling_Deal?⠀⇛

                   A crucial part of the clean energy transition is

                   swept up in the high-pressure negotiations

                   happening in Washington.

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ Kurdish_politician_Aysel_Tuğluk’s_sentence_suspended_for

              one_year_for_health_reasons⠀⇛

                   Diagnosed with dementia, Tuğluk was released from

                   prison in October last year. The prosecutors

                   concluded that her health condition is not suitable

                   for a return to the prison.

            # ⚓ The Straits Times ☛ ‘Wang_hong’_culture_booms_in_China_as

              more_young_people_dream_of_becoming_influencers⠀⇛

                   But many underestimate the difficulties in having

                   to constantly come up with new content.

            # ⚓ Ruben Schade ☛ No_more_@Rubenerd_Blog_Twitter_posts⠀⇛

                   With changes to Twitter’s API, it’s no longer

                   feasible for me to auto-post new entries to the

                   @Rubenerd_blog account. I apologise if that’s how

                   you tracked stuff here.

                   As an alternative, I’d recommend opening an account

                   with one of the RSS reader services below, and

                   adding my feed so you don’t miss a post: [...]

            # ⚓ New York Times ☛ Alberta_Election_Tests_Conservatives’_Far-

              Right_Shift⠀⇛

                   The pandemic took the conservative party in the

                   oil-rich province of Alberta far to the right. An

                   election on Monday will test if voters,

                   traditionally among Canada’s most conservative,

                   will follow.

            # ⚓ RSF_attests_media_system_is_rigged,_denounces_biased

              coverage_of_Turkey’s_election⠀⇛

                   The campaign of opposition candidate Kemal

                   Kılıçdaroğlu has been significantly impeded by an

                   unjust distribution of airtime and editorial

                   control, while the incumbent Erdoğan has utilized

                   tactics like intimidating and detaining independent

                   journalists, as well as acquiring around 85% of the

                   media.

            # ⚓ Turkey_elections:_Latest_polls_ahead_of_second_round⠀⇛

                   While AREA research predicts a win for the

                   oppositional contender on May 28, two other polling

                   companies foresee a win for the incumbent.

            # ⚓ New York Times ☛ Burhan_Sönmez_on_the_Tensions_Between

              Politics_and_Art_in_Turkey⠀⇛

                   Burhan Sönmez, who is president of PEN

                   international, discusses the tension between

                   politics and art and the role of literature in

                   authoritarian societies.

            # ⚓ New York Times ☛ Turkey’s_Presidential_Runoff_Election_on

              Sunday:_What_to_Know⠀⇛

                   President Recep Tayyip Erdogan led his main

                   challenger, Kemal Kilicdaroglu, by a comfortable

                   margin after the first round of voting.

            # ⚓ New York Times ☛ How_Turkey’s_Erdogan_Rose_to_Power⠀⇛

                   Turkey’s leader faced a criminal conviction, mass

                   protests and a coup. Instead of hurting or ending

                   his political career, they helped him accumulate

                   ever more control.

            # ⚓ New York Times ☛ Turkey’s_Erdogan_Woos_Voters_in_Re-

              Election_Campaign⠀⇛

                   President Recep Tayyip Erdogan has rock star appeal

                   at his election rallies, promising to lead Turkey

                   to claim its rightful place as a global power if he

                   is re-elected in a runoff on Sunday.

            # ⚓ CS Monitor ☛ Why_quakes_that_razed_homes_may_raise_up

              Turkey’s_Erdoğan⠀⇛

                   Expectations that a weak response to earthquakes

                   would cost the Turkish government votes proved

                   false. Political preferences have become

                   identities.

            # ⚓ The Atlantic ☛ Photos_From_Turkey’s_Convulsive_Decade⠀⇛

                   The photographer Emin Özmen has spent his career

                   documenting life in Erdoğan’s shadow, watching his

                   country transform from an aspiring democracy to a

                   vision of the dystopian autocratic future.

            # ⚓ RFERL ☛ Georgian_President_Criticizes_Government_In

              Independence_Day_Speech⠀⇛

                   Georgian President Salome Zurabishvili has used a

                   speech during the South Caucasus nation’s

                   Independence Day celebrations to criticize the

                   government over fears it is backsliding on

                   democratic reforms.

            # § Misinformation/Disinformation/Propaganda⠀➾

                  # ⚓ Michael West Media ☛ Twitter_abandons_EU_pact_against

                    disinformation⠀⇛

                         Twitter has dropped out of a voluntary

                         European Union agreement to combat online

                         disinformation, a top EU official says.

                         European Commissioner Thierry Breton tweeted

                         that Twitter had pulled out of the EU’s

                         disinformation “code of practice” that other

                         major social media platforms have pledged to

                         support.

      o § Censorship/Free Speech⠀➾

            # ⚓ Meduza ☛ Russia’s_Justice_Ministry_adds_lead_singer_of_rock

              group_Bi-2,_journalists,_and_scholars_to_its_list_of_‘foreign

              agents’_—_Meduza⠀⇛

                   Russia’s Justice Ministry updated its registry of

                   “foreign agents.” New additions include Lyova Bi-2

                   (real name Yegor Bortnik), lead singer of the band

                   Bi-2, and other individuals and organizations:

            # ⚓ China_deletes_1.4_million_social_media_posts_in_crack_down

              on_‘self-media’_accounts

              ⠀⇛

                   China’s cyberspace regulator said 1.4 million

                   social media posts have been deleted following a

                   two-month probe into alleged misinformation,

                   illegal profiteering, and impersonation of state

                   officials, among other “pronounced problems.”

                   The Cyberspace Administration of China (CAC) said

                   in a statement on Friday it had closed 67,000

                   social media accounts and deleted hundreds of

                   thousands of posts between March 10 and May 22 as

                   part of a broader “rectification” campaign.

                   Since 2021, China has targeted billions of social

                   media accounts in a bid to “clean” its cyberspace

                   and make it easier for authorities to control.

                   The latest crackdown targeted accounts on popular

                   Chinese social media apps including WeChat, Douyin,

                   and Weibo that fall under the category of “self

                   media,” a term that broadly refers to accounts that

                   publish news and information but are not

                   government-run or state-approved.

      o § Civil Rights/Policing⠀➾

            # ⚓ RFERL ☛ Kosovar_Police_Clash_With_Protesters_In_Serb-

              Majority_Northern_Towns,_Drawing_U.S.,_EU_Rebukes⠀⇛

                   Police in northern Kosovo used tear gas and stun

                   grenades to disperse crowds in three Serb-majority

                   towns and enter municipal buildings in support of

                   recently elected ethnic Albanian mayors — security

                   actions that drew quick rebukes from Pristina’s

                   Western allies, who urged dialogue.

            # ⚓ Axios ☛ Judge_temporarily_blocks_South_Carolina’s_6-week

              abortion_ban⠀⇛

                   A state judge on Friday temporarily blocked South

                   Carolina’s_recently_enacted_six-week_abortion_ban

                   until the state supreme court has a chance to

                   review it, Axios has confirmed.

            # ⚓ Neritam ☛ This_Labor_Day,_Remember_That_Martin_Luther

              King’s_Last_Campaign_Was_for_Workers’_Rights⠀⇛

                   Most Americans today know that Reverend Martin

                   Luther King Jr. was killed in Memphis, Tennessee in

                   1968, but few know why he was there.

            # ⚓ France24 ☛ Tear_gas_fills_the_air_as_TotalEnergies_AGM

              rejects_climate_activist_resolution⠀⇛

                   TotalEnergies shareholders rejected an activist

                   resolution on Friday urging faster cuts to the oil

                   major’s greenhouse gas emissions programme after

                   police intervened to stop climate protesters

                   disrupting its annual general meeting.

            # ⚓ RFERL ☛ Iranian_Lawyers_Say_Courts_Issuing_Them_Dozens_Of

              Summonses_With_No_Charges⠀⇛

                   A leading member of one of Iran’s legal

                   associations says more than 100 lawyers from across

                   the country have been summoned to Tehran’s security

                   court, even though there is no mention of any

                   charges against them.

            # ⚓ RFA ☛ Childhood_friend_of_North_Korea’s_Kim_Jong_Un_says_he

              has_never_heard_about_Kim’s_son⠀⇛

                   Focus on daughter Ju Ae seems to undermine South

                   Korean claims that Kim has a son

            # ⚓ Mexico News Daily ☛ Girls_develop_phone_apps_to_solve

              problems_in_their_community [Ed: Well, phone apps, however,

              create rather than solve problems]⠀⇛

                   The nonprofit Technovation is teaching young

                   Mexican girls to develop technology to help others

                   and also see a better future for themselves.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ Hackaday ☛ Where_Exactly_Did_That_Network_Packet_Come

              From?⠀⇛

                   Have you ever noticed that some websites can figure

                   out, at least roughly, where you are? Sometimes

                   they use it to find you a closer content provider.

                   Or they might block you from seeing certain things

                   while offering you other things specific to your

                   location. This is possible because there are

                   databases that map IPs to locations. [Mark

                   Litwintschik] looks at using those databases from

                   an API or downloading them into your own database.

                   He also shows some very large database queries,

                   which is interesting, too. He uses IPInfo, although

                   there are other providers. Some only provide a

                   limited number of lookups, but there are plenty of

                   free tiers for low-volume usage.

      o § Monopolies⠀➾

            # § Patents⠀➾

                  # ⚓ USPTO’s_ANPRM_Has_Major_Problems⠀⇛

                         Throughout my 26 years in Congress, including

                         three terms as Chairman of the House

                         Judiciary Committee, there was a clear need

                         to strengthen our patent system in order to

                         protect the rights of innovators and

                         entrepreneurs.

                  # ⚓ Europe_embarks_on_a_new_era_of_patent_protection [Ed:

                    EPO is celebrating illegal and unconstitutional

                    program. Europe embarks on a new era of criminality and

                    law-breaking -- all this to appease lobbyists with

                    their moles running the EPO.]⠀⇛

                         The Unitary Patent system enters into

                         operation

                  # ⚓ JUVE ☛ Top_ten_most-read_UPC_articles [Ed: Those "UPC

                    articles" are sponsored by Team UPC. JUVE got paid to

                    promote crimes, and is now taking stock of fake "news"

                    is produced for a fee. We nowadays have a press

                    apparatus sponsored to promote crime on behalf of

                    criminals, including reputation-laundering PR. There's

                    money in that.]⠀⇛

                         With the Unified Patent Court just days away

                         from launch, JUVE Patent has rounded up the

                         top ten most-read articles concerning the

                         pan-European court published on the site

                         since 2018.

                  # ⚓ Unified Patents ☛ Mel_NavIP_automobile_speech

                    recognition_patent_likely_invalid⠀⇛

                         On May 23, 2023, the Patent Trial and Appeal

                         Board (PTAB) instituted trial on all

                         challenged claims in an IPR filed by Unified

                         against U.S._Patent_8,060,368, owned and

                         asserted by Mel NavIP, LLC. The ’368 patent

                         is generally directed to navigation and

                         speech recognition for a vehicle. The patent

                         had been asserted against Toyota and is

                         currently asserted against GM and Hyundai.

                  # ⚓ Dennis Crouch/Patently-O ☛ The_Silent_Echo:_Supreme

                    Court’s_Non-Engagement_with_the_Federal_Circuit_in

                    Amgen_v._Sanofi⠀⇛

                         Prof. Chris Holman recently characterized

                         Amgen v. Sanofi as an “endorsement of the

                         Federal Circuit’s current interpretation and

                         application of the enablement requirement,

                         and maintenance of the status quo.”  Although

                         I largely align with Holman’s views, I note

                         that the Supreme Court did not explicitly

                         engage with Federal Circuit precedent. More

                         specifically, the Court neither cited nor

                         discussed any Federal Circuit or CCPA

                         decision outside of case-specific historical

                         documents.

            # § Trademarks⠀➾

                  # ⚓ TTAB Blog ☛ TTABlog_Test:_How_Did_These_Three_Appeals

                    from_Section_2(d)_Refusals_Turn_Out?⠀⇛

                         By my count, the TTAB has affirmed about 83%

                         of the Section 2(d) refusals it has reviewed

                         on appeal this year. How do you think these

                         latest three appeals came out? Results will

                         be found in the first comment.

* § Gemini* and Gopher⠀➾

      o § Personal⠀➾

            # ⚓ Birotam_emi⠀⇛

                   Two weeks ago I finally bought a bicycle. I went to

                   a bike shop where

                   they do measure you and based on your criteria that

                   you gave them

                   beforehand, they propose a bike that should fit

                   your needs. They also

                   mount everything based on your sizes.

                   Of course it costs more than buying in a shopping

                   mall, but as I have

                   no idea about bicycles it was a safe choice. This

                   way I also do not

                   have to worry about maintenance, they do everything

                   and I just have to

                   reserve a time slot online and drop off the bike in

                   the shop. They

                   also have a bike wash.

      o § Politics⠀➾

            # ⚓ End_the_slaughter_age⠀⇛

                   EU citizens: there is time until 5th June to sign

                   the ECI petition to close animal farms and

                   slaughterhouses.

      o § Technical⠀➾

            # ⚓ Love_is_all_I_need⠀⇛

                   The trouble with so fantastic a read/review is now

                   I’d rather read CircaDian than play Half-Life Alyx.

            # § Internet/Gemini⠀➾

                  # ⚓ About_the_Domain_“Geminispace.org”⠀⇛

                         I have encountered a few complaints that the

                         domain name of this site, Geminispace.org, is

                         problematic because it can be somewhat

                         ambiguous and misleading: it may be unclear

                         whether one means just this capsule or

                         Geminispace as a whole — a collection of

                         Gemini capsules and the people who maintain

                         them. One might react to this dismissively

                         and think that a name is just a name, but I

                         want to give this topic some serious

                         consideration.

=> =============================================================================

Gemini_(Primer) links can be opened using Gemini_software. It’s like the

World Wide Web but a lot lighter.

╘══════════════════════════════════════════════════════════════════════════════╛

                   ¶ Lines in total: 8871

➮ Generation completed at 02:54, i.e. 115 seconds to (re)generate ⟲

Proxy Information

Original URL: gemini://gemini.techrights.org/tr_text_version/techrights-2023-05-27.txt
Status Code: Success (20)
Meta: text/plain;lang=en-GB
Capsule Response Time: 348.127364 milliseconds
Gemini-to-HTML Time: 67.534632 milliseconds

This content has been proxied by September (3851b).