𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, February 07, 2024
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Gemini index for the day: gemini://gemini.techrights.org/2024/02/07/


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

⦿ Techrights  -  Decision From the Paris Court of Appeal Can Challenge the Diplomatic Immunity of the European Patent Office

⦿ Techrights  -  IRC Proceedings: Tuesday, February 06, 2024

⦿ Techrights  -  [Meme] Buying a Government

⦿ Techrights  -  Microsoft Back Doors Exploited, Many Dead Products, and More Backlash After Mass Layoffs

⦿ Techrights  -  Over at Tux Machines...

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://news.techrights.org/n/2024/02/07/Decision_From_the_Paris_Court_of_Appeal_Can_Challenge_the_Diplo.shtml
https://news.techrights.org/n/2024/02/07/IRC_Proceedings_Tuesday_February_06_2024.shtml
https://news.techrights.org/n/2024/02/07/Meme_Buying_a_Government.shtml
https://news.techrights.org/n/2024/02/07/Microsoft_Back_Doors_Exploited_Many_Dead_Products_and_More_Back.shtml
https://news.techrights.org/n/2024/02/07/Over_at_Tux_Machines.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://news.techrights.org/n/2024/02/07/Gemini_Links_07_02_2024_Alternative_Protocols_and_Scammers_From.shtml
https://news.techrights.org/n/2024/02/07/Links_07_02_2024_Taylor_Swift_s_Lawyers_Take_on_Stalkers_GOP_Pu.shtml
https://news.techrights.org/n/2024/02/07/Links_07_02_2024_Voice_Synthesis_Causing_More_Problems.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 61

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/02/07/Decision_From_the_Paris_Court_of_Appeal_Can_Challenge_the_Diplo.shtml
    Gemini version at gemini://gemini.techrights.org/n/2024/02/07/Decision_From_the_Paris_Court_of_Appeal_Can_Challenge_the_Diplo.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Decision From the Paris Court of Appeal Can
Challenge the Diplomatic Immunity of the European Patent
Office⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 07, 2024


A few weeks ago the Paris Court of Appeal served to "end [...] a period of
lawlessness", according to a new article


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Le suicide d’un ingénieur de l’Agence spatiale européenne
         relance le débat sur l’immunité juridique de telles entités⦈


THE staff union of the EPO is circulating a translation of this_new_article_in
French. It recalls Benoît_Battistelli's suicide wave and speaks of what the
implications might be for António_Campinos, seeing that the European Space
Agency has its immunity legally questioned after a death. The latest outcome,
after an appeal, is negative for apologists of impunity.


Here is the English translation (deficient, automated):


     SOCIETY - JUSTICE


     § The suicide of a European Space Agency engineer reopens the debate
     on the legal immunity of such entities⠀➾


     An internal report by the agency concluded that the employee had
     taken his own life in 2011 due to "work-related problems". When the
     case was brought by his parents, the French courts had to dismiss the
     case because of the legal immunity of European agencies vis-à-vis the
     country that hosts them. A decision by the Paris Court of Appeal has
     changed all that.


     By Benoît Hopquin


     Published yesterday at 17:45, modified at 08:44 - Reading time 3 min.


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇European Space Agency⦈


     At the European Space Agency's European Space Research and Technology
     Centre in Noordwijk, the Netherlands, in 2009. BALINT PORNECZI / AFP


     Can European law be altered because a man and a woman want to know
     why their husband committed suicide and are denied this simple
     request? This is the issue at stake in a decision handed down by the
     Paris Court of Appeal on 16 January. In what is bound to be an
     arduous piece of prose, its ruling puts a nail in the coffin of a
     fundamental principle that governs the many European agencies set up
     throughout the European Union: their legal immunity from the country
     that hosts them.


     Read also | The investigation that is shaking up the European Space
     Agency


     Denise and Daniel Kie er have been fighting for twelve years to bring
     to justice those who, in the couple's view, drove their son Philippe
     to take his own life at his home in Leiden, the Netherlands, on 20
     December 2011, at the age of 38. An accomplished mountaineer,
     musician and polyglot, Philippe Kie er was an engineer at the
     prestigious European Space Agency (ESA). A gifted man, in short.


     The Frenchman had been working at an ESA technical centre in the
     Netherlands since 2003. However, from 2009 onwards, he began to tell
     his parents about the systematic harassment to which he was subjected
     by some of his superiors. His appraisals soon described him as
     'asocial' or 'antisocial'.


     "autistic". The humiliations were public. "I don't want to see you
     any more", a boss shouted at her during a meeting. And then there was
     the irreparable: "I've been suffering martyrdom in my workplace for
     three years now. It had to end", he wrote in a farewell letter to his
     parents, found at the scene of the tragedy.


     § Impossible searches


     An ESA internal audit report left little doubt as to why Philippe Kie
     er committed suicide. It concluded that "Philippe Kie er's suicide
     was caused by work-related problems". His act was "due to a chain of
     unintentional but fateful omissions at many levels", the audit added.
     The agency even decided to pay 189,722.40 euros in compensation to
     the parents. However, the ESA refused to accept the idea of moral
     harassment and the implication of the protagonists.


     The family then brought criminal charges before the French courts,
     the country in which the ESA is headquartered. However, two
     investigating judges successively came up against the legal immunity
     enjoyed by the European organisation since its creation in 1975. This
     immunity is enshrined in an agreement signed at the time between the
     agency and France. The same principle governs the operation of all
     European agencies, in whichever EU country they are based. The idea
     is to avoid the cacophony (and competition) of local social rights.
     Only internal appeals are possible if a decision or sanction is
     contested. For the rest, the host country can go to court, but under
     limited conditions and only before an international arbitration
     tribunal.


     Read also | Social situation worsens at the European Patent Office


     The two French judges dealing with the case came up against this
     legal bulwark in turn. Requests for documents and letters rogatory
     went unheeded. Searches were impossible. Each time, the principle of
     immunity was referred back to them. Wearily, the last judge dismissed
     the case. But the Kieers did not give up. In 2014, their defence
     team, William Bourdon, decided to challenge the very principle of
     immunity before the French courts. An initial ruling on 4 November
     2020 found against the Kieers and reiterated its absolute principle.
     "In short, immunity cannot be challenged... because of immunity",
     explains Bertrand Repolt, one of the couple's lawyers.


     § "End of a period of lawlessness".


     However, on 16 January, the Paris Court of Appeal overturned this
     decision. In doing so, it relied on the case law of the European
     Court of Human Rights, which places a caveat on this principle of
     immunity if it results in a denial of justice. The Court of Appeal
     considered that this was the case, since the Kie er couple had no
     access to any legal remedy, even domestic. The judgement therefore
     rejected "the n de non-recevoir based on immunity" and decided that
     the Kie er couple had the right to bring their case before the French
     courts so that the latter could look into what had happened to their
     son.


     ESA's lawyer did not respond to requests from Le Monde. This decision
     marks the end of a period of lawlessness in which international
     organisations were able to escape all judicial control by hiding
     behind their immunity, often to the detriment of their staff", says a
     pleased Mr Bourdon. They will now have to answer to the courts for
     their decision, particularly regarding the lifting of their
     immunity". In fact, the stakes in the judgment go beyond the Kie er
     case and even beyond that of the ESA. Other agencies have taken
     refuge behind this principle of immunity, which is assimilated by
     detractors to impunity, to introduce authoritarian management and
     allow hierarchies to establish a form of nepotism.


     Read also | Such a good office


     In 2012, a wave of suicides at the European Patent Office (EPO),
     which has its headquarters in Munich, Bavaria, and offices in The
     Hague, Netherlands, caused controversy. A Dutch court ruled in 2015
     that the immunity was "disproportionate" and did not guarantee "the
     protection of the fundamental rights" of employees. At the time,
     however, the Dutch government refused to implement this court ruling,
     fearing that the manna represented by the EPO and the other European
     agencies present on its territory would be lost.


     Benoît Hopquin


Around the same time the Dutch government also engaged in corruption with the
EPO and participated in illegal acts, partly connected to a new building that
was built there. Many EPO insiders have knowledge of it, but it never came out.
Even if it did come out in full, who would hold the Dutch government
accountable? It fancies the concept of immunity from the international
community.


There is always a structural and functional deficiency when states resort to
giving some organisations immunity, typically the ones which guard
corporations' (and thus oligarchs') interests. WIPO, the World Intellectual
Property Organization, is_another_example_of_this. █




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣉⣉⣑⣉⣿⣽⣏⣉⣭⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⠿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠸⠏⠤⣿⠔⡃⠷⠷⠏⠦⠆⠡⠆⡣⢼⡏⠶⢷⡇⠇⠇⠤⢹⡇⡇⠄⠇⠂⡇⠬⠦⠎⠆⡣⢼⠸⠸⠠⣾⠱⠾⠡⢼⡇⢷⢓⠸⠑⢸⠠⠴⢰⢸⠰⡇⠬⣿⠀⡆⠆⠓⠸⠰⠆⠓⠸⠸⠠⢼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⣥⣿⣿⣿⢻⣿⣿⣿⡟⣿⢻⣻⣿⣿⣿⢿⣿⣿⣿⣿⣬⣽⡟⡟⡟⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⢻⢿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠠⢄⠷⠷⢰⠰⢨⠰⢸⠠⢄⠤⡇⡆⠇⠶⢇⠤⣿⠦⡆⠤⠿⠣⠸⢰⠸⠰⠆⠤⣿⠸⠠⢼⡇⠆⠇⠤⡷⢎⠢⢰⠰⡇⠄⡆⠇⠇⣾⡇⣿⠆⠆⡆⡆⠇⠶⠶⢱⠳⠰⢰⠸⠸⠰⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠻⢿⢿⠿⠟⡿⠛⠌⡿⠿⠿⠿⡿⢿⣿⠟⢻⠿⣿⠟⡿⢿⣻⣻⡿⢿⠿⣿⡿⡿⠿⡿⠻⢟⠿⡿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣘⣸⣰⣇⣑⣃⣇⣕⡃⣇⣃⣇⣁⣯⣚⣈⣀⣿⣇⣃⣁⣿⣿⣈⣸⣀⣿⣈⣸⣸⣸⣘⣿⣟⣃⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⢿⡶⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⡿⣿⠿⣿⣿⢿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⠿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣦⣴⣄⣄⡤⡤⣦⣤⣤⣤⣴⢴⣼⣤⣤⣿⡤⣐⣤⡤⣤⣼⣴⣤⣴⣼⣤⣤⣤⣤⣼⣦⣤⣤⣧⣼⣤⣤⢤⣤⣤⣧⣧⡤⣬⣤⣧⣤⣴⣷⣤⣧⣼⣤⣤⣴⣼⣤⣼⣤⣬⣧⣼⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣼⣤⣠⣤⣤⣤⣤⣤⣤⣥⣧⣤⣷⣴⣤⣤⣤⣧⣭⣷⣥⣥⣤⣼⣠⣤⣼⣬⣤⣼⣬⣤⣦⣥⣦⣌⣧⣼⣠⣤⣴⣵⣤⣧⣤⣤⣄⣤⣥⣤⣼⣤⣤⣤⣼⣤⣼⣠⣤⣤⣤⣤⣤⣤⣴⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣍⣉⣩⣀⣉⣻⣏⣈⣹⣌⣫⣹⣉⣹⣰⣩⣉⣍⣉⣉⣀⣉⢏⣋⣍⣹⡉⣉⣉⣏⣈⣉⣏⠉⣍⣉⣉⣉⣹⣉⣋⣍⣉⣁⣉⣉⣉⣉⣹⣩⣈⣭⣩⣩⣉⣏⣘⣹⣉⡉⣍⣏⢉⣁⣈⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⠉⠛⠛⠛⠛⢿⠏⡛⢻⠋⠋⠛⠛⠙⠛⢛⢛⢻⠙⠟⠟⠛⠛⡿⠹⠛⠟⠟⠋⡿⠛⡏⡙⠛⠙⢟⡋⠛⣿⠟⠏⠛⠛⠛⠛⢻⡟⢻⢟⢟⡟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣆⠀⠹⣄⠈⣧⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⠃⠀⠀⣀⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⡀⠀⠘⢆⠀⠘⢆⠀⢹⣾⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⡈⠁⢀⠀⣰⣿⠟⠀⠀⠀⣼
⠀⠀⠀⠀⠂⠀⠀⠘⢄⠀⠈⢣⠀⠈⢧⠀⠹⣞⠛⠇⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠁⠠⠋⣼⣿⠏⢠⣤⣶⣼⣿
⠀⠀⠀⠀⠀⠑⠄⠀⠈⢣⡀⠀⠳⡀⠈⢣⠀⠙⣀⣤⣾⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠁⢠⣿⣾⣿⣇⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠑⡄⠀⠙⠀⢀⣴⣾⣿⣿⣿⣿⣫⣿⣾⣿⣯⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⢿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⠁⠃⠄⢰⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣟⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⣿⣿⣿⠋⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿
⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠺⢿⣶⣶⢿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠞⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣉⠙⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠀⠉⢷⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣟
⢀⣾⠇⠀⠀⢈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⣠⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣿⣿⣽⡿⠦⣄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣴⠿⣧⣛⣹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠉⠀⠉⢩⣲⣾⣿⣿⣦⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣟⣀⡬⣽⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡁⣠⣾⣿⣿⠁⠸⠁⠉⠳⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠉⠠⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠘⠂⠀⢦⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢄⢇⡼⠁⣰⣉⣃⠈⢠⣾⣛⡛⣷⡄⢀⣤⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⢀⢟⣭⣄⣀⣀⠀⠀⠀⠀⢠⣾⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣂⣈⠉⠉⠀⢻⣇⣉⣹⣛⢃⡘⠿⣶⣬⡛⠀⠰⠿⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡠⢀⣴⣿⣿⣿⣿⢿⣿⣶⣿⣿⣿⣿⡵⠏⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠋⠁⠘⢿⣦⣤⣿⡿⢰⣾⡟⠛⠛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⡵⠋⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠻⠷⣶⠶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⣿⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⢿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠇⠈⠁⠀⢰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠛⠿⣿⠻⣿⣿⣿⠃⠀⠀⠀⢤⣟⣽⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠈⠙⣿⣿⡿⠁⠀⠀⠀⠀⢀⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 317

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/02/07/IRC_Proceedings_Tuesday_February_06_2024.shtml
    Gemini version at gemini://gemini.techrights.org/n/2024/02/07/IRC_Proceedings_Tuesday_February_06_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Tuesday, February 06,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 07, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


===============================================================================
The corresponding text-only bulletins for_Tux_Machines and for_Techrights
contain all the text.


                          Enter_the_IRC_channels_now




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⣀⡤⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠲⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡇⡁⠀⠀⠐⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡃⠀⢰⠀⢠⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣷⣿⠟⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⣿⣿⠯⡐⠀⢸⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡇⣿⢏⡄⠀⢹⣺⡀⠀⠀⠀⠉⠓⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣾⢸⡟⣿⣿⣷⢏⡾⢓⣃⣥⣴⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡜⣾⡿⣿⣯⣽⣾⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⡿⠟⠛⠉⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣤⣄⣀⣀⠀⠤⢤⠤⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠃⠀⢛⣛⣛⣛⣛⣛⣛⠛⠛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⡛⠛⣛⣛⣛⣛⣛⣻⡇⠀⠀⣛⣛⣛⣛⣛⣛⣛⣿⡇⠀⠀⢘⣛⣛⡛⠀⠀⠀⢘⣛⣛⣛⣛⣛
⣉⣿⣿⣿⠋⠻⠿⠛⠛⠁⣽⣿⣿⣿⠛⠉⢻⡇⠋⠀⣹⠏⠁⠒⠛⠻⠿⠋⠉⠻⠿⠿⠄⢈⡿⣿⠗⠀⢿⡼⠛⠛⠻⠀⠀⠘⠛⠛⡿⣿⣇⠁⠀⠀⠿⢩⢿⡿⠿⠿⠿⢿⠃⠀⠀⠘⢿⠻⠃⠀⠀⠀⠸⠿⠟⢹⣧⡈
⠀⠈⠙⠋⠀⠈⠁⠀⢐⣲⣿⡿⠻⠁⠀⠀⠀⠀⡀⠙⡿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 543

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Buying a
Government⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 07, 2024


The EPO's Benoît_Battistelli engaged in serious_corruption_in_The_Netherlands.
In the coming weeks we'll take a closer look at EPO affairs on Dutch territory.


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇We built this new building; the government protects us⦈




⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣛⡛⠛⠛⠻
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⣿⣿⡇⠀⠀⠀⠀⠀⠠⠅⢸⣿⠀⠗⢀⠀⠇⠀⢀⠀⠀⢿⡇⠸⠀⡇⢀⢸⠢⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⡏⠋⢒⠒⠛⠃⠀⠐⣀⠈⡶⣶⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⠋⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣍⣛⡛⠛⠛⠛⠋⠉⠶⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠈⠉⠟⠃⠀⣤⡄⢐⠚⠟⣿⠛⠒⠀⠟⡛⠀⠒⠛⡛⢻⠟⡛⢻⣿⣿⣿⣿⣿⣿⢻⠀⣐⣿⣦⡀⠈⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣶⣤⠀
⣿⣿⣿⠀⠷⢰⡐⢂⣴⠀⡆⢰⣿⠃⠘⠃⠂⠛⠐⠀⠀⢀⠛⠀⠀⠀⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣽⣿⣧⣼⣧⣾⣾⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠛⠛⠛⢛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠾⡇⠀⠀⢸⣿⣿⣿⣿⣿⢸⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠂⠀⠀⣿⢷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⢸⣿⡟⠀⠀⠉⠙⠃⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖
⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⠿⡋⠀⠀⡀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⠤⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⡆⠀⠀⠨⠉⠽⣿⡶⠾⢛⠘⠉⠐⢤⠈⠋⠈⠀⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⡙⠛⡿⣷⣿⢀⣿⣗⣦⣝⠲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣀⣿⣧⡅⡠⠀⠂⠐⠀⠀⠀⠄⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⠃⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢸⢏⣿⣿⡮⠙⠪⡙⠻⣿⢿⡿⣿⡿⠿⠿⠿⠿⠿⠃⠀
⣿⣿⣿⣿⣿⣿⣤⡴⡶⢿⢟⣽⣷⣿⡥⣥⠀⣄⡩⣠⣠⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣴⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠄⠀⠈⢑⠀⠈⠨⢶⢶⢅⠣⣶⣮⡒⣄⠒⣿⢿⣰⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⠼⢿⣿⡟⣭⢶⣴⡴⢛⣫⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⡀⠀⣄⣷⠀⢰⣖⡦⡀⢶⣴⣄⠈⠻⣿⣾⣽⣿⣷⣕⣬⡻⣿⣿⣷⣷⣷⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣿⡄⠐⠀⠂⣤⢻⡷⠞⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣃⣾⣷⡄⢽⣿⠀⣹⡹⠴⠾⢦⡙⠋⣖⢠⡀⠙⠾⣿⣏⣻⣿⠝⣌⠻⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣷⠃⠄⠘⣊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡘⣝⠀⡯⣻⣿⠫⢰⡦⢢⡀⠺⣕⣶⣄⠀⠘⠛⢩⡇⠤⡁⣌⠉⣍⣉⡉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣲⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⢀⢿⣿⢣⡇⣿⠁⠀⠉⠠⡈⠙⣿⠩⠄⡀⠈⠉⠛⣧⢊⠃⠈⠛⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⡈⣫⣈⠻⢛⠀⠀⠀⠀⠈⢂⡈⠳⡙⡶⠷⠄⠀⠈⠀⠳⠝⠦⠙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⢱⡉⢛⠀⡏⠀⠀⠀⠀⠀⠀⠙⢦⡘⢮⣳⣽⣿⣦⡀⠀⠀⠀⠢⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣤⠁⠽⣭⢭⢁⣅⣀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⡈⠻⢸⣤⣿⣌⡢⣄
⠸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢧⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠰⠀⡄⢦⡀⠢⣤⡄⣤⣀
⡠⣤⣿⣻⣿⣧⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣼⣧⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠻⣄⢳⣀⢈⠳⣤⣼
⣿⣿⣿⣿⣿⠿⢿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣟⢛⢛⠛⠻
⣯⠉⠉⠀⠀⠀⠘⢀⠟⠛⢿⣿⠀⠛⢿⠛⡟⠃⠀⠈⠉⢿⡏⠙⠀⠛⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠀⠀⠀
⣿⡆⠀⠄⠀⠠⠀⢸⠀⠀⢸⣿⠀⠗⢀⠀⠇⠀⠀⠈⠀⢿⡇⠸⠀⡇⢸⢸⠠⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠌⠀⠀⠀⠀⠀
⣿⣇⠀⠀⠀⠀⠀⢿⣿⡶⠻⠛⠒⠶⠋⠃⠂⢒⣊⢼⡶⣾⣿⢿⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⠟⠁⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣛⣙⠛⠟⠋⠛⠛⠑⠾⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠠⠈⠉⠟⠇⠀⠀⣤⡆⢐⠛⠟⣿⠛⠒⠀⠟⡛⠀⠒⠛⡛⢻⠟⡛⢻⣿⣿⣿⣿⣿⣏⣹⢠⢘⣿⣆⡀⢸⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣶⣶⣶⣆⡆⠀
⣿⣿⣿⠀⡗⢰⡐⢂⣴⢀⡄⢰⡟⠃⠘⠃⠂⠛⠐⠀⠀⣄⠛⠀⠀⠀⣏⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣼⣤⣿⣷⣷⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠾⡿⠀⠀⠀⢻⣿⣿⣿⣿⣇⣻⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⠐⠀⠀⣸⣿⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⡏⠉⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⣿⣿⠇⠀⠀⠈⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⡿⢟⡃⠀⢀⣀⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⣿⣿⡭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀
⣿⣿⣿⣿⡆⠀⠀⠈⠍⠩⣿⡶⠶⠟⣷⠩⢁⠪⣌⠘⠑⠐⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠙⢛⡿⣦⢿⢸⣿⣷⢮⣙⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿⣬⢀⠀⠐⠀⠂⠈⠀⠠⠀⠀⢸⣿⣿⣿⣜⣿⣿⣿⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠊⠀⢸⢹⣿⣿⡮⠓⠌⡛⢿⣿⢿⢿⣿⣿⠿⠿⠿⠿⣿⠀⠀
⣿⣿⣿⣿⣿⣤⣤⣶⠾⣿⣻⣿⣾⣿⢨⡅⢀⣈⣅⣌⣁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢠⣦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠄⠀⠀⠀⠉⠕⠀⡉⠰⢶⢶⢁⢦⣶⣬⡢⣄⠻⡾⣟⣰⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠇⢿⣿⡿⢛⣥⢶⣵⡾⢛⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⠀⠀⠀⣴⣷⠀⣴⣦⢦⠠⣶⣶⣄⠈⠻⣿⣮⣽⣾⣮⣵⣌⠻⣿⣿⣿⣿⣦⣤⣄⣀
⣿⣿⣿⣿⣿⣿⡄⠀⠄⠐⢀⣽⣷⠶⢚⣫⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⡀⣿⣿⠀⣿⡻⠸⠾⣦⡙⠏⣶⢠⡈⠙⠾⣯⣏⣻⣿⠷⣌⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠔⢡⠀⠖⣪⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣷⡘⠉⠀⡿⣻⣿⠫⢰⡦⢤⡀⠺⣕⣦⣄⠀⠘⠛⢩⡇⠮⡡⡈⠩⣍⣉⠀⡉
⣿⣿⣿⣿⣿⣿⣿⣇⢤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⢣⡇⣿⠁⠀⠉⠨⡈⠻⣟⢩⠄⡀⠈⠁⢫⡆⢉⠃⡙⢛⠛⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣃⠀⣘⣣⣈⢻⠛⠀⠀⠀⠀⠈⢂⡈⠳⡓⡿⠶⠄⠀⠀⠈⠳⠽⠆⠹⢿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⢳⠉⣻⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⣷⣿⣿⣦⡀⠀⠈⠀⢢⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⢹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠁⠽⡩⣭⢩⣥⡄⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⡇⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⡘⢿⢸⣤⣿⣌⡦⣄
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣧⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠰⡀⠈⢦⠀⠲⣤⡀⡤⣀
⣿⣴⣿⣻⣿⣧⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠄⣼⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢃⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠸⡌⢧⣀⢈⠳⣥⣾
⣿⣿⣿⣿⣿⠿⢿⣿⣟⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣟⠛⠛⠛⠻
⣯⠉⠉⠀⠀⠀⠘⢀⠟⠛⢿⣿⠀⠛⢿⠻⡟⠃⠀⠘⠉⢿⡏⠙⠀⠛⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠩⠈⠁⠀
⣿⡆⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠗⢀⠀⠇⠀⠀⠰⠀⢿⡇⠘⠀⡇⢸⢸⠠⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠁⠀⠀⠀⠀
⣿⣇⠀⠀⠀⠀⠀⢿⣿⡦⠿⠻⡖⠢⠏⠁⠀⢒⣀⠼⡶⣾⣿⢿⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⠟⠁⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣟⣍⣟⠛⠟⠋⠛⠋⠓⠿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠠⠈⠉⠟⡇⠀⠀⣤⡄⢐⠛⡟⣿⠛⠒⠀⠟⡛⠀⠒⠛⡛⢻⠟⡛⢻⣿⣿⣿⣿⣿⣏⢹⢠⣘⣿⣆⡀⢸⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣷⣶⣶⣶⡂⠀
⣿⣿⣿⠀⡷⢰⡐⢂⣴⢀⡄⢰⡟⠃⠘⠃⠂⠛⠐⠀⠀⣄⠛⠀⠀⠀⣏⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣼⣤⣿⣷⣷⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠴⢿⠀⠀⠀⢻⣿⣿⣿⣿⣇⣻⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢻⣿⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⠐⠀⠀⣸⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⡏⠉⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⣿⣿⠇⠀⠀⠈⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⡿⢟⡃⠀⢀⣀⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⣿⣿⣿⣿⡆⠀⠀⠈⠍⠩⣿⡶⠶⡟⣷⠹⢁⠪⣌⠘⠑⠐⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠙⢛⡿⣧⣿⢸⣿⣗⢮⣙⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣽⣿⡬⢄⠀⠐⠀⠀⠈⠀⠠⠀⠀⢹⣿⣿⣿⣼⣿⣿⣿⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠊⠈⢸⢹⣿⣿⡮⠓⠌⡛⢿⣿⣿⣿⣿⢿⠿⠿⠿⠿⣿⠀⠀
⣿⣿⣿⣿⣿⣤⣤⣶⠾⣿⣻⣿⣾⣿⢨⡅⢀⣈⣅⣌⣁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢠⣦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠄⠀⠀⠀⠉⠕⡀⡉⠰⢶⢶⢁⢧⣶⣬⡢⣌⠻⡿⣗⣶⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠇⢿⣿⡿⢛⣥⢶⣵⡾⢛⣫⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⠀⠀⠀⣴⣷⠀⣴⣦⢦⠠⣶⣶⣄⠈⠻⣿⣮⣽⣾⣮⣵⣌⠻⣿⣿⣿⣿⣷⣤⣀⣀
⣿⣿⣿⣿⣿⣿⡄⠀⠄⠐⢀⣽⣷⠶⢚⣫⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⡄⣿⣿⠀⣿⣻⠰⠾⣦⡙⠏⣶⢠⡈⠙⠾⣯⣏⣻⣻⠷⣌⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠔⢡⠀⠖⣪⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣷⡘⠉⠀⡿⣻⣿⠫⢰⡦⢤⡀⠺⣕⣦⣄⠀⠘⠛⢩⡇⠮⡡⡈⠩⣍⣉⣁⠉
⣿⣿⣿⣿⣿⣿⣿⣇⢤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⢣⡇⣿⠁⠀⠉⠠⡈⠻⣟⢩⠄⡀⠈⠁⢫⡆⢉⠃⡙⠛⠛⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⣘⣣⣊⢻⠛⠀⠀⠀⠀⠈⢂⡈⠳⡓⡿⠶⠀⠀⠀⠈⠳⠽⠆⠹⢷
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⢳⠉⣻⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⣷⣿⣿⣦⡀⠀⠈⠀⠢⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⢹⠄⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠁⠽⡩⣭⢩⣥⡄⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⡇⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⡘⢿⢸⣤⣿⣌⡦⣄
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣧⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠰⡀⠌⢦⠀⠲⣤⡀⡤⣀
⣿⣤⣿⣻⣿⣧⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠄⣼⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢃⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠸⡌⢧⣀⢈⠳⣥⣾
⣿⣿⣿⣿⠿⣿⣿⣟⣯⣹⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⡛⠛⠛⠛⠛
⠉⠁⠀⠀⠀⠀⢹⠁⠟⠛⣿⣿⠀⠛⢿⠻⡟⠃⠀⠘⠉⢿⡏⠙⠀⠛⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢘⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣸⠀⠄⠈⢝⠀⠗⢀⠀⠇⠀⠀⠘⠀⢿⡇⠘⠀⡅⢸⢸⠪⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡫⠭⠁⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠰⣿⣇⠀⠁⠠⡖⠒⠝⠓⠐⣂⣠⢶⡶⣿⣿⢷⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣙⡛⠟⠋⠋⠉⠹⠖⠁⠀⠀⠀⠀⠀⠀
⣷⡀⣀⠀⠀⠠⠊⡛⠏⠄⠠⠀⣴⡆⢘⠛⡟⣿⠛⠒⠀⠟⡛⠀⠒⠛⢛⢻⠟⡛⢻⣿⣿⣿⣿⣿⣟⡇⣠⠾⣿⣆⡀⣹⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣶⣶⣄⡀
⣿⣿⣿⠀⡗⢰⡐⢂⣶⠀⡄⢰⠟⠃⠘⠃⠂⠛⠐⠀⠀⣄⠛⠀⠀⡀⣉⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠛⠛⢛⡛⠛⠛⠛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⢾⢷⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⢿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠒⠀⠀⣽⣿⡧⠂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒
⣿⣿⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠸⣿⣿⠁⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⣿⣿⣇⠀⠀⠘⣿⣿⣿⣿⣿⠿⣛⠀⠀⣀⢀⣀⣀⡀⠀⠀⢸⣿⣿⣿⡧⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⣿⣿⣿⡄⠀⠀⠁⠩⠉⣿⣷⠶⠶⢻⡆⠏⡀⠡⡁⠟⠂⡃⠸⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⠙⢻⡿⣾⡧⣸⣿⣶⢮⣛⢷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣇⠀⠀⠀⠀⠅⢸⣿⣠⡅⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠊⠃⣿⣸⣿⣷⡯⠓⢌⡛⢿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣟⠀⠀
⣿⣿⣿⣿⣀⣤⣴⡶⣿⣿⣿⣶⣿⡇⣿⡀⣁⣉⣁⣉⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣶⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢄⠀⠀⠀⠉⠖⠀⠉⠱⠶⣮⣘⢶⣶⣭⡢⡘⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣏⠁⠀⠀⠸⠸⣿⣿⠿⣋⡵⣦⣮⠽⣛⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣠⣄⠠⣴⣶⠀⣶⣶⢦⠰⣶⣶⣄⠘⠻⣿⣯⣽⣾⣮⣷⣌⠻⣿⣿⣿⣿⣷⣤⣀⣀
⣿⣿⣿⣿⣿⡀⠀⠠⠀⠠⣸⣿⡤⠖⢛⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣿⣿⠀⣟⣻⠰⠾⣮⡙⠏⣶⢠⡀⠑⠿⣿⣟⣿⣯⠳⣌⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠠⠊⡄⠰⢘⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠹⠁⠀⠿⣿⡿⠋⣠⠅⢤⡈⠸⣷⣶⣄⠀⠙⠛⣹⠂⠌⡢⡈⢩⣅⣀⣀⠉
⣿⣿⣿⣿⣿⣿⡆⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⡀⣿⣿⢳⣧⡿⠀⠀⠽⠀⡈⠻⣟⢩⢠⣀⠈⠉⠹⡆⣉⢀⠙⠉⠛⠟
⣿⣿⣿⣿⣿⣿⣿⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⡂⢀⢙⣣⢉⢻⠟⠀⠀⠀⠀⠙⢂⡈⢊⡓⡾⠷⠀⠀⠀⠈⠦⠳⠄⠹⢿
⣿⣿⣿⣿⣿⣿⣿⡾⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡌⢧⢛⣻⠀⠄⠀⠀⠀⠀⠀⠀⠛⢦⡙⢾⣿⣿⣿⣦⣀⠀⠀⠈⠢⡈
⣿⣿⣿⣿⣿⣿⣿⣇⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⠉⠻⡩⡭⢩⣥⡀⡀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠠⡈⠻⣶⣭⣿⣜⢦⣄
⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣷⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣇⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⡄⠘⢆⠀⠰⣤⢠⣤⡀
⣿⣤⣿⣻⣿⣧⣼⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢆⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠁⠀⠈⢧⣀⣌⠑⢥⣿
⣿⣿⡿⠿⢿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠛⠛⠛⠛
⠀⠀⠀⠀⠸⠀⢻⠀⠟⠻⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠉⢿⡏⠹⠀⠛⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⡀⠀⠀
⠀⠀⠀⠀⠀⢸⠈⢨⠀⠄⢸⣿⠀⠗⢀⠀⠇⠀⠀⠸⠀⢿⡇⠘⠀⡅⢸⢸⠪⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡭⠽⡉⠀⠀⠀
⠀⠀⠀⠀⠂⠸⣿⣿⠓⡐⠿⣿⠶⠶⠿⠗⣒⣂⣼⣶⡶⣿⣿⢶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡟⠋⢀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⠛⠿⠿⠟⠉⠻⠆⠀⠀⠀⠀⠀⠀⠀
⣀⡀⢀⠀⠀⠢⢛⡛⠀⠄⠠⠀⣶⡆⢘⠛⡟⣿⠛⠒⠀⠟⡛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣿⣿⣿⣿⣍⡇⣴⠿⣿⣆⠀⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⣶⣦⠀
⡟⠛⣿⠀⡗⢰⡐⢂⣤⠀⡄⢰⠛⠃⠘⠃⠂⠛⠐⠀⠀⣄⠛⠀⠀⡇⣹⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⡟⠛⠛⠛⣛⣛⠛⠛⠛⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠴⣿⣇⠀⠐⢸⣿⣿⣿⣿⣿⢸⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⢿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠚⠀⢀⣿⣿⡗⠒⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝
⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠸⣿⡿⠀⠀⠀⠀⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⡿⢟⡃⠀⠀⡀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⣿⣷⠀⠀⠀⢈⠈⠉⣹⣷⣶⡶⢾⣿⠸⢃⠉⢤⠺⠛⠚⠀⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣍⠛⢻⢿⣾⡇⣼⣿⣲⢬⡛⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⡆⠀⠀⠀⠀⠡⢸⣿⡀⣠⢀⠠⠀⠀⠐⠌⢀⠀⠄⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠐⠀⠀⠀⡁⠃⠃⡿⣿⣿⣷⠭⡳⢍⠻⢿⣿⣿⣿⣿⡿⠿⠿⠿⢿⡟⠀⠀
⣿⣿⣷⣀⣠⣤⣶⢾⣿⣿⣧⣶⣿⣰⣇⢉⣈⣉⣈⣉⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⣀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⢠⢠⠀⢀⠉⣒⢀⠁⠳⢶⡮⣜⢶⣷⣕⢦⡙⢿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀
⣿⣿⣿⡏⠉⠀⠀⠀⡇⢿⣿⣿⢟⣪⡵⣴⣯⠿⣛⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣱⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⣴⣶⣾⣶⠀⣶⣲⠦⠰⣶⣦⣄⠘⠿⣷⣿⣿⣿⣮⣢⣍⢿⣿⣿⣿⣿⣷⣤⣤⣤
⣿⣿⣿⣿⠀⠀⠀⠄⠠⢘⣿⣤⠼⠶⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⣟⢿⢳⢿⣮⡙⠏⣶⢠⡀⠑⠿⣿⣟⣿⣯⠳⣝⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠴⢀⠀⠮⢻⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢫⡃⢸⠿⣿⡿⡫⣨⠅⢤⡈⢸⣶⣦⡄⠀⠙⠋⣹⠠⢌⢢⡈⢥⣄⣀⣀⣁
⣿⣿⣿⣿⣿⡤⢀⣨⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣆⠁⡸⣿⣿⣳⢧⡿⠀⠀⠽⠀⡉⢻⡟⢭⢠⡀⠈⠉⢹⡄⡙⢀⠉⢉⢻⡟
⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢁⢹⣣⢽⢸⠇⠀⠀⠀⠀⠙⢂⡙⢊⣓⡾⠗⠀⠀⠀⠘⠮⠳⠌⠻⣿
⣿⣿⣿⣿⣿⣿⣴⠞⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡌⢯⢻⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡙⢽⣿⣿⣿⣦⢀⠀⠀⠘⠦⡈
⣿⣿⣿⣿⣿⣿⣇⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠺⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣎⢻⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⠈⢻⡩⡭⣨⣥⡀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣎⠠⠋⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠢⡙⠧⣧⣬⣷⣝⢦⡄
⣿⣿⣿⣿⠿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣆⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠐⣄⠀⠲⣤⢠⢤⡀
⣿⣴⣿⣻⣦⣄⣼⣬⢤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⠆⠄⣀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠙⠀⠘⢦⢤⣌⠳⣥⣿
⣿⠿⠿⢻⣿⡏⠉⡑⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⢛⠛⠛
⠀⠀⠀⠀⢻⠁⠙⠀⠞⠻⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠉⢿⡟⠹⠀⠻⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢧⠄⠠
⠀⠀⠀⠀⠀⣼⠀⢀⠀⠄⢸⣿⠀⠗⢀⠀⠇⠀⠀⠸⠀⢿⡇⠸⠠⡇⢸⢸⠪⠅⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠏⠅⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣷⡈⠀⠖⠭⡽⡶⠲⠿⠗⣒⣲⣾⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⡟⠁⣀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⠿⠃⠁⠀⣀⡀⠀⠀⠀
⣀⣀⣀⠀⠀⢻⢛⡀⠀⠄⠠⠐⣶⡆⢘⠛⡟⣿⢻⠒⠀⠟⣛⠀⠒⠛⣛⢻⠟⡛⢻⣿⣿⣿⣿⣿⣻⣀⣴⠽⣿⢦⢀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆
⠛⢻⣿⠀⡟⢸⣐⢂⣠⠀⡄⠐⠛⠃⠘⠃⠂⠛⠘⠀⠀⣄⠛⠀⢀⡄⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⡟⠛⠛⠛⣛⣛⡿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣾⣿⡆⠀⠐⢻⣿⣿⣿⣿⣧⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠻⠿⢿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠗⠀⢬⣿⣿⣿⠔⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⢸⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⢛⠀⠀⢀⢀⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⡍⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣇⠀⠀⠀⠈⠁⠋⢹⣯⣤⣶⠶⣟⡇⠿⡨⠫⣜⠚⡑⢳⠆⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣍⠛⢻⢿⣿⡇⣿⣿⣶⣍⡻⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⡀⠀⠀⠀⠁⠈⠙⣿⡆⣀⡃⡂⢀⠠⠀⠆⠉⠀⠠⠠⠀⢻⣿⣿⣿⣼⣿⣿⣿⣿⡿⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠑⠁⠀⠀⡑⠁⢀⣏⣿⣿⣷⠝⠲⢍⠻⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠟⠀⠀
⣿⣇⢀⣀⣤⣴⡶⣿⣿⣧⣤⣾⣟⣸⡀⣁⣈⣁⣉⣁⡀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣀⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⣀⡠⠀⠉⠹⠂⢀⠉⠶⢶⣏⡹⣶⣶⣕⢤⡙⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀
⣿⣿⡏⠉⠁⠈⠂⢸⢹⣿⣿⡿⢓⣭⢧⣾⡽⢟⣫⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⢉⣤⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⢼⣿⣷⡀⣶⣲⠄⢴⣶⣦⣄⠙⢿⣷⣯⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣷⣦⣤⣤
⣿⣿⣇⠀⠀⠀⣠⠀⡄⣿⣇⣠⠽⠟⣋⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⢺⣿⡿⢙⡟⣿⢷⣷⣬⡻⡏⣴⢀⡈⠑⢿⣿⣙⣿⡿⢦⡙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⢠⠒⡀⢤⢿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⢋⡃⢸⠛⣿⡿⠋⣨⠅⣄⠙⢬⣲⣦⡀⠀⠙⠋⣽⠰⢜⢦⡈⢤⣤⣀⣈⣀
⣿⣿⣿⣧⠀⠐⢈⣡⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠁⣸⣾⡿⣱⢧⡏⠀⠈⠷⠀⠙⢿⡃⣥⢤⡀⠈⠈⢹⡄⡙⣀⠉⣉⣻⡛
⣿⣿⣿⣿⡆⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⢅⣻⣣⢽⢸⠇⠀⠀⠀⠀⠙⢂⠙⢞⢻⠿⠗⠀⠀⠀⠙⠮⠳⠌⠻⣿
⣿⣿⣿⣿⣷⣠⡴⠟⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⡘⣎⢿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡳⣽⣿⣿⣿⣦⣀⠀⠀⠙⢆⡙
⣿⣿⣿⣿⣿⡏⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡟⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣎⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠠⣥⡄⠈⢯⣭⡍⣬⣥⡠⡀⠀⠀
⣿⣿⣿⣿⣿⣿⡾⠟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⠠⠓⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢢⡙⠧⣧⣾⣷⣝⢦⡄
⣿⣿⣿⣿⠿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣧⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠐⠆⢀⠰⣄⡀⠲⣤⢠⣤⡀
⣿⣴⣿⣣⣤⣤⣼⣭⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⡌⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠘⠄⠘⣆⡠⣈⠢⣤⣿
⠿⠟⢿⣿⡏⢉⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⠛⠛⠛
⠀⠀⢸⡆⢻⠀⢹⠀⠿⠻⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠉⢿⡟⠙⠈⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠰⠀
⠀⠀⠀⣷⠀⢠⠀⢠⠀⠄⢸⣿⠀⠗⢀⠀⠇⠀⠀⠸⠀⢿⣇⠸⠀⡇⢸⢸⠪⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠊⠀⠀
⠀⠀⠀⢸⣿⣷⠂⠘⠃⡴⣿⢿⠶⠖⠿⣗⣒⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁⣀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⠿⠿⠿⠛⠉⢊⣁⠀⠀⠀⠀
⣀⣀⣀⠈⡛⢻⠀⡀⠀⠄⠰⠒⣶⡇⢘⠛⡟⣿⢻⠒⠀⠟⣛⠀⠒⠛⣛⢻⠟⡛⢻⣿⣿⣿⣿⣯⣿⣀⣴⠽⣿⢦⢀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆
⠛⣻⣿⠀⣟⢸⡐⢂⣠⠀⡆⠐⠛⠃⠘⢃⠂⠛⠘⠀⡀⣄⢛⠀⢀⠀⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠛⠉⢛⣿⣟⣛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢼⣿⣿⠀⠐⠒⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠻⠿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠃⠀⣼⣿⣿⣿⡳⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⢽⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣛⠀⠀⡀⢀⣀⣀⣀⡀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀
⠀⠀⠀⠀⠉⢙⢻⣿⢭⣴⡶⢶⢿⠸⢟⠝⢵⡓⠏⡺⠆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⡙⠛⡿⣷⣿⢄⣿⣿⡶⣝⡻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠁⠀⢸⣿⡆⢀⣙⠐⠨⡀⠇⠰⠈⠃⠀⠄⠁⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠃⠁⠀⢀⡑⠹⢸⣯⣿⣿⣾⢝⠢⣙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠋⠀⠀
⡄⠀⣀⣀⣤⣶⢶⣿⣿⣤⣰⣿⣇⣇⢈⣁⢛⣀⣙⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣺⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢠⣤⣀⠈⠱⠂⢈⠙⠶⣶⣥⡳⣶⣮⣕⢌⠛⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀
⣿⠛⠋⠉⠀⠡⠸⣿⣿⣿⣿⡿⣚⣭⣴⣯⠿⢟⣫⣥⣶⣿⣿⣿⣿⣿⣿⣿⡟⢋⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢦⣍⡻⢿⣷⣲⠄⢶⣶⣦⡀⠛⢿⣿⣯⣷⣷⣽⣦⡹⢿⣿⣿⣿⣿⣿⣦⣤⣤
⣿⡄⠀⠀⠀⢀⡄⢙⣿⣏⣁⣤⠽⠟⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢿⣿⡇⢘⡛⣿⣼⣷⣍⠻⡟⣤⢀⡈⠻⢿⣿⣛⣿⡝⢦⡙⢿⣿⣿⣿⣿⣿⣿
⣿⣷⠀⠀⠀⡄⢂⠠⣽⣿⣃⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡌⠟⡁⢸⣛⣿⣿⠣⡩⠅⣄⠙⢨⣲⣦⡀⠈⠛⢋⣷⠱⢕⢄⠉⣤⣤⣄⣈⣀
⣿⣿⡆⠀⠀⠐⢉⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡌⠀⢸⣾⡿⣱⢧⡏⠀⠨⣷⠀⠙⢿⡏⡥⣄⡀⠉⠉⢷⢨⡱⣈⠉⣉⣿⢛
⣿⣿⣷⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠈⠿⣃⢻⢸⠃⠀⠀⠀⠀⠑⣈⠙⣙⢺⠿⠖⠀⠀⠀⠙⠞⠦⠘⠿⡿
⣿⣿⣿⣇⢠⣤⡶⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠸⡝⣿⡾⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣿⣷⣦⣀⠀⠀⠙⢄⠑
⣿⣿⣿⣿⡛⠋⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠨⣥⡈⠘⢏⢭⡍⣭⣥⢀⡀⠀⠀
⣿⣿⣿⣿⣷⣶⣶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡜⢰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⢦⠙⢧⣯⣿⣧⣳⣤⡄
⣿⣿⣿⣿⠿⡄⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣦⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⡶⠂⠳⡀⠐⠶⣄⣤⣄⠀
⣿⣤⣾⣠⣤⣥⣼⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⡔⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣆⠹⣄⡠⡈⠪⣼⣷
⠿⠿⣻⣿⡏⣍⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠟⠛⠛⠛
⠀⠀⠸⡇⢻⠀⠹⠀⠿⠻⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠉⢿⡟⠙⠈⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣂⠠⠀
⠀⠀⠀⣷⠀⠠⠀⢠⠀⠄⢸⣿⠀⠗⢀⠀⠇⠀⠀⠸⠀⢿⣇⠸⠀⡇⢸⢸⠪⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⠏⠀⠀⠀
⠀⠀⠀⢺⣿⣿⠒⠀⠑⡴⣿⣿⠶⠶⠿⣗⣒⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠿⠋⠁⣀⣀⠀⠀⠀⠀
⣀⣀⣀⠈⡛⢻⠀⡀⠀⠄⠰⠒⣶⡇⢘⠛⡟⣿⢻⠒⠀⠟⣛⠀⠒⠛⣛⢻⠟⡛⢻⣿⣿⣿⣿⣯⣿⣀⣼⠽⣿⢦⢀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⠆
⠛⢻⣿⠀⣟⢸⡐⢂⣠⠀⡆⠐⠛⠃⠘⠃⠂⠛⠘⠀⡀⣄⢛⠀⢀⠀⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠉⢻⣿⣛⣟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⣿⣿⡀⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠻⠿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠚⠇⠀⣼⣿⣿⡿⣷⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⢽⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣛⠀⠀⡀⢀⣀⣀⣀⡀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⠀⠀⠀⠀⠉⢙⢻⣿⢭⣴⡶⢶⢿⡸⢗⠝⢵⡓⠟⠺⠆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⡙⠛⡿⣷⣿⢄⣿⣿⡶⣝⡻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠁⠀⢸⣿⡆⢀⣙⠐⠨⠀⠇⠰⠈⠃⠀⠄⠁⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠃⠁⠀⢀⡑⠹⢸⣯⣿⣿⣾⢝⠢⣙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠀⠀
⡄⠀⣀⣀⣤⣶⢶⣿⣿⣤⣰⣿⣇⢇⢀⣁⢛⣀⣙⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣺⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢠⣤⣀⠈⠱⠂⠈⠙⠶⢶⣥⡳⣶⣮⣕⢌⠛⢿⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀
⣿⠛⠋⠉⠀⠡⠸⣿⣿⣿⣿⡿⣚⣭⣴⣯⠿⢟⣫⣥⣶⣿⣿⣿⣿⣿⣿⣿⡟⢋⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⢦⣍⡿⢿⣶⣲⠄⢶⣶⣦⡀⠛⢿⣿⣯⣷⣷⣽⣦⡙⢿⣿⣿⣿⣿⣿⣦⣤⣤
⣿⡄⠀⠀⠀⢀⡄⢩⣿⣏⣁⣤⠽⠟⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢿⣿⡇⢘⡛⣿⣼⣷⣍⠻⡟⣤⢀⡈⠻⢿⣿⣛⣿⡝⢦⡙⢿⣿⣿⣿⣿⣿⣿
⣿⣷⠀⠀⠀⡄⢂⠠⣽⣿⣃⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡌⠟⡁⢸⣛⣿⣿⠣⡩⠅⣄⠙⢨⣶⣦⡀⠈⠛⢋⣷⠱⢕⢄⠁⣤⣤⣄⣈⣀
⣿⣿⡆⠀⠀⠀⢉⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡈⠀⢸⣾⡿⣱⢧⡏⠀⠨⣷⠀⠙⢿⡏⡥⣄⡀⠉⠉⢵⢨⡱⣈⠉⣉⣟⣛
⣿⣿⣷⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠈⠿⣃⢻⢸⠃⠀⠀⠀⠀⠑⣈⠙⣙⢺⠿⠖⠀⠀⠀⠙⠞⠦⠘⠿⡿
⣿⣿⣿⡇⢠⣤⡶⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠹⡝⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣿⣷⣦⣀⠀⠀⠙⢄⠑
⣿⣿⣿⣿⡟⠋⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠨⣥⡈⠘⢏⢭⡍⣭⣥⢀⡀⠀⠀
⣿⣿⣿⣿⣷⣶⣶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣶⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡜⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢦⠙⢧⣯⣾⣧⣳⣤⡄
⣿⣿⣿⣿⠿⡄⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣦⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⡶⠂⠳⡄⠐⠶⣄⣤⣄⠀
⣿⣤⣾⣡⣤⣥⣼⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⡔⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣆⠹⣄⡠⡈⠪⣼⣷
⠟⣿⣿⣩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡟⠛⠛⠛
⠀⢻⣿⡆⠹⠀⠹⠀⠿⠛⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠉⢿⡟⠙⠘⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠀
⠀⠘⣿⣧⠀⢰⠀⢨⠀⠄⢸⣿⠀⠗⢀⠠⠇⠀⠀⠸⠀⢿⣟⠸⠀⡇⢸⢸⠪⠅⣿⣿⣽⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⢻⣿⣖⡋⠐⠚⢷⢾⣿⠿⠲⠶⢛⣓⣲⣶⣾⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⠟⠙⠉⣀⡀⠀⠀⠀⠀
⣀⣀⣸⠛⡋⢡⠀⡀⠀⠄⠲⠒⣿⡇⢘⠛⡟⣿⢻⠒⠀⠟⣛⠀⠒⠟⣛⢻⠟⡛⢻⣿⣿⣿⣿⣯⣿⣀⣮⢽⣿⢤⢈⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡮
⠛⣿⣿⠀⣿⢠⡐⢂⣤⠀⡆⠐⠛⠃⠘⠃⠂⠛⠘⠀⡀⣄⢛⢀⣀⡀⣿⢸⣘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠛⠉⣻⣿⣟⡿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣇⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠈⣼⣿⣿⣿⣿⣿⠻⠃⠠⣿⣿⣿⣿⣶⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⢿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⢟⡃⠀⠀⠀⢀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣯⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀
⠀⠀⠀⠋⠉⣻⣯⠩⢥⣶⣶⡾⣧⠻⡫⠉⣝⠻⠻⠵⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⡙⠛⡿⣷⣿⢸⣿⣗⣦⣝⠻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠈⠀⢘⣿⣄⠀⣈⣋⠂⠅⠰⠈⠂⠙⢀⠀⡈⠄⢸⣿⣿⣿⡇⣿⣿⣿⣿⡿⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠊⠁⠀⢀⠙⠘⢸⣿⣿⣿⡾⢝⠮⡙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠇⠀⠀
⠀⠀⣀⣠⣤⣴⣿⣿⣊⣌⣼⣿⣘⡀⢈⠐⣊⣘⣓⣀⠀⢈⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣠⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⠀⠀⠀⢠⣶⣴⣌⢱⡂⡈⠙⢶⣶⣥⣷⣶⣮⣳⣌⠻⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀
⠞⠛⠋⠉⠘⠀⢿⣿⣿⣽⣿⠟⣋⣥⣨⣽⠿⢟⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⠟⣡⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⡀⣶⣦⡍⢻⣿⢴⡤⢷⣶⣤⡈⠻⢿⣿⣿⣿⣷⣵⣬⡻⣿⣿⣿⣿⣿⣿⣦⣤⣤
⠀⠀⠀⠀⠀⣄⢸⣿⡟⡋⣁⣮⡽⢟⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⣿⣿⡇⢘⡻⡇⣼⣶⣝⠿⡟⣤⢀⠈⠻⣿⣿⣻⣿⡝⢮⡻⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⠀⢀⠍⠀⣽⣿⠘⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡘⡿⠀⢸⣿⣿⣶⠞⠙⠃⣀⠻⢐⣶⣤⡀⠈⠛⢩⡇⠦⡑⣄⠩⣤⣤⣄⣀⣀
⣷⠀⠀⠀⠡⠈⡃⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡈⠀⢸⣾⡿⣱⢣⠇⠀⢨⣷⠈⠙⣿⠯⡇⣄⠀⠉⠉⣧⢪⠃⡈⠉⣉⣟⡛
⣿⣆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡧⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⠈⠘⠿⡣⢻⢸⠀⠀⠀⠀⠀⠓⣈⠳⣙⣶⠿⠆⠀⠀⠀⠳⠝⠦⠙⢿⡿
⣿⣿⡀⠀⣀⣤⡶⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⢳⡹⣷⡾⠈⠀⠀⠀⠀⠀⠀⠙⠷⣌⠻⣿⣿⣿⣷⣄⡀⠀⠀⠱⢄⠱
⣿⣿⣷⠾⠿⠋⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳⡹⣧⠐⡂⠀⠀⠀⠀⠀⠀⠀⢨⣤⡈⠙⣏⢭⠅⣭⣥⢀⠀⠀⠁
⣿⣿⣿⣄⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳⡹⢠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡔⢌⠹⣶⣮⣽⣦⡳⣤⡀
⣿⣿⣿⣿⠉⠉⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⡈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⢢⡀⠐⢦⡄⣤⣄⠀
⣿⣤⣾⣹⣤⣤⣼⣥⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢷⡰⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⠀⣄⠱⡄⣠⡙⠪⣼⣷
⡏⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠟⠛⠛
⣷⠀⠀⠀⠀⠀⠩⠀⠟⠛⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠉⣿⡏⠙⠈⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐
⣿⡆⡀⠀⠀⠀⠀⠀⠀⠄⢸⣿⠀⠗⢀⠠⠇⠀⠀⢸⠀⣿⣷⠸⠀⡇⢸⢸⠪⠅⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠏⠁⠀⠐
⣿⣿⡄⣀⡀⠀⠀⠉⠅⠐⠹⠏⠆⠒⢛⣃⣦⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠟⠛⠏⣈⣉⠀⠀⠀⠀⠀
⣿⣿⣧⠈⡀⠠⠀⡀⠀⠖⠲⠚⣿⡇⢘⠛⡟⣿⢻⠒⠀⠟⣛⠀⠒⠛⣛⢻⠟⡛⢻⣿⣿⣿⣿⣹⣿⢀⣴⢿⣿⣄⢈⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⠁
⣿⣿⣿⠀⡇⢠⡐⢂⣠⠀⠂⠐⠛⠃⠘⠃⠂⠛⠘⠀⡀⣄⢛⢀⢀⡀⣿⢸⣘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠋⠛⣻⣿⡟⠿⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣼⣿⣷⡀⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠻⠀⢠⣿⣿⣿⣷⠖⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⣿⣿⣿⠀⠀⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⢺⣿⣿⣿⣿⣿⣿⣿⠿⣃⠀⠀⠀⠀⣀⣀⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠈⠛⣿⡟⠛⢋⣭⣄⣶⡶⢦⢸⠋⡝⣙⠛⡯⠴⠎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣍⠛⠻⣿⣾⡯⣸⣿⣷⣮⣛⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⣿⣷⠀⢀⠉⢁⣂⠉⡉⠀⠀⠠⣘⠃⠈⣂⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠋⠃⣿⣹⣿⣿⡯⡓⢌⡛⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠀⠀⠀
⠀⠀⢀⣸⣿⣆⡴⢆⣩⣵⣿⢰⡔⠐⠐⠒⠐⠓⠂⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡆⠀⠀⠸⢿⣿⡆⠈⡖⠀⠉⠹⣶⣮⣙⢷⣶⣭⡢⡝⠻⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀
⠾⠛⠋⠉⣿⣿⣿⣿⣿⣿⡯⢟⣫⡈⣛⣯⡿⣛⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠠⣶⣶⠛⣳⡶⣬⠸⣷⣦⣄⠙⠿⣿⣯⣿⣿⣮⣷⣌⠻⣿⣿⣿⣿⣿⣿⣦⣤⣤
⠀⠀⠀⠀⣸⣿⡍⠋⠛⠉⣐⣿⠿⢟⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠰⣿⣿⠀⢿⢽⣇⣼⣮⡛⢿⡷⣀⠀⠙⠿⣿⣟⣻⣿⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⡉⣿⣯⢴⡕⢙⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⢻⠛⠀⡿⢶⣧⣭⠍⠻⠆⠁⠻⢨⣦⣄⠀⠙⠻⢹⡇⣮⡲⣈⠢⣤⣤⣀⣁⣀
⠀⠀⠀⠋⠐⠻⣿⣤⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⠉⠀⣷⣾⣿⣣⠃⠀⠂⢹⣦⡈⠻⣿⢸⣄⡀⠈⠁⢻⣦⢉⢃⡉⢉⣹⣟⡛
⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⢘⠸⣿⢳⢿⣈⠀⠀⠀⠀⠀⢀⠉⠫⡓⣿⠷⢄⠀⠈⠈⠳⠹⠆⠹⢿⠿
⠀⢀⣄⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡄⢦⢲⣧⡜⠎⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣾⣽⣿⣦⡀⠀⠈⠈⢣⡈⠳
⠀⣀⣾⣿⠏⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣧⢻⡇⠠⠆⠀⠀⠀⠀⠀⠀⠀⢭⣄⠁⠻⡯⣭⢉⣥⡄⠀⠀⠈⠂
⡞⠋⠉⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣏⢿⢈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡠⡙⢿⣰⣬⣿⣎⢦⣀⠀
⣇⠀⠚⠿⠛⠋⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡌⢦⠁⠢⣤⡄⣥⣀⠀
⣿⡄⠀⢀⣤⣤⣼⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣆⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠙⠿⠈⠳⣀⣈⠳⣕⣼⣧
⠉⠀⠀⠀⠀⢠⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡍⡛⠛⠛
⠀⠀⠀⠀⠀⠀⠹⠀⠟⠛⢿⣿⠀⠛⢿⠻⡟⠃⠈⠘⠙⣿⡏⠹⠸⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⠀⠗⢠⠀⠇⠀⠀⢸⠀⣿⡧⠸⢰⡇⢸⢘⠪⠅⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠙⠁⠀⠐
⡄⠀⢀⣀⠀⠀⠀⠉⠃⠐⠛⠩⠒⠒⣛⣣⣤⣶⣾⣿⡷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠻⠟⠟⠉⠃⣉⣁⠀⠀⠀⠀⠀
⣗⣢⣤⠀⡀⠠⠀⡀⠄⠖⠲⠛⣿⡇⢘⠛⡟⣿⠛⠒⠀⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣿⣿⣯⣽⣿⠀⣴⣿⣷⣄⠘⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇⠀
⣿⣿⣿⠀⡇⢠⡐⢂⣴⠀⠂⠐⠛⠃⠘⠃⠂⠛⢰⠀⡀⣄⢛⢀⡀⡇⣿⢸⣘⡃⢸⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣶⣾⣿⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⡟⠛⠋⠛⣿⣿⡛⠛⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡆⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢓⠀⢼⣿⣿⣿⣶⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⣿⣿⣿⠀⠈⠉⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⢹⣿⣿⣿⣿⣿⣿⣿⡿⢟⡀⠀⠀⠀⠀⣀⣀⢀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⢿⣿⠟⠛⠛⣉⣥⣰⣴⡶⡆⡟⢊⢏⡛⢹⠴⠴⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣙⠟⢻⢿⣾⡇⣽⣿⣶⣭⡻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠘⣿⡇⠀⠁⠈⠉⢒⠈⠉⠁⠀⠀⡄⡛⠀⢁⡈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠙⠀⠀⠐⠁⠃⣿⣿⣿⣷⠝⠳⢍⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠏⠀⠀⠀
⠀⠀⢻⣿⡀⣠⠤⡈⣭⣶⡇⣦⠄⠆⠰⠂⠘⠂⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠿⣿⣧⠀⠀⢉⠆⢀⠉⠷⣶⣯⣸⣶⣶⣝⢦⡙⢿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀
⠾⠛⠛⣿⣿⢻⣿⣛⣿⣿⠷⢛⣃⠛⣓⣵⠿⣛⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢀⣰⣿⣷⠀⣴⡤⣌⢼⣧⣤⡀⠙⢿⣷⣿⣿⣿⣮⣢⣝⢿⣿⣿⣿⣿⣿⣶⣤⣤⣤
⠀⠀⠀⢿⣿⡈⠛⠽⠛⢡⣚⣿⠿⣛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⢸⣿⣿⠀⡿⢳⣇⣷⣍⠻⣿⣶⢀⠈⠻⢿⣿⣟⣿⣯⠳⣝⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣗⡡⣞⠒⢉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⢟⠏⠀⡿⢮⣯⣭⠟⠷⠄⠁⢯⠀⣦⡀⠀⠛⠿⠹⠆⣌⢢⡈⢤⣤⣄⣈⣀⣀
⠀⠀⠚⠈⣿⣿⣈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡎⠂⠀⣯⣾⣿⣣⢂⠂⠀⢣⣄⠘⢿⡿⢁⢀⠀⠉⠓⢻⡆⡙⢂⠉⢉⣹⡛⠛
⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠢⢻⣿⠳⡿⡄⠀⠀⠀⠈⠁⠀⠙⠮⠷⡿⠦⠀⠀⠁⠘⠮⠳⠌⠻⣿⠿
⠀⣀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⡐⣖⢷⣏⡅⠟⠀⠀⠀⠀⠀⠈⠳⣄⠻⣝⣦⣶⣷⣤⡀⠀⠉⠈⢦⡈⢶
⠀⣹⣷⣾⠋⠉⣿⡏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢸⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣎⣿⡂⠀⠆⠀⠀⠀⠀⠀⠀⠈⣥⣌⠩⣻⣩⣍⢉⣠⡀⠀⠀⠉⠀
⠞⠻⠉⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⣯⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⡹⢷⣰⣯⣿⣔⢦⣀⠀
⠀⠴⡶⠿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡄⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡐⣌⠀⢤⣬⡍⣅⡁⢠
⠀⠀⠀⢀⣠⣤⣾⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⣷⡈⢦⢀⠙⢧⣅⣽⣆
⠀⠀⠀⠀⠀⢐⡥⠍⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠹⠀⠞⠛⢿⣿⠀⠛⢿⠻⡟⠃⠀⠘⠙⢻⡏⠹⠈⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠣⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⠀⠗⢠⠀⠇⠀⠀⢰⠈⣿⡧⠸⠀⡇⢸⢘⠨⠅⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠧⠀⠀⠒
⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⠒⠙⢀⡀⣉⣤⣴⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠿⠟⠻⠛⠛⠁⠁⣀⣀⠀⠀⠀⠀⠀
⣐⣀⣤⠀⡀⠠⠀⡀⠔⠖⠺⠛⣿⡇⢘⠛⡟⣿⢛⠒⠀⠟⡛⠀⠒⠛⣛⢻⠟⡛⢻⣿⣿⣿⣏⣿⣿⠀⣰⣾⣷⡀⠸⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀
⣵⣿⣿⠀⡇⢠⡐⢂⡔⠀⠂⠐⠛⠃⠘⠃⠂⠛⢀⠀⡀⣄⣛⢀⢀⡁⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣾⣿⣮⣿⣽⣾⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠛⠉⢉⣫⣽⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣷⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠇⠀⣼⣿⣿⡿⠂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿⣿⡏⠉⠉⠙⠃⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣃⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⣿⡿⠿⠛⠛⢛⣩⢤⣤⣶⢶⢸⠃⡹⣉⠋⡧⠦⠦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣮⡙⠟⢿⣷⣿⡇⣿⣿⡶⣝⡻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⢿⣿⠁⠀⠀⠈⠉⠁⠂⠉⠉⠀⡀⢠⢘⠇⡈⣀⢁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠈⠐⠛⢰⡏⣿⣿⣾⠝⠢⣙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠃⠀⠀⠀
⠸⣿⣇⡀⣄⡤⠄⢋⣭⣶⠰⠤⠰⠀⠴⠀⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⡃⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⢻⣿⣌⠀⢀⠀⠀⠣⠄⠈⠉⢶⡶⡍⡻⣴⣮⣕⢌⠛⢿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀
⠾⢻⣿⣛⠛⣿⣛⣻⣿⣟⠾⣓⠘⡳⣮⣾⠿⣛⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⢿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠋⣠⣾⣴⠀⣤⣄⡅⣼⣤⣄⡈⠻⣿⣿⣽⣿⣷⣿⣦⡙⢿⣿⣿⣿⣿⣿⣦⣤⣤⣤
⠀⠘⣿⣏⠀⠙⠻⠟⠋⢵⣻⣯⠿⣛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⢼⣿⡧⠀⣿⣿⢣⣦⣝⠻⣿⣦⠀⠙⠻⣿⣿⣻⣿⣟⢦⡙⢿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⢻⣿⡀⠂⠤⡴⠊⢉⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡜⡟⡇⠠⢷⢼⣾⣟⡛⢦⠈⠁⢿⠠⣄⠀⠁⠻⠟⢽⢰⣝⢄⡀⢤⣄⣀⣈⣀⣀
⠀⠠⠙⣿⡧⢋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⡘⠃⢸⣌⣾⡿⣣⢂⠀⠀⣦⡀⠘⢿⡧⢂⢀⠈⠙⠙⣳⡄⡙⣈⠉⣉⣻⠛⠛
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠆⣿⣿⢱⡟⠀⠀⠀⠀⠉⠀⠀⠙⠝⠾⡷⠤⠀⠈⠁⠙⠮⠳⠈⠿⡿⠿
⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣤⠱⡌⣵⣅⡇⡇⠀⠀⠀⠀⠀⠈⢦⡈⢻⣵⣶⣶⣦⣄⠀⠈⠑⠙⣄⠑⢶
⢈⣷⣶⠟⢻⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡹⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⣥⡉⢙⢿⢉⣛⢁⣀⡀⠀⠈⠓⠄
⢿⠛⠉⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡸⡇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠈⠳⣆⣶⣫⣷⡰⣄⠀⠀
⠀⢤⣶⡾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢳⡁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣥⠠⡉⠨⣭⣭⢍⣀⡁⣀
⠀⠀⠀⢀⣠⣤⣾⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠙⣆⡈⠻⣮⣋⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡈⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⣙⡛⠛⠛
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⢝⠀⠛⢿⠻⡟⠃⠀⠸⠉⢿⡟⠹⠈⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠷⢀⠀⠇⠀⠀⢈⠐⣿⣿⠸⠀⡇⢸⢘⠪⠅⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠫⠿⠀⠀⠒
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⠻⠿⠟⠋⣍⣀⡀⠀⠀⠀⠀⠀
⣀⣀⣤⠀⡀⢠⠀⡀⠖⠖⠺⠛⣿⡇⢘⠛⡟⣿⢛⠒⠀⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣿⣿⣍⣿⣿⠀⣰⢶⣦⡀⠙⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠀⠀
⣿⣿⣿⠀⡇⢠⡐⢂⠐⠀⠂⠐⠛⠃⠘⠃⠂⠛⢀⠀⡀⣄⢛⢀⢀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣼⣯⣽⣿⣽⣼⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⠉⠛⠛⢛⣛⣛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⡆⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣾⣿⣿⣿⣿⣿⠛⠂⠠⣽⣿⣿⡷⠂⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿⣿⡏⠉⠙⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⢭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀
⠙⠿⠿⠛⠛⣋⡡⣤⣥⡶⡆⡮⢈⠛⡉⢽⠷⠴⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⡻⠿⢿⣷⣿⢀⣿⣷⣮⣝⠿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀
⡆⠀⠀⠀⠈⠀⠉⠉⠀⠀⠁⠀⠀⡄⠰⢀⠀⠀⡀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠪⠹⢸⣟⣿⣿⣮⠕⢮⡙⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠃⠀⠀⠀
⣷⠀⠀⠠⣀⠄⠘⢋⡴⡆⠆⠄⠒⠠⠄⠘⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢀⣤⣞⠀⠀⠀⠀⠀⢴⣻⣷⠆⠀⠀⠀⣀⠀⠀⠰⡀⠈⠩⣷⢾⣍⢻⣶⣮⡲⣌⠻⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀
⣿⡇⢺⡚⣷⣟⢟⣿⣿⣸⠿⡂⢳⠶⣷⡾⢟⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢰⣿⣿⣗⠀⠀⠀⠀⠀⢸⣿⣯⡀⠀⣶⣦⡴⠀⣤⣌⡁⣿⣤⣄⠉⢾⣿⣯⣿⣯⣷⣕⣬⡻⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤
⢿⣿⠀⠃⠛⠛⡻⠟⡫⢔⣻⡽⠞⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿⣷⡀⣾⣿⡇⢰⡿⣾⠑⣮⡙⢿⣷⣤⠈⠛⢿⣿⣿⢻⣿⣝⢎⡻⣿⣿⣿⣿⣿⣿⣿⣏
⠘⣿⣆⠀⠄⠠⢢⠔⠚⣉⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣷⡸⡿⠇⢰⣧⣝⣘⣿⠿⣦⡨⡋⣔⠀⣄⠈⠙⢿⠟⠷⢠⡑⢄⠩⣤⣄⣀⣉⣈⠀
⠀⢿⣿⠀⠖⢀⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣧⠑⠃⢸⣀⣿⣿⢫⠀⠀⠀⢄⡈⠑⣿⠇⣀⠀⠉⠻⠸⣻⡈⠓⡈⠛⣛⣿⠛⠛
⠀⠘⣿⣇⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠀⠜⣿⣿⣳⡏⠀⠀⠀⠀⠉⠀⠨⠳⠽⠾⡶⡄⠀⠙⠃⠳⠜⠦⠘⢿⡿⠷
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⢠⠹⣵⠁⡇⡆⠀⠀⠀⠀⠀⠑⢄⠘⢾⣲⣶⣶⣄⡀⠀⠈⠢⠱⣄⠱⣶
⣻⣤⡶⣿⣏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢧⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⢝⣟⣙⣛⣀⣀⠀⠀⠈⠣⡈
⡿⠛⠁⠸⣿⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠈⢿⡇⣯⣽⣧⣠⡀⠀⠀
⠀⢠⡠⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣧⠃⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣄⢠⡙⢩⣭⣭⢉⣈⠀⣀
⠀⠀⠀⢀⣤⣥⣼⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠱⣄⠘⢿⣎⣋⣷⡙
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⡛⠛⠛⠛
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⢿⠀⠛⢿⠻⡟⠃⢸⠘⠉⢿⡟⠹⠸⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠷⠀⠀⠇⠀⠈⢸⠀⢿⣿⠸⠐⣿⢘⢘⠪⠅⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠐⠒
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⣴⣶⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠋⠻⠿⠟⢻⣀⣀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⠀⡀⠠⠀⡒⠖⠞⠻⠛⣿⡇⢘⠛⡟⣿⠛⠒⠇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣿⣯⣹⣿⣿⠀⣠⣤⣄⠀⢻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠀⠀
⢾⣿⣿⠀⡇⢠⡐⠂⠐⠀⠂⠐⠛⠃⠘⠃⠂⠛⢘⠀⡀⣄⢛⢀⢀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣸⣗⣻⣟⣢⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠙⠛⠛⣛⣿⡛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣰⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⡗⠻⠂⢤⣿⢿⣿⠲⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠘⣿⣿⡋⠙⠛⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⠨⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀
⠿⠿⠿⠛⢛⣉⣠⣬⣥⡄⠶⢐⠛⠻⠭⣕⢕⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡙⠻⠿⣿⣾⣷⢸⣿⣶⣬⡻⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠀⠀⠀
⠂⠀⠀⠉⠑⠊⠍⠙⠂⠁⢠⠀⡈⠱⠀⠐⡀⠂⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠑⠝⠇⣾⢹⣿⣷⣭⠳⢍⡻⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⠁⠀⠀⠀
⠀⠀⠀⢀⡀⠐⠒⣰⡆⠄⡄⡔⠀⠥⠸⠀⠁⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠔⣀⠲⢦⣄⠀⡄⠀⠀⡀⠀⡀⠀⠐⡄⠀⠛⢪⣿⢯⢃⣯⣴⣝⢦⡙⠿⣿⣿⣿⣾⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠞⣵⠶⠾⣿⣷⢰⠶⢄⠲⢦⣶⣶⡶⢖⣂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⢠⣾⣿⣿⣥⡼⢿⢋⣼⣇⠀⢀⣥⣦⡇⢀⣄⣀⢠⣤⣄⠉⠩⣿⣿⣽⣿⣿⣮⣦⣍⢿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄
⠀⠀⠀⠿⠿⣻⡿⢋⠥⢾⣻⡾⢖⣩⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⠑⠈⠘⣿⣿⣿⣆⢡⣿⣿⡇⢸⣿⣽⣰⣍⠻⣷⣦⡈⠙⢿⣿⣿⣿⢿⣮⡳⣍⠻⣿⣿⣿⣿⣿⣿⣟⣉
⠀⠀⢆⠐⠈⢅⡠⠔⠚⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⢻⠿⠀⢸⡅⡿⠻⢿⣦⡀⢝⠟⡠⠀⠈⠙⠽⡿⠟⡧⣨⡣⡈⠩⣤⣀⣈⣉⡉⠀
⡤⠀⠠⡄⠘⢚⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠶⠀⣸⢅⣿⣿⢟⠀⠉⠀⡁⠙⠃⣿⣀⡀⠉⠛⠟⠺⣏⢙⢂⡙⢛⣻⡟⠛⠋
⣧⠀⠀⢐⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⢀⢸⣿⣿⢣⡏⠀⠀⠁⠉⠂⠐⠝⢦⠳⢤⠄⠀⠉⠻⠈⠷⠽⠆⠹⣿⠷⠶
⣿⡄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⡀⣀⠛⣣⠟⡇⡄⠀⠀⠀⠀⠀⠠⡁⠙⣾⣦⣶⣤⡀⠀⠐⠰⣎⢢⡈⠢⣶
⣿⣧⡴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣞⣏⣀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢀⡈⢻⡻⣟⣛⡂⣀⠀⠀⠀⠙⣢⠙
⣿⣿⡆⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⣿⡄⠠⠂⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢝⣾⣥⣽⣳⣄⠀⠀⠈⠓
⠀⢹⣿⡄⠄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⡄⠉⠇⢭⣭⣭⢁⡀⢀⠀
⠀⠀⣿⣃⣤⣤⣼⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⢢⡈⢿⣿⣜⢝⣦⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡛⠛⠛⠛
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠻⢿⠀⠛⢿⠻⡟⠃⢸⠘⠉⢿⡟⠹⠸⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠷⢀⠀⠇⠀⠈⢸⠀⢿⣿⠸⠐⣿⢘⢘⠪⠅⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠍⠀⠐⠒
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⣴⣾⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠛⠛⠿⠟⢻⣁⣀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⠀⡀⠠⠀⡒⠖⠟⠻⠛⣿⡇⢘⠛⡟⣿⠛⠒⠇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣿⣯⣽⣿⣿⠀⣠⣤⣄⠀⢻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠀⠀
⣿⣿⣿⠀⡇⢠⡐⠂⠐⠀⠂⠐⠛⠃⠘⠃⠂⠛⢈⠀⡀⣄⣛⢀⢀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣸⣗⣻⣟⣢⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠙⠙⠛⣛⣟⡛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣾⣆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠻⠂⣤⣿⣿⣿⠢⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠘⣿⣿⡋⠙⠛⠏⠀⠀⡀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⠨⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠿⠿⠿⠛⢛⣉⢀⣬⣥⡄⠶⢐⠙⠻⠯⣕⢕⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡙⠻⠿⣿⣾⣷⢸⣿⣶⣬⡻⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀
⠂⠀⠀⠈⠑⠊⠍⠙⠂⠁⢠⠀⡈⠱⠀⠑⡀⠂⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠀⠑⠝⠇⣺⢹⣿⣷⣭⠳⢍⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠟⠁⠀⠀⠀
⠀⠀⠀⢀⡀⠰⠒⣰⡆⠀⡄⡔⠀⠥⠸⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠔⣀⠲⢦⣄⠀⡄⠀⠀⡀⠀⡀⠀⠐⡄⠀⠛⢫⣿⢯⢃⣯⣴⣝⢢⡙⠿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠞⣵⠶⠾⣿⣷⢰⠶⢆⠲⢦⣶⣶⡶⢖⣂⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⢠⣾⣿⣿⣥⡼⢿⢋⣼⣇⠀⢀⣥⣧⡇⢀⣄⣀⢠⣤⣄⠉⠩⣿⣿⣽⣿⣿⣮⣦⣍⢿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄
⠀⠀⠀⠿⠿⣻⡿⢋⠥⢾⣻⡾⢖⣩⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⠑⠈⠘⣿⣿⣿⣇⢡⣿⣿⠇⢸⣿⣽⣰⣍⠻⣷⣦⡈⠙⢿⣿⣿⣟⢿⣯⡳⣍⠻⣿⣿⣿⣿⣿⣿⣟⣉
⠀⠀⢆⠀⠈⢄⡠⠔⠛⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⢻⠿⠀⢸⡅⡿⠻⢿⣦⡀⢝⠟⡠⠀⠈⠙⠽⡿⠟⡧⣌⡣⡈⠩⣤⣀⣈⣉⡉⠀
⡄⠀⠠⡄⠘⢚⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠶⠀⣸⢅⣿⣿⢟⠀⠉⠀⡁⠙⠃⣿⣀⡀⠉⠛⠟⠺⣏⢙⢂⡙⢛⣻⡟⠛⠛
⣧⠀⠀⢐⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⢀⢸⣿⣿⢣⡏⠀⠀⠁⠉⠂⠐⠝⢦⠳⢤⠄⠀⠉⠻⠈⠷⠽⠆⠹⣿⠿⠶
⣿⡄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⡀⣀⠛⣣⠟⡇⡄⠀⠀⠀⠀⠀⠠⡁⠙⣾⣦⣶⣤⡀⠀⠐⠰⣎⢢⡈⠲⣶
⣿⣧⡴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣞⣏⣐⠀⠃⠀⠀⠀⠀⠀⠀⠈⢀⡈⢻⡻⣟⣛⡂⣀⠀⠀⠀⠙⣢⠙
⣿⣿⡆⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⣿⡄⠠⠂⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢝⣾⣥⣿⣳⣄⠀⠀⠈⠓
⠀⢹⣿⡄⠀⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⡇⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⣥⡄⠉⠇⢭⣭⣭⢁⡀⢀⠀
⠀⠀⣿⣃⣤⣤⣼⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⢢⡈⢻⣿⣜⢝⣦⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢍⣙⠛⠛⠛
⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠰⣿⠀⠛⢿⠻⡟⠯⠀⠘⠙⣿⡟⠹⠸⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠗⢀⠀⠇⠀⢸⢰⠘⣿⣿⠸⢰⡏⢸⢸⠪⠅⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠁⠀⠲⠒
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡤⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⠿⠿⠻⠿⠿⠯⣛⣁⡀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⠀⡀⠠⠒⡒⠖⠟⠻⠛⣿⡇⢘⠛⠟⣿⢻⠒⠀⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣿⣍⣿⣿⡏⢀⣤⣤⠀⠘⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡖⠀⠀
⣿⣿⣿⠀⣇⢠⡐⠂⠐⠀⠂⠐⠛⠃⠘⠃⢂⠛⢘⢀⡀⣄⢛⢀⢀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣇⣿⣻⣿⣳⣄⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠛⠛⢛⣟⣛⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣶⡀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠗⠀⣼⣿⣿⣷⠒⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⢻⣿⣿⠙⠛⠿⠇⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠿⠿⠿⠛⣋⡐⣈⣭⡄⠖⠂⠺⠻⠟⣍⣌⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⠛⡿⢿⣷⣽⡇⣿⣷⣦⣝⠻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠱⠀⠀⠀
⠀⠀⠚⠉⠚⡋⠉⠁⠀⠠⠈⡀⢹⠄⠀⠀⠐⠀⢹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠀⠈⠨⠃⠁⣿⣿⣿⣮⡝⠮⣙⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠠⠖⣠⡆⣀⡄⠠⠁⣀⠀⠇⠈⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⡜⣀⡀⢤⣄⡀⢠⠀⠀⠀⠀⡀⠀⠀⢀⠄⠐⠇⣿⣿⡝⡰⣥⣮⣗⣌⡻⢿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠘
⠀⠶⣯⢥⣴⣾⣯⢱⣶⡄⢠⣤⡴⣴⣦⠶⢂⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣶⣿⣿⣖⡀⢰⡿⠛⣾⡄⠀⠈⣼⣠⡁⢀⣄⠀⣰⣄⡈⠣⣽⣿⣮⣿⣿⣵⣽⣦⡙⢿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀
⠀⠀⠿⡷⢾⣯⠇⣫⣴⣞⣦⠦⢚⣩⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠁⠂⠀⢳⣾⣿⣿⡀⢹⣿⣿⠀⣸⣿⣡⣌⠙⢿⣶⣄⠉⠻⣭⣽⣿⡿⣿⣟⢦⡙⢿⣿⣿⣿⣿⣿⣿⣏⣁
⢠⠀⠀⠐⡉⣀⢤⠶⠚⣩⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡘⡿⡿⠀⣽⠻⣯⣾⣷⣅⢨⡻⡷⢀⠈⠙⠫⠿⢿⢻⡄⣝⢄⡉⢥⣄⣀⣉⣉⠁⠀
⠀⢈⢀⡠⠝⣀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡰⠠⠀⡏⢸⣶⣶⡦⠉⠓⠙⠂⠻⠆⣦⠀⠈⠙⠻⠗⠿⣅⠙⢀⠛⣛⣿⠛⠛⠛
⠀⠈⠡⢐⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⢀⢿⣾⣿⢫⡆⠀⠀⠀⠁⠀⠤⡻⣾⢧⡄⠀⠀⠻⠿⠘⠮⠷⡌⠻⣿⠷⠶
⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠨⠘⠿⠃⢿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠳⣾⣥⣤⡀⠀⠀⠂⢲⣘⢦⠐⢶⣶
⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳⡱⠗⣐⠀⠃⠀⠀⠀⠀⠀⠀⠁⡀⠙⢛⢿⣛⣓⡀⠀⠀⠉⠈⠓⣄⠛
⠋⠁⠈⠻⠿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⣻⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡈⠻⣷⣭⣭⣓⣦⡀⠀⠀⠘⠦
⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⡇⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣣⠉⠙⡏⣉⣍⡉⠀⠀⠀⠀
⣧⠀⠀⢀⣤⣄⣬⣤⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣧⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠹⣿⣧⡻⢳⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⡍⠙⠛⠛
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⢿⢿⡟⠃⢸⠘⠙⣿⡟⠹⠸⠿⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠑⢀⠀⠇⠀⢸⢸⠸⣿⣿⠸⢀⡇⢸⢸⠠⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠠⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡶⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⠁⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠿⠿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⠀⡒⠺⠛⡛⠟⠟⠻⠛⣿⡇⢘⠛⡟⣿⢛⠒⠀⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣍⣿⣿⢠⠾⣿⠦⡀⢹⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡖⠀⠀⠀
⣿⣿⣿⠀⡇⠐⠐⠂⠐⠀⠂⠐⠛⠃⠘⢃⣄⠛⢀⣀⡀⣄⢛⢀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⢼⡆⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠿⣷⣶⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢲⠂⣼⣿⣿⣿⣷⣢⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⣿⣿⡇⠉⠉⠛⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠂⠀⠀
⠿⠟⠋⠑⢒⣉⡄⢠⠂⠲⢖⠛⣻⢤⡉⡕⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡛⢿⣿⣿⣮⣿⢸⣯⣶⣬⡻⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣸
⠚⠋⢑⠚⠋⠉⠁⠀⠈⠁⠀⡄⠘⠈⡀⠅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠐⢽⠈⢸⢿⣿⣷⣽⡳⢍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⢀⣿
⠀⠀⢀⠀⣠⠄⠀⡆⠀⠀⠐⠁⣘⢀⠑⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠘⢷⣦⢀⠀⠀⡀⣀⠀⠺⢸⣿⣯⣃⣮⣶⣝⣢⡙⠿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠸⠻
⣀⡠⣤⣔⣝⢰⢤⡃⢠⡀⣠⣄⣤⣤⡤⠄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣦⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠨⢯⣎⣤⠀⣤⠡⣀⣤⡀⠙⢼⣽⣿⣿⣿⣿⣮⣶⣌⠻⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀
⣅⣢⣿⣟⠇⢎⣪⡴⢄⣡⠽⠟⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠚⣯⣿⡏⠀⣿⡇⣤⡉⠻⣷⣄⡈⠛⢿⣽⣟⣿⢿⣿⣳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣏⡀
⢀⡀⠘⠁⣀⡬⠵⠞⡋⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡎⢿⣿⡇⠐⡻⢿⣷⣽⣮⡪⣙⢿⡢⡀⠉⠻⠫⣿⡿⣿⢨⡡⣌⠩⣭⣍⣹⣋⣉⠀⠀
⠁⢀⣲⠉⢈⢥⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡌⡌⡀⢰⢿⢠⣥⣝⡉⠙⢎⡳⢝⢰⣦⠀⠀⠙⠓⢾⢪⢿⡚⠓⡘⠛⣻⣿⠛⠛⠋
⢈⡀⢔⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡈⠀⢸⣯⣾⣿⠟⠀⠀⠀⠁⠈⠀⠜⢠⡳⣤⠀⠈⠘⢿⣇⠳⡝⢦⠙⢿⡿⠶⠶
⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠃⢻⣿⢏⡆⠀⠀⠀⠀⠀⠀⠄⠢⡐⣶⣧⣤⣄⠀⠈⠐⠔⣦⡲⣄⠰⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠰⡄⣅⠀⠠⢰⡄⠀⠀⠀⠀⠀⠀⢈⠊⠻⡻⣿⠓⣂⠀⠀⠘⠋⠘⢣⡈⠛
⠋⢰⠺⠟⠻⠟⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡜⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⣿⢮⣟⢘⠢⣄⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣈⠛⣻⣙⣛⣛⣓⠀⠀⠀⠈
⠀⠀⣀⣠⣤⣅⣼⣴⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢳⡙⠇⢸⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣆⠀⠡⢻⣿⣇⢿⢦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣍⠙⠛⠛
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠛⢿⢿⡟⠃⢸⠘⠙⣿⡟⠹⠸⠿⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠑⠀⠀⠇⠀⢸⢸⠸⣿⣿⠸⢀⡇⢸⢸⠠⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠻⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⠀⡒⠲⠛⡛⠛⠟⠻⠛⣿⡇⢘⠛⡟⣿⠻⠒⠀⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣍⣿⣿⢠⠿⣿⠦⡀⢹⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡖⠀⠀⠀
⣿⣿⣿⠀⡇⠐⠐⠂⠐⠀⠂⠐⠛⠃⠘⢃⣄⠛⢀⣀⡄⣄⢛⢀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⢼⣆⠀⠀⠠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠿⣷⣶⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢓⠂⢬⣿⣿⣿⣷⣶⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⣿⣿⡇⠉⠉⠛⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀
⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⠄⠀⠀
⠿⠟⠋⠑⢒⣉⣄⢠⠂⠲⢖⠛⣻⢤⡉⡕⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡛⢻⣿⣿⣮⣿⢸⣯⣶⣬⡻⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⣸
⠒⠋⠑⠛⠋⠉⠃⠀⠈⠁⠀⡄⠘⠈⡀⠅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠐⢝⠘⢸⣿⣿⣿⣽⡳⢍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣿
⠀⠀⢀⠀⣠⠄⠀⡄⠀⠀⠐⠁⣐⣀⠐⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠘⣷⣦⢀⠀⠀⡀⣀⠀⠻⢸⣿⣯⣋⣮⣴⣝⣢⡙⠿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠸⠛
⣀⡠⣤⣔⣼⢰⢤⣃⢠⡀⣠⣄⣤⣤⡤⠄⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣦⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠨⢯⣎⣤⠀⣤⠡⣂⣦⡀⠙⢬⣽⣷⣿⣿⣿⣮⣷⣌⠻⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀
⣅⣣⣿⣛⠇⢎⣪⡴⢄⣡⠽⠟⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠊⣯⣿⡏⠀⣿⡇⣤⡉⠻⣷⣄⡈⠛⢿⣽⣿⣿⢿⣿⣳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣍⡀
⢀⡀⠚⠁⣀⡬⠵⠞⣋⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡎⢿⣿⡇⠐⡻⢿⣷⣽⣮⡪⣙⢿⡢⡀⠉⠻⠯⣿⡿⣿⢨⡱⣌⠩⣭⣍⣩⣋⣉⠀⠀
⢁⠀⣶⠉⢈⣥⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡌⡌⡀⢰⢿⢠⣥⣝⡉⠙⢎⡳⢝⢰⣦⠀⠀⠙⠓⢾⢪⢿⡚⠓⡘⠛⣻⣿⠛⠛⠋
⢈⡀⢐⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡈⠀⢸⣯⣾⣿⠟⠀⠀⠀⠁⠈⠀⠝⢠⡳⣤⠀⠈⠘⢿⣇⠳⡝⢦⠙⢿⡿⠶⠶
⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠃⢻⣿⢏⡆⠀⠀⠀⠀⠀⠀⠄⠢⡐⣶⣧⣤⣄⠀⠈⠐⠔⣦⡲⣄⠰⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠰⡄⡅⡀⠠⢰⡄⠀⠀⠀⠀⠀⠀⢈⠊⠻⡻⣿⠓⣂⠀⠀⠘⠋⠘⢣⡈⠛
⠉⢖⠾⡿⠻⠛⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡼⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⣿⢮⣟⢘⠢⣄⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣈⠛⣻⣙⣛⣛⣓⠀⠀⠀⠀
⠀⠀⣀⣠⣶⡅⣼⣴⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢳⡙⠇⢰⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣆⠀⠡⢻⣿⣇⢿⢦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣩⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢼⣿⠀⠛⢿⢿⡟⠃⢼⠸⠙⣿⡟⠹⠸⠿⢿⢼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠿⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠁⢀⠸⠇⠀⢸⢸⠸⣿⣿⠸⢐⡇⢸⢸⠠⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿⢁⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣟⠫⠌⠀⠀⠀⠀⠀
⣤⣤⣴⠒⡒⠺⠛⡛⠟⠟⠻⠛⣿⡇⢘⠛⡟⣿⢻⠒⡇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣹⣿⣧⣚⣿⣟⣄⠈⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣟⠀⠀⠀
⣿⣿⣿⠀⠃⠐⠐⠂⠐⠀⠂⠐⠛⠃⠘⢃⣆⠛⢸⡀⡇⣄⢛⢀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠟⠛⢻⣿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣿⣿⣿⡄⠀⠀⠀⠀⣴⣶⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠗⠀⣼⣿⣿⣿⣶⣦⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠀⢼⣿⣿⠀⠉⠙⠻⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠈⠁⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣁⠀⠀⠀
⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⢠
⠟⠋⠉⢒⣈⣡⢠⠀⠰⢶⡒⣚⡧⣤⣍⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠛⣿⣿⣿⣾⣿⢸⣿⣶⣍⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡄⠀⣼
⠋⠑⠚⠛⠅⠙⠀⠌⠉⠀⣦⠄⠋⠁⠨⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣾⣥⣾⡿⡇⣿⢻⣿⣿⣽⡳⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢠⣿
⠀⢀⡀⢀⡄⠀⣠⠀⡈⠐⠈⢠⠂⠱⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⠀⠀⠀⠀⠛⠛⠛⠁⣀⠁⠻⢺⣿⣿⣃⣿⣴⣝⢦⡙⢿⣿⣿⣿⣿⣿⣤⡈⠀⠀⠀⠀⠸⠿
⡠⣤⣤⣸⢱⣥⡁⡀⣄⢀⣄⣠⣄⣥⠤⠀⣄⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣿⣷⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢠⣄⣄⡅⢀⣅⠁⢀⣤⡈⠙⢽⣿⣿⣿⣿⣿⣮⣲⣌⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀
⣃⣿⣿⡋⠬⣘⣥⡦⣉⢫⠾⢛⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡌⢘⣿⣿⡇⠀⣟⡇⣨⡙⠻⣷⣄⠉⠻⢿⣿⣿⣿⢿⣿⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣋⠀
⣉⠐⠋⢀⣈⣭⠷⠛⢩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡜⣿⣿⡇⠸⡿⢿⣯⣹⣮⡪⡙⢿⡢⡀⠉⠻⢿⣿⡿⣿⢨⡣⡈⠩⣭⣍⣽⣋⣉⠁⠀
⢀⣤⡚⠙⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⡘⡬⡀⢰⢿⢪⣃⣛⠉⠙⢌⠲⣝⠎⣤⡀⠀⠙⠖⢿⢪⢿⡚⠳⡙⢛⣻⣿⠛⠛⠛
⣈⠥⣲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡘⠀⢸⣽⣾⣿⡿⠀⠀⠈⠑⠈⠂⠙⠇⣱⣠⠀⠈⠘⢿⡇⠳⣝⢦⠙⢿⡿⠶⠶
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠎⢿⣿⡟⡁⠀⠀⠀⠀⠀⠀⢄⠠⡱⣾⢯⣤⣄⠀⠈⠐⢔⣦⡲⣄⠰⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄⢱⡈⣋⠀⠡⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣿⠳⢂⠀⠀⠈⠋⠘⢣⡈⠛
⠁⠿⡻⠿⠿⠛⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳⡹⣿⣶⠀⠋⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⣟⣾⣛⢹⡢⣄⠀⠀⠀⠹⣄
⠀⠁⠀⢀⠤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⡹⣿⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠈⢳⡈⠻⣻⣛⣛⣛⣓⡀⠀⠀⠀
⠀⢀⣤⡠⣬⣄⣼⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢷⢻⡇⢠⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⣆⠀⠡⢿⣿⣏⢶⢮⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠀⠛⢿⢿⡟⠫⢸⠘⠙⣿⡟⠹⠸⠿⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠗⢀⠸⠇⠀⢸⢸⠸⣿⣿⠸⢀⡇⢸⢰⠠⠅⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠚⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣶⡾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣄⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣟⠛⠛⠁⠀⠀⠀⠀
⣤⣴⣶⠒⡚⠻⠛⡛⠟⠟⠻⠛⣿⡇⢘⠛⡟⣿⢻⠒⡇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣿⣹⣿⣰⣩⣿⣳⡄⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡗⠀⠀⠀
⣿⣿⣿⠀⠓⠐⠐⠂⠐⠀⠂⠐⠛⠃⠘⢁⣇⠛⢸⢀⡇⣄⣛⣀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠛⠛⢻⣿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣷⠀⠀⠐⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⡗⠀⣽⣿⣿⣿⠿⣢⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⢿⣿⡿⠀⠉⠙⠻⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠈⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣅⠀⠀⠀
⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢩⣭⣭⣭⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⢠
⠛⠋⠑⣒⣉⡄⢠⠀⠲⠶⣶⣚⢦⣈⡕⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣅⠛⣿⣿⣿⣼⣿⣸⣿⣶⣍⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣼
⠉⠑⠛⠛⠈⠑⠀⠘⠁⠐⡄⠈⠈⠀⠥⠀⢻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⣾⡿⡇⣿⢻⣿⣿⣽⡳⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⠀⢰⣿
⠀⣀⠀⣠⢀⢰⡆⢀⠁⠀⠁⠸⠄⠑⠘⠀⢸⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⣠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⠀⠀⠀⠀⢈⠙⠉⠁⣄⠁⠿⢺⣿⣿⣃⣿⣴⣝⢦⡙⢿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠺⠿
⢠⣤⣄⡏⣼⣈⠁⢀⡀⢀⣀⣤⣨⣥⠄⢀⣨⣿⣿⣿⣿⣷⣤⣶⣶⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⠀⢠⣌⡄⡅⢀⣁⢑⢰⣄⡈⠙⢾⣿⣾⣿⣿⣿⣮⣲⣌⢿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀
⣽⣿⣟⢣⠧⣋⣅⠀⣙⡟⠿⣛⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡌⢘⣿⣿⡇⠀⣿⡷⣈⠙⠿⣷⣄⡈⠛⢿⣿⣿⣿⢿⣯⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣏⠀
⡉⠛⠁⢀⣈⣭⠶⢛⣩⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡘⣿⣿⡇⠸⡿⢿⡯⣹⣎⠪⡛⢿⣢⡀⠉⠻⢯⣿⡿⣯⢨⡣⣈⠩⣭⣉⣽⣋⣉⠁⠀
⣠⣔⠚⠛⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣷⡸⡩⠀⢰⢷⢨⣓⡛⠉⠳⣌⠲⡙⠿⢣⡀⠀⠙⠒⢿⢪⢿⡚⠳⡙⢛⣻⣿⠟⠛⠋
⣉⠅⣢⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠙⠀⢸⣟⣼⣿⡿⠀⠀⠈⠙⠈⠣⠙⢧⢠⣠⡀⠈⠐⢾⡇⠳⣝⢦⡙⢿⣿⡶⢶
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠎⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⢄⠠⡰⣾⢯⣤⣀⠀⠀⠐⠔⣦⡲⣄⠰⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢢⡈⡛⠀⠃⠄⣀⠀⠀⠀⠀⠀⠁⠀⠈⠿⡿⣿⠷⠦⠀⠀⠈⠛⠘⢳⡈⠛
⡙⣛⡟⡿⠟⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢳⡻⣿⣦⠀⠟⠀⠀⠀⠀⠀⠀⠀⠰⣄⠹⣿⢾⣻⢹⢶⣄⠀⠀⠀⠹⢆
⠀⠁⠀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠫⢻⡞⣛⣛⣓⡀⠀⠀⠀
⠀⢠⣤⡠⣬⣄⣼⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢧⢻⡇⠠⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢆⠀⠡⢻⣿⣟⢶⢦⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⡭⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⠀⠛⢿⢿⡟⠯⢸⠘⠙⣿⡟⠹⠸⠿⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠟⠀⠑⢸⠀⠅⠀⢸⢸⠸⣿⣧⠸⢠⡇⢸⢰⠢⠅⣿⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠓⠛⠃
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⡾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢋⣤⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠻⠟⠉⠈⠀⠀⠀
⣤⣶⣶⠚⡛⠻⠛⡛⠟⠟⠻⠛⣿⡇⢘⠻⡟⣿⢻⠒⠇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣯⣿⣇⣾⣽⣿⣵⡀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣟⠀⠀⠀
⣿⣿⣿⠀⠃⠐⠐⠂⠐⠀⠂⠐⠛⠃⠘⢁⣇⠛⢸⢀⡆⣄⣛⣀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⣿⣿⣭⣿⠿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣧⠀⠀⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⠿⢻⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡗⠰⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠐⢿⣿⡇⠀⠉⠙⢻⠁⠀⠀⠀⣻⣿⣿⣿⣿⡿⠀⠀⠀⠈⠁⠀⠉⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡄⠀⠀
⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢰
⠛⠉⠐⣊⣉⠀⡄⡄⡶⢖⣖⣻⢤⣬⣃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣅⠛⣿⣿⣷⣽⣯⣸⣿⣶⣝⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾
⠉⠒⠛⠫⠈⠃⠀⠙⠀⢢⡠⠈⠁⠈⠅⠈⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡿⡟⡇⣿⣻⣿⣿⣽⡲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⢰⣿
⢀⡀⢈⡤⡀⢰⠀⢀⠁⠊⠃⠆⠀⠄⠀⠀⢻⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠁⠿⢻⣿⣿⣃⣿⣴⣕⢦⡙⢿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠾⠿
⣬⣤⣸⢣⣇⡘⢀⢀⡀⣀⢀⣭⣩⣤⠄⢀⣸⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⢠⣬⡌⡅⠀⣁⣐⢰⣄⡈⠙⢾⣿⣾⣿⣿⣿⣮⣲⣌⢿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀
⣿⡿⡟⣨⠎⣋⣀⢈⣙⣳⠿⣛⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡘⢚⣿⣿⡇⠀⣾⡶⣈⠙⠿⣷⣄⠈⠛⢿⣿⣿⣿⢿⣯⡳⣍⠻⣿⣿⣿⣿⣿⣿⣿⣋⠀
⠉⠛⡁⢀⣩⡽⠾⢛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡐⣿⣿⡇⠸⡿⣷⡟⣹⣎⠪⡛⢿⣢⡀⠉⠻⠯⣿⡿⣯⢨⡳⣌⠩⣭⣭⣽⣉⣉⠉⠀
⢠⡔⠚⢛⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣷⡹⡹⠀⢰⣷⢨⣃⡻⠋⠳⣌⠢⡙⢾⢓⡀⠀⠙⠒⢿⢬⣿⡚⠳⡘⠛⣻⣿⠟⠛⠛
⡉⠀⣢⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠙⠀⢸⣟⣼⣿⡿⠀⠀⠈⠑⠈⠢⠘⢯⡄⣠⡀⠈⠐⠾⡗⠳⣝⢦⡙⢿⣿⣷⣶
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⡎⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢄⠀⡰⣜⢿⣀⣀⠀⠀⠐⠔⣦⡲⣄⠰⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢢⡘⠟⠁⠂⡄⣀⠀⠀⠀⠀⠀⠁⠀⠈⠿⡿⣿⠿⠦⠀⠀⠈⠛⠘⢳⡈⠛
⠩⣯⣟⠟⠛⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢷⣻⣿⣤⡄⡿⠈⠀⠀⠀⠀⠀⠀⠠⣄⠹⣟⢾⣿⢻⢷⣄⠀⠀⠀⠙⢆
⠀⠉⠀⣀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⣿⡇⠀⡀⠀⠀⠀⠀⠠⠀⠀⠈⠳⡌⠫⢻⡞⡛⠛⠓⠀⠀⠀⠀
⠀⢠⣤⣢⣤⣀⣼⣾⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢧⢻⡇⢠⣅⠀⠈⠀⠀⠀⠉⠀⠀⠀⠙⢆⠀⠡⢻⣿⣿⢰⢦⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣍⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⢿⣿⠀⠛⢿⢿⡿⠧⢼⠘⠙⣿⡟⠹⠸⠿⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠀⠓⢸⠠⠅⠀⢸⢸⠸⣿⣇⠸⢠⡇⢸⢰⠢⠅⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠂
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⡾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡟⢁⣤⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠛⠟⠉⠀⠀⠀⣀
⣶⣶⣶⠚⡛⢻⠛⡛⠟⠟⠻⠛⣿⡇⢘⠛⡟⣿⢻⠒⡇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣏⣿⣧⣭⣽⣯⣧⢈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠀⠀⠀
⣿⣿⣿⠀⠓⠐⠐⠂⠐⠀⠂⠐⠛⠃⠘⢃⣆⠛⢸⣀⡇⣄⣛⣀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⡏⠋⣿⣭⣯⣿⡿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀
⣿⣿⣿⡄⠀⠀⠀⠀⢰⣿⡆⠀⠠⠦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⡗⠰⣿⣿⣿⣿⣿⡶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠸⣿⣿⠆⠈⠉⠙⢿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠁⠈⠉⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁⠀⠀
⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰
⠋⠉⢒⣊⣡⢠⡠⠰⠶⢶⣖⡲⣄⣩⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣅⣻⣿⣿⣿⣿⣯⣸⣿⣶⣝⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣾
⠑⠚⠛⠁⠙⠀⠀⠋⠀⢢⢄⠉⠁⠨⡀⠘⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠟⠻⡟⡇⣿⢻⣿⣿⣽⡲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢰⣿
⠀⠀⣈⠄⠀⣧⠀⡈⠀⠉⠀⠧⠈⠂⠃⠀⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠁⠿⣻⣿⣿⣃⣿⣴⣕⢦⡙⢿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠾⠿
⣤⢆⣺⣰⣁⡃⡀⡀⢀⡁⣨⣍⣩⡤⠄⣀⣽⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⢠⣬⡍⡅⠀⣅⣐⢰⣄⡈⠙⢿⣿⣾⣿⣿⣿⣮⣲⣌⢿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀
⣿⡿⢃⡕⢜⣋⡄⣈⢛⡾⠿⣛⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡘⢺⣿⣿⡇⠀⣾⣶⣈⠙⢿⣷⣄⠈⠛⢿⣿⣿⣿⢿⣯⡳⣍⠻⣿⣿⣿⣿⣿⣿⣿⣉⠀
⠩⢋⠈⢀⣩⡽⠞⢛⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡰⣿⣿⡇⠰⣿⣷⣿⣹⣖⠪⡛⢿⣢⡀⠉⠻⠯⣷⡿⣯⣨⡳⣌⠩⣭⣍⣽⣉⣉⠉⠀
⢠⠖⠛⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣷⠹⣹⠀⢠⣷⢨⡣⠻⠉⢳⣌⠪⡙⢾⡷⡀⠀⠙⠒⢿⣮⣿⡚⠳⡘⢛⣻⣿⠛⠛⠛
⡉⢔⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠙⠀⢸⣿⣸⣿⡿⠀⠀⠈⠑⠎⠢⡁⢧⡧⢠⡀⠀⠐⠾⣷⡳⣝⣦⡙⢿⣿⣾⢶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⡎⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢄⠀⡁⣼⢿⣒⣄⠀⠀⠐⠔⣦⡰⣄⠰⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢢⠘⠏⠁⠂⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠿⡿⣿⠿⠦⠀⠀⠈⠛⠚⠷⡌⠛
⢱⡿⡿⠿⠛⢛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⣿⣄⡅⢹⠋⠄⠀⠀⠀⠀⠙⠀⣀⠹⣿⢞⣿⢻⢷⣄⠀⠀⠀⠙⢦
⠀⠁⠀⢀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠳⠌⠋⢻⡞⠷⠞⠓⠀⠀⠀⠀
⠀⣠⣴⣂⡤⣀⣼⣾⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣧⢻⣧⠀⢡⠀⠀⠀⠀⠀⠈⠀⠀⠂⠘⢆⢀⠑⢻⣿⣿⢱⣦⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣚⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠚⠏⠿⠈⠻⠿⢻⡿⠯⢼⠸⠙⣿⡟⠹⠸⠿⢿⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠀⠿⢀⠀⠇⠀⢸⢸⠸⣿⣷⠸⢠⡇⢸⢸⠢⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠿⠃
⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣶⣶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠋⣤⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⢿⣿⣿⣿⠻⠟⠉⠀⠀⢀⣀
⣶⣶⣾⠛⡛⠻⠛⡛⠟⠟⠻⠛⣿⡇⢘⠛⡟⣿⢻⠒⡇⠟⣛⠀⠒⡟⣛⢻⠟⡛⢻⣏⣅⣮⣽⣯⣵⡄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠀⠀⠀
⣿⣿⡛⠀⠃⠐⠐⠂⠐⠀⠂⠐⠛⠃⡘⣃⣆⠛⢸⡀⡇⣄⣛⣀⣀⡇⣿⢸⢘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠉⣯⣯⣽⣿⡿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀
⣿⣿⣧⠀⠀⠀⠀⠀⢼⣿⣀⠀⠠⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⢿⣿⡇⠀⠉⠙⠻⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠁⠀⠀⠁⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⣿⣿⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢰
⠉⠀⣂⣉⠀⡄⡄⡶⢶⣶⣒⢦⢌⣑⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣴⣿⠿⣿⣿⣿⣽⡏⣸⣿⣶⣝⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠒⠛⠃⠨⠁⠀⠐⠀⠁⡨⡈⠈⠀⣩⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⢉⠳⠆⠁⠸⡟⡇⣿⢻⣿⣿⣽⡶⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠁⢸⣿
⠀⠈⡀⡀⠆⠀⠀⠀⠈⠃⠵⠀⠢⠐⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠁⠿⢻⣿⣿⣓⣿⣾⣝⣦⡙⢿⣿⣿⣿⣿⣷⣌⡀⠀⠀⠀⠀⠾⠿
⡖⢸⢃⣇⢘⢐⢀⠀⣀⠀⣈⣉⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢠⣨⡍⣅⠀⡀⣐⢐⣄⣈⠙⢾⣿⣾⣿⣿⣟⣮⣲⣌⠻⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣀
⣿⠎⣘⡨⢗⠉⡀⠓⣫⡿⠟⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡠⢺⣿⣿⡟⠀⣿⣱⢈⡛⢿⣷⣄⡈⠛⢿⣿⣿⣿⣿⣯⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣋⠀
⠟⠁⠁⣚⣫⡵⠞⣃⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠸⣿⣿⡇⠀⣿⢿⣾⠛⣆⠉⡻⣿⣦⣀⠉⠛⢿⣵⣿⣯⡉⡳⣌⠫⣭⣉⣽⣍⣉⠉⠐
⠬⠒⠛⢉⣠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⢹⣙⠁⠀⣿⣈⠿⠑⠙⣻⣮⠪⡻⢾⣷⡄⠀⠈⠫⢿⡅⣿⡚⠳⡘⠛⣻⣿⡿⠛⠓
⡡⢴⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠳⠃⢸⡧⢿⣿⡗⠀⠀⠉⠛⠮⡪⡛⢠⢵⡀⢀⠀⠀⠳⣿⠱⣝⢦⡘⢿⣿⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⡍⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢬⡈⠡⡅⢘⣓⣤⡀⠀⠀⠂⢶⡐⣆⠀⢦⣤
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⢿⠏⠠⢄⠀⠀⠀⠀⠀⠀⠝⢦⠀⢿⡿⣿⠿⠶⠄⠀⠀⠙⠪⠳⡄⠻
⡹⣿⡻⠿⠛⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢲⣾⣄⠸⢰⡆⠀⠀⠠⠀⠀⠛⠷⠀⠙⢽⢖⣾⠇⣷⣤⡀⠀⠀⠙⠢
⠈⠁⠀⢀⢴⡿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣰⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⢻⣿⣿⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⢻⡟⠿⠾⠿⠔⠄⠀⠀
⠀⣠⣴⠂⣤⣄⣼⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣧⢻⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠳⡄⠀⠀⡙⠹⣿⣿⢯⣥⡐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢀⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⠀⠘⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⢃⣤⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⠟⠛⠻⠛⠛⣛⣙⣉⠀⠂⠀⠀⠀⠀⠀
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣁⣈⣽⣏⣦⠀⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠃⠀⠀⠀
⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⢩⣭⣍⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⡆⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠂⠠⣼⣿⣿⡽⠒⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠘⢿⣿⠇⠉⠙⠛⢿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡂⠀⠀⠀
⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⡄⣭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⠉⠐⣊⣋⠀⠄⡀⣶⠶⣶⠒⠆⠌⡁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣼⣶⠟⢜⠻⣿⣿⣷⣽⡯⣸⣿⣶⣝⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠄⠀⠀⣾
⠒⠛⠃⠉⠀⠀⠒⠀⠁⢈⠈⠈⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⢈⠓⠄⠁⠨⠏⡇⣿⢹⣿⣿⣽⠲⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠁⠀⢰⣿
⠀⠀⡀⡀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢺⣯⣽⡋⣮⣢⣝⣦⡙⠿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠘⠛
⡀⡐⣰⠃⠃⡂⠀⠀⣀⢀⣀⣈⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢠⡈⡍⣄⠀⡀⢐⢐⣄⣀⠙⢺⣽⣾⣿⡿⣟⣮⣲⣌⠻⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⡀
⣳⠆⣫⠹⠋⠈⠘⠐⢫⡿⠟⣋⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⠀⢜⣿⣿⡟⠀⣵⢱⣈⠙⢿⣷⣄⡈⠛⢿⣟⣿⣟⢿⣯⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿⡉⠀
⠞⠈⠁⣚⣫⡵⠞⠋⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠨⣿⣿⡇⠀⣿⣾⣼⢟⣆⠉⡻⣿⣦⣀⠉⠛⢟⣵⣿⢯⡉⡱⣌⠩⣭⣉⣹⣉⠉⠁⠀
⠤⠒⠉⢁⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠹⠙⠁⠀⣶⣉⠿⡘⠘⠻⣮⠪⡻⢾⣷⡄⠀⠀⠪⢮⡅⣿⡊⠳⠈⠛⣻⣿⠛⠛⠒
⠁⢀⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠣⠂⠀⡇⡏⣿⡆⠀⠀⠉⠛⠮⡢⡙⠆⢴⣀⠀⠀⠀⠳⣿⠰⣜⢦⡈⢻⣷⣦⣤
⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⡀⢿⣾⣿⡇⠀⠀⠀⠀⠀⠀⢈⡀⠡⣍⠀⣓⣤⡀⠀⠀⠀⢤⡔⢄⠁⢤⣄
⠿⢟⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠐⢌⠝⠡⢀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢶⡿⣿⡿⠶⠄⠀⠀⠙⠪⠳⣄⠹
⠀⠈⠙⠋⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠠⣶⡄⠀⠀⣤⠀⠀⠀⠀⠀⠐⢶⡦⠙⢟⢆⢶⡗⣶⣦⡀⠀⠀⠈⠢
⠀⠀⠀⢀⠴⠾⣫⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣼⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢧⠻⣿⡘⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⢻⡇⠿⠮⠿⠖⠄⠀⠀
⠀⣀⣤⠀⣤⣄⣴⣷⣼⣧⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣼⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢧⢻⣷⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠲⣄⠀⠠⡙⠸⣿⣿⡟⣥⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣘⠘⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠥⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⣈⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠀⠘⠛⠁
⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠟⢁⣄⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠟⠛⠻⠛⠛⣛⣙⣀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢰⣉⣿⣉⣄⢘⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠁⠀⠀⠀
⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⢩⣭⡍⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠂⠠⣼⣿⢿⣷⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠸⣿⣿⠈⠉⠛⠻⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣃⠀⠀⠀
⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡄⣭⣯⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡂⠀⠀⢀
⠁⢐⣚⡃⢠⢠⢠⡶⠶⡶⠒⡔⡀⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⣾⣿⠟⢜⠻⣿⣿⣷⣽⡯⣸⣷⣶⣝⡻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠂⠀⠀⣼
⠒⠛⠀⠉⠀⠀⠂⠈⢁⠈⠉⠉⠀⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢈⠓⠄⠁⠨⠏⡇⣿⢹⣿⣿⣝⡲⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢠⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠙⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢺⣭⣽⡃⣶⣢⣝⡦⡙⠿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠘⠛
⠀⡆⣸⠀⡂⡀⠀⢀⣀⢀⣀⣀⣀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢠⡈⡍⣀⠀⣀⠐⢐⣄⣀⠙⢸⣿⣾⣿⣿⣿⣮⣳⣌⠻⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣀
⣖⠘⢍⠽⠂⠁⠘⠖⢩⡿⠟⣋⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⢜⣿⣿⡿⠀⢡⢧⡈⠛⢿⣷⣄⡈⠛⢿⣟⣿⣿⢿⣿⡷⣌⠻⣿⣿⣿⣿⣿⣿⣟⡁⠀
⠂⠊⠐⢚⣫⡵⠞⡊⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠨⣿⣿⡇⠀⣿⣾⣵⡿⢆⠉⡻⣿⣦⣀⠉⠛⠟⣵⣿⢯⡍⡑⣌⠩⢍⣉⣹⡉⠉⠁⠀
⠤⠒⠋⢉⠀⣰⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠹⠹⠃⠀⣵⡅⢻⡟⠘⠻⣮⠪⡻⢾⣷⡆⠀⠀⠪⢨⡧⣻⡪⠳⡌⠛⢛⣿⠟⠛⠒
⠀⢀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠣⠆⠀⣏⡅⣷⡆⠀⠀⠉⠛⠮⡢⡙⢦⢡⡀⡀⠀⠀⠱⢿⡾⣌⢧⡌⢻⣿⣦⣤
⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢿⣾⣿⣇⠀⠀⠀⠀⠀⠀⠈⡀⠀⣍⢇⠘⣠⡀⠀⠀⠀⢠⣌⢦⡁⢤⣤
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⠈⠝⠽⠃⠀⡀⠀⠀⠀⠀⠀⠙⠢⡈⢡⡾⣿⡿⠶⠄⠀⠀⠉⠪⠻⣄⠙
⠀⠈⠉⠉⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠠⣥⡄⠀⡁⢠⠀⠀⠀⠀⠀⠰⢶⣦⡘⢞⢆⢶⡾⣰⣦⡀⠀⠀⠈⠢
⠀⠀⠀⢀⢴⢾⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣾⡏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢧⠻⣿⡒⠆⠸⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠈⠻⣧⠿⠯⠿⠦⠦⠀⠀
⠀⣀⣴⢂⡤⣀⣼⣾⣼⡧⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢧⠹⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠠⡘⠸⣾⣶⡶⣡⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣸⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⠈⠋⠉
⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠏⣀⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣛⣿⣳⡄⢹⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠃⠀⠀⠀
⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⢩⣭⣍⡍⠍⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠂⠠⣼⣿⣿⡿⠗⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠻⣿⡯⠈⠉⠛⠿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡆⠀⠀⠀
⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢀⢽⣭⣽⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢀
⠁⢐⣛⡃⠠⢀⢠⡶⠶⡖⠒⡔⢀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⣾⣿⣟⠻⣿⣿⣿⣽⣯⢸⣷⣶⣌⡳⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠀⠀⠀⣸
⠒⠓⠘⠈⠈⠐⠂⠈⠁⠁⠁⠁⠈⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢈⠓⡄⠁⠉⠟⡇⣽⢻⣿⣿⣽⡳⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⢄⠐⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠻⢸⣿⣽⠋⣮⣢⣝⣦⡙⠿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠘⠛
⢀⢂⣆⠀⢐⠀⠀⠀⡀⢀⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣠⣤⣤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢀⢀⡘⣀⠀⢀⠐⢐⣂⣀⠙⠻⣿⣾⣿⣿⣿⣮⣳⣌⠻⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀
⡓⠘⢍⠳⢁⠁⠀⠞⣵⡿⠟⣋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠼⣿⣿⡿⠀⢩⣟⡈⠛⢿⣷⣦⡈⠙⠿⣛⣻⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣟⡉⠀
⠀⠉⠐⢚⣫⡴⠞⡉⢁⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠨⣿⣿⡇⠀⣼⡿⣥⡿⢦⡉⠻⣿⣦⣄⠈⠛⠟⣷⣿⣿⡍⡙⢌⠉⢭⣉⣹⠋⠉⠉⠐
⠤⠒⠋⠉⠠⣰⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠹⠹⠇⠀⣹⡅⢻⡇⠈⠻⣦⡪⡻⢾⣷⡦⠀⠈⠛⠨⡯⢛⡪⠳⠄⠛⢻⡿⠿⠓⠒
⠀⢐⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠃⡆⠀⣿⣵⣷⡆⠀⠀⠉⠛⠮⡀⠙⢯⡉⡀⡀⠀⠈⠈⢿⡞⣎⢣⣌⠻⣷⣤⣤
⢶⣯⣽⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢿⣾⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠁⢍⢃⡀⠀⠀⠀⠀⠈⠠⣌⢤⡀⢤⣤
⠿⢻⣿⣤⣟⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢙⠈⠭⠛⠟⡀⠀⠀⠀⠀⠀⠀⠘⢢⡈⠓⢁⣾⣿⣷⣤⡀⠀⠈⠢⠻⣦⠙
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢦⢨⣡⡄⠀⠀⢀⡀⠀⠀⠀⠀⠰⢶⣦⡘⠚⢧⢶⣶⢰⣶⣄⠀⠀⠈⠒
⠀⠀⠀⠀⠠⡾⣿⣾⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢧⡻⣿⡄⠁⠸⠇⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠻⣷⢾⣯⡽⠦⠦⠀⠀
⠀⣀⣤⣀⣀⣀⣼⣾⣭⡦⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢧⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠠⡈⠐⣶⣶⣶⢒⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣤⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠂⠛⠉
⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢁⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⢿⣿⣏⣃⠙⠐⠀⠀⠀⠀⠀
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡒⣻⣟⣢⠈⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡏⠀⠀⠀
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⢭⣭⣭⡭⢽⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⠈⣳⠀⠀⠠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⡗⠠⣽⣿⣿⣿⣷⢶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠸⣿⣿⠈⠙⠛⠿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀
⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⣭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡄⠀⢀
⠀⣒⢛⠀⠀⠀⣴⡶⢶⠶⢢⢒⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣽⣿⢸⣷⣶⣌⡳⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣸
⠒⠂⠃⠁⠁⠒⠀⠉⠈⠉⠙⠉⢘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⠳⠤⠁⠉⠿⡏⢸⢿⣿⣿⣝⡳⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠃⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠂⢡⡀⠠⠄⠀⠀⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠁⠻⢘⣿⣿⡟⣶⣂⣝⡢⣙⠻⣿⣿⣿⣿⣧⣈⡁⠀⠀⠀⠀⠸⠿
⡄⢰⡀⠄⡆⠀⠈⠀⠀⣀⡐⢂⣀⠀⠀⢻⣿⣿⣿⣿⣀⣀⣠⣤⣤⣤⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⢀⡘⣐⡀⠀⡀⠂⣂⣀⠙⠙⣻⣾⣿⣿⣻⣪⣳⣌⡻⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀
⠁⠋⣓⠆⡘⠀⠠⢍⣾⡿⠟⣫⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⠐⠼⡾⣿⣾⡇⢘⣽⢈⠛⢿⣷⣦⡈⠙⠻⣛⣿⣟⣿⣿⣿⢮⡻⣿⣿⣿⣿⣿⣿⣿⣏⠁
⠜⠉⠴⢖⣪⡷⠆⡉⣁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠨⣿⣿⣿⠀⢸⣧⣟⣼⣦⡙⠻⣿⣶⡄⠈⠙⠿⣳⣽⣯⣝⢙⢌⠙⢯⣉⣩⡏⠉⠉⠓
⠤⠒⠋⠉⢡⣶⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⢹⡙⡏⠀⢨⡝⠹⡟⠀⢻⣦⡈⠻⣿⣿⣦⠀⠈⠉⠡⣿⢺⡶⠿⠆⠻⠿⣿⡿⠿⠒
⠀⢐⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠳⡥⠀⢸⢻⢰⡍⠀⠈⠉⠳⢦⡀⠙⢾⣘⡇⠄⠀⠈⠈⢽⡆⢮⡳⣌⠻⣿⣦⣤
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⢸⣮⣼⣿⡀⠀⠀⠀⠀⠈⢠⡈⠑⡁⢪⡿⠄⢀⠀⠀⠈⠩⣍⢡⡈⠡⣄
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⡄⢿⠽⢉⠇⠀⠀⠀⠀⠀⠀⠀⢠⣀⠑⣿⡶⢨⣷⣦⡀⠀⠈⠑⠽⣦⡘
⠀⠉⠳⠙⠛⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣼⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢡⡈⡳⣁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢾⣦⡀⠠⢶⣠⣶⡆⣶⣄⠀⠀⠈⠑
⠀⠀⠀⠀⠰⣾⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⡹⣿⣆⠀⠀⢻⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠹⣾⣸⣿⣻⣧⡢⣄⠀
⠀⢀⣠⠀⠠⣄⣼⣾⣼⣷⡿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢷⡹⣿⣯⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣍⡀⠀⣌⠀⢶⣶⣶⡶⡄⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣄⣀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⢾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠌⠃⠛⠉
⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⢁⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⢟⣿⣯⣃⠉⠘⠀⠀⠀⠀⠀
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡒⣻⣟⣢⠈⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡏⠀⠀⠀
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣩⠉⠉⢭⣭⣭⡭⠩⡭⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⢀⣵⡀⠀⠠⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⡗⠠⣽⣿⣿⣿⣷⡶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠸⣿⣿⠈⠙⠛⠿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀
⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⣭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⡆⠀⠀
⠀⣒⢛⠀⠀⠀⣴⡶⢶⠶⢢⢒⢐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣽⣿⢸⣷⣶⣌⡳⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⣸
⠒⠂⠃⠁⠁⠒⠀⠉⠈⠁⠙⠉⢘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⠳⠤⠁⠉⠿⡏⢸⢿⣿⣿⣝⡳⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠂⢡⡀⠠⠄⠀⠀⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠁⠻⢘⣿⣿⡟⣶⣂⣝⡢⣙⠻⣿⣿⣿⣿⣧⣈⡁⠀⠀⠀⠀⠸⠿
⡄⢰⡀⠄⡆⠀⠈⠀⠀⣀⡒⢂⣀⠀⠀⢻⣿⣿⣿⣿⣀⣀⣠⣤⣤⣤⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⢀⡘⣐⡀⠀⡀⠂⣂⣀⠙⠛⣻⣾⣿⣿⣻⣪⣳⣌⡻⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀
⠁⠋⣓⠆⡘⠀⠠⢍⣾⡿⠟⣫⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⠐⠼⡾⣿⣾⡇⢘⡽⢈⠛⢿⣷⣦⡈⠙⠻⣛⣿⣟⣿⣿⣿⢮⡻⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠜⠉⠴⢖⣪⡷⠆⡉⣁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠨⣿⣿⣿⠀⢸⣧⣟⣼⣦⡙⠻⣿⣶⡄⠈⠙⠿⣳⣽⣯⣝⠙⢌⠙⢯⣉⣩⣏⠉⠙⠓
⠤⠒⠋⠉⢡⣶⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⢹⡙⡏⠀⢨⡝⠹⡟⠀⢻⣦⡈⡻⣿⣿⣦⠀⠈⠉⠡⣿⢺⡶⠻⠆⠻⠿⣿⡿⠿⠒
⠀⢐⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠳⡥⠀⢸⢻⢰⡍⠀⠀⠉⠳⢦⡀⠙⢿⣘⡗⠄⠀⠈⠘⢽⡆⣮⡳⣌⠻⣿⣦⣤
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⢸⣮⣼⣿⡀⠀⠀⠀⠀⠈⢠⡈⠑⡁⢪⡿⠄⢀⠀⠀⠈⠩⣍⢡⡈⠡⣄
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⡄⢿⠿⢉⠇⡀⠀⠀⠀⠀⠀⠀⢠⣀⠙⣿⡶⢨⣷⣦⡀⠀⠈⠑⠽⣦⡘
⠀⠉⠉⠋⠛⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣼⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢡⡈⡳⣁⠀⢀⠁⠀⠀⠀⠀⠀⠀⢾⣦⡀⠠⢶⣠⣶⡆⣶⣄⠀⠀⠈⠑
⠀⠀⠀⠀⠰⣾⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⡹⣿⣆⠀⠀⢻⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠹⣾⣸⣿⣻⣧⡢⣄⠀
⠀⢀⣠⠀⠠⣄⣼⣾⣼⣷⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢷⡹⣿⣯⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣍⡀⠀⣌⠀⢶⣶⣶⡶⡄⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣤⣀⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡖⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠁⠛⠉
⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠛⠛⠛⢛⣻⣏⣉⠉⠉⠀⠀⠀⠀⠀
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠚⣿⢓⡄⢸⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡏⠀⠀⠀
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⢩⣭⣭⠭⡭⠭⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠗⢠⣽⣿⣿⣷⠖⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠠⣿⣿⡏⠙⠻⠿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀
⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⣿⣭⣭⣭⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠄⠀⠀
⠐⡚⡃⠀⠀⢠⣴⡶⡶⠖⣂⡂⡢⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⣠⣞⣽⡿⣿⣿⣿⣽⣿⢰⣷⣶⣌⡲⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢠
⠖⠉⠛⠈⠀⠂⠈⠉⠨⠘⠘⠁⢋⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠸⡿⠿⠛⠳⢠⠙⠉⢙⠙⢸⣿⣿⣿⣝⡳⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⠃⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠚⠈⡀⠀⢃⠈⠀⢸⣟⣿⣿⣿⣿⣷⠀⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠸⢛⣻⣿⡻⢱⣂⣽⡢⣙⠻⣿⣿⣿⣿⣧⣈⠉⠀⠀⠀⠀⠠⠿
⠄⢄⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣀⣀⣀⣠⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⢀⡀⣒⢓⡐⠀⠀⠀⣦⢀⠙⠛⣛⣿⣟⣿⣿⣪⣳⣌⡻⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀
⠸⠛⡢⠂⠃⠰⡬⣛⣾⡿⠟⣋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡰⠨⣘⣿⣾⡇⠀⣯⠈⠻⢿⣿⣦⡈⠙⠻⣿⣿⣿⣿⣿⣟⢮⡙⢿⣿⣿⣿⣿⣿⣿⡟⠉
⠒⠨⠴⢖⣠⡴⠘⠈⢥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠠⣿⣿⣽⠀⢀⣿⢸⢃⣦⡙⠻⣿⣷⣄⠈⠙⠿⢟⣬⣿⣗⢙⢦⡙⢛⣛⢛⣟⠋⠋⠁
⠠⠒⠚⠉⢡⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠹⡛⣿⠀⠈⣛⠟⡿⠋⠹⣦⡈⠻⣯⣿⣦⠀⠀⠉⠃⣿⡳⠷⠽⠦⠙⠿⢿⣿⠷⠶
⠀⢐⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⢢⠀⢰⡿⡆⡌⠀⠀⠁⠳⢦⣄⠙⢿⡚⡵⢦⡀⠈⠁⠫⣧⢠⡻⣄⠙⢿⣦⣤
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⠀⠸⣏⣣⠧⡄⠀⠀⠀⠀⠈⢓⣈⠙⣙⠛⢁⡤⠀⠀⠈⠀⠉⢌⠡⣌⠉⣉
⣾⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⠆⢻⢿⣅⢾⠀⠀⠀⠀⠀⠀⠉⠁⢈⠣⠰⣦⣿⡆⢢⣄⠀⠀⠑⠝⢦⡈
⠀⠙⠉⠘⠙⠋⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢂⡈⢾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⡀⠈⠛⠁⣨⣭⣠⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠠⣼⢟⣽⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⡱⣶⣧⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⢿⣆⠀⡙⢯⡅⣯⣟⣷⡰⣄⡀
⠀⠀⣠⡠⢬⣄⣬⣴⣼⣷⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⡘⣿⡆⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠭⠥⠑⠀⠁⢩⣭⣭⣤⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠆⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⡏⠛⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢹⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠘⠉
⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠛⠻⠿⢛⣻⣏⣑⠀⠀⠀⠀⠀⠀⠀
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠚⣿⠧⡀⢹⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇⠀⠀⠀
⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⢩⣭⣭⠭⠭⠭⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠇⠠⣼⣿⣿⣿⠗⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠀⢸⣿⣿⡉⠛⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀
⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠀
⠔⠚⠃⠀⠀⢠⣤⡶⡶⠶⡐⡒⡲⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⣠⡆⣩⡿⢿⣿⣿⣾⣷⢐⣷⣶⣤⡲⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⢀
⠞⠉⠑⠀⠀⠂⠈⠉⠈⠘⠑⠁⠃⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠀⢀⣾⣿⡿⠛⠳⢠⠈⠉⢛⢹⢸⡇⣿⣷⣝⡳⣌⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠌⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⢄⠨⠀⢸⣿⣿⣿⣿⣿⣯⠉⠉⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠸⠻⣻⣟⡻⢱⣢⣽⡢⣉⠻⣿⣿⣿⣿⣷⣈⡉⠀⠀⠀⠀⠀⠿
⠀⡄⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠉⠋⠀⠀⣀⣀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣾⠀⠀⢀⡀⣒⢂⡀⠀⠀⠄⣦⢀⠉⠻⣟⣿⣟⣿⣿⣮⣗⢄⡛⢿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀
⡞⢓⡬⠘⠂⠁⣼⢫⣾⣿⠿⢋⣁⣤⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡰⢨⣹⣽⣺⣟⠀⢞⠀⠻⢿⣿⣦⣀⠉⠻⣿⠿⣿⣿⣿⣝⢦⡙⢿⣿⣿⣿⣿⣿⣿⡟⠉
⠒⠨⠴⠎⣢⡴⠐⠛⢭⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣻⣾⣿⡏⢠⣿⣷⡷⣦⡙⠳⣿⣷⡄⠀⠙⠻⢿⣨⣿⣗⠛⢦⡙⢛⣛⠛⣿⠛⠛⠃
⠠⠔⠚⠋⠡⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠹⡛⣿⠁⠈⣛⠏⣿⠛⠉⢦⣌⠻⣯⣿⣶⡄⠀⠉⠛⣻⡇⠷⢝⢦⠙⠿⢿⣿⠷⠶
⠀⢀⣨⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠱⢸⠀⠀⣿⣇⡌⠀⠀⠀⠲⢦⣄⠙⢾⡃⠧⢢⣀⠀⠁⠋⣷⡤⡙⣦⡘⢿⣦⣄
⣶⡟⣯⣶⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠀⡀⣿⠚⡡⣠⠀⠀⠀⠀⠈⢓⣀⠛⢝⠷⡛⢃⠀⠀⠀⠁⠉⢈⡉⣄⠉⢉
⣽⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠄⢹⠻⣇⢸⡄⠀⠀⠀⠀⠀⠉⠓⠈⠻⡅⢤⣿⣷⡀⢄⠀⠀⠉⠈⢷⣄
⠉⠙⠃⠃⠊⠉⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠸⡀⢲⡦⠄⠁⠀⠀⠀⠀⠀⠀⠀⡄⢠⡀⠈⠻⠍⠁⣨⢠⣤⡀⠀⠀⠉
⠀⠀⠀⠀⠀⣴⣟⣻⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⡔⣶⣶⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣆⠠⡐⢮⣿⣸⠻⢿⣔⣤⡀
⠀⠀⢀⣠⢤⣀⣨⣴⣼⣷⡿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⡜⣿⠅⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢙⣣⡙⢆⠉⠩⣭⣭⣭⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢹⣿⡝⠛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⡻⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣍⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣝⡀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⣷⠷⠛⠒⠉⠋
⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢂⣀⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⠿⡟⡟⣿⠿⡋⠁⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡔⠺⣿⠧⠀⢹⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣨⣼⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣶⣿⣿⣿⠁⠀⠀
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡩⠉⠉⢩⣭⣭⣭⣽⣯⠍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡗⠠⣼⣿⣿⣿⣿⣦⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⣹⣿⣿⠙⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠁⠀⠁⠉⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠔⠚⠂⠀⡀⢠⣤⣴⡶⢶⡐⡒⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⡦⢉⠻⢿⣿⣿⣎⣿⠀⣿⣶⣤⡲⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀
⠞⠉⠁⠀⠀⠀⠁⠈⠉⢒⠓⠁⡃⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⣀⣶⣫⣥⡞⠳⢠⡈⠋⠛⢿⢸⡟⣿⣷⣿⡳⢬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖⠀⠀⣸
⠀⠀⡀⠀⠀⠀⢀⠲⠐⡀⠀⢄⡠⠀⢻⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⡟⠃⠀⠁⠈⠋⠄⠀⠈⠸⠷⣛⣟⡻⢫⣦⣹⡢⣌⠻⣿⣿⣿⣿⣿⣀⡉⠉⠀⠀⠀⠀⠿
⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣤⣤⣤⠀⡐⢀⡀⢀⠒⣀⠀⠀⠄⣦⢀⠉⠻⢟⣿⣟⣿⣿⡮⣗⢤⡙⢿⣿⣿⣿⣿⣷⣶⣄⣀⣀⣀
⠟⢗⡔⠸⠂⠁⣔⢣⣾⣿⠿⣋⣁⣤⣾⣿⣿⣿⣿⣄⣠⣤⣶⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡠⢊⢿⣿⣮⣿⠀⠾⠃⠻⢿⣿⣦⣀⠉⠻⢿⠿⣿⣿⣿⣟⢦⡙⢿⣿⣿⣿⣿⣿⣿⣿⠋
⠔⢨⡤⠄⣢⣄⠂⠛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣾⣿⡏⠀⢸⡇⡿⢠⡙⠳⣿⣷⡤⡀⠙⠿⡿⣝⣿⣟⡛⠢⡙⠛⣛⠛⣻⠛⠛⠓
⠠⠴⠒⠛⢩⣔⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡛⣿⠇⠀⢿⢧⢷⠺⠛⢢⣌⠻⣯⣿⣶⡄⠀⠙⠛⣻⡗⢷⣝⢦⡙⠿⢿⣿⡶⠶
⠀⢀⣦⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠱⡬⡀⠀⣾⣧⡌⠀⠀⠀⠹⢦⣄⠙⢾⡃⠷⢢⣀⠀⠁⠺⣶⡔⣜⢦⡘⢿⣦⣄
⣶⠿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣰⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠁⡀⣿⢸⠀⣀⡀⠀⠀⠀⠈⠓⣄⠛⠟⡷⢞⡗⠀⠀⠀⠁⠙⢋⡛⣂⠉⢉
⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⣄⠹⣿⣇⢨⡇⠀⠀⠀⠀⠀⠙⠳⠌⠻⣵⠀⣟⣷⣆⠀⠀⠀⠉⠊⢳⣄
⠉⠛⠻⢫⠽⠟⢋⣩⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⣿⣧⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠸⡀⢻⣿⡄⢋⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⠁⠹⣍⡉⡁⠁⣤⣀⠀⠀⠉
⠀⠀⠀⠀⠀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡔⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣆⠠⡈⢩⣠⢸⣻⢿⣆⢤⡀
⠀⠀⢀⣠⡔⢁⣴⣤⣼⣷⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⡜⣿⣷⠀⠀⠀⣷⠀⠀⠀⢀⠀⠀⢙⣓⡘⢦⡉⠈⣁⣫⣉⣈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣵⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠂⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⣿⡛⠛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⣻⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣝⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⣿⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⡾⣷⡗⠛⠒⠀⠋
⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣀⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⠿⡟⡟⣿⠿⡋⠈⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡄⠻⣿⡦⠀⢻⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣨⣼⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣶⣿⣿⣿⠁⠀⠀
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠩⠉⠉⢩⣭⣭⡭⢽⣽⠍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⡗⠠⣼⣿⣿⣿⣿⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⠀⠀⣿⣿⡏⠛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠁⠈⠉⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⠀⠀
⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⢙⣿⣿⣿⣿⠀⠀⠀⠀⣛⣿⣛⣟⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠔⠚⠀⠀⡀⢠⣤⣤⡤⢤⡐⢒⠆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣿⡏⠀⠀⠀⠀⣦⢉⠻⢿⣿⣿⣯⣷⡃⣿⣶⣤⡒⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀
⠏⠉⠂⠀⠠⠉⠑⠈⠋⠂⠃⠁⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢀⡀⠁⠈⠳⢦⡀⠉⠛⢿⢨⡿⣿⣷⣿⡳⢬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠦⠁⡄⠠⣀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⣴⣿⣿⡶⠞⠀⠁⢈⠃⠀⠀⠈⠸⡇⣿⣛⡻⢯⣦⣩⡲⣌⠻⣿⣿⣿⣿⣿⣈⡉⠀⠀⠀⠀⠀⠾
⢠⠀⡀⢠⠀⠀⠀⠀⠈⠉⠤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⣀⣀⠀⢙⣿⠋⡀⢀⡀⠀⠒⠀⠄⠀⠀⠤⢄⠉⠋⢿⣷⣟⣿⡿⣾⣕⢤⡙⢿⣿⣿⣿⣿⣷⣶⣦⣀⣀⡀
⠿⢧⡂⠸⠄⡄⡰⢧⣾⣿⠾⡛⣁⣤⣾⣿⣿⣿⣿⡟⠛⢁⣤⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡠⢊⣷⣿⣧⣿⡂⢰⠇⡻⢿⣿⣦⣄⠉⠻⠿⠷⣿⣿⣿⣟⣶⡝⢿⣿⣿⣿⣿⣿⣿⣿⠋
⠄⣫⣤⠄⣢⡄⠎⠛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⣺⣾⣟⡏⠁⢴⣿⣶⣤⡙⠻⣿⣷⡤⡀⠙⠻⢿⢟⣻⣛⡟⠶⡙⠻⡛⠛⢻⠛⠛⠓
⡠⠴⠒⠛⣉⣔⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⡛⢿⡇⠀⠸⢿⢻⡘⠟⠲⣌⠙⢯⣿⣶⣄⠀⠙⠻⢫⣷⢵⣭⢶⡌⠿⣿⣿⡶⠶
⠀⠀⣢⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡨⡁⠀⢸⣷⢀⠁⠀⠀⠹⣥⣄⠙⢾⡣⢶⣦⣀⠀⠉⠰⢲⣄⣔⢦⡀⢿⣦⣄
⣴⣿⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣦⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠑⠃⠀⣾⣩⠇⡀⡀⠀⠀⠀⠉⠓⣄⠙⠯⡷⢟⣷⡆⠀⠀⠉⠙⢓⡛⣂⠙⢛
⣷⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⠸⣷⣆⠩⣧⠀⠀⠀⠀⠀⠙⠳⣄⠙⢕⢶⠀⣶⣦⡀⠀⠀⠉⠪⠳⣆
⠉⠋⢈⠉⠟⠙⠏⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⠀⢉⣿⣓⠙⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠉⠘⢏⠉⣉⡀⢠⣀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⡄⣝⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢦⠠⡀⠈⠛⠁⡘⣿⣧⢢⣀
⠀⠀⠀⣠⡴⢁⣼⣤⣼⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⡌⢿⣷⡀⠀⠀⢰⡄⠀⠀⢀⠀⠀⠘⣳⡘⢦⡈⠛⣛⣒⣛⣃⡉
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣶⣮⣢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⣏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡛⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣝⡂⠀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⣳⢷⠛⠒⠀⠉
⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⠿⡟⡟⣿⠿⡋⠁⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣴⣾⢿⣿⡀⢹⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣨⣼⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣾⣿⣿⠁⠀⠀
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⡍⠉⣩⣭⣭⡭⠭⢽⠽⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⣨⡄⠀⠀⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡗⠀⣼⣿⣿⣿⣿⣷⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⢸⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠉⠉⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠀⠈⡿⣿⣿⣿⣿⠀⠀⠀⠀⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⠀
⠐⠒⠀⢀⠀⡤⣤⣤⠤⢤⣐⢒⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢹⣿⣿⡟⠀⠀⠀⠀⣦⢉⠹⢿⣿⣿⣯⣷⡆⣾⣶⣤⡒⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀
⠍⠏⠀⠀⠠⠉⠓⠈⠃⠂⠂⠘⡂⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠁⠀⡳⣦⣁⠉⠛⠻⠇⣿⢹⣿⣿⣳⢮⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠆⠂⠀⠀⣈⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣄⣠⡄⡐⠀⠈⠐⠀⠫⠀⠀⠀⠀⠟⢿⣛⣻⡟⡥⣍⣳⣌⡛⢿⣿⣿⣿⣿⣍⠉⠉⠀⠀⠀⠀⠸
⡀⠈⠃⡄⠀⠐⠀⠀⠨⠠⠤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣤⡀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⢨⣿⣿⣿⣿⡇⠀⠀⠀⠰⠰⠧⠀⠀⠀⠠⠄⠈⠻⠽⢶⣽⣿⣿⢶⢝⢦⡙⢿⣿⣿⣿⣿⣶⣶⣤⣀⣀⡀
⠿⣄⠄⠷⠀⢂⡶⣦⣾⣷⠾⢛⣁⣠⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣈⣿⣿⣿⣿⣷⡀⡄⡋⣿⣷⣺⡧⠀⡴⡘⢿⣿⣦⣄⠉⠻⢿⣿⣿⡿⣿⣿⡷⣍⠻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⣩⣔⠦⣀⡨⠼⠛⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣹⣯⣿⣿⠃⢰⣶⣏⣦⢉⠻⣿⣷⡦⡀⠉⠻⢿⡽⣻⣿⡮⠳⣌⠻⠿⠛⠛⡿⠛⠻
⣠⠤⠶⠚⣋⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡿⢿⣿⠀⠘⣿⡟⡏⣼⡷⣄⠛⢿⣲⣶⣄⠀⠈⠛⠟⣿⢎⣮⡳⣌⠻⣿⣿⣶⣦
⠀⠀⣂⣵⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⡌⡃⠀⠂⣶⡅⠀⠁⠀⠈⣥⣄⠙⢿⡿⢸⣢⣄⠀⠉⠃⠶⣤⢀⢲⣄⠹⣷⣄
⣴⡾⣻⣭⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣷⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠞⠀⢸⡟⡃⠀⠀⠀⠀⠀⠉⠻⣦⡙⢾⠲⢽⢷⣦⠀⠀⠉⠋⠓⢙⢓⡈⠛
⣩⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠀⠈⣷⡅⠀⠲⡆⠀⠀⠀⠀⠙⢿⣦⠙⢶⢯⣉⠶⠁⣀⠀⠀⠈⠓⠙⢦
⠉⠋⠁⠁⠈⠞⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡃⠸⣿⣗⡘⡷⠀⠀⠀⠀⠀⠀⠈⡑⠀⠑⠻⡇⠘⢛⣛⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠡⣆⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠐⢌⠈⠳⠿⢸⠇⠀⡀⣄
⠀⠀⠀⣀⣤⢆⣼⣤⣤⣶⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣎⢿⣟⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠌⠳⡀⠈⠉⠀⠘⠓⠙
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣿⣬⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⣿⡟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣏⣭⢩⢹⢫⣝⡍⡍⣯⣽⡀⠀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⣷⣷⠟⠒⠁⠈
⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⠿⡟⡟⣿⠿⡛⠛⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢠⣶⣿⣿⡆⢸⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣨⣽⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣾⣿⣿⠍⠀⠀
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠏⠉⢩⣭⣭⡭⢿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⠀⣼⣿⣿⣿⡿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⢸⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠉⠈⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠛⠏⠀⠀⠀⠀⡿⣿⣿⣿⣿⠀⠀⠀⠀⣛⣛⣛⣛⣛⡛⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠀⠀
⠐⠆⠀⢀⠀⡠⣤⣤⠤⢄⢀⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢹⣿⣿⡿⠀⠀⠀⠀⣶⢍⠹⢿⣿⣿⣭⣳⡆⢾⣶⣤⣒⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀
⠉⠟⠀⠀⠠⠉⠓⠈⡂⠊⠊⠘⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣸⣿⣿⣷⠀⠀⠀⠀⠁⠀⡻⡦⣉⠉⠙⠟⡇⣿⢻⣿⣿⣳⢮⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢂⠀⢀⡀⡁⢹⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣿⣿⣿⣄⣠⡄⠀⠀⠘⠀⠢⠻⠀⠄⠀⠁⢿⢾⣟⣿⡿⣥⢍⣳⢌⡛⢿⣿⣿⣿⣿⣍⡉⠉⠀⠀⠀⠀⢸
⡀⠈⠀⡄⠀⠐⠀⠀⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠰⠅⠀⠀⠀⠀⡄⠈⠛⠽⣷⣽⣿⣿⣷⢝⡦⣙⠿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠳⠔⠀⠦⠐⢂⠴⣠⣶⣶⠶⢒⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⢸⣿⣿⣿⣿⣿⣷⡔⡤⡻⣿⣷⣹⡷⠀⡦⠐⢿⣿⣶⣄⠉⠻⢿⣿⣿⣿⣿⣯⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⣈⣐⠨⣀⢨⠰⠛⢩⣴⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣿⣶⠦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣱⣯⣿⢿⢻⢀⢰⡾⣤⣙⠳⣿⣿⣦⡀⠈⠻⢿⡽⣻⣿⡮⠳⢎⠛⠿⠟⠛⣿⠛⠿
⣀⠤⠶⠚⣋⣠⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡿⢻⣿⠋⠸⣿⣗⠏⢻⣷⣄⡛⢯⣲⣶⣄⡀⠈⠛⠿⢿⡆⣮⡳⣄⠙⣿⣿⣷⣶
⠀⠠⣰⣭⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡌⣛⠀⠀⣵⣌⠀⠈⠀⠈⣭⣤⡙⢿⣿⡴⣦⣄⠀⠉⠁⠔⣬⡀⡲⣄⠘⣧⣀
⣴⣾⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢼⠀⠀⣿⠛⠀⠀⠀⠀⠀⠉⠛⣦⡙⢶⡲⣼⢿⣦⠄⠀⠈⠃⠻⠚⠳⣌⠛
⣉⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠂⢿⡄⠀⠦⡆⠀⠀⠀⠀⠙⢿⣦⡘⠶⣯⣭⢷⣷⠤⠀⠀⠈⠑⠝⢧
⠋⠋⠃⠉⠙⠿⠿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢣⠈⣯⣒⠈⢻⠀⠀⠀⠀⠀⠀⠈⠛⠄⠈⠛⣿⡃⠐⣛⡂⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⣆⠙⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⢌⠃⠐⠿⠇⣿⡆⠀⢄
⠀⠀⠀⢀⣤⢄⣬⣤⣤⣶⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣆⢲⡶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⠳⡄⠈⠘⠧⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢔⡀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⡋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡙⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣝⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣿⣄⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⡷⡳⠛⠒⠀⠀
⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⠻⡟⡟⣿⠿⣋⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣴⣾⣿⣆⠈⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣨⣼⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⡇⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣟⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠉⠉⢩⣭⣭⡭⡽⠯⠍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢗⠀⣼⣿⣿⣿⣷⢦⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⢹⣿⡿⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠁⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⡿⣿⣿⣿⣿⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀
⠰⠆⠀⠀⠀⡠⣤⣤⠤⢔⠄⠒⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢼⣿⣿⡿⠀⠀⠀⠀⢶⡍⡹⢿⣿⣿⣯⣳⡖⢰⣶⣤⣒⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠑⠧⠀⠀⠈⠉⠓⠈⠃⠪⠞⠸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⣿⣿⣷⠀⠀⠀⠀⠁⠀⡻⡦⣈⠙⠙⠿⡏⣾⣿⣿⣯⣻⢮⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⢀⡀⡁⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⣠⡄⠀⠐⠀⠀⠂⠹⠁⠀⠀⠁⢿⢸⣿⣿⣿⣣⢌⣓⢬⡙⢿⣿⣿⣿⣿⣅⠉⠉⠀⠀⠀⠀⢠
⠀⠘⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠀⠈⠛⠿⣧⣼⣿⣿⣷⣽⡦⣌⠻⣿⣿⣿⣿⣶⣦⣤⣀⣀⡈
⠀⠠⡠⡦⢐⠀⠴⣠⣶⣶⡶⢖⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠸⣦⡀⣴⣿⣿⣿⣿⣿⣿⣷⡔⡦⣻⣽⣷⣱⣷⠅⢀⠘⢿⣿⣷⣄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢀⣀⠨⣀⢩⠰⠟⣋⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣾⣿⣷⣤⡄⠀⠀⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⢡⣯⣿⣿⡿⠀⣮⣼⢧⡉⠻⣽⣿⣦⣄⠈⠒⢿⣵⠛⣿⠿⠿⢦⠙⠿⠿⠿⢿⠿⠷
⢀⠭⠴⠞⣋⢡⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⡽⢿⣿⡇⠀⢻⣿⠺⠁⣷⣤⡙⢯⣳⣷⣦⡀⠀⠛⠿⢻⣷⣠⣑⣦⡙⢷⣿⣶⣦
⠀⠀⣐⣩⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡌⣻⡀⠀⢨⣍⠀⠀⠉⠉⢩⣤⡙⢿⣿⡧⣷⢤⡀⠈⠀⠨⢭⡈⡱⣄⡘⢿⣄
⣤⣾⣿⣉⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢲⠂⠀⣾⠇⠀⠀⠀⠀⠀⠉⠻⢦⡙⢷⡺⣬⠿⣦⠄⠀⠀⠙⠸⠮⠳⢆⠙
⢀⣴⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢻⡇⠀⠠⢠⠀⠀⠀⠀⠘⢿⣦⡈⠢⣫⣍⢙⣚⣦⣄⠀⠀⠑⠈⠳
⠛⠉⠉⠙⠊⠹⠟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠳⠈⣌⣄⡀⠻⡆⠀⠀⠀⠀⠀⠈⠛⠆⠈⠛⢿⡿⠛⠀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠘⣠⠘⢧⠀⠐⠁⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠙⠀⠸⠏⣾⣿⡄⠀
⠀⠀⠀⢀⣤⣄⣬⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣧⠢⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠱⣆⠀⠀⠷⠏⠻⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣧⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⢻⣿⡍⠙⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡙⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣝⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⣿⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⢳⠳⠛⠒⠀⠀
⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠉⠁⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⠛⡟⡟⣿⠿⣋⠉⠃⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⢀⣤⣷⣆⠈⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣨⣽⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⡇⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⡉⠉⢉⣭⣭⡭⠽⠿⠍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀
⡆⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⢗⠀⣬⣿⣿⣿⣿⢶⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠁⠈⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⠃⠀⠀⠀⠈⡿⣿⣿⣿⣿⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀
⠴⠆⠀⠀⢀⡠⣤⣤⡤⢄⠄⠠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢸⣿⣿⡿⠀⠀⠀⠀⢶⡌⡙⢿⣿⣿⣯⣲⣶⢰⣶⣦⣐⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠒⠣⠀⡀⡈⠉⠓⢐⠢⠸⠘⠸⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣨⣿⣿⣷⠀⠀⠀⠀⠁⠀⠙⡦⣈⠋⠙⠻⠟⢸⣿⣿⣯⣻⢦⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀
⠀⠁⠀⠀⠀⠀⠰⠀⢀⠁⠀⠀⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣄⣠⡄⠀⠀⠀⠈⠂⠙⠁⠀⠀⠀⢿⢹⣿⣿⢿⢧⢬⣓⢦⡙⢿⣿⣿⣿⣿⣅⠉⠉⠀⠀⠀⠀⢀
⠀⠐⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠀⡀⠤⠤⠀⠀⠀⠀⢠⠀⠙⠻⣷⣾⣿⣿⣷⣭⡲⣌⠻⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀
⠀⠀⠰⡆⠐⠠⣴⣠⣶⣶⡶⠖⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⢠⠀⢀⣹⣿⣿⣿⣿⣿⣿⣷⡌⡇⢻⢹⢷⣅⣿⡅⢀⠰⢸⣿⣷⣤⡈⠛⢿⣿⣿⣿⣿⣿⣿⢮⡛⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣀⠈⢀⢩⠲⠟⢋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣷⡶⠄⠀⠀⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠉⣷⣿⣿⡿⠇⡀⣤⣗⣍⠻⣽⣿⣦⣄⠀⠒⠿⣵⡛⢿⠷⢝⢦⡙⠿⠿⠿⢿⠿⠷
⠀⡨⠵⠞⢋⠠⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣿⡇⠀⢿⣿⡿⠿⣸⣦⡙⢯⣷⣷⣦⣀⠀⠙⠿⡟⣷⢰⣝⢦⡙⢳⣾⣷⣦
⠀⠀⢄⣨⣿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣆⠻⡃⠀⢈⣭⠃⠀⠈⠉⠙⣦⡙⢿⣿⢇⡷⣤⡀⠈⠀⠨⢭⣅⠉⢤⡈⢿⣄
⣤⡶⠟⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢮⠆⢠⢸⡿⠀⠀⠀⠀⠀⠉⠛⢦⣌⠷⡾⣯⡿⣷⡤⠀⠀⠙⠚⠮⠻⠦⡙
⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠆⠠⢸⣇⠀⠠⣀⡀⠀⠀⠀⠘⢿⣦⡀⠣⡫⣟⢋⣐⣢⣄⠀⠀⠉⠊⠳
⠞⠋⠋⠉⠘⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠶⡀⢍⣀⠀⠰⣧⠀⠀⠀⠀⠀⠈⠛⠦⠈⠛⢿⡿⠿⠟⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢧⠈⢿⡉⠀⠘⠀⠀⠀⠀⠀⠀⠐⢶⣄⠈⠀⠙⠐⠄⢸⢸⣿⣦⠀
⠀⠀⠀⠀⣠⣤⣨⢄⣤⣶⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢧⠠⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠰⣦⠀⠀⠲⠜⠹⠷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠘⣿⣏⠈⠹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡙⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣝⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣇⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⣗⡓⠛⠒⠀⠀
⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠈⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⣛⡟⡟⣿⠿⣫⡉⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⢀⣠⡄⠘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣨⣼⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣾⣿⣼⣿⣿⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠙⠉⠉⣭⣭⡭⠽⠿⠝⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀
⡄⠀⠀⠀⠀⠀⢀⣆⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢿⠂⢨⣿⣿⣿⣿⢖⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠀⠁⠁⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀
⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠸⠁⠈⡿⣿⣿⣿⣿⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀
⠴⠀⠀⠀⢀⣀⣠⣤⣤⠄⠤⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠀⣉⡸⣿⣿⣿⠀⠀⠀⠀⠰⣌⠙⠿⣿⣿⣯⣴⣶⢰⣶⣦⣔⠲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠒⠀⠀⠀⠚⠈⠁⠲⠠⠹⠁⠻⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⠈⢁⣿⣿⣷⠀⠀⠀⠀⠘⠀⠸⢦⣌⠙⠛⠻⣿⢸⡏⣿⣯⣟⠶⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠓⠀⠀
⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣽⣿⣿⣿⣆⣀⡄⠀⠂⠀⠂⠠⠙⠟⠄⠀⠀⠸⣧⠿⣿⢿⣟⣬⣙⢦⣉⠻⣿⣿⣿⣿⣯⡉⠉⠁⠀⠀⠀⠀
⠀⠲⢀⠀⠀⠀⠀⠀⠋⢀⠀⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠄⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠙⠿⣿⣪⣿⣿⣷⣮⣷⢬⡙⢿⣿⣿⣿⣷⣦⣤⣄⡀⠀
⠀⠀⠈⠀⠤⢀⡄⣠⣤⣤⡤⠔⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⠏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡌⠤⠹⣶⣾⡞⣼⣖⠀⠀⠦⣾⣷⣤⡈⠙⠻⣿⣿⣿⣿⣷⣟⢦⣝⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡓⣼⠿⢛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠛⠿⠏⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠚⣼⣻⣿⣿⡿⢀⢑⣴⢌⠻⣿⣿⣷⣄⡀⠑⠿⣽⣿⠿⡿⣿⠷⣌⠻⠿⠿⠿⡿⠷
⠀⣀⡤⠾⠓⡁⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢟⠿⣿⣿⠀⢸⣺⡿⢾⠇⣦⡙⢿⣷⣿⣶⣄⠀⠐⠻⢿⣷⡆⣬⡲⣌⠳⣾⣧⣤
⠀⠀⢄⣂⣴⡾⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢮⠻⡟⠀⠀⢛⠃⠘⠂⠉⢛⢳⡙⠻⣿⢿⢹⠦⣀⠀⠈⠁⠩⣍⡉⢡⣌⠹⢯
⢠⡴⠿⠋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠎⣭⠀⡄⣿⠀⠀⠀⠀⠀⠁⠻⢷⣌⠳⢼⢭⣻⣷⣤⡀⠀⠈⠓⠱⢝⠷⠌
⠀⢀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢡⠀⠁⣿⠀⠀⢀⠀⠀⠀⠀⠀⠿⣷⣄⠐⠬⣞⣒⣦⣴⣄⡀⠀⠀⠐⠙
⡶⠋⠁⠈⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢠⡄⢩⡃⠀⠘⣼⡇⠀⠀⠀⠀⠈⠛⢦⡀⠈⠻⣾⠿⠿⠿⠷⠤⠀⠀
⠀⠀⠀⠀⠀⠁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⢸⠀⠋⠏⠈⠈⡷⠀⠀⠀⠀⠀⠀⢀⣈⠂⠲⡌⠋⢢⣾⡆⠀⣤⣄
⠀⠀⠀⠀⢀⣤⡜⣤⣠⣴⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢳⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠇⠀⢟⢿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠙⣿⣏⠈⠹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⣿⣿⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⡝⡽⢯⢫⣏⡏⣭⡍⡍⣯⣭⢩⢹⢫⣝⡍⡍⣯⣽⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⢿⣇⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣷⣷⣿⣷⣷⣷⣾⣾⣾⣷⣾⣷⠗⠛⠒⠀⠀
⠀⠀⠀⠀⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠈⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⣛⡟⡟⣿⠿⣻⡛⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⣠⡄⠘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣨⣼⣭⣿⣮⣼⣮⣷⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⣾⣿⣿⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠉⠉⢉⣭⣭⡭⠿⠿⠝⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀
⡄⠀⠀⠀⠀⠀⢀⣤⠀⠀⠸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⠂⢨⣿⣿⣿⣿⡶⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠁⠉⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀
⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠸⠁⠈⡿⣿⣿⣿⣿⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀
⠴⠀⠀⠀⢀⣀⣠⣤⣤⠄⠤⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣉⡸⣿⣿⣿⠀⠀⠀⠀⠰⣌⠙⠿⣿⣿⣯⣴⣶⠰⣶⣦⣔⠲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⢒⠀⠀⠀⠚⠈⠁⠲⠠⠹⠑⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⠈⢁⣿⣿⣷⠂⠀⠀⠀⠘⠀⠸⢦⣌⠙⠛⠻⣿⢸⡏⣿⣯⣟⢶⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣽⣿⣿⣿⣆⣀⡄⠀⠂⠀⠂⠠⠙⠟⠄⠀⠀⠸⣧⢿⣿⢿⣟⣬⣙⠦⣉⠻⣿⣿⣿⣿⣏⠉⠉⠀⠀⠀⠀⠀
⠀⠲⢀⠀⠀⠀⠀⠀⠊⡀⠈⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠄⠀⠀⠀⠄⠠⠀⠀⠀⡄⠀⠙⠟⣿⣪⣿⣿⣷⣮⣷⢤⡙⢿⣿⣿⣿⣷⣦⣤⣄⡀⠀
⠀⠀⠘⠀⠤⢀⡄⣠⣤⣤⡤⠔⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡌⠥⠹⣶⣾⡞⣼⣖⠀⠀⠆⣾⣷⣤⡈⠙⠻⣿⣿⣿⣿⣷⣟⢦⣝⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡓⣼⠿⢛⣍⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠛⠿⠏⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠘⣼⣻⣿⣿⡿⢀⢑⣴⢌⠻⣿⣿⣷⣄⡀⠑⠿⣽⣿⠿⡿⣿⠷⣌⠻⠿⠿⠿⡿⠷
⠀⣀⡤⠾⠓⠁⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢟⠿⣿⣿⠀⢸⣺⡿⢾⠇⣦⡙⢿⣷⣿⣶⣄⠀⠐⠻⢿⣷⡆⣌⡲⣌⠳⣶⣧⣤
⠀⡀⢄⣂⣵⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢮⠻⡟⠀⠀⢛⠃⠘⠐⠉⢛⢳⡙⠻⣿⢿⢹⠦⣄⠀⠈⠁⠩⣍⠉⢡⣌⠹⢯
⢠⣴⠿⠋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠎⣭⠀⡄⣿⠀⠀⠀⠀⠀⠁⠻⢷⣌⠳⢼⢭⣻⣷⣤⡀⠀⠈⠓⠱⢝⠷⠌
⠀⢀⣴⡾⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢡⠀⠁⣿⠀⠀⢀⠀⠀⠀⠀⠀⠿⣷⣄⠘⠬⣞⣒⣦⣴⣄⡀⠀⠀⠐⠙
⡶⠋⠁⠘⢻⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢠⡄⢩⡃⠀⠘⣾⡇⠀⠀⠀⠀⠈⠛⢦⡀⠈⠻⣾⠿⠿⠿⠷⠤⠀⠀
⠀⠀⠀⠀⠀⠋⣀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⢸⠀⠋⠏⠁⠉⡳⠀⠀⠀⠀⠀⠀⢀⣈⠂⠲⡌⠋⢢⣻⡆⠀⣤⣄
⠀⠀⠀⠀⢀⣤⡜⣤⣠⣴⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⠈⠇⠈⢟⢿
⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⢩⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⠕⠂⠀⠀⠀⠀⢀⡀⠀⠀
⠸⣿⣇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⣿⢨⢹⢫⣍⣿⡟⣭⢹⢹⠙⡽⢯⢫⣍⡏⣭⡍⡍⣯⣭⢩⢱⢫⣕⡍⠍⣮⣝⠀⠀
⠀⢿⣿⣅⡈⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣗⣓⣓⠛⠓⠓⠓⠚⠚⠚⠑⠊⠓⠓⠛⠂⠀⠀
⠀⢸⣿⣏⣁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⡟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢖⣶⡖⡖⣦⠶⣲⣶⣶⣶⣶⣆⣉
⣀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⠋⠁⠀⠀⢹⣿⣿⣿⣿⡿⠻⠟⠋⠉⣿⣿⣿⣨⣼⣥⣿⣮⣼⣮⣵⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⣿⣿
⠉⠛⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡀⠀⠀⢠⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣤⣶⣆⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⡏⠋⠋⠀⣤⣿⡿⠿⠿⠖⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⣿⡷⣯⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⠉⠙⢻⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠸⠻⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢤⣉⠻⢿⣿⣷⣶⣶⠶⣶⣶⠄⣤⡄⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠾⡆⠈⡙⠻⢿⢿⡽⣿⢀⠿⠿⣟⠷⣦⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⣀⡀⢈⢀⡈⢠⠀⠐⢿⣶⠀⢈⠁⠃⢸⣿⢸⣿⣿⣮⣍⡳⢦⡈⠛⠻⠟⠉⠉⠉⠁⠉
⣀⣠⣤⡶⠞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠈⢻⡇⢈⠈⠁⠊⠀⡦⠑⠬⡛⠟⠁⠆⣄⠀⠙⠛⣻⠿⣿⠹⣶⡌⠓⢄⡀⠀⠀⠀⠀⠀
⠋⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠙⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⢀⡇⠀⠁⠀⠠⠀⠠⠆⠀⠄⠀⢈⠀⢿⠆⣠⡄⢀⠈⠀⠀⠁⣶⣿⣶⣤⡒⢦⣀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣿⣟⠀⢔⡆⣴⣖⣦⣶⣶⣆⣤⣆⢰⡰⣄⢿⣜⣴⣶⡆⠀⠀⠈⠙⠿⢿⣏⣷⣽⡻⣦
⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⡴⣻⣿⣿⣯⣿⣞⢇⣴⠄⡙⠸⣜⢉⠛⠀⠀⣼⠓⣂⡀⠀⠉⠙⠻⣿⣦
⣿⡤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠓⡛⣫⣿⣻⢵⣿⣷⠀⢾⣿⣶⡉⠛⠂⠀⠈⡙⡇⠛⠛⢀⠀⠀⡀⠀⠉
⣿⣧⢀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣝⢷⣮⣺⣿⠁⠈⠀⠙⠛⠇⣶⠀⠀⢠⡄⠰⣶⣾⡏⠀⢠⠶⣶⣤
⣿⣿⡇⠀⠀⠀⣠⡾⠛⢿⣿⢻⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢮⢻⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⠨⣮⡙⠃⠀⠠⣤⣤⡀
⠈⢿⣷⣀⣴⠟⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢳⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⣤⣀⠁⢤⡁⢀⠀⠙⢷
⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡎⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣓⣌⠉⠀⠙⠀⠀
⠞⠀⢸⣣⡄⠀⠀⠀⢀⣤⡾⠃⣳⣿⣿⠟⠉⢛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡆⠀⠐⢦⡀
⣿⡅⠀⢿⣿⣿⣿⣾⣿⣿⡼⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣘⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣷⣴⠆⠀⠀⠀⠀⠀⢀⡀⠀⠀
⣿⣇⠀⢺⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⣿⢨⢹⢫⣍⣿⡏⣭⢹⢹⠙⡝⢯⢫⣍⡏⡭⡍⡍⣯⣭⢩⢱⢫⣕⡍⠍⣮⣕⠀⠀
⢿⣿⣂⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣿⣒⣼⣾⣾⣷⣿⣷⣓⣓⡋⠓⠓⠓⠚⠚⠚⠑⠊⠓⠓⠛⠂⠀⠀
⢸⣿⣇⢈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⡟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⣶⡖⡖⣶⠶⣲⣶⣶⣶⣖⡄⠀
⣬⣿⣿⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⡟⠁⠀⠀⠈⣿⣿⣿⣿⠟⠛⠉⠉⠉⣿⣿⣿⣨⣼⣥⣿⣮⣼⣮⣵⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⣿⣯
⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢿⣻⣿⣿⣿⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠤⣿⡿⠿⠷⠦⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣷⣷⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠛⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠟⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡈⠻⠿⣿⣷⣶⣶⡶⣶⣦⡆⣤⣤⠀⠤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠱⢶⠈⠙⠛⠿⡿⣪⢻⠇⠽⠵⢟⠳⢦⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⣀⠀⢀⠘⡈⠀⡀⡀⢾⣷⠠⢀⠉⠘⠀⣿⢲⣿⣿⣶⣍⡛⢦⡌⠙⠛⠛⠉⠉⠁⠀⠀
⣀⣠⣤⡶⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠙⠃⠈⠈⠧⢸⠁⢰⠄⠨⡙⠿⠃⠂⢀⡀⠈⠻⠿⠿⣿⠟⡓⣾⣧⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠙⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⢀⣄⠀⠘⢠⠀⠄⠀⠤⠀⢠⠐⠀⡀⢴⡇⠐⣠⡀⠈⠀⠀⠁⠉⣹⣷⣦⣙⠶⢄⡀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⡀⢀⣶⢰⣤⣲⣴⣤⣦⢐⣤⠀⣆⢤⡂⣯⡳⣸⣷⡆⠀⠀⠙⠻⠿⣿⣷⣮⡛⢶
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡄⠀⠀⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡄⢻⡞⢝⢿⠸⣿⣻⣧⢻⣰⣬⠈⢦⢙⡽⢛⠛⠁⠀⠐⠒⠀⠀⠀⠉⠛⢿⣷
⢀⡦⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⡻⠛⣽⣟⡯⣾⣷⡌⢡⣾⣷⡄⠛⢮⡇⠀⠀⠛⠋⠐⠛⠂⠀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣎⢾⣯⡅⣿⠏⠁⠀⠈⠻⠿⡆⣤⡀⠀⢀⡈⠀⣤⣤⢰⡆⠀⢲⣶
⣷⠀⠀⠀⠀⠀⣠⡾⢿⣿⡟⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢷⡹⣷⢻⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠫⢤⡝⠻⡈⠀⠀⢠⣄
⣿⣇⠀⢀⣴⠞⠁⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⡜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠙⠃⠀⠀⠀⠈⠻
⢻⣿⡶⠋⠀⠀⠀⠀⠀⢸⣿⣟⢻⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠄⠙⠁⡙⠒⠀
⠞⢤⣧⠀⠀⠀⠀⠀⢀⣠⡿⠫⣤⣿⣿⡟⠹⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣄⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣇⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢈⣹⣻⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠡⡹⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⣧⠀⠙⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⢨⢹⢪⣍⣿⡏⣭⢹⢹⠙⡝⢯⢫⣍⡏⡭⡍⡍⡯⣭⢩⢱⢨⣕⡍⠍⣮⣅⠀⠀
⣿⣄⡤⢻⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣷⣒⣼⣾⣾⣷⣿⣷⣓⣑⣋⠓⠓⠓⠚⠚⠚⠐⠊⠓⠓⠛⠂⠀⠀
⣿⣇⢀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⡟⣟⢻⡻⢹⡟⠿⠻⣻⣻⢸⡿⢟⣷⡖⡖⣶⠶⣲⣶⣶⣶⣶⢀⠀
⣿⣿⡍⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡿⠁⠀⠀⠀⢹⣿⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣨⣼⣥⣿⣮⣼⣮⣵⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⣿⣮
⠹⣿⣿⢹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⡀⠀⠀⣰⣾⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠛⣿⣿⣿⣿⠃⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⠈⠈⠀⠠⣼⣿⠿⠷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡟⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣀⠛⠿⣿⣷⣶⣶⡶⣦⣶⣤⢠⣤⡀⠠⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠱⢶⠌⠉⠛⠻⣿⢇⡟⡇⠨⣿⠿⡳⢶⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⣀⠁⡀⠀⠸⣷⡆⠀⠉⠁⠂⣾⡆⣿⣿⣷⣬⣙⠶⣄⡉⠛⠛⠉⠉⠉⠀⠀
⣀⣠⣤⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⢻⠀⡀⠉⠀⠉⠀⣄⠢⣙⠲⠟⠰⠀⡀⠀⠛⠿⠿⢿⣿⢓⡀⣬⣆⠄⠀⠀⠀⠀⠀
⠋⠉⠀⠀⠘⣿⣯⣽⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⡎⠀⠘⠀⠀⣄⠀⢨⡀⠀⡄⠂⡀⠠⣯⢠⡆⢀⠀⠁⠁⠸⠀⠘⢻⣦⣄⠰⢤⡀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣗⡀⢠⣶⠠⣤⣴⣴⣦⣴⡄⣄⡄⣰⡄⠘⢰⣿⠷⣰⣦⡄⠀⠀⠘⠿⣯⡽⣶⣝⠳
⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣄⠹⣧⠟⢿⡇⢿⣟⣿⡜⣃⣤⡙⢰⡅⠹⣻⠛⢛⠃⠀⠀⠠⠀⠀⠉⠙⠻⢷
⠀⡦⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢞⠿⢛⣾⢿⠫⣿⣮⠛⣣⣶⣬⡈⠶⣜⠆⠀⠀⠘⠛⠉⠰⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢦⢫⣿⣛⢸⡏⠉⠁⠉⠻⠿⣷⡄⣈⠁⠀⠀⠈⠠⣄⡀⢀⠗⡀⠀
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⢾⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢳⡽⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⢛⠃⠀⠀⢖⡁⠘⠃⠉⠈⠁⠀
⠀⠀⠀⢀⣠⠾⠋⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣦⡀⠈⠡⢅⠃⠀⠀⠀
⣧⢀⣴⠟⠁⠀⠀⠀⠸⣿⡷⡿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠤⡀⠀⠀⠲⠄
⣿⡄⠀⠀⠀⠀⠀⠀⠀⣤⡿⠒⣻⣿⣿⡿⠿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠄⠀⠀⠄
⠀⣸⣿⣿⣿⣿⢻⣿⣿⡀⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⡀⣁⣓⣋⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠈⣿⣿⣿⣿⡾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⣽⢨⢹⢪⣍⣯⡏⣭⢹⢹⠙⡝⢯⢫⣍⡏⡭⡍⡍⡮⣭⢩⢡⢨⣕⡍⠅⣮⣅⠀⠀
⠄⠀⢹⣿⣿⣿⣷⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣾⣷⣷⣿⣗⣒⣼⣾⣾⣷⣷⣵⣧⣑⣋⡓⠓⠓⠚⠚⠚⠐⠊⠓⠑⠈⠒⠀⠀
⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡿⢟⣿⡖⡖⣶⠶⣲⣶⣶⣶⣀⠀⠀
⣿⡀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⡏⠉⠉⠉⠉⢻⣿⣿⣨⣼⣥⣿⣮⣼⣮⣵⣭⣾⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⣖⠀
⣿⡏⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣆⠀⠀⢀⣶⣾⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀
⣿⣿⡷⠋⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠃⠀⠈⠻⣿⣿⣿⠇⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣸⡿⠿⠧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡷⠻⢸⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣷⣸⡿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣀⠘⠿⢿⣷⣶⣶⣶⠦⣤⣤⠄⣤⣄⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢿⣿⣫⣼⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇⠀⠁⠉⠶⠄⠉⠛⠿⢿⠷⡝⢻⠀⢭⡯⠟⠶⣬⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠸⣿⣟⣡⣾⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⣷⡆⠀⠈⠁⠀⢸⣷⢸⣿⣷⢮⣉⠳⢤⠉⠉⠉⠉⠉⠉⠀⠀
⢀⣀⣤⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠀⠀⢀⠀⠁⠙⠀⡌⠀⠀⠀⢍⠲⠾⠠⠀⢀⠀⠘⠿⠿⢿⣾⠛⢀⠀⢀⣀⡀⠀⠀⠀⠀
⠛⠉⠁⠘⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣽⠀⠀⠂⡀⢀⠀⠀⣄⠀⠀⡀⢀⠀⣤⠀⣀⡤⠀⠀⠈⠌⢧⡌⠈⠿⢧⡀⢤⣄⠀
⠀⠀⠀⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⣰⡄⣤⡄⣤⣴⣄⣤⠤⠀⠀⣤⡀⠿⢠⡶⣤⢰⣤⣀⠀⠀⠀⢟⣿⣲⣬⡻
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣮⠀⠹⣧⣫⠿⣿⠹⣿⢻⣏⠃⣤⡙⠃⢵⡈⢛⣶⣾⣿⡟⠀⠀⠀⠀⠈⠙⠛⠿
⠀⡠⠀⠀⠀⢸⣿⣿⡷⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡢⠘⣶⠿⡟⣶⡿⡾⡿⣧⡛⠿⢃⣬⡓⠰⢝⠠⡌⠃⠀⠀⠶⠒⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣇⣹⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⢢⡪⣟⣗⠃⡟⠛⠛⠀⠛⠿⣿⣦⡈⠳⠆⠀⠀⠀⢀⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢌⣿⣿⣿⣷⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠳⡝⢿⣷⠁⠀⠀⠀⠀⠀⠈⠉⠁⠷⠄⠀⠀⢀⠢⠘⠂⠂⠊⠁
⠀⠀⠀⠀⣠⡴⠛⢻⣿⢻⢻⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣎⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⠀⠒⠤⠰⠀⠀⠀
⠀⢀⣤⠞⠋⠀⠀⠘⣿⣾⣬⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠈⠓⠂⠂⠀
⡴⠄⠀⠀⠀⠀⠀⠀⢠⣦⡬⠹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀
⣿⣿⣿⣿⡀⣿⣿⣷⠘⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⣀⠉⢝⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⣿⣿⣿⣿⣧⢿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣶⡎⣭⢹⢙⠙⡝⢯⢫⣍⡏⡭⡍⡍⡎⣭⢩⢠⢨⣕⡍⠅⣮⡅⠀⠀
⢻⣿⣿⣿⣿⡼⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣷⣿⣗⣒⣼⣾⣾⣷⣿⣷⣦⣕⣋⣓⡑⠓⠒⠚⠊⠐⠊⠑⠑⠈⠂⠉⠀
⠺⣿⣿⣿⣿⣧⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡗⡖⣶⠶⣲⣶⣶⣦⡀⠀⠀
⠀⢻⣿⣿⣿⣿⣹⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣨⣼⣥⣿⣮⣼⣮⣵⣭⣶⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣿⡗⠀
⠀⠘⣿⣿⣿⣿⡗⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣆⠀⠀⢠⣿⣾⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣯⠀
⠂⠉⢿⣿⣿⣿⣿⣿⣿⣿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠟⠀⠀⠀⠹⠿⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⣿⠿⠧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯
⡦⠦⠸⣿⣿⣿⣿⣟⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠻⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⢁⡸⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡒⠶⠶⠶⠶⠶⠶⠦⢤⡤⣤⢀⣄⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⠈⠁⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠈⠑⠱⠦⡉⠙⠻⢿⣵⢎⡳⡏⢘⣝⣬⠇⣦⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⠃
⢻⣿⣼⠊⠹⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣦⠀⠀⠉⠁⠀⢰⡄⢰⡿⠆⣍⡛⠦⢄⠉⠉⠉⠉⠁⠀⠀
⠘⣿⣷⢼⠗⢻⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⢀⠄⠈⠀⠖⠀⠂⠀⠀⠈⠓⠤⡅⢠⠀⠀⠁⠙⠿⣖⣢⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠾⢻⣿⣶⡶⢺⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣿⡂⠀⠠⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⣀⠀⣀⣀⡀⠀⠁⠀⣦⣀⣠⣠⠀⢴⣦⡀
⠀⠀⣿⣿⡄⢾⢿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢁⠀⡠⣤⠀⣍⢀⡈⣭⢀⣌⢀⡁⢠⠌⠈⢿⣿⣇⣀⣄⠀⠀⠉⠻⠇⠀⠐⠣⣔
⠀⠀⠸⣿⣇⡥⠾⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⡄⡿⣯⣿⢿⢻⢻⣎⠁⡛⠸⢗⡀⢉⠸⣿⠙⠃⢸⣶⣤⠀⠀⠀⠀⠻
⢀⡀⠀⢿⣿⣥⢶⢿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢯⣡⣌⡿⣍⣿⣾⣿⣆⠻⣷⣬⡁⢲⣅⠹⣿⡿⠶⣦⡄⠀⠀⠀⠀⠀
⠈⠀⠀⠘⣿⣷⡴⠸⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⡄⠱⠉⡡⣿⡯⡇⠇⠿⠷⠈⢩⣤⣤⣀⠈⠢⣄⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⢹⣿⡅⠰⢹⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⣎⢻⢶⡅⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⠈⠓⠀⠀⠀⠠⠀⠗⠀
⠀⠀⠀⠀⠈⣿⣷⠀⠈⣿⣿⣿⣿⣻⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢷⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠞⠛⣿⡇⠀⢹⣿⣿⣿⡿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠠⣀⠀
⢀⣤⠌⠀⠀⠀⢸⣤⡀⠀⢼⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⣿⣿⣿⡇⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠀⣀⣀⡀⢊⠙⠿⢿⢿⠿⣻⡿⢿⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⣿⣿⣷⠸⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣶⡎⣭⢹⢹⠙⡍⢯⢪⣍⡏⡭⡍⡍⡎⣭⢨⢠⢨⣕⡄⠅⣮⡅⠀⠀
⣿⣿⣿⣿⡆⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣿⣷⣦⣕⣃⣓⡑⠓⠒⠚⠊⠐⠊⠑⠑⠈⠀⠉⠁
⣿⣿⣿⣿⣧⢹⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡗⡖⣶⠶⣲⣶⣶⡆⠀⠀⠀
⢻⣿⣿⣿⣿⡜⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⡟⠉⠉⠉⠉⢹⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⣖⠀⠀
⠘⣿⣿⣿⣿⣷⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⡀⠀⠀⣰⣷⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠙⢿⣿⣿⣿⣿⣼⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠃⠀⠀⠀⠿⠿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠿⠿⠷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⢸⣿⣿⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠀⣀⣿⣿⣿⣿⣿⣾⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠈⠋⠹⣿⣿⣿⣿⣧⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡐⠲⢶⣶⣶⣶⣤⣤⡤⣤⢤⡄⣀⣀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⡷⠘⠁⢿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠣⢣⢦⣈⠛⠻⢻⣿⡦⡻⢶⠀⣻⣧⣲⢠⣌⡛⠿⣿⣿⣿⣿⣿⣿⡿⠀
⣿⡠⠔⠻⣿⣿⣿⣿⣯⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⣀⡀⠈⠀⠁⠈⢀⣦⠁⣶⠶⠍⡙⠲⠄⠉⠀⠉⠉⠁⠀⠀
⣿⣧⢠⣦⢿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⢠⢀⠀⠀⠀⠰⠀⠐⠀⠀⠈⡃⠤⣤⠀⠀⠀⠉⠈⢹⣆⣠⡝⠅⠨⠁⠀⠀⠀⠀⠀⠀
⣿⣿⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⡃⠀⠀⠀⡀⠅⠀⠘⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠉⠃⢠⣄⣀⣀⣀⠀⢀⣀
⠸⣿⣷⡉⢠⢿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠇⠀⠀⣀⡁⢈⠀⣀⢈⡁⢀⠁⡈⢐⣈⡁⢽⣿⣯⡰⢀⡀⠀⠉⠉⠭⣤⡄⠀⠙
⠀⢻⣿⡇⠈⣸⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣤⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⡀⠘⢿⡇⠿⣿⣻⡾⡟⡟⣷⠉⡐⠫⠰⡢⠉⠛⠃⣿⠻⠅⢰⣤⣀⠀⠀⠀⠀
⠀⠈⣿⣿⠇⣀⣻⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⡚⣬⣻⣇⢳⣷⣿⣷⡹⣷⣤⡙⠇⣭⡂⢰⣶⣦⣖⣤⣬⡅⠀⠀⠀
⠀⠀⢸⣿⡗⠈⠈⣿⣿⣿⣿⡟⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠄⠙⣕⠛⣨⣿⠻⢛⢝⢷⠬⡛⢛⡀⠈⠙⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⠁⠀⣸⣿⣿⣿⣿⢻⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⠘⢮⠲⣯⡜⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀⠳⢤⡀⠀⠀⠀⠠⠄
⠀⠀⠀⠘⣿⣷⠀⠀⣿⣿⣿⣿⡟⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢳⡝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡍⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠼⣿⡄⠀⠸⣿⣿⣿⣷⢻⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀
⠀⢀⡄⠀⠀⢄⣬⣠⠀⢠⣿⣿⣿⡎⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⡆⢻⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⢀⣀⡀⢘⠛⠻⠟⠻⠿⢿⡿⢿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⣿⣷⠈⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣶⡎⣭⢹⢩⠙⡍⢯⢪⣅⡏⡭⡍⡍⡎⣭⢨⢠⢨⣕⡄⠄⣮⡅⠀⠀
⣿⣿⣿⡄⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣿⣷⣶⣵⣁⣐⡑⠓⠒⠊⠊⠐⠀⠁⠑⠈⠀⠈⠉
⣿⣿⣿⣷⢸⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡗⡖⣶⠶⣲⣶⣦⡄⠀⠀⠀
⣿⣿⣿⣿⡆⣿⣿⣿⡂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⡟⠉⠉⠉⠉⠙⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣮⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣷⢹⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⡀⠀⠀⣐⣶⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡧⠀⠀
⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠟⠀⠀⠈⠸⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡶⠧⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠂⠀
⢸⣿⣿⣿⣿⣷⢻⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶
⠀⣿⣿⣿⣿⣿⡞⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡧⠇
⠈⠻⣿⣿⣿⣿⣷⢻⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠲⣶⣶⣴⣶⣤⣤⣤⣤⡤⣤⢀⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠛⠖⢤⣄⠘⠻⠶⣯⣧⠹⠯⠇⢘⣻⣑⡆⣌⡙⠻⢿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠼⣿⣿⣿⣿⣷⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⡀⠈⠁⠚⠈⠁⡬⡉⠭⣶⠌⡉⠲⠄⠈⠁⠉⠉⠈⠁⠀
⡀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡶⡤⠀⠀⠰⠄⢀⠀⠀⠈⠑⠄⣔⠂⡄⠀⠁⠀⠹⣥⣄⣝⠓⠀⠉⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠂⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡼⣾⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠃⠀⣄⠀⠀⣀⡀⠀⠀
⣿⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⡗⠀⡀⢀⡀⠀⠃⠃⢀⣉⠀⠈⠢⠀⢌⡁⢸⣿⣿⡀⢤⡀⠀⠉⠛⠿⣍⣀⣄⣄
⣿⣿⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⡀⠈⢾⣿⢸⣷⡾⣧⣿⢿⢻⡜⠐⠸⠟⡃⠉⠛⢿⡏⣴⡷⠄⠠⣀⠀⠉⠑⠀
⠿⣿⣧⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⡃⠁⠘⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠳⡎⢎⣻⣿⢼⣼⡝⣷⡌⢷⣄⡈⠳⡄⡢⡀⢭⣤⣀⣀⣉⣉⣀⠀⠀
⠀⢻⣿⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢞⠽⠏⣳⡿⡷⠟⠹⢎⡻⢿⠂⠀⠈⢶⠈⠉⠁⠉⠁⠀⠀⠀⠀
⠀⠘⢿⣷⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⠈⢦⡪⣍⣃⠂⠀⠀⠀⠀⠀⠐⠶⣶⣄⡀⠀⢠⡀⢠⡀⠀⠀⠀
⠀⠀⠸⣿⣇⠀⠀⢿⣿⣿⣿⣿⢿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡧⡈⠳⡔⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣉⡀⠀⠉⠓⠀⠀⠀⠀
⠀⠀⠀⢹⠿⠀⠀⠸⣿⣿⣿⣿⡌⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⡄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⣀⡀⠀⠀⠀⠀
⠀⠀⣀⠀⣤⣄⠀⠀⢠⣤⣾⣿⣧⣸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⡆⢸⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣀⡀⢀⠀⠐⠒⠂⠐⠀⠀⠝⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⣿⣷⠈⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣶⡎⣭⢹⢩⠙⡍⢯⢪⣅⡎⡭⡍⡍⡎⣭⢨⢠⢨⣔⡄⠄⣮⡅⠀⠀
⣿⣿⡆⢻⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣿⣷⣶⣵⣁⣐⡑⠑⠒⠊⠊⠀⠀⠁⠁⠈⠀⠀⠉
⣿⣿⣷⢸⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡟⡖⣶⠶⣲⣶⣦⡀⠀⠀⠀
⣿⣿⣿⡆⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⠉⠉⠉⠉⠉⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣯⣵⣿⣷⣥⣽⣭⣾⣿⣿⣿⡖⠀⠀
⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⢤⣽⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⠀⠀
⣿⣿⣿⣿⡇⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠂⠀⠈⠩⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⢸⡶⠦⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡅⠀
⣿⣿⣿⣿⣿⣸⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢶
⣿⣿⣿⣿⣿⡟⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡽⠑
⢿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⠀⣀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀
⠘⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠙⠱⢠⣀⠒⠲⠶⣶⣲⡜⠯⠍⠀⣻⣏⣦⢬⡙⠻⢿⣿⣿⣿⣿⣿⠀⠀
⠀⣻⣿⣿⣿⣿⣷⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⢀⡈⠉⠐⠃⠁⢠⣉⢩⢥⡌⠉⠐⢠⣈⠁⠉⠉⠉⠀⠀
⠀⠙⣿⣿⣿⣿⣿⡟⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠈⡤⠀⡀⠀⠀⠛⠄⣀⡠⢀⠀⠀⠀⠀⢆⠀⣌⠓⡠⠀⠂⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠂⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⡰⣖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠉⠙⠳⠂⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣿⣿⣿⣿⣿⡿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣽⣾⡿⠀⠀⠀⠀⠀⠐⠐⠀⠐⠂⠀⠂⠆⠀⠑⠀⣿⣿⡖⢄⡀⠀⠈⠛⢛⣛⣀⣀⣀
⡆⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣠⣴⣿⢿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠈⢾⣿⠃⣷⣤⣷⣹⡗⡞⣦⠃⠤⢹⡆⠉⠻⢿⣿⡿⢋⡀⡀⠀⠈⠉⠋⠲
⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣟⢍⠙⠈⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⡄⠀⠳⡥⢯⠿⣿⡏⣇⣷⢹⣤⠰⣄⡀⠓⣅⡀⢌⡁⢌⣁⠨⠀⠀⠀⠀⠀
⣿⣇⠀⠀⠘⣿⣿⣿⣿⣷⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣤⡅⠀⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⡞⠟⣿⠱⣽⣿⣼⠟⣧⡙⢿⡶⠈⠁⢰⣅⠈⠉⠀⠀⠉⠉⠉⠁
⢿⣿⡄⠀⠀⢹⣿⣿⣿⣿⡞⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⢠⡢⡺⠿⠀⠀⠄⠀⠌⠀⠉⠀⣀⣀⠈⠀⠀⠐⠀⢀⡀⠀⠀
⠘⣿⣧⠀⠀⠈⣿⣿⣿⣿⣷⢻⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣳⡀⠳⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⡒⠄⠈⠳⢄⠋⠀⠀
⠀⠹⣿⡆⠀⠀⢹⣿⣿⣿⣿⡎⣻⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠀⢤⣤⣤⣾⣿⡘⠸⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠂⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⡯⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⠀⣀⡀⢀⠀⠀⠐⠒⠒⠆⠂⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣶⡆⣭⢹⢩⠑⡍⢫⢪⣅⡏⡭⡍⠍⡎⣭⢨⢠⢠⣕⡄⠀⣮⡅⠀⠀
⠈⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣾⣷⣶⣵⣆⣐⡑⠒⠒⠊⠊⠐⠀⠁⠁⠈⠀⠀⠀
⡄⢹⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡟⡖⣶⠶⣲⣤⣶⣀⠀⠀⠀
⣧⠘⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠘⣿⣿⠉⠉⠉⠉⠉⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣮⣵⣿⣧⣥⣽⣭⣾⣿⣿⣿⡧⠀⠀
⣿⡆⢹⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣘⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀
⣿⣿⠘⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠒⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣿⣷⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⡇⢹⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⢕
⣿⣿⣿⡘⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡕
⣿⣿⣿⣇⢿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠭⣭⣭⣥⣤⣤⣤⣤⣄⣀⣀⣀⢀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂
⣿⣿⣿⣿⠘⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠘⠷⢄⣉⠛⠿⢿⣿⣟⣇⢻⣦⡍⠸⢿⠠⣌⣉⠻⢿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣇⢿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠈⠉⠋⠼⠐⠂⡈⠒⢋⡡⠙⠳⠂⡌⠉⠈⠉⠉⠁⠀
⣿⣿⣿⣿⣿⣸⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣠⡇⠀⠀⢀⡁⠀⠀⠀⠀⢆⢀⣀⠀⠀⠀⠋⠃⠀⡇⢨⡓⠂⠈⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⢿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⣦⣂⠁⠀⠀⠠⠀⠀⠀⠀⠀⠐⠈⠈⠀⠃⠀⠀⠀⠀⠑⠙⠓⢤⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢷⣍⣿⠀⠀⠀⠀⠄⠀⠄⠄⠀⠠⠀⠀⢠⠀⡐⠆⢰⣶⣶⠄⠀⠀⠀⠘⢒⣒⠀⢀⡂
⢹⣿⣿⣿⣿⣿⣇⢿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⢤⣶⣶⢰⣔⣠⣔⢶⣦⡐⡔⢠⠚⢢⣌⠻⢿⣷⣿⣷⣶⠄⡀⠈⠙⠻⠟
⠀⢿⣿⣿⣿⣿⣿⡼⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣶⣾⣿⡟⢛⠛⠃⢟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠻⡵⡸⡻⣧⣽⡼⡏⣇⢃⡀⠈⠈⠵⢁⡠⠈⠛⠛⠓⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣧⢿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣠⢀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠙⣦⢡⢍⣿⢇⢷⣿⣸⣿⣆⢻⣶⡄⠘⠶⠀⠲⠄⠘⠋⠀⠒⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⡌⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠡⡉⠋⢠⡏⠉⠁⠁⠘⠂⠙⠷⣴⣤⠀⠀⢤⡀⠠⡀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣷⢹⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⠸⣄⢼⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢦⡦⢄⠑⠄⠀⠳⠀⠀
⠀⠀⠀⠘⠿⣿⣿⣿⣿⡆⢿⢹⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢤⣄⣼⣤⣤⣤⠀⠀⢻⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠂⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀
⢸⡏⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⢸⣿⣻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣶⡆⣭⢹⢩⠑⡍⢫⢪⣅⡏⡭⡍⡍⡎⣭⢨⢠⢠⣔⡄⠄⣮⡅⠀⠀
⠈⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣾⣷⣶⣵⣅⣐⡑⠓⠒⠊⠊⠐⠀⠁⠁⠈⠀⠀⠀
⡄⢹⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡟⡖⣶⠶⣲⣴⣶⣆⠀⠀⠀
⣧⠘⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⠉⠉⠉⠉⠉⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣮⣵⣿⣧⣥⣽⣭⣾⣿⣿⣿⣇⠀⠀
⣿⡆⢹⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣘⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⠘⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠒⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡷⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⡇⢹⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣗⢢
⣿⣿⣿⠘⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⡢
⣿⣿⣿⣇⢿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠩⣭⣭⣥⣤⣤⣤⣤⣄⣀⣀⣀⢀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂
⣿⣿⣿⣿⠘⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠘⠗⢄⣉⠛⠿⢿⣿⣟⣇⢻⣦⡅⠸⢿⠠⡌⣉⠻⢿⣿⣿⣿⣿⣿⡁⠀
⣿⣿⣿⣿⣇⢿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠈⠉⠉⠸⠐⠂⣈⠒⠋⣡⠙⠓⠀⠈⠉⠉⠉⠉⠁⠀
⣿⣿⣿⣿⣿⣸⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣤⡇⠀⠀⠀⡁⠀⠀⠀⠀⠆⢀⣀⠀⠀⠀⠛⠃⢂⠀⢠⡗⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⢿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⡀⣆⡀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠐⠈⠈⠀⠁⠀⠀⠀⠀⠑⠙⠃⢤⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣓⣍⣾⠀⠀⠀⠀⠀⠀⠄⠄⠀⠠⠀⠀⢠⠀⡐⠆⢰⣶⣶⠄⠀⠀⠀⠘⢒⣒⠀⠀⡀
⢹⣿⣿⣿⣿⣿⣇⢿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⢤⣶⣶⢰⣔⣠⣔⢶⣦⡐⡔⢠⠚⢢⣌⠻⢿⣷⣿⣷⣶⠄⡀⠈⠙⠻⠟
⠀⢿⣿⣿⣿⣿⣿⡼⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣶⣶⣾⣿⡟⠉⠃⠈⢹⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣷⡄⠀⠳⡵⡸⡻⣧⣽⡼⡏⣇⢃⡀⠈⠈⠵⢁⡠⠈⠛⠛⠓⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣧⢿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⡗⣠⣠⣀⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠙⣦⢡⢍⣿⢇⢷⣿⣸⣿⣆⢻⣶⡄⠘⠶⠀⠲⠀⠘⠋⠀⠒⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⡌⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠡⡉⠋⢠⡏⠉⠁⠁⠘⠂⠙⠷⣴⣤⠀⠀⠤⡀⠀⡀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣷⢹⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡀⠸⣄⢼⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢤⡤⢄⠑⠄⠀⠳⠀⠀
⠀⠀⠀⠘⠿⣿⣿⣿⣿⡆⣿⢹⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣄⣼⣤⣤⣤⠀⠀⢻⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⣀⡀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣷⡆⣭⢹⢩⠑⡍⢫⢪⣅⡏⡭⡍⠅⡎⣭⢨⢠⢨⣔⡄⠀⣮⡅⠀⠀
⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣿⣷⣶⣵⣁⣐⡑⠒⠂⠊⠊⠀⠀⠀⠁⠈⠀⠀⠀
⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡗⡖⣶⠶⣲⣴⣆⢀⠀⠀⠀
⣿⣿⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⣿⣿⠉⠉⠉⠉⠉⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣮⣵⣿⣧⣥⣽⣭⣾⣿⣿⣿⡆⠀⠀
⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀
⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⣦⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⢤⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀
⠹⣟⣿⣿⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠟⠃⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣗⠠
⠈⣻⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀
⡄⢻⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠁⠉⠉⣉⣉⣅⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀
⣧⠸⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠐⠶⡤⡉⠉⠭⣭⣭⣭⢭⡸⣿⣚⠁⣿⡖⣈⡙⠛⠿⣿⣿⣿⣿⣿⡃⠀
⣿⡆⢻⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠓⠀⠀⠀⠙⠛⢁⡎⠑⢀⡉⠜⠚⢑⠻⠆⠀⠉⠈⠉⠉⠁⠀
⣿⣷⠘⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣆⢹⣿⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠀⠀⠀⠀⠐⠔⠣⢤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡘⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠁⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢟⡔⣄⣶⡃⠀⠈⠀⢀⠀⢀⠀⡀⡀⣄⠀⠀⡄⠀⢤⠀⣤⣦⡄⠀⠀⠈⠀⠦⠤⠤⠀⠀
⣿⣿⣿⣧⢹⣿⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⡄⠀⠀⠀⠀⠀⢰⣿⠿⢿⣿⣿⡁⠀⢄⣴⣤⡄⣤⡄⢂⢠⣦⡄⢠⠁⡰⢦⡄⠻⢿⣷⣼⣶⣤⣄⠀⠈⠛⠻⢾
⣿⣿⣿⣿⡈⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣤⣤⣤⣴⢾⠻⠋⠂⠩⡇⠀⠀⠀⠀⠀⣾⣯⣼⢿⣿⣿⣷⡄⠀⠳⡿⡁⡿⣿⡸⣧⢻⡇⡏⠀⠉⠀⠂⣑⠀⠉⠛⠿⠻⠇⠀⠷⠠⠀⠀
⣿⣿⣿⣿⣧⠹⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣆⠀⠙⣶⠱⡘⣻⣿⢸⢇⣷⢸⣷⡀⣤⣈⠃⠢⣕⠄⠈⠒⠶⠀⠤⠤⠀
⣿⣿⣿⣿⣿⡄⢻⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠳⡣⢻⠏⠞⠘⠛⠈⠉⠹⠌⢻⣀⣄⠀⠱⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⠈⣿⢻⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⣿⣽⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠁⣔⢐⠂⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠆⠀⠀⢠⣄⠀⢠⡤
⡿⢿⣿⣿⠿⣿⡆⠈⠈⢻⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠄⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⡁⠀⠀⠂⠀⠀
⠀⢠⣄⣀⣤⣄⣤⠀⠀⠀⣴⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠠⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢨⢹⢫⣍⣿⡆⣭⢹⢩⠑⡍⢫⢪⣅⡌⡭⡍⠅⡎⣭⢨⢠⢠⣔⡄⠀⣮⡀⠀⠀
⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣷⣶⣿⣇⣒⣼⣾⣾⣷⣾⣷⣶⣵⣤⣀⣑⡐⠀⠈⠊⠀⠀⠀⠁⠈⠀⠀⠀
⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⡟⣟⢻⠻⢹⡟⠿⠻⣻⣻⢸⡟⢟⣿⡗⡖⣶⠶⣢⣤⣖⡀⠀⠀⠀
⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⣿⡟⠉⠉⠉⠉⠉⣿⣿⣨⣼⣥⣿⣬⣼⣮⣴⣭⣶⣬⣾⣬⣮⣵⣿⣧⣥⣽⣭⣾⣿⣿⣷⡄⠀⠀
⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡃⠀⠀
⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣦⠀⠀⠠⢿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⣴⠄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠂⠀
⢸⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⢿⣿⣿⡿⠟⠃⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡲⠀
⡌⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠘⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡓⠀
⣿⣿⣿⣇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠉⠉⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠂⠀
⢹⣷⢹⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠶⡨⠉⠉⠭⣭⣭⣭⢭⡁⣷⣛⠃⣸⣷⣀⡉⠛⠿⣿⣿⣿⣿⣿⠀⠀
⠘⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠙⠓⠃⠊⠱⠀⠐⠼⠒⠃⠛⠆⠄⠉⠈⠉⠉⠀⠀
⠀⢿⣿⣿⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠁⠠⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠄⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠘⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⡄⠠⡃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠍⠐⠀⠀⠀⠀⠀⠦⠲⢀⠀⡀⠀⠀⠀⠀⠀
⣿⡄⢿⣿⣿⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠑⣄⣠⡆⠀⢈⠄⠀⡀⠀⠀⡀⠀⢤⠀⠀⢀⠀⠤⡄⢠⣤⣤⠀⠀⠈⠁⠰⠤⠄⠀⠀
⣿⣷⠘⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣦⣴⣾⡄⠀⠀⠀⠀⠀⢰⣿⠿⣿⣿⣿⠃⠀⢀⢠⣤⡄⣠⢀⠤⠀⣤⣤⠀⡀⢨⣤⡄⠺⢿⣿⣦⣒⣢⣄⡀⠀⠐⠺⢷
⣿⣿⡆⢹⣿⣿⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣠⣤⡤⠞⠋⠉⠀⠉⠅⠀⠀⠀⠀⠀⣼⣿⡴⢿⣿⣿⣷⡄⠀⠳⡽⡇⣿⣷⡾⢷⣹⣿⢠⠁⡈⠋⠀⠑⠐⠉⠛⠿⣿⣿⠁⠲⠦⠀⠀
⣿⣿⣿⠀⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣄⠀⠙⣦⠼⠜⠿⣿⡇⡿⢸⡆⣿⣄⢀⣀⠻⠆⣀⠤⡀⠐⢶⠶⠀⠀⠀
⣿⣿⣿⡇⠘⣿⡹⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣪⣿⣿⣿⣿⣿⣧⢀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣞⣿⣿⣆⠀⠈⢳⠻⢡⢿⠃⠃⠛⠃⠛⠻⣆⠙⣥⠀⠀⠉⠨⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⠙⠀⢿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠻⢿⣄⣀⠁⠀⡀⠂⠀⠀
⡿⢿⣿⣿⠇⠀⠀⠀⢿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠔⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣉⠀⠀⠉⠑⠂⠀
⣣⣤⣄⣀⣤⠀⠀⠀⠀⣤⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⡄⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1667

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/02/07/Microsoft_Back_Doors_Exploited_Many_Dead_Products_and_More_Back.shtml
    Gemini version at gemini://gemini.techrights.org/n/2024/02/07/Microsoft_Back_Doors_Exploited_Many_Dead_Products_and_More_Back.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Back Doors Exploited, Many Dead
Products, and More Backlash After Mass Layoffs⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Feb 07, 2024


    * ⚓ The Register UK ☛ Raspberry_Pi_Pico_cracks_BitLocker_in_under_a_minute
      •_The_Register [Ed: BitLocker has back doors [1, 2]]⠀⇛


    * ⚓ Ghacks ☛ Microsoft_Graveyard:_last_honor_for_dead_Microsoft_products_-
      gHacks_Tech_News⠀⇛


           Microsoft Graveyard is an open source website that lists dead
           Microsoft products, including software and hardware, and
           studios.


    * ⚓ Bloomberg ☛ FTC_Dings_Microsoft_Over_Activision_Blizzard_Layoffs_in
      Court⠀⇛


           FTC is appealing decision that allowed deal to close last year


    * ⚓ Engadget ☛ FTC_accuses_Microsoft_of_misrepresenting_its_Activision
      Blizzard_plans_after_layoffs⠀⇛


           The FTC isn't done questioning gaming's biggest acquisition.


    * ⚓ FTC_files_complaint_against_Microsoft_for_recent_Xbox_layoffs⠀⇛


           The regulatory battle over Microsoft's acquisition of
           Activision Blizzard isn't over yet. Per the Verge, the FTC has
           filed a complaint after the Xbox maker laid off 1,900 employees
           in January.


           In its complaint, the FTC claims Microsoft contradicted an
           earlier promise to "maintain a pre-merger status quo." It wants
           the acquisition paused until it completes a proper antitrust
           evaluation.


           By eliminating overlapping positions, Microsoft went back on
           its word. As such, Activision Blizzard isn't actually operating
           independently, making it hard for the FTC to "order effective
           relief" in potential administrative proceedings.


    * ⚓ Half_of_Microsoft's_Recent_Layoffs_Affect_Activision_Blizzard⠀⇛


           While it was not initially clear whether this was a new wave of
           reductions, The Verge's Tom Warren said this is a part of the
           cuts that have already been announced, meaning almost half of
           the aforementioned fired employees were from Activision, while
           Xbox lost 1,000 people.


           Earlier, Microsoft Gaming CEO Phil Spencer addressed the issue,
           saying that Xbox layoffs were "painful choices" needed for
           "long-term success."


           Endless job cuts keep ravaging the industry, with big companies
           like Amazon, Meta, and Embracer firing more and more workers.
           According to Kotaku, over 6,000 positions in the game industry
           were eliminated in the first month of the year only.





                    ䷩ 𝚕𝚒𝚗𝚎 1754

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/02/07/Over_at_Tux_Machines.shtml
    Gemini version at gemini://gemini.techrights.org/n/2024/02/07/Over_at_Tux_Machines.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Over at Tux
Machines...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 07, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Ubuntu:_Newsletter,_Repositories,_and_Microsoft_Spyware⠀⇛


           Some Ubuntu picks


   2. ⚓ IBM_LinuxONE_4_Express_and_Ubuntu_Server_drive_data_centre_performance
      and_economics⠀⇛


           Canonical is pleased to announce that Ubuntu Server is
           optimised and fully supported on IBM LinuxONE 4 Express


      ⚓  New⠀⇛


   3. ⚓ today's_leftovers⠀⇛


           LF, FSF-EEE, and OpenSUSE


   4. ⚓ Android_Leftovers⠀⇛


           Ayaneo reveals details of new Android gaming handheld set to
           rival the Ayn Odin2


   5. ⚓ OS_8_Now_Available_in_Early_Access⠀⇛


           I’m super excited to let you know that OS 8 builds are
           available in Early Access and they are now installable


   6. ⚓ Programming_Leftovers⠀⇛


           Raku and more


   7. ⚓ Best_Linux_Distro_for_Gaming_–_Top_Distros_for_Enhanced_Linux_Gaming
      Experience⠀⇛


           Thanks to the big push made by Valve


   8. ⚓ Open_Hardware/Modding:_Arduino_Uno,_ESP32-S2,_and_3D_Printing⠀⇛


           4 projects or stories


   9. ⚓ Security_Leftovers⠀⇛


           flaws, patches, and more


  10. ⚓ A_Complete_Guide_to_Xubuntu_Default_Apps_and_Their_Purposes⠀⇛


           This is a full list of all Xubuntu default applications


  11. ⚓ Review:_wattOS_R13⠀⇛


           wattOS wattOS is a fast and lightweight desktop Linux
           distribution based on Debian


  12. ⚓ OKdo_ROCK_5_AIO_Edge_Media_Board_with_3_TOPs_NPU_and_Pre-integrated_AI
      Stack⠀⇛


           The board runs on the Debian 10 LTS operating system, providing
           a mature and actively developed software environment


  13. ⚓ European_Events:_Hackaday_Europe_2024_and_FOSDEM_2024⠀⇛


           4 reports/invitationss


  14. ⚓ Red_Hat_/_IBM_Leftovers⠀⇛


           corporate and technical articles from Red Hat


  15. ⚓ GNU/Linux_Applications:_FSearch,_Note_Taking,_and_Lux⠀⇛


           5 new articles about software


  16. ⚓ Audiocasts/Shows:_WordPress_Briefing,_Late_Night_Linux,_Linux_User
      Space,_Destination_Linux,_and_LINUX_Unplugged⠀⇛


           5 new episodes


  17. ⚓ today's_howtos⠀⇛


           many howtos for Tuesday


  18. ⚓ Why_the_future_of_manufacturing_will_rely_on_open_source⠀⇛


           Let’s look at a few examples of how Red Hat is working with our
           ecosystem to put this effort into action


  19. ⚓ Open_Hardware/Modding:_How_I_Also_Hacked_my_Car_and_Raspberry_Pi
      Project⠀⇛


           Some devices and hacking


  20. ⚓ Free,_Libre,_and_Open_Source_Software_and_the_World_Wide_Web⠀⇛


           Web-centric news picks


  21. ⚓ Programming_Leftovers⠀⇛


           many picks for this week


  22. ⚓ Windows_TCO_Leftovers⠀⇛


           3 Windows TCO examples


  23. ⚓ today's_howtos⠀⇛


           morning batch of howtos


  24. ⚓ Android_Leftovers⠀⇛


           Google Maps is now bringing 3D buildings during navigation to
           more Android Auto users


  25. ⚓ Beyond_2038:_Debian_Strengthens_32-Bit_Builds_with_Critical_Patches⠀⇛


           No worries. Your 32-bit packages won't break after 2038 since
           the Debian team already started working on it.


  26. ⚓ IPFire_2.27_-_Core_Update_182_released⠀⇛


           The first update of the year 2024 is out: IPFire 2.27


  27. ⚓ Stable_kernels:_Linux_6.7.4,_Linux_6.6.16,_and_Linux_6.1.77⠀⇛


           I'm announcing the release of the 6.7.4 kernel


  28. ⚓ These_two_old-school_music_players_for_Linux_let_me_fine-tune_my
      listening_experience⠀⇛


           Both Clementine and Qmmp include 10-band EQs


  29. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


      =========================================================================
      The corresponding text-only bulletin for Tuesday contains all the text.


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠈⢰⢿⠁⡿⢩⣽⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⣧⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⡿⡿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1992

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 07/02/2024: Alternative
Protocols and Scammers From Microsoft's
LinkedIn⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 07, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Health
          o Retro
          o Technology_and_Free_Software
                # Internet/Gemini
                # Programming
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ the_clown_show⠀⇛


                       My second grade teacher, Mrs. Cervantes, was an old
                       lady who liked to smoke during breaks. The fact
                       that those breaks would happen in the classroom can
                       tell you more or less how old I am. I remember
                       little about the things I learned during second
                       grade. Most of my school memories are blurred
                       together and there are bad memories here and there.
                       You could say that some things I put away on
                       purpose.


                       As a kid I didn’t have the concept of resentment.
                       That’s something that I wouldn’t think of. Bad
                       things happened and I would be told to man up and
                       that was the end of it, but as an adult, I look
                       back on those moments and realize how messed up the
                       world was around me. I feel cheated and want
                       revenge, impossible now that so many years have
                       passed, even the people who wronged me are not
                       around anymore.


                # ⚓ Supermarket_Nightmare⠀⇛


                       I gathered around with four friends. We were
                       shopping for chocolate and potato chips to spend
                       some time at a park, especially since the weather
                       was great.


                       We pay for our stuff and head to the park.
                       Suddenly, the store's staff stopped one of our
                       friends AFTER we exited the store and paid for our
                       stuff(we got the receipts too). They believe he
                       stole a chocolate bar from the store. We all saw
                       him paying for the chocolate bars so we intervened
                       and they made us go to the back of the supermarket
                       to speak with the manager. They made us wait for
                       half an hour to check the camera recordings.


                       Now here comes the infuriating part. They couldn't
                       find anything, so they settled for showing a
                       recording of two strangers who pocketed some stuff
                       from the supermarket. I don't know how showing
                       completely unrelated individuals serves their point
                       but WHATEVER I guess.


                       But it gets WORSE. After we told them we didn't
                       know those guys, the manager started talking about
                       how our friend was *about to* steal something but
                       got scared out and paid for it at the last minute
                       instead.


                       ????????????????????? We were put away for 30
                       minutes because of some piece of poorly thought-out
                       speculative fiction. It makes even less sense
                       because we have been regulars to the store for the
                       last two years.


                       But It got even WORSE as the manager started
                       yelling at our friend who told them they had no
                       reason to be wasting our time when we didn't steal
                       anything and paid for everything we left the store
                       with. After that, a heated argument broke out and
                       after another 10 minutes of our time wasted we were
                       let go. I got kind of hot and let out a slur to the
                       manager on our way to the park which caused one of
                       the staff to try to charge at us but he was stopped
                       by his colleagues.


                # ⚓ Just_a_Little_Sad_and_Jealous_That_The_World_I_Came_From
                  Was_Gone:_Nikkiana's_vintage_throwback_secret_internet
                  journal,_and_the_Reverberations_of_What_Came_Before⠀⇛


                       I found her site the way I suspect a lot of
                       neocities sites are found: via neocities' browse
                       function. Periodically I go see if there's anything
                       interesting. Go to the site, filter by tag: diary,
                       journal, blog. I look for something that catches my
                       eye. So many of the sites are dead, or garish, or
                       both. I'm not interested in the pixie-puke Win95-
                       ish sites covered with fifty buttons and webrings
                       and little else. Her journal, when I found it, was
                       none of those things. Black and white. It would
                       have been minimal in 1997. It feels even more so
                       now. It's perfect.


                # ⚓ My_Musical_Journey⠀⇛


                       Forewarning: this will be a bit of a long one. So
                       grab a drink, go pee, and get some headphones. This
                       is my history as a musician.


                       There'll be links to samples throughout. All of
                       these are Creative Commons BY-NC-SA 4.0. They're
                       listed in the format [album] - [song] ([year]).


                       I've written a few hundred songs in my life,
                       easily, so I likely missed some things here. Oh
                       well, it's long enough as it is ^_^


                # ⚓ Academiology_0:_On_the_willingness_to_know_the_value_of
                  university⠀⇛


                       A significant part of my writing process involves
                       not actually writing, but rather just allowing
                       myself to be bored. When I do this, I find my mind
                       starts racing, and I get all these ideas that can
                       often be distilled into very terse one-liners.
                       Whenever this happens, I put the respective one-
                       liner in the notes app on my phone, and then one
                       day, that one-liner becomes the title of an article
                       I write.


          o § Health⠀➾


                # ⚓ Flossing_Teeth_Considered_Harmful?⠀⇛


                       I am not 100% convinced yet, but I think flossing
                       teeth can cause more damage than good.


                       While every dental heath professional will tell you
                       to floss, if you think about it, there are
                       problems.


                       Getting rid of remaining food and bacterial
                       accumulations forming on sugary residues on your
                       teeth is a good thing. However, driving it around
                       with a piece of string can just as easily shove it
                       deeper under the gum and make matters worse. There
                       is also a significant possibility of cutting with a
                       bacterial-laden floss.


          o § Retro⠀➾


                # ⚓ 1971_Schwinn_Varsity⠀⇛


                       Last year I bought a 1971 Schwinn Varsity bicycle
                       from my mechanic for 20 USD (143 CNY/1800 RUB).
                       Schwinn seat, tires, original brake cables. That's
                       why he hadn't cut it up or gotten rid of it. It was
                       a bike in search of...me.


                       I'm not much of a mechanic. If I could easily pay
                       or trade for all the fixing on my bicycles, car,
                       motorcycle, old computers, I would. But having a
                       fleet of old stuff you want to actually use means
                       learning to care for it yourself to some degree.


          o § Technology and Free Software⠀➾


                # ⚓ FLENG_as_a_"Plan_B"⠀⇛


                       I like KL1, but KLIC is taking a long time to be
                       put on a software forge; and a lot of the things I
                       think would be a good idea (e.g. kqueue, pthreads)
                       are already in FLENG. So I've been taking a look at
                       the latter again.


                # ⚓ Oh_Boy,_it's_Steam_Next_Fest_-_Day_1⠀⇛


                       It's that time again, Steam Next Fest! Where a good
                       chunk of games put out playable demo for the masses
                       to try out and see if it's something they want to
                       wishlist and wait ever-so-patiently for it to come
                       out!


                       Last Next Fest I paid attention to, Enshrouded
                       really took the audience by storm. I say, it worked
                       pretty well, since I ended up getting the game on
                       Early Access release. I'm also waiting on Deep Rock
                       Galactic: Survivor. That one had their demo out
                       about a week early, but it was available until a
                       good couple weeks after Next Fest was over. That's
                       another one I'm waiting on.


                       After trying a few demos on the PC and wished I had
                       played it on my Deck, I've finally got it in my
                       head to install a bunch of them on the Deck. I'm
                       going to try and put up a batch of quick impression
                       reviews each day for this week on the different
                       demos I'm trying. Keep in mind that, unless I say
                       so, these were tested on the Steam Deck.


                # ⚓ Letter_Score⠀⇛


                       Or how much "weight" does a character in a font
                       have? The stupid, brute force way follows: write
                       each letter to a (cleared) image, and count how
                       many pixels have values. Higher count, higher
                       scoring letter. (ASCII only, Unicode will obviously
                       take longer and may have more bounding box issues.)
                       The count is font specific: a bold font will score
                       different from regular or italic, and some fonts
                       are more chonky than others. The following score
                       list is for a "Doves Type" TTF that I got somewhere
                       on the Internet some time ago.


                # § Internet/Gemini⠀➾


                      # ⚓ Why_all_those_protocols⠀⇛


                             This post was made because someone on BBS
                             made clear that he's done with gopher since
                             gemini exists. Here is my answer to that.


                      # ⚓ Okay!_I'll_answer_your_question,_LinkedIn._Also,
                        Orange_Site!_Orange_Site!_Orange_Site!⠀⇛


                             Today's “you're one of the few experts
                             invited to add this collaborative article”
                             from {^https://www.linked.com/ LinkedIn [1]
                             is “How do you become a senior application
                             developer?” My answer? Stay in a programming
                             job for three years. Boom! You're a senior
                             application developer. I know, I know, that's
                             a big ask these days when everybody is
                             jumping ship every two years. But hey, if you
                             want to be a “senior application developer,”
                             you got to make sacrifices.


                      # ⚓ So_you_want_to_amplify_my_SEO⠀⇛


                             Since you neglected to include a link (in an
                             email sent as HTML (HyperText Markup
                             Language) no less!) it's hard for me judge
                             the value Next Publisher will provide for my
                             site, so I'm going to have to adjust my
                             prices accordingly. My fee for both guest
                             posts and link insertions is $10,000 (US
                             (United States)) per. So if a guest post also
                             includes a link insertion, that would be a
                             total of $20,000 (US). If I'm going to be
                             [DELETED-whoring-DELETED] selling out what
                             Google Page Rank [1] I have, it's going to
                             cost.


                      # ⚓ Solo_Campaign_1_-_Some_preliminary_thoughts⠀⇛


                             I'm tired of constantly thinking, "Oh, I'll
                             start a solo TTRPG campaign and write about
                             it in this gemlog." All I did was think,
                             think, think. Time to do!


                             Of course, this prelim post will be more
                             stream of consciousness. There isn't going to
                             be any meaningful structure, I don't think.
                             Mostly because I'm just jumping into it head
                             first. But, I'll put each section into its
                             own section so it won't be a huge wall of
                             text that jumps all over the place. There
                             will be markers!


                # § Programming⠀➾


                      # ⚓ agrajag_dev_log_5⠀⇛


                             did your boy write the most half-assed,
                             mostly-broken CSS implementation the world
                             has ever seen? yes. does it make it possible
                             to do offline conversion from certain epubs
                             to edf?


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





                    ䷩ 𝚕𝚒𝚗𝚎 2345

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 07/02/2024: Taylor Swift’s Lawyers
Take on 'Stalkers', GOP Pundits to Meet Putin⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Feb 07, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # 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 Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Robert Pfotenhauer ☛ I'm_currently_building_a_webring⠀⇛


                 My little blog is celebrating its six-month anniversary
                 these days and I am very pleased that I am posting quite
                 frequently by my standards, which was not the case with
                 my first blog in 2004. I can't say why, a lot of water
                 has flowed down the Tiber since then. (And by water I
                 also mean beer and by Tiber I also mean my throat).


          o ⚓ Marty Day ☛ Miss_the_old_internet?_These_video_games_do_too.⠀⇛


                 First, I have to adjust my brain for having lived through
                 an age that people have nostalgic fondness for.


          o ⚓ Kev Quirk ☛ Ending_my_Kagi_Search_Subscription⠀⇛


                 I figured 300 searches would be fine, since the 100
                 search free trial lasted me a couple weeks. Turns out
                 that 300 searches a month isn't enough for me, as my
                 quota just ran out, 12 days shy of my monthly renewal.


                 It's interesting that a search who prides itself on being
                 privacy respecting only offers Google and Bing as
                 alternative searches...


          o ⚓ Marcel Kolaja ☛ How_Do_You_Spend_Your_Time?⠀⇛


                 I set myself a time budget. Five or six themes, and an
                 explicit goal for how I should divide my time between
                 these themes. Then, over the long-term (weeks and
                 months), I hold myself accountable to approximately
                 spending my time in the way that I planned. I also, twice
                 a year or so, calibrate with my manager that they agree
                 with this time budget, and adjust accordingly.


          o ⚓ Victor Kropp ☛ My_private_garden⠀⇛


                 This website is very own private garden on the world wide
                 web. Here I express myself, here I can experiment and do
                 whatever I want. I enjoy improving it when I have some
                 free time, it’s like watering plants or removing weeds
                 from the lawn.


                 Here are some enhancements I implemented in the last few
                 months.


          o § Science⠀➾


                # ⚓ Science News ☛ A_rare_3-D_tree_fossil_may_be_the_earliest
                  glimpse_at_a_forest_understory⠀⇛


                       With its fluffed, spiraling top and thin trunk, the
                       Sanfordiacaulis densifolia tree looks like it came
                       straight out of Dr. Seuss’ The Lorax. But this
                       isn’t a truffula come to life. It’s a 3-D rendering
                       of a 350 million-year-old fossil that shows
                       something very few other fossils in the world ever
                       have — both a trunk and the leaves of a tree
                       species from a somewhat fuzzy time period in plant
                       history, researchers report February 2 in Current
                       Biology.


          o § Education⠀➾


                # ⚓ Reason ☛ The_Real_Student_Loan_Crisis_Isn't_From
                  Undergraduate_Degrees⠀⇛


                       The real story is more complicated. It's true that
                       yearly increases in college tuition have long
                       outstripped inflation, rising more than 200 percent
                       since 1980. But the conversation around student
                       loan debt has become seriously miscalibrated: Not
                       only do small, expensive, elite universities
                       command the conversation about tuition costs, but
                       there's a misplaced focus on undergraduate degree
                       programs.


                       Even after decades of tuition hikes, it is still a
                       good time to be a motivated first-time
                       undergraduate student. The average public
                       university tuition bill is less than $10,000 per
                       year, and the most selective universities tend to
                       offer extremely generous financial aid. Despite
                       tuition increases, most undergraduates don't pay
                       full price. In 2020, around half of students at
                       four-year public colleges received federal grants
                       and about half received institutional grants. At
                       private nonprofit colleges, 84 percent received
                       institutional grants; only about 40 percent
                       received federal student loans. The Association of
                       Public and Land-Grant Universities, a membership
                       association of public research universities,
                       estimates that at four-year public colleges, 78
                       percent of undergraduate students graduate with
                       less than $30,000 in debt and 42 percent graduate
                       with no debt at all.


                # ⚓ Quillette ☛ Concordia_University_'Decolonises'
                  Engineering⠀⇛


                       Goodleaf is quite clear about the intent of the new
                       curriculum. It “creates a path where everyone is
                       equal and no worldview is superior.” But as nice as
                       this claim sounds, it simply isn’t true. Not
                       everyone is equal. Some people are more talented
                       musicians than others. Some are more gifted
                       athletes. Some have better mathematical skills.
                       Some are taller. Of course, it is important to
                       treat everyone with equal respect, in spite of the
                       obvious physiological and intellectual inequities
                       that exist between individual human beings. This is
                       a wonderful tenet that stems from the
                       Enlightenment. (I don’t know enough about their
                       cosmogeny to be certain, but I bet that the peoples
                       of the Six Nations Confederacy also recognized that
                       individuals differ in their skills and abilities
                       and therefore probably did not consider everyone to
                       be equal—especially people outside the
                       Confederacy.) Indeed, the very notion Goodleaf
                       espouses—that people should be considered equals,
                       and their differing worldviews should all be
                       granted equal consideration—is uniquely Western. In
                       fact, it could be seen as one of the Western
                       cultural norms that she is supposedly critiquing.


                       And some worldviews are superior to others:
                       especially those that conform to reality, rather
                       than myth. Some people still believe that the Earth
                       is flat, but that view is not consistent with
                       building and launching of satellites that help us
                       predict the weather, guide our travel, and save
                       many lives. A worldview that helps create
                       knowledge, including a better understanding of the
                       realities of being human and of the laws that
                       govern the cosmos, will help produce structures and
                       technologies that improve our lives. A worldview
                       based on myth and superstition, governed by
                       ideological strictures that discourage or punish
                       open questioning will diminish the quality of human
                       existence. Human history has demonstrated this time
                       and again.


          o § Hardware⠀➾


                # ⚓ The Register UK ☛ EU_repair_rights_bill_tells_manufacturers
                  to_fix_up_or_ship_out⠀⇛


                       Negotiations over the bill have been ongoing for a
                       while now - the rules were first proposed in March
                       2022, and the hope is that new requirements will be
                       finalized in 2024.


                       The thinking is that consumers should be better
                       informed about the lifespan and repairability of
                       products before buying them, and there should be
                       measures to boost repair after the legal guarantee
                       period has expired.


                # ⚓ European Parliament ☛ Deal_on_strengthening_consumers’
                  right_to_repair⠀⇛


                       On Thursday, Parliament and Council reached a
                       political agreement on a stronger “right to repair”
                       for consumers. The agreed rules clarify the
                       obligations for manufacturers and encourage
                       consumers to extend a product’s lifecycle through
                       repair.


                # ⚓ European Council ☛ Circular_economy:_Council_and_Parliament
                  strike_provisional_deal_on_the_right_to_repair_directive⠀⇛


                       The provisional agreement applies to all products
                       with repair requirements on EU law, sets an
                       obligation to repair on manufacturers of goods with
                       repair requirements, establishes a European
                       information form providing consumers with key data
                       on the repair service, and unifies the national
                       repair information platforms into a European online
                       platform.


                       With the agreement reached today, Europe makes a
                       clear choice for repair instead of disposal. By
                       Facilitating the repair of defective goods, we not
                       only give a new life to our products, but also
                       create good quality jobs, reduce our waste, limit
                       our dependency on foreign raw materials and protect
                       our environment.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ El País ☛ Elon,_the_monkeys_and_you:_the_atrocity_of_giving
                  up_control_of_our_thoughts⠀⇛


                       I’ve been ruminating on the first since Elon Musk
                       decided to create a company to develop brain chips.
                       I already had a shock when he killed a dozen
                       monkeys that had been implanted with these devices.
                       After that, he asked for human volunteers… and he
                       got them.


                       Through his Twitter account (I refuse to call it
                       “X”), Musk announced that his company had
                       transplanted one of its devices into a human,
                       without giving more technical details other than
                       noting that the subject had survived. We don’t know
                       for sure if the transplant recipient has any
                       disease related to motor skills, but what Musk has
                       promised everyone is that we’ll be able to go on
                       our mobile phones using nothing but our minds.


                       Anyone who has observed how he’s been managing his
                       social media site should have no doubt about what
                       will happen to their identity, ideas and secrets if
                       they decide to put them in the hands of a depraved
                       oligarch.


                # ⚓ The Nation ☛ In_the_US,_Mental_Health_Treatment_Can_Be_a
                  Death_Sentence⠀⇛


                       Perhaps one reason to study such issues is to
                       ensure that someone is paying attention when
                       lawmakers of virtually every political stripe seek
                       to answer a mental health crisis by forcing people
                       into institutionalized treatment. Notably, such
                       “treatment” can increase the odds of accidental
                       death. Allow us to explain.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Tom's Hardware ☛ $10,000_for_a_$3,500_Fashion_Company_Apple
                  Vision_Pro?_Scalpers_mark_up_Apple's_headset,_despite_the
                  fact_that_it's_still_in_stock [Ed: So "demand" for it is
                  being faked already by scalping]⠀⇛


                       Scalpers have taken to eBay and Facebook
                       (Farcebook) Marketplace with Fashion Company Apple
                       Vision Pro, some asking for sky-high premiums. Most
                       may lose money, and it's not the best way to buy.


                # ⚓ [Repeat] Ali Reza Hayati ☛ Apple_(and_other)_VR_headsets
                  are_proprietary_tyrants⠀⇛


                       Tivoized products are injustices to users.
                       Specifically regarding to giant companies such as
                       Apple, they can be very harmful to people. These
                       headsets will track users and violate their
                       privacy. As they use proprietary operating systems,
                       they violate people’s right to operate freely.
                       Software used in them is not libre and people won’t
                       have any control over how they use their computers
                       or how they do their computing.


                # ⚓ The Register UK ☛ Oracle_partner_gets_multimillion_top-up
                  after_Edinburgh_Uni_disaster⠀⇛


                       It appears as though the new system, Oracle ERP
                       Cloud and Oracle HCM Cloud, is taking a bit of time
                       to bed in. In May last year, the university's
                       academic representative body issued a statement of
                       no confidence in the institution over its
                       disastrous enterprise software migration, which
                       left research students and suppliers unpaid.


                # ⚓ Silicon Angle ☛ Meta_will_label_AI-generated_images_across
                  Facebook,_Instagram_and_Threads⠀⇛


                       The development effort is set to focus on two open-
                       source technologies called C2PA and IPTC. They make
                       it possible to equip an image with metadata, or
                       contextual information, that describes when it was
                       created and related details. That contextual
                       information can also be used to flag if the image
                       was generated by an AI tool.


                       According to Meta, its engineers are building
                       classifiers that can detect if an image’s C2PA or
                       IPTC metadata indicates it was created with AI. The
                       company says the classifiers will enable it to spot
                       files generated by a variety of popular image
                       generators. The goal is to “label images from
                       Google, OpenAI, Microsoft, Adobe, Midjourney and
                       Shutterstock as they implement their plans for
                       adding metadata to images created by their tools,”
                       Meta President of Global Affairs Nick Clegg
                       detailed in a blog post.


                # ⚓ The Verge ☛ OpenAI_is_adding_new_watermarks_to_DALL-E_3⠀⇛


                       OpenAI’s image generator DALL-E 3 will add
                       watermarks to image metadata as more companies roll
                       out support for standards from the Coalition for
                       Content Provenance and Authenticity (C2PA).


                # ⚓ 404 Media ☛ Inside_the_Underground_Site_Where_‘Neural
                  Networks’_Churn_Out_Fake_IDs⠀⇛


                       Rather than painstakingly crafting a fake ID by
                       hand—a highly skilled criminal profession that can
                       take years to master—or waiting for a purchased one
                       to arrive in the mail with the risk of
                       interception, OnlyFake lets essentially anyone
                       generate fake IDs in minutes that may seem real
                       enough to bypass various online verification
                       systems. Or at least fool some people.


                # ⚓ The Hill ☛ Facebook,_Instagram_ramping_up_labels_on_AI-
                  generated_images_ahead_of_election⠀⇛


                       For AI-generated or altered images, video or audio
                       that “creates a particularly high risk of
                       materially deceiving the public on a matter of
                       importance,” Meta may add a “more prominent label
                       if appropriate” to provide users with additional
                       information and context, he said.


                # ⚓ 404 Media ☛ AI-Generated_Grandma_Porn_Is_Flooding_the
                  Internet⠀⇛


                       All the videos follow the same format: they have an
                       AI-generated thumbnail of a naked woman or a woman
                       showing cleavage, a title that describes the
                       content, and the video itself consists of an AI
                       voice reading some kind of erotic scene. All the
                       videos feature the exact same female, breathy,
                       monotone voice, which an analysis by the deepfake
                       detection firm Reality_Defender found it was “99%
                       likely manipulated” by AI. The videos are very
                       subtly and eerily animated, with the woman in the
                       thumbnail and the background slightly and eerily
                       shifting across the frame.


                # ⚓ Zimbabwe ☛ These_guys_used_AI_to_impersonate_company
                  executives_(deepfake)_and_stole_US$25.6_million⠀⇛


                       Scammers used digitally recreated versions of the
                       company’s CFO and other employees in a convincing
                       video conference, instructing an employee to
                       transfer funds.


                       My friend, these guys had a video meeting with an
                       employee of the unnamed company where the only real
                       person was that employee. There were multiple
                       deepfakes of other company employees that fooled
                       this particular employee into thinking they were
                       real.


                # ⚓ Futurism ☛ Hackers_Steal_$25_Million_by_Deepfaking_Finance
                  Boss⠀⇛


                       As the South China Morning Post reports, scammers
                       are believed to have used publicly available
                       footage to create deepfake representations of the
                       staff. Some of the fake video calls apparently only
                       had a single human on the line, with the rest being
                       deepfakes created by the hackers.


                       "This time, in a multi-person video conference, it
                       turns out that everyone you see is fake," senior
                       superintendent Baron Chan Shun-ching told the SCMP.


                # ⚓ SCMP ☛ ‘Everyone_looked_real’:_multinational_firm’s_Hong
                  Kong_office_loses_HK$200_million_after_scammers_stage
                  deepfake_video_meeting⠀⇛


                       A multinational company lost HK$200 million
                       (US$25.6 million) in a scam after employees at its
                       Hong Kong branch were fooled by deepfake
                       technology, with one incident involving a digitally
                       recreated version of its chief financial officer
                       ordering money transfers in a video conference
                       call, police said.


                       Everyone present on the video calls except the
                       victim was a fake representation of real people.
                       The scammers applied deepfake technology to turn
                       publicly available video and other footage into
                       convincing versions of the meeting’s participants.


                # ⚓ The Verge ☛ /_A_year_after_debuting_in_private_beta,_the
                  decentralized_Twitter_competitor_is_dropping_its_invite
                  system_and_preparing_to_release_its_underlying_protocol.⠀⇛


                       The app quickly amassed over two million users
                       while in closed beta and became a hot topic of
                       conversation in newsrooms like The Verge’s. Now,
                       the conversation about what comes after the
                       platform-now-called-X has largely shifted to
                       ActivityPub, the decentralized protocol powering
                       Mastodon, a budding ecosystem of other services,
                       and eventually, Meta’s Threads.


                # ⚓ Techdirt ☛ Bluesky_Opens_Up⠀⇛


                       Bluesky is now open to anyone without an invite.
                       And a bunch of other exciting things are coming
                       soon.


                # ⚓ [Old] Cloudbooklet ☛ Bluesky_No-Login_Mode:_View_Profiles
                  and_Posts_Without_Login⠀⇛


                       Bluesky No-Login Mode is a feature that allows you
                       to view profiles and posts on Bluesky without
                       logging in.


                # ⚓ OMG Ubuntu ☛ Open-Source_Social_Network_Bluesky_is_Now_Open
                  to_Everyone [Ed: omgubuntu is openwashing proprietary
                  software and uses a hyphen/dash in "open-source"]⠀⇛


                       Bluesky, the much-hyped open-source alternative to
                       X/Twitter, is now open for all — invites code no
                       longer needed! Launched in the spring of last year,
                       Bluesky is a decentralised social network modelled
                       after early Twitter. You sign up, post, follow
                       people, repost, and generally enjoy seeing content
                       from people you choose in a reverse-chronological
                       feed. And for fans of algorithms, Bluesky has an
                       open marketplace where developers can share custom
                       feeds that users can add, access, and even make
                       their default experience.


                # ⚓ India Times ☛ Meta_to_start_labelling_AI-generated_deepfake
                  images,_hopes_move_will_pressure_industry_to_follow_suit⠀⇛


                       Global social media conglomerate Meta will soon
                       start labelling deep fake or artificial
                       intelligence (AI) generated images posted on
                       Facebook, Instagram, and Threads as ‘Imagined with
                       AI’ to differentiate with from other human-
                       generated content shared on these platforms, the
                       company’s president of global affairs Nick Clegg
                       told ET.


                       The move is likely to put pressure on Meta’s peers
                       in the social media and internet space to come up
                       with respective tools to fight deep fakes on their
                       respective platforms. By labelling images or
                       content generated with the help of AI tools,
                       especially those offered by Meta, the company hopes
                       to give users more information about the content
                       they are interacting with and subsequently sharing,
                       Clegg said at a select media roundtable.


                # ⚓ Modus Create LLC ☛ Evaluating_Retrieval_in_RAGs:_A_Gentle
                  Introduction⠀⇛


                       Updating the knowledge of an LLM can take two
                       forms: fine-tuning, which we will address in a
                       future post, and the ever-present RAG. RAG, short
                       for Retrieval Augmented Generation, has garnered a
                       lot of attention in the GenAI community and for
                       good reasons. You “simply” hook the LLM up to your
                       documents (more on that later), and it can suddenly
                       tackle any question, as long as the answer is
                       somewhere in the documents.


                       [...]


                       In this article, the first of a series on
                       evaluation in LLMs, we will unpack how retrieval
                       impacts the performance of RAG systems, why we need
                       systematic evaluation and what the different
                       schools and frameworks of evaluation are. If you’ve
                       been wondering about evaluating your own RAG system
                       and needed an introduction, look no further.


                # ⚓ 404 Media ☛ ‘Neural_Network’_Fake_ID_Site_Goes_Dark_After
                  404_Media_Investigation⠀⇛


                       OnlyFake, an underground website that lets
                       essentially anyone generate highly convincing
                       photos of fake IDs in minutes, has gone offline.
                       The move comes after 404 Media used the service to
                       create two, highly convincing photos of IDs, and
                       used one of them to successfully step through the
                       identity verification check of a cryptocurrency
                       exchange.


                # ⚓ Vice Media Group ☛ 3_Students_Reveal_Secrets_of_2000-Year-
                  Old_Scroll_In_Breakthrough_Discovery⠀⇛


                       Youssef Nader, Luke Farritor, and Julian Schilliger
                       created a series of machine learning algorithms to
                       digitally unfurl and read 15 panels of a
                       Herculaneum papyrus, revealing ancient reflections
                       on life, food, and music. The papyrus is a part of
                       an ancient library of scrolls in Naples, Italy that
                       was buried when the neighboring volcano Mount
                       Vesuvius erupted in 79 AD. The eruption carbonized
                       the works and made them impossible to open.


                # ⚓ Silicon Angle ☛ AI_helps_scholars_decipher_ancient_scroll
                  buried_by_Vesuvius_eruption⠀⇛


                       The scroll is part of the Herculaneum Papyri, which
                       includes about 1,800 scrolls that were discovered
                       in the 18th century in Villa of the Papyri in
                       Herculaneum, Southern Italy. Most of them were
                       badly charred after being buried by the eruption
                       that famously destroyed the city of Pompeii.


                       The carbonized documents, described as looking like
                       leftover logs in a campfire, are extremely
                       difficult to decipher given that even the slightest
                       touch could turn them to ash. Although some of them
                       have been carefully unfurled, with new technology,
                       it has been possible to unspool them virtually.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Unmitigated Risk ☛ Challenges_in_Digital_Content
                        Authentication_and_the_Persistent_Battle_Against
                        Fakes⠀⇛


                             Efforts have been made for years to detect
                             modified content by enabling content-creation
                             devices, such as cameras, to digitally sign
                             or watermark the content they produce.
                             Significant efforts in this area include the
                             Content Authenticity Initiative and the
                             Coalition for Content Provenance and
                             Authenticity. However, these initiatives face
                             numerous issues, including privacy concerns
                             and fundamental flaws in their operation, as
                             discussed here.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Scoop News Group ☛ State_Department_will_not_issue
                        visas_to_individuals_linked_to_spyware_abuse⠀⇛


                             The State Department will on a case-by-case
                             basis deny visas for individuals seeking to
                             travel to the United States and who have been
                             implicated in the misuse of commercial
                             spyware, Secretary of State Antony Blinken
                             announced Monday. 


                      # ⚓ Quartz ☛ Palantir's_stock_surged_as_AI_demand_drives
                        revenue⠀⇛


                             Karp said that the company’s latest
                             generative AI-driven platform, simply called
                             “AIP” for “artificial intelligence platform,”
                             is bringing new revenue and customers. Data
                             integration used to take weeks and months,
                             but the latest platform can be up and running
                             in as little as a few hours, he boasts.


                      # ⚓ Silicon Angle ☛ Palantir_shares_surge_on_revenue
                        beat,_revised_outlook_driven_by_AI_growth⠀⇛


                             In a letter to shareholders, Palantir Chief
                             Executive Officer Alex Karp said that the
                             company’s expansion and growth had “never
                             been greater” and that “after nearly two
                             decades of investment, we have positioned
                             ourselves as a fundamentally new software
                             business and our results reflect this ongoing
                             transformation.”


                      # ⚓ [Old] El País ☛ Neurotechnology_can_already_read
                        minds:_so_how_do_we_protect_our_thoughts?⠀⇛


                             On account of these and other developments, a
                             group of 25 scientific experts – clinical
                             engineers, psychologists, lawyers,
                             philosophers and representatives of different
                             brain projects from all over the world – met
                             in 2017 at Columbia University, New York, and
                             proposed ethical rules for the use of these
                             neurotechnologies. We believe we are facing a
                             problem that affects human rights, since the
                             brain generates the mind, which defines us as
                             a species. At the end of the day, it is about
                             our essence – our thoughts, perceptions,
                             memories, imagination, emotions and
                             decisions.


                             To protect citizens from the misuse of these
                             technologies, we have proposed a new set of
                             human rights, called “neurorights.” The most
                             urgent of these to establish is the right to
                             the privacy of our thoughts, since the
                             technologies for reading mental activity are
                             more developed than the technologies for
                             manipulating it.


                      # ⚓ India Times ☛ Google_names_and_shames_spyware
                        companies_that_are_‘dangerous’_for_free_speech,
                        elections⠀⇛


                             Google has named a bunch of spyware – a type
                             of surveillance software – and called on
                             countries to do more to curb the sale and
                             misuse of commercial spy tools that have been
                             used to target high-risk users like
                             journalists, human rights defenders,
                             dissidents and opposition party politicians
                             in the past.


                             The company’s Threat Analysis Group (TAG)
                             released a report that details how 40
                             Commercial Surveillance Vendors (CSVs) of
                             varying levels of sophistication and public
                             exposure are developed, sold and deployed
                             spyware.


                      # ⚓ Tech Central (South Africa) ☛ Google_calls_out
                        spyware_firms⠀⇛


                             In a report on Tuesday, Google researchers
                             said that while NSO is better known, there
                             are dozens of smaller firms helping the
                             proliferation of spy technology for malicious
                             uses.


                             The findings by Google are significant
                             because the company has some of the best
                             visibility into hacking campaigns globally,
                             given the vast breadth of its online
                             offerings.


                      # ⚓ Security Week ☛ Millions_of_User_Records_Stolen_From
                        65_Websites_via_SQL_Injection_Attacks⠀⇛


                             Between November and December 2023, a threat
                             actor successfully stole more than two
                             million email addresses and other personal
                             information from at least 65 websites, threat
                             intelligence firm Group-IB reports.


          o § Defence/Aggression⠀➾


                # ⚓ The Register UK ☛ AI_models_just_love_escalating_conflict
                  to_all-out_nuclear_war⠀⇛


                       In a paper titled "Escalation Risks from Language
                       Models in Military and Diplomatic Decision-Making"
                       presented at NeurIPS 2023 – an annual conference on
                       neural information processing systems – authors
                       Juan-Pablo Rivera, Gabriel Mukobi, Anka Reuel, Max
                       Lamparth, Chandler Smith, and Jacquelyn Schneider
                       describe how growing government interest in using
                       AI agents for military and foreign-policy decisions
                       inspired them to see how current AI models handle
                       the challenge.


                       The boffins took five off-the-shelf LLMs – GPT-4,
                       GPT-3.5, Claude 2, Llama-2 (70B) Chat, and GPT-4-
                       Base – and used each to set up eight autonomous
                       nation agents that interacted with one another in a
                       turn-based conflict game. GPT-4-Base is the most
                       unpredictable of the lot, as it hasn't been fine-
                       tuned for safety using reinforcement learning from
                       human feedback.


                # ⚓ Lusaka ZM ☛ Is_China_delaying_Zambia_Debt_Restructuring
                  Deal?_An_Independent_Analysis⠀⇛


                       However, there are two latest stumbling blocks that
                       the public should know about as being responsible
                       the Debt restructuring stalemate, which need to be
                       resolved. The first is the delay in signing the
                       Memorandum of Understanding (Mou) agreed in
                       October,2023 by all Official Creditors. The Zambia
                       government has stated that 98% of them have signed.
                       The second issue is the impasse regarding the
                       rejection by Official Creditors of the proposal by
                       Private Creditors. There is a need to analyse these
                       issues critically in order to establish who is
                       possibly responsible for the delay, and how Zambia
                       should strategise to resolve the issue.


                # ⚓ Tech Central (South Africa) ☛ Fears_of_Red_Sea_attack_on
                  internet_cables⠀⇛


                       Apart from being one of the world’s busiest
                       shipping corridors, the Red Sea is also host to
                       some of the world’s biggest intercontinental subsea
                       cables, including several that run along Africa’s
                       east coast.


                # ⚓ The Guardian UK ☛ Houthis_may_sabotage_western_internet
                  cables_in_Red_Sea,_Yemen_telecoms_firms_warn⠀⇛


                # ⚓ Atlantic Council ☛ No_more_business_as_usual:_The_US_needs
                  a_broader_engagement_strategy_in_West_Africa⠀⇛


                       The Pentagon is reportedly in preliminary talks
                       with the governments of Benin, Ghana, and Côte
                       d’Ivoire about opening a drone base in one of those
                       countries, presumably to compensate for the likely
                       closure of the US drone base in Niger, following a
                       coup there in July 2023. Even though there are
                       contradictory reports about the talks, their
                       possibility underscores an unsettling reality: US
                       influence in the Sahel has waned, and Washington
                       needs to rethink its engagement there and in West
                       Africa as a whole.


                       If left to its own devices, US policy probably
                       would default to a business-as-usual approach in
                       West Africa. Unfortunately, that approach has not
                       worked and is even less likely to work now that the
                       French have been ousted from the region. US
                       rhetoric about governments transitioning to
                       civilian rule often falls on deaf ears, and many
                       people in the region are convinced that Russia is a
                       better partner than the United States was and is
                       likely to be in the future. Worse, it is not clear
                       that they are wrong.


                # ⚓ Gizmodo ☛ TikTok's_Newest_Trend:_Cross_The_Southern_Border
                  With_Me⠀⇛


                       TikTok is allegedly being used by Chinese migrants
                       to cross the United States’ southern border, first
                       reported by 60 Minutes on Sunday. In interviews at
                       the border of the U.S. and Mexico, Chinese migrants
                       said they were able to discover weak points in
                       America’s border wall through TikTok.


                       Videos on TikTok written in Mandarin provided step-
                       by-step instructions for crossing the border and
                       even hiring a smuggler, according to the report.
                       Chinese migrants are the fastest-growing group
                       crossing illegally into the United States from
                       Mexico.


                # ⚓ Vox ☛ Welcome_to_the_“neomedieval_era”⠀⇛


                       The result is that the US now finds itself
                       operating in two strategic eras at the same time.
                       In one, heavily armed industrial militaries fight a
                       catastrophic war over a chunk of Europe (with a
                       potentially even more catastrophic invasion
                       scenario lurking in Asia). And in another, a Yemeni
                       rebel group using rudimentary drone and missile
                       technology shows itself capable of causing a
                       disruption to global supply chains on par with
                       Covid-19.


                       To comprehend this chaotic era — one in which
                       nation-states boast historically destructive
                       firepower but in many ways appear weaker than ever,
                       unable to mobilize their populations around a
                       common call or control their international
                       environment — we need to go beyond the well-worn
                       20th-century analogies. We need to get medieval.


                # ⚓ The Hindu ☛ India_to_fence_entire_border_with_Myanmar⠀⇛


                       The 1,643-km-long India-Myanmar border, which
                       passes through Mizoram, Manipur, Nagaland and
                       Arunachal Pradesh, currently has FMR. It was
                       implemented in 2018 as part of India's Act East
                       policy.


                       Fencing along the border has been a persistent
                       demand of the Imphal Valley-based Meitei groups
                       which have been alleging that tribal militants
                       often enter into India through the porous border.


                # ⚓ ANF News ☛ 85_ISIS_members_arrested_in_Hol_Camp⠀⇛


                       According to the statement, YPJ rescued a Yazidi
                       woman named Kovan Ido Xorto, who had been kidnapped
                       by ISIS gangs 10 years ago.


                # ⚓ ADF ☛ Dismantling_al-Shabaab_Finances_a_Tough_Task_For
                  Somalia⠀⇛


                       More than a dozen bombings in and around Somalia’s
                       capital, Mogadishu, in November and December 2023
                       revealed a clear pattern — telecommunications
                       company Hormuud Telecom was being targeted. Bombs
                       killed at least three employees and destroyed
                       offices, communications towers and vehicles.


                       Analysts believe al-Shabaab has targeted the
                       country’s largest telecommunications provider for
                       refusing to pay “taxes” to the terrorist group.


                # ⚓ The Strategist ☛ China’s_recognition_of_the_Taliban_sets_a
                  dangerous_precedent⠀⇛


                       Prior to the Taliban’s resurgence, China maintained
                       a cooperative relationship with the Afghan
                       government, which included security collaboration
                       against Uyghur militants. Following the Taliban’s
                       takeover, China initiated engagement with the new
                       regime, aiming to prevent terrorism from affecting
                       its regional interests and to secure its
                       investments, including those related to the Belt
                       and Road Initiative.


                       The ethical dimensions of China’s interactions with
                       the Taliban are seemingly complex, even on the
                       surface. On one hand, China’s engagement is driven
                       by security concerns and economic interests,
                       particularly in mining and infrastructure. On the
                       other hand, the Taliban’s lack of international
                       recognition and domestic legitimacy raises
                       questions about the long-term viability of these
                       agreements.


                # ⚓ The Dissenter ☛ 'Terrorism_Enhancement'_Applied_Against_Ex-
                  CIA_Programmer_For_Leaking_Represents_A_Stark_Development⠀⇛


                # ⚓ FAIR ☛ ACTION_ALERT:_Friedman’s_Vermin_Analogies_Echo_Ugly
                  Pro-Genocide_Propaganda⠀⇛


                       New York Times columnist Thomas Friedman had a
                       piece in the Point (2/2/24), an online Times
                       feature the paper describes as “conversations and
                       insights about the moment,” that compared the
                       targets of US bombs to vermin. It’s the sort of
                       metaphor that propagandists have historically used
                       to justify genocide.


                # ⚓ Common Dreams ☛ Let_Us_Pray:_God's_Gullible,_Ugly,_Sad_Army
                  Limps_to_the_Border⠀⇛


                       As GOP House leaders trash as "a stinking pile of
                       crap" a border deal that (unconscionably) gives
                       them most of what they've demanded to "solve" a
                       crisis they in fact have no interest in solving,
                       several dozen witless MAGA nativists - a tad shy of
                       their avowed 700,000 - joined a bedraggled "Take
                       Our Border Back" convoy to the southern border to
                       wave flags, preach hate, hawk merch, get baptized,
                       hear Sarah Palin babble, and decry a migrant
                       "invasion" that, once there, failed to materialize.
                       SAD!


                # ⚓ teleSUR ☛ UN_Security_Council_Convenes_to_Address_Middle
                  East_Tensions⠀⇛


                       The U.S. actions in the region were just the latest
                       in a litany of unlawful and irresponsible
                       attacks, Russian diplomat Nebenzia pointed out.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ Meduza ☛ Russian_court_arrests_exiled_writer_Boris
                        Akunin_in_absentia_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Mobilized_Russian_soldier_given_six_years_in
                        prison_for_desertion,_400_servicemen_present_at
                        sentencing_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia’s_Health_Ministry_approves_two
                        popular_emergency_contraceptives_for_over-the-counter
                        sale_—_Meduza⠀⇛


                      # ⚓ Latvia ☛ Latvia-Belarus_border_point_Silene_to_remain
                        closed⠀⇛


                             Taking into account the need to prevent
                             possible threats to Latvia's internal
                             security, on Tuesday, February 6, the
                             government decided not to reinstate the
                             operation of the Silene border post on the
                             Latvian-Belarusian border.


                      # ⚓ LRT ☛ Lithuania_looks_to_close_2_more_checkpoints_on
                        Belarus_border_quoting_national_security⠀⇛


                             Lithuania’s National Security Commission has
                             proposed closing down two more checkpoints on
                             the Belarusian border and taking steps to
                             reduce travel between the two neighbouring
                             countries.


                      # ⚓ Meduza ☛ Russia_arrests_former_Zelensky_adviser
                        Oleksiy_Arestovych_in_absentia_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_anti-war_presidential_hopeful_Boris
                        Nadezhdin_asks_authorities_for_three_more_days_to
                        review_claims_of_paperwork_errors,_Russia’s_election
                        commission_gives_him_one_more_day_—_Meduza⠀⇛


                      # ⚓ France24 ☛ France_sells_Riviera_chateau_seized_from
                        late_Putin_foe⠀⇛


                             A French Riviera chateau seized from late
                             Russian oligarch Boris Berezovsky has been
                             sold to an undisclosed buyer, according to
                             France's agency for handling confiscated
                             assets.


                      # ⚓ Atlantic Council ☛ Ukraine_opens_new_front_with_drone
                        strikes_on_Russia’s_energy_sector⠀⇛


                             Ukraine is seeking to bring the war home to
                             Russia in 2024 with a new long-range drone
                             strike campaign against Putin's oil and gas
                             industry, writes Mykola Bielieskov.


                      # ⚓ Atlantic Council ☛ Russia’s_Bashkortostan_protests:
                        Separatism_isn’t_the_real_threat_facing_Putin⠀⇛


                             The main risk to the Putin regime is unity
                             and solidarity across regions between
                             Russians protesting shared forms of
                             mistreatment at the hands of the state, write
                             Dylan Myles-Primakoff and Lillian Posner.


                      # ⚓ Meduza ☛ Putin_reportedly_to_address_Russia’s_Federal
                        Assembly_in_late_February_or_early_March_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Former_Fox_News_host_Tucker_Carlson
                        announces_interview_with_Putin_in_Moscow_—_Meduza⠀⇛


                      # ⚓ New York Times ☛ Tucker_Carlson_Says_He_Will_Soon
                        Interview_Putin⠀⇛


                             The Kremlin did not immediately confirm an
                             interview with Mr. Carlson. It would be Mr.
                             Putin’s first formal interview with Western
                             media since the start of his full-scale
                             invasion of Ukraine.


                      # ⚓ The Straits Times ☛ 'Very_good'_deals_worked_on_for
                        Putin's_visit_to_N._Korea_-Russian_envoy⠀⇛


                             February 07, 2024 8:49 AM



                             Russia and North Korea are working on a
                             \"very good\" package of agreements to be
                             signed when President Vladimir Putin visits
                             Pyongyang, Russia's envoy to North Korea told
                             the Russian TASS state news agency in remarks
                             published on Wednesday.


                      # ⚓ RFERL ☛ Wagner_Group_Defector_Reportedly_Granted
                        Temporary_Residence_In_Norway⠀⇛


                             A Russian man who reportedly defected from a
                             high-ranking position in the Wagner Group has
                             been given permission to stay in Norway but
                             was refused permanent asylum, a Norwegian
                             newspaper reported.


                      # ⚓ European Commission ☛ Speech_by_President_von_der
                        Leyen_at_the_European_Parliament_Plenary_on_the_need
                        for_unwavering_EU_support_for_Ukraine,_after_two_years
                        of_Russia's_war_of_aggression_against_Ukraine⠀⇛


                             European Commission Speech Strasbourg, 06 Feb
                             2024 The President of the European
                             Commission, Ursula von der Leyen, delivered a
                             speech at the European Parliament Plenary on
                             the need for unwavering EU support for
                             Ukraine, after two years of Russia's war of
                             aggression against Ukraine.


                      # ⚓ Latvia ☛ Osokin_Freedom_Festival_for_Ukraine_to
                        return_April,_May⠀⇛


                             From April 5 to May 12, the fifth Osokin
                             Freedom Festival will be held in Rīga and
                             elsewhere in Latvia. Since the Russian
                             invasion of Ukraine, it has been dedicated to
                             supporting the Ukrainian army, civilians, and
                             especially Ukrainian children.


                      # ⚓ The Strategist ☛ The_anniversary_of_war_in_Ukraine—10
                        years,_not_two_years⠀⇛


                             In the coming weeks, a flood of analysis can
                             be expected marking the end of the second
                             year of war in Ukraine.


                      # ⚓ JURIST ☛ Russia_accuses_Ukraine_of_attack_on_bakery
                        in_Lysychansk⠀⇛


                             Russian officials accused Ukraine on Saturday
                             of attacking a bakery in a Russian-occupied
                             town, Lysychansk, in eastern Ukraine, killing
                             civilians and several representatives of the
                             Russian occupation authorities. Kremlin
                             spokesman Dmitry Peskov also called the
                             attack a terrorist act against civilian
                             infrastructure.


                      # ⚓ JURIST ☛ Moscow_court_orders_arrest_of_exiled
                        novelist_Boris_Akunin_over_Ukraine_support⠀⇛


                             A Moscow court issued an arrest warrant in
                             absentia on Tuesday for exiled novelist
                             Grigori Chkhartishvili (under pen name Boris
                             Akunin) over his critique of Russia’s war
                             against Ukraine.


                      # ⚓ RFERL ☛ Ukraine's_Parliament_Extends_Martial_Law,
                        Military_Mobilization_By_90_Days⠀⇛


                             Ukraine's parliament, the Verkhovna Rada, on
                             February 6 passed laws to extend martial law
                             and military mobilization for another 90 days
                             as Russia's full-scale invasion nears the
                             two-year mark.


                      # ⚓ RFERL ☛ Moscow_Court_Issues_Arrest_Warrant_For_Former
                        Adviser_To_Ukraine's_Presidential_Office⠀⇛


                             A court in Moscow issued an arrest warrant
                             for the former adviser to Ukraine's
                             presidential office, Oleksiy Arestovych, on
                             February 6, on charges of calling for
                             terrorism and distributing false information
                             about Russian armed forces involved in
                             Moscow’s ongoing invasion of Ukraine.


                      # ⚓ RFERL ☛ Three_Belarusians_On_Trial_Over_Online_Chat
                        Supporting_Ukraine⠀⇛


                             Three men went on trial on February 6 in the
                             Belarusian city of Homel over an online chat
                             in which they supported Ukraine's efforts to
                             stand against Russia's ongoing invasion.


                      # ⚓ RFERL ☛ Romanian_Defense_Minister_Rules_Out
                        Reintroducing_Mandatory_Military_Service⠀⇛


                             Romanian Defense Minister Angel Tilvar has
                             ruled out reintroducing a mandatory military
                             service in Romania amid discussions about
                             measures to better prepare the NATO member
                             country in case Russia's war against Ukraine
                             spreads.


                      # ⚓ RFERL ☛ UN_Nuclear_Chief_Says_Security_Still_Fragile
                        At_Ukraine's_Russian-Occupied_Power_Plant⠀⇛


                             Security at Ukraine's Zaporizhzhya Nuclear
                             Power Plant remains fragile amid worrying
                             recent staff cuts enacted by Russian
                             authorities occupying the facility, which is
                             one of the 10 biggest atomic power plants in
                             the world, the United Nations nuclear
                             watchdog chief said on February 6.


                      # ⚓ RFERL ☛ Russia_Issues_Arrest_Warrant_In_Absentia_For
                        Writer,_War_Critic_Akunin⠀⇛


                             A Moscow court has issued an arrest warrant
                             in absentia for prominent Russian writer
                             Boris Akunin (aka Grigory Chkhartishvili),
                             who has been accused of calling for
                             "terrorism" and disseminating "fake
                             information" about the Russian Army.


                      # ⚓ New Yorker ☛ Was_an_Antiwar_Russian_Tricked_Into
                        Carrying_Out_an_Assassination_Plot?⠀⇛


                             Darya Trepova admits that a network of
                             handlers in Ukraine recruited her to hand an
                             explosive device to a far-right propagandist
                             in St. Petersburg—but, she says, they never
                             told her it was a bomb.


                      # ⚓ New York Times ☛ Dysfunction_Reigns_in_Congress_as
                        G.O.P._Defeats_Multiply⠀⇛


                             In a day of chaos in the Capitol, Republicans
                             failed to impeach the homeland security
                             secretary, lost a vote to speed aid to Israel
                             and cheered the demise of a border deal they
                             had demanded.


                      # ⚓ New York Times ☛ U.S._Ambassadors_in_the_Pacific_Urge
                        Action_on_Ukraine,_Israel_and_Border_Bill⠀⇛


                             With the package teetering on the brink of
                             collapse, diplomats said the nation’s
                             credibility was on the line.


                      # ⚓ LRT ☛ Russian_reconnaissance_sonar_discovered_on
                        Curonian_Spit_in_Lithuania⠀⇛


                             A Russian hydroacoustic sonar designed to
                             detect and locate submarines was found in the
                             Curonian Spit in Lithuania on Saturday, the
                             military has reported.


                      # ⚓ RFERL ☛ Russia_Summons_Israeli_Ambassador_Amid_Anger
                        At_Criticisms_Of_Lavrov,_Middle_East_Policy⠀⇛


                             The Russian Foreign Ministry said on February
                             6 that it had informed Israeli Ambassador
                             Simona Halperin of its "negative reaction" to
                             her comments about Foreign Minister Sergei
                             Lavrov and Russian policy in the Middle East.


                      # ⚓ RFERL ☛ Russia_Labels_Japanese_Association_Seeking
                        Return_Of_Islands_'Undesirable'⠀⇛


                             The Russian Justice Ministry on February 6
                             declared as "undesirable" Japan's Northern
                             Territories Issue Association, which seeks
                             the return to Japan of four islands
                             incorporated to Russia by the then-Soviet
                             Union after World War II.


                      # ⚓ RFERL ☛ Inmate_With_Central_Asian_Roots_Who_Was
                        Tortured_In_Russian_Prison_Found_Hanged⠀⇛


                             Tahirjon Bakiev, an inmate with Central Asian
                             roots who was tortured in a Siberian
                             penitentiary, has been found dead at the
                             correctional colony No. 6 in the Irkutsk
                             region.


                      # ⚓ RFERL ☛ Anti-War_Presidential_Hopeful_Nadezhdin_Says
                        Russia_Needs_To_Stick_To_Its_Constitution⠀⇛


                             Anti-war presidential hopeful Boris
                             Nadezhdin, whose official registration as a
                             candidate for the March 15-17 presidential
                             election in Russia is under question by
                             authorities, says Russia should stick to its
                             constitution and act like a real federation
                             by giving more freedom to its regions and
                             ethnic republics.


                      # ⚓ RFERL ☛ Kremlin_Critic_Navalny_Placed_In_Solitary
                        Confinement_For_26th_Time⠀⇛


                             The press secretary of imprisoned Russian
                             opposition politician Aleksei Navalny said on
                             February 6 that the outspoken Kremlin critic
                             had been placed in solitary confinement five
                             days earlier for unspecified reasons.


                      # ⚓ Marcy Wheeler ☛ John_Durham_Feigns_Totally_Dumb_about
                        Russian_“Collusion”⠀⇛


                             During John Durham's testimony to Congress,
                             he played dumb about how willingly Trump
                             pursued Russian help.


                      # ⚓ RFERL ☛ EU's_Borrell,_IAEA's_Grossi_In_Kyiv_As
                        Russian_Strike_On_Kharkiv_Kills_2-Month-Old_Baby⠀⇛


                             EU foreign policy chief Josep Borrell and UN
                             nuclear chief Rafael Grossi have arrived on
                             separate visits to Kyiv on February 6 as
                             Russian missile strikes continued to claim
                             victims among Ukrainian civilians, killing a
                             2-month old baby boy on February 6 in the
                             Kharkiv region.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ JURIST ☛ Canada_Supreme_Court_rules_disclosure_of_Premier
                  Doug_Ford’s_mandate_letters_are_not_required⠀⇛


                       The Supreme Court of Canada ruled that Ontario
                       Premier Doug Ford’s mandate letters to his cabinet
                       fell under an exemption of the Freedom of
                       Information and Protection of Privacy Act (FIPPA)
                       on Friday. The request for the mandate letters by a
                       journalist from the Canadian news outlet Canadian
                       Broadcast Corporation (CBC) was denied...


                # ⚓ Bruce Schneier ☛ Documents_about_the_NSA’s_Banning_of_Furby
                  Toys_in_the_1990s⠀⇛


                       Via a FOIA request, we have documents from the NSA
                       about their banning of Furby toys.


                # ⚓ Rolling Stone ☛ Taylor_Swift’s_Lawyers_Threaten_Private_Jet
                  Flight_Tracker_Over_‘Stalking_and_Harassing_Behavior’⠀⇛


                       As The Washington Post reports, the letter was sent
                       to Jack Sweeney, the same programmer and University
                       of Central Florida student briefly suspended from X
                       in Dec. 2022 after his jet tracking account rankled
                       Elon Musk. At the time, Musk characterized the
                       tracking of aircraft as a form of “doxxing,” and
                       compared sharing this flight info — which, again,
                       is culled from publicly available Federal Aviation
                       Administration data — to dropping his
                       “assassination coordinates.”


                       (Sweeney was eventually able to relaunch his flight
                       tracker account on X, though all data is shared
                       with a 24-hour delay to abide by the site’s real-
                       time location tracking rules.)


                # ⚓ TMZ ☛ Taylor_Swift_Sends_Cease_&_Desist_to_Jet_Tracker_...
                  You're_Inviting_Stalkers!!!⠀⇛


                       Sweeney had one page that was completely dedicated
                       to tracking Taylor's private jet -- as well as a
                       general celebrity jet page, where her jet would at
                       times be tracked too -- and he was using publicly
                       available data from the FAA and amateurs who'd
                       throw out data for fun.


                # ⚓ The Verge ☛ Taylor_Swift_joins_Elon_Musk_in_trying_to
                  silence_student_who_tracks_celebrity_jets⠀⇛


                       Along with data on private jets landing and taking
                       off, Sweeney also posts estimates of the associated
                       fuel use and greenhouse gas emissions of the
                       flights. “Flight shame” really took off in 2018
                       after an environmental campaign in Sweden urged
                       people to find less polluting ways to travel.
                       Swedish activist Greta Thunberg then made waves for
                       taking a two-week by sea journey to attend a
                       climate conference in New York the following year.


          o § Environment⠀➾


                # ⚓ The Hill ☛ Record_rain_dumped_on_parts_of_Los_Angeles⠀⇛


                       On Sunday, the NWS said an atmospheric river event
                       would continue bringing “heavy rain, strong wind,
                       high surf and heavy snows” over a sizable part of
                       Central and Southern California for the next few
                       days. More than 200,000 people had lost power in
                       California Sunday afternoon, according to
                       poweroutage.us.


                # ⚓ Omicron Limited ☛ Researchers_find_that_dust_in_the
                  atmosphere_is_feeding_algae_in_mountain_lakes⠀⇛


                       Researchers are trying to understand what is
                       driving recent and troubling changes to mountain
                       headwaters across the globe, which support roughly
                       half the world's population with freshwater for
                       drinking, irrigation, hydropower, industry and use
                       in homes. The latest from the team is a publication
                       in Global Change Biology showing how algae growth
                       is connected to atmospheric dust, with lead author
                       Juan Manuel González-Olalla and James Powell.


                # § Energy/Transportation⠀➾


                      # ⚓ The Sun ☛ Real_identity_of_Bitcoin_founder_‘Satoshi
                        Nakamoto’_could_FINALLY_be_revealed_in_court…and_may
                        unlock_£36billion_fortune⠀⇛


                             The real identity of Bitcoin founder Satoshi
                             Nakamoto could finally be revealed, unlocking
                             the key to his £36billion fortune.


                             A UK court will now decide if Craig Wright,
                             54, is the mysterious, anonymous crypto-king
                             who disappeared from the internet over a
                             decade ago.


                             Wright, an Australian computer scientist who
                             lives in London, has been arguing since 2016
                             that he is the real Nakamoto – a claim
                             largely dismissed by the cryptocurrency
                             world.


                             Whoever did invent Bitcoin is sitting on an
                             enormous stash of cryptocurrency now worth
                             £36billion ($46b) – which would make them one
                             of the world’s richest people.


                      # ⚓ India Times ☛ Apple_wants_'speculative'_consumer
                        lawsuit_over_[cryptocurrency]_tech_dismissed⠀⇛


                             Apple asks U.S. judge to dismiss consumer
                             lawsuit accusing it of unlawfully barring
                             cryptocurrency transaction apps. The lawsuit
                             claims Apple's restrictions on cryptocurrency
                             tech harm competition and increase fees on
                             Venmo and Cash App. Apple argues there are no
                             unlawful app rules or business agreements.


                      # ⚓ The Verge ☛ Fossil_fuels_are_losing_ground_to
                        renewable_energy_in_Europe⠀⇛


                             Fossil fuels dropped to their lowest point
                             since reliable record-keeping started in
                             1990, making up less than a third of EU’s
                             electricity generation in 2023. Carbon-
                             pollution-free power generation — which
                             includes renewables and nuclear energy — made
                             up more than two-thirds of the electricity
                             mix, and twice as much as fossil fuels.


                             “What’s encouraging is it’s just continuing
                             that structural decline in fossil fuels,”
                             says Sarah Brown, Ember’s Europe program
                             director. And while records started in 1990,
                             she says, “We think it’s the lowest point
                             ever, because before that fossil fuels were
                             making up the majority and there wasn’t
                             anything else to replace it.”


                      # ⚓ DeSmog ☛ New_Liz_Truss_Faction_‘Pops’_With_Climate
                        Science_Denial_and_Fossil_Fuel_Ties⠀⇛


                             Liz Truss’s new ‘Popular Conservatism’
                             faction of the Conservative Party launched
                             today with attacks on net zero targets and
                             environmental bodies, using the playbook
                             established by libertarian lobby groups.


                             The self-styled PopCons included politicians
                             critical of climate policies and science,
                             including Lord Frost, who is a director of
                             the climate science denial Global Warming
                             Policy Foundation, as well as Conservative MP
                             Lee Anderson and Reform party president Nigel
                             Farage. 


                      # ⚓ DeSmog ☛ How_the_Oil_Industry_Indefinitely_Delays
                        Cleaning_up_Oil_and_Gas_Wells_in_California⠀⇛


                             A new report from the Sierra Club has found
                             that more than 40,000 unplugged oil and gas
                             wells are sitting idle across California —
                             potentially leaking planet-warming gas and
                             unsafe chemicals, but no longer actively
                             extracting fossil fuels. 


                             In theory, it shouldn’t be possible to leave
                             so many wells in that neglected state.
                             Companies that operate in California are
                             required to safely “abandon” wells that are
                             no longer in use, removing pumpjacks and
                             sealing off openings forever with concrete.
                             And yet, the report found that more than 40
                             percent of unplugged wells in California
                             haven’t produced oil or gas in at least two
                             years, which is the state’s formal criteria
                             for an “idle” well. According to Sierra
                             Club’s review of California Geologic Energy
                             Management Division (CalGEM) data, only three
                             companies are responsible for most of these
                             wells: Chevron, Aera Energy, and California
                             Resources Corporation. And while operators do
                             pay modest fees for letting their wells stay
                             idle so long, aggressive industry lobbying
                             has helped to keep those penalties as low as
                             possible. 


                # § Overpopulation⠀➾


                      # ⚓ Overpopulation ☛ Birth_rates_have_been_falling_in
                        Nigeria,_though_slowly._What_factors_cause_declining
                        fertility,_according_to_educated_people_in_Nigeria?⠀⇛


                             Since 1970, birth rates have been falling in
                             most developing countries. An earlier study
                             by TOP researchers found that Swedes
                             generally think that improved living
                             conditions, including economic and
                             educational progress, are the cause for
                             declining fertility. What do Nigerians,
                             living in a developing country, think about
                             declining fertility in their country?


                      # ⚓ [Old] Sierra Club ☛ What_Does_“Dead_Pool”_Mean_for
                        the_American_West?⠀⇛


                             If Powell hit dead pool, the delta would
                             advance toward the dam at a faster rate,
                             filling the reservoir with sediment. Power
                             generation would get stuck in a loop of
                             diminishing returns until the water level
                             fell below what's called “power pool,” at
                             3,470 feet.


                             "The Bureau of Reclamation would have to re-
                             engineer those tubes to make sure they can
                             withstand the abrasiveness of the sediment,"
                             Schmidt told Sierra. "They're going to do
                             everything possible to prevent that
                             condition."


                             Dead pool into perpetuity could lead to so-
                             called water wars—lawsuits between the
                             federal government, states, municipal
                             leaders, and agricultural business owners—and
                             even mass exodus.


                      # ⚓ CBS ☛ Northern_Colorado_communities_partner_to_build
                        $150_million_water_pump_station_and_pipeline_for
                        pending_population_boom⠀⇛


                             Northern Colorado's population is expected to
                             double in the coming 25 years.


                             With that in mind, the previously mentioned
                             communities and water districts are forming
                             the Cobb Lake Regional Water Treatment
                             Authority.


          o § Finance⠀➾


                # ⚓ Techdirt ☛ I_Remain_Confused_By_The_Ruling_On_Elon_Musk’s
                  Compensation_Package⠀⇛


                       There are a number of people, both those who agree
                       with me and those who disagree with me, who seem to
                       think I have some sort of personal dislike of Elon
                       Musk. That’s not true. I find it amazing that he
                       gets away with some of the stuff he gets away with,
                       and I am perplexed at why anyone thinks he
                       “supports free speech,” when he clearly does not. I
                       also have pointed out the many times he seems to
                       make counterproductive decisions at ExTwitter.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Pro Publica ☛ Nevada_Republicans’_Caucus_Adds_Chaos_and
                  Confusion_to_the_State’s_Presidential_Primary⠀⇛


                       When Sarah Lee Hooper’s mail-in ballot for Nevada’s
                       presidential primary arrived last month, the Las
                       Vegas Republican was utterly confused.


                       The candidate she wanted to vote for, Vivek
                       Ramaswamy, wasn’t included. Neither were Florida
                       Gov. Ron DeSantis and, most notably, former
                       President Donald Trump. The only name she
                       recognized was former South Carolina Gov. Nikki
                       Haley.


                # ⚓ Silicon Angle ☛ DocuSign_cuts_400_jobs_in_third_round_of
                  layoffs_since_2022⠀⇛


                       DocuSign Inc. today announced plans to let go about
                       400 employees, or 6% of its workforce, in a bid to
                       cut costs and redirect more resources to growth
                       initiatives.


                       The electronic signature provider detailed in a
                       regulatory filing that the layoffs will mainly
                       affect its sales and marketing teams. According to
                       DocuSign, those employees in the U.S. will receive
                       at least 12 weeks of severance pay. The company
                       also plans to provide healthcare benefits,
                       accelerated stock vesting and outplacement support.


                # ⚓ US News And World Report ☛ EU_Proposes_Stronger_Rules
                  Against_Child_Abuse_and_Pornography⠀⇛


                       The new rules would adapt those implemented in
                       2011, and expand the definition of criminal
                       offences related to child abuse to include
                       livestreaming and AI content.


                # ⚓ Pete Brown ☛ Never_trust_a_simple_solution.⠀⇛


                       So, two things:


                       1. This is not something that a US president has
                       the power to do.


                       2. If the President did try to do something like
                       this, every company CEO and all of the usual right-
                       wing suspects would immediately start screaming
                       about authoritarian overreach.


                # ⚓ CBC ☛ Meta_says_users_must_label_AI-generated_audio_and
                  video_—_or_they_could_be_penalized⠀⇛


                       Meta Platforms could penalize users who fail to
                       label AI-generated audio and visual content posted
                       on its platforms, its top policy executive said on
                       Tuesday.


                       The comments were made by Nick Clegg, the company's
                       president of global affairs, during an interview
                       with Reuters.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Silicon Angle ☛ Oversight_Board_calls_for_changes_to
                        Meta’s_manipulated-content_policy⠀⇛


                             Meta Platforms Inc.’s Oversight Board, an
                             expert panel that advises the company on
                             moderation decisions, today called for
                             changes to its manipulated-content policy.
                             Meta formed the Oversight Board in 2020 to
                             field appeals that users submit over
                             moderation decisions across Facebook
                             (Farcebook) and Instagram. Additionally, the
                             panel can recommend ways to improve the
                             company’s content policies.


                      # ⚓ Reason ☛ "Times_Less_Than"⠀⇛


                             A Facebook (Farcebook) comment reminded me
                             again of this debate — some people argue that
                             "A times less than B" is "mathematically
                             incorrect," "simply wrong," and so on.


                      # ⚓ AI_and_the_election:_a_voters_guide⠀⇛


                             The UK's National Cyber Security Centre
                             (NCSC) recently raised concerns about the
                             threat of AI to free and fair elections


                             So what is AI in this context? How does it
                             impact you? Can you defend against it, making
                             yourself less prone to its influence?


                             § NPD


                             Think of all the people you dislike because
                             they are manipulative. Do you know a person
                             who always seems to know which of your
                             buttons to press? Is there someone who always
                             seems to know what you're thinking, or
                             mirrors back your own fears and desires in a
                             way that strangely seems to suit them?


                             Narcissistic Personality Disorder (NPD) is
                             what psychologists call a trait of habitual
                             lying and manipulation from otherwise
                             intelligent people who seem to lack a part of
                             their mind that cares about others. Someone
                             lacking empathy or acting very selfishlu is
                             sometimes labelled a "psychopath" or
                             "sociopath".


                             The narcissistic psychopath (NP) watches very
                             carefully and learns from things you do and
                             say, with one goal, to manipulate and use
                             you.


                      # ⚓ Futurism ☛ Embattled_Sheriff_Caught_Posting_AI-
                        Generated_Headlines_About_How_She’s_Awesome⠀⇛


                             As it turns out, the 31 Bilal-boosting
                             headlines were made up by AI, and either
                             nobody caught it ahead of time, or nobody
                             cared to change it.


                             "After review," the unattributed statement
                             from Bilal's campaign provided to the
                             Inquirer reads, "it has been determined that
                             an outside consultant for the reelection
                             campaign utilized ChatGPT."


                      # ⚓ The Philadelphia Inquirer ☛ The_Philly_sheriff’s_good
                        news_headlines?_AI_generated_them.⠀⇛


                             The campaign broke its silence, releasing a
                             statement in response to an Inquirer article
                             published Monday morning that raised
                             questions about the veracity of 31 favorable
                             headlines attributed to local news
                             organizations including NBC10, CBS3, WHYY,
                             and The Inquirer, each with supposed dates of
                             publication.


                             Representatives for those organizations were
                             not able to find any of the articles.


                      # ⚓ ADF ☛ AI-Generated_‘Fake_News’_Fuels_Misinformation,
                        Puts_Peacekeepers_at_Risk⠀⇛


                             Recent research shows a dramatic rise over
                             the past year in misinformation generated by
                             artificial intelligence and presented as
                             authentic news that, experts say, puts at
                             risk international peacekeeping operations in
                             Africa.


                             At last count, more than 675 websites publish
                             what one group of experts describes as
                             “unreliable” news articles generated by
                             artificial intelligence (AI) — articles that
                             frequently present falsehoods and
                             misinformation as the truth.


                             NewsGuard, a group that monitors
                             misinformation efforts, identified the sites.
                             Researchers found AI-generated content
                             published in 15 languages, including Arabic,
                             Chinese, English, French and Portuguese, on
                             sites whose names make them seem like
                             legitimate sources of information.


          o § Censorship/Free Speech⠀➾


                # ⚓ RFERL ☛ 'Revenge_For_My_Activism':_Extremism_Cases
                  Skyrocket_In_Russia⠀⇛


                       Yet very few of these “extremists” are prosecuted
                       for something they did, according to Yevgeny
                       Smirnov, a lawyer with the legal-aid organization
                       First Department. Instead, he said, the statistics
                       “indicate a tendency toward the mass persecution of
                       people for speech.”


                # ⚓ RFA ☛ China_jails_feminist_labor_activist_Li_Qiaochu_for
                  ‘subversion’⠀⇛


                       But rights activists have said Li’s detention came
                       after she publicly shared details of her husband’s
                       torture by state security police while in
                       detention.


                       “Li has been ruthlessly targeted for expressing
                       views the Chinese authorities would prefer to
                       suppress – on the premise that her speech could
                       somehow topple the government,” Amnesty
                       International China director Sarah Brooks said in a
                       statement on Monday.


                       “It is shameful that the Chinese authorities have
                       jailed Li for speaking out against torture and ill-
                       treatment rather than properly investigating the
                       allegations she made,” Brooks said, calling for
                       Li’s immediate and unconditional release.


                # ⚓ Techdirt ☛ Content_Moderation_At_Scale_Is_Impossible_To_Do
                  Well,_Child_Safety_Edition⠀⇛


                       Last week, as you likely heard, the Senate had a
                       big hearing on “child safety” where they
                       grandstanded in front of a semi-random collection
                       of tech CEOs, with zero interest in actually
                       learning about the actual challenges of child
                       safety online, or what the companies had done that
                       worked, or where they might need help. The
                       companies, of course, insisted they were working
                       hard on the problem, and the Senators could just
                       keep shouting “not enough,” without getting into
                       any of the details.


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


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_media_mogul_Jimmy_Lai_told
                  Apple_Daily_to_play_up_business_sector_concerns_on
                  extradition_law,_court_hears⠀⇛


                       The founder of pro-democracy newspaper Apple Daily
                       Jimmy Lai asked senior staff to play up the
                       business sector’s concerns over a since-axed
                       extradition law, a former publisher at the paper
                       has said as she testified against her former
                       employer in his national security trial.


                # ⚓ Kansas Reflector ☛ Former_Marion_police_chief_had_‘pizza
                  party’_after_raid,_turned_off_body_cam,_new_lawsuit_says⠀⇛


                       The lawsuit describes the chief rummaging through
                       Gruver’s desk drawer and rifling through her files
                       on him. Captured audio depicts Cody stating that he
                       is hungry and that the officers should “just take
                       them all” in reference to the Record’s computers
                       and equipment, so they could “get the f*** out of
                       here.”


                       Other footage includes Cody using the bathroom at
                       Casey’s General Store between raiding homes.


                       “While Chief Cody did not turn off his body camera
                       while relieving himself, he apparently chose to
                       turn it off while he reviewed Gruver’s file on him,
                       for the Marion Police Department did not produce
                       any body camera footage from Cody of him looking
                       through Gruver’s file on him,” the lawsuit reads.


                # ⚓ US News And World Report ☛ A_Reporter_Is_Suing_a_Kansas
                  Town_and_Various_Officials_Over_a_Police_Raid_on_Her
                  Newspaper⠀⇛


                       Marion County Record reporter Phyllis Zorn is
                       seeking $950,000 in damages from the city of
                       Marion, its former mayor, its former police chief,
                       its current interim police chief, the Marion County
                       Commission, the county sheriff and a former
                       sheriff's deputy. The lawsuit calls them “co-
                       conspirators” who deprived her of press and speech
                       freedoms and the protection from unreasonable
                       police searches guaranteed by the U.S.
                       Constitution.


                       Officers raided the newspaper's offices on Aug. 11,
                       2023, as well as the home of Publisher Eric Meyer,
                       seizing equipment and personal cellphones. Then-
                       Marion Chief Gideon Cody said he was investigating
                       whether the newspaper committed identity theft or
                       other crimes in accessing a local restaurant
                       owner's state driving record.


                # ⚓ ANF News ☛ Journalist_detained_in_Hewlêr⠀⇛


                       "This kind of mistreatment is part of the pressure
                       exerted by the KRI authorities on freedom of
                       expression, which leads to the number of charges
                       against Kurdish officials increasing day by day and
                       the country losing its friends in the international
                       community," said Standard Kurd officials. They see
                       Husen's safety under threat and call for his
                       immediate release.


                # ⚓ Joan Westenberg ☛ The_creator_economy_can't_rely_on
                  Patreon.⠀⇛


                       She felt like she had no creative freedom or joy in
                       her creations. And the only answer had been a pivot
                       to direct financial support. But despite racking up
                       tens of thousands of views per video, she struggled
                       to convert more than a tiny fraction into paid
                       subscribers.


                       Finally, we were grabbing coffee, and she just
                       broke down. She asked me, "At what point am I
                       selling out? And is it even worth it?"


                # ⚓ Hamilton Nolan ☛ Public_Funding_of_Journalism_Is_the_Only
                  Way⠀⇛


                       So next time that you wonder, “What happened to all
                       the nice newspapers and magazines and perhaps even
                       websites that I remember reading from my halcyon
                       youth?” just imagine Google and Facebook and Amazon
                       as three vampires, sticking a straw into the media
                       business and sucking it dry. The tech platforms
                       figured out how to insert themselves between the
                       news producers and the news audience. The ad money
                       that used to fund news now goes to the tech
                       companies. They took it and now the news companies
                       don’t have it to hire journalists with. That’s why
                       your local paper sucks and your favorite website is
                       dying. When you pull back, it’s pretty simple.


                       This is not a case of publications dying because
                       they weren’t good enough and consumers made the
                       independent choice of moving their dollars to new
                       and better publications, which flourished anew. No.
                       This is the attack of the middlemen. I must admit
                       that I kind of admire the cleverness of the big
                       tech companies in figuring out how to extract all
                       of the revenue from journalism without actually
                       making any journalism. Smooth move. Also a problem.
                       Did you see the problem? That’s right: the places
                       that make the journalism are not getting the money
                       and therefore they stop making journalism and the
                       places that are getting the money instead do not
                       make journalism. So where does that leave
                       journalism? Nowhere. Which is to say, the place we
                       are rapidly approaching now.


                # ⚓ CPJ ☛ Iranian_journalist_Nasrin_Hassani_begins_7-month
                  prison_sentence⠀⇛


                       On Sunday, Hassani, a reporter for the state-run
                       local newspaper Etefaghyeh, and editor-in-chief of
                       the social media-based outlet East Adventure Press,
                       responded to a summons to appear before Branch 2 of
                       the Bojnourd Revolutionary Court in the
                       northeastern city of Bojnourd. She was arrested and
                       taken to the city’s central prison to serve a
                       seven-month sentence for “false news” that was
                       issued in November 2023, according to multiple news
                       reports.


                # ⚓ The Atlantic ☛ You’ll_Miss_Sports_Journalism_When_It’s
                  Gone⠀⇛


                       The new sports-media reality is troubling—and
                       paradoxical. Sports fans are awash in more
                       “content” than ever before. The sports-talk-podcast
                       industry is booming; many professional athletes
                       host their own shows. Netflix cranks out one gauzy,
                       player-approved documentary series after another,
                       and every armchair quarterback or would-be pundit
                       has an opinion to share on social media. Yet
                       despite all of this entertainment, all of these
                       shows, and all of these hot takes, true sports-
                       accountability journalism is disappearing.


          o § Civil Rights/Policing⠀➾


                # ⚓ ANF News ☛ Over_17_thousand_girls_at_risk_of_genital
                  mutilation_in_Germany,_says_human_rights_organization⠀⇛


                       With global migration, the brutal tradition of
                       female genital mutilation of girls and women is
                       becoming increasingly common in Europe. According
                       to the women's rights organization Terre des
                       Femmes, there are currently more than 100,000 girls
                       and women who have suffered genital mutilation in
                       Germany, and more than 17,000 girls in Germany are
                       potentially at risk.


                # ⚓ The Kent Stater ☛ FGM_in_Sierra_Leone:_Girls_continue_to
                  bleed_to_death_but_an_alternative_ritual_could_save_lives_and
                  preserve_tradition⠀⇛


                       FGM involves the partial or total removal of the
                       external female genitalia. There are differing
                       numbers from various UN agencies (due to
                       inconsistent data collection in-country) about
                       prevalence rates but the United Nations Children’s
                       Fund (UNICEF) estimates that at least 200 million
                       girls and women in 31 countries have undergone one
                       of four types of FGM. The practice is said to be
                       happening on every continent, though it is most
                       prevalent in the Arab states and in Africa.


                # ⚓ PHR ☛ ICE_Used_Solitary_Confinement_More_Than_14,000_Times
                  Since_2018:_Report⠀⇛


                       U.S. Immigration and Customs Enforcement (ICE) used
                       solitary confinement at least 14,264 times from
                       2018 to 2023, according to a new report issued by
                       experts at Physicians for Human Rights, Harvard Law
                       School, and Harvard Medical School.


                       The report, “Endless Nightmare”: Torture and
                       Inhuman Treatment in Solitary Confinement in U.S.
                       Immigration Detention, documents that people placed
                       in ICE solitary confinement spent a staggering 27
                       days in isolation on average, exceeding the 15-day
                       period that constitutes torture as currently
                       defined by United Nations experts.


                # ⚓ RFA ☛ Tibetan_monk_arrested_for_publishing_books_on_Tibet
                  from_exiles⠀⇛


                       “The primary charge that was leveled against him
                       was that he had published and disseminated books
                       that had origins in the Tibetan exiled community
                       while he was in charge of the library at Kirti
                       monastery and he communicated with people outside
                       Tibet,” another source said.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ India Times ☛ Alphabet_is_seeking_outside_investment_for
                  its_GFiber_internet_business⠀⇛


                       Alphabet plans to seek external investment for
                       GFiber, its business selling Wi-Fi and internet
                       connectivity in parts of the United States, the
                       company told Reuters on Monday, as it looks to ramp
                       up its expansion to more cities.


                       GFiber, owned by Google's parent company, competes
                       with larger internet service providers including
                       Comcast, Verizon Communications and AT&T.


                # ⚓ Troy Patterson ☛ Enshittification_and_Owning_Your_Own
                  Land⠀⇛


                       I saw this somewhere today (lost exactly where, so
                       I can’t link to it). The basic premise is don’t
                       create all your stuff somewhere that someone else
                       owns. We’ve seen this play out with Facebook and
                       Twitter. Now more than ever, it is possible to own
                       your own website and post to it. Not only that, but
                       with the Fediverse, you can also automatically have
                       those posts show up on a social media site. This
                       was incredibly hard in the past. Thus, we were
                       forced to choose between having your own website
                       and the network effect of other sites.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Digital Music News ☛ Indies_Speak_Out_Against_Fashion
                  Company_Apple_Music’s_Heightened_Spatial_Audio_Royalties,
                  Target_Policy-Change_Talks⠀⇛


                       Indie labels are reportedly criticizing – and
                       signaling their openness to pursuing legal action
                       against – Fashion Company Apple Music’s royalty
                       bump for works made available in spatial audio. The
                       newest twist in the Apple-developed streaming
                       platform’s own royalties pivot (Spotify, Deezer,
                       and others have likewise retooled their models)
                       just recently entered the media spotlight.


                # ⚓ Quartz ☛ Spotify_raised_prices_and_still_hit_a_record_for
                  new_subscribers⠀⇛


                       The music streaming giant now boasts 236 million
                       paid subscribers, according to its news released
                       fourth quarter earnings report. That growth came
                       even as the company raised prices to $10.99 a month
                       in 2023. It was Spotify’s first price increase in
                       12 years. A monthly subscription to Spotify had
                       previously cost $9.99.


      § Monopolies/Monopsonies⠀➾


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ AirVPN_Stops_Serving_Italians_due_to
                  “Piracy_Shield”_Blocking_Requirements⠀⇛


                       Starting later this month, VPN provider AirVPN will
                       no longer accept Italian customers. This drastic
                       decision is a direct response to the Government's
                       piracy-blocking requirements, enforced through the
                       "Piracy Shield" system. AirVPN says that the
                       requirements are too burdensome, while opening the
                       door to potential overblocking and violations of
                       users' fundamental rights.


                # ⚓ Torrent Freak ☛ Piracy_Shield's_First_Targets_Blocked,
                  Pirate_Boxes_Discovered_in_Italian_Prison⠀⇛


                       The much anticipated Piracy Shield blocking system
                       is now fully operational according to Italian
                       authorities. The system's first three official
                       targets appear in legal documents and are web-
                       based, not traditional IPTV providers as some
                       expected. Meanwhile, an operation carried out by
                       over 100 officers to seize contraband from an
                       Italian prison has turned up pirate set-top boxes
                       in prisoners' cells.





                    ䷩ 𝚕𝚒𝚗𝚎 4677

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 07/02/2024: Voice Synthesis Causing
More Problems⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Feb 07, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
                # 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 Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
                # Gemini*_and_Gopher
                      # Personal/Opinions
                      # Politics_and_World_Events
                      # Technology_and_Free_Software
    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ Science Alert ☛ 90,000_Years_Ago,_Humans_Walked_on_a
                  Moroccan_Beach._We_Just_Found_Their_Footprints.⠀⇛


                # ⚓ Science Alert ☛ This_Poor_Puppy_Lost_Part_of_His_Jaw_to
                  Cancer._Astonishingly,_It_Grew_Back!⠀⇛


                       The healing power of youth.


                # ⚓ Hackaday ☛ They_Want_To_Put_A_Telescope_In_A_Crater_On_The
                  Moon⠀⇛


                       When we first developed telescopes, we started
                       using them on the ground. Humanity was yet to
                       master powered flight, you see, to say nothing of
                       going beyond into space. As technology developed,
                       we realized that putting a telescope up on a
                       satellite might be useful, since it would get rid
                       of all that horrible distortion from that pesky old
                       atmosphere. We also developed radio telescopes,
                       when we realized there were electromagnetic signals
                       beyond visible light that were of great interest to
                       us.


          o § Hardware⠀➾


                # ⚓ MIT Technology Review ☛ Why_China_is_betting_big_on
                  chiplets⠀⇛


                       For the past couple of years, US sanctions have had
                       the Chinese semiconductor industry locked in a
                       stranglehold. While Chinese companies can still
                       manufacture chips for today’s uses, they are not
                       allowed to import certain chipmaking technologies,
                       making it almost impossible for them to produce
                       more advanced products.


                # ⚓ Hackaday ☛ It_Wasn’t_DOOM_That_Killed_The_Amiga⠀⇛


                       If you were the type of person who might have read
                       Hackaday had we been around in the late 1980s or
                       early 1990s, it’s a reasonable guess that you would
                       have had a 16-bit home computer on your desk, and
                       furthermore that it might have been a Commodore
                       Amiga. These machines gave the best bang for the
                       buck in those days with their impressive multimedia
                       capabilities, and they gained a fervent following
                       which persists to this day. [Carl Svensson] was one
                       of them, and he’s penned a retrospective on the
                       demise of the platform with the benefit of much
                       hindsight.


                # ⚓ Hackaday ☛ Evidence_For_Graphite_As_A_Room_Temperature
                  Superconductor⠀⇛


                       Little has to be said about why superconducting
                       materials are so tantalizing, or what the benefits
                       of an ambient pressure, room temperature material
                       with superconducting properties would be. The main
                       problem here is not so much the ‘room temperature’
                       part, as metallic hydrogen is already capable of
                       this feat, if at pressures far too high for
                       reasonable use. Now a recent research article in
                       Advanced Quantum Technologies by Yakov Kopelevich
                       and colleagues provides evidence that
                       superconducting properties can be found in cleaved
                       highly oriented pyrolytic graphite (HOPG). The fact
                       that this feat was reported as having been measured
                       at ambient pressure and room temperature makes this
                       quite noteworthy.


                # ⚓ Hackaday ☛ IoT_Air_Purifier_Makes_A_Great_Case_Study_In
                  Reverse_Engineering⠀⇛


                       Here at Hackaday, about the only thing we like more
                       than writing up tales of reverse engineering
                       heroics is writing up tales of reverse engineering
                       heroics that succeed in jailbreaking expensive
                       widgets from their needless IoT dependency. It’s
                       got a real “stick it to the man” vibe that’s hard
                       to resist.


                # ⚓ Hackaday ☛ Human-Interfacing_Devices:_Packing_For_The
                  Descriptor_Heist⠀⇛


                       We started with figuring out HID descriptors a week
                       ago, and I’ve shown you how to send raw HID packets
                       using a MicroPython fork. We do still have the task
                       in front of us – making a touchscreen device. For
                       that, let’s give you the tools to capture an
                       existing descriptor from a touchscreen, then show
                       you how to tweak it and how it turns out in the
                       end.


                # ⚓ CNX Software ☛ Maxtang_MTN-FP750_business_mini_PC_review_–
                  Part_3:_Ubuntu_22.04 [Ed: In exchange for gifts they keep
                  promoting Windows products as if they are with GNU/Linux
                  distributions]⠀⇛


                # ⚓ IT Wire ☛ Chinese_company_set_to_make_5nm_chips_this_year:
                  report⠀⇛


                       The US has been trying, for at least the last five
                       years, to place hurdles in the way of China and
                       limit the country to making only older generations
                       of chips.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Pro Publica ☛ NY_Wage_Theft_Law_Would_Bar_Violators_From
                  Doing_Business_in_the_State⠀⇛


                       New York lawmakers proposed three new bills last
                       week that would make it difficult for wage theft
                       violators to conduct business in the state.


                       The legislation would bolster the power of state
                       agencies to crack down on wage theft by stripping
                       violators of their liquor licenses or business
                       licenses, as well as issuing stop-work orders
                       against them.


                # ⚓ Barry Kauler ☛ Surgery_on_thumb⠀⇛


                       Accident yesterday; I was drilling 3.5mm holes in
                       some aluminium sheet, with a handheld electric
                       drill, and holding the workpiece steady with my
                       right hand. The drill-bit snapped, the drill veared
                       sideways and down, and drilled right through my
                       thumb. I know it was careless; should have used a
                       g-clamp to hold the workpiece.


                # ⚓ Science Alert ☛ A_Daily_Diet_of_Burgers_And_Pizzas_Could_Be
                  Putting_You_at_Risk_of_Alzheimer's⠀⇛


                       Never too late to change.


                # ⚓ Science Alert ☛ Caffeine_in_Your_Blood_Might_Affect_Body
                  Fat_And_Diabetes_Risk,_Study_Finds⠀⇛


                # ⚓ Latvia ☛ Campaign_to_raise_awareness_of_rare_diseases_in
                  Latvia⠀⇛


                       In February, awareness of rare diseases is raised
                       in Latvia, this year through a campaign "Color your
                       strength!" This campaign aims to inform the public
                       about the rare diseases in Latvia and the world,
                       Latvian Television reported on February 6.


                # ⚓ Latvia ☛ Stradiņš_hospital_to_break_contract_with_builder⠀⇛


                       Pauls Stradiņš Clinical University Hospital (PSKUS)
                       will terminate its contract with LLC “Velve” to
                       build the new A2 hospital building complex
                       on February 13 due to the company's breach of
                       contract obligations and delays in execution of
                       construction works, the hospital council announced
                       on Tuesday, February 6.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ New York Times ☛ Vision_Pro_Goggles_are_not_Safe_While
                  Driving_a_Tesla,_U.S._Says⠀⇛


                       Videos, many of them stunts or jokes, of people
                       wearing Apple’s new virtual reality headset while
                       driving Teslas in Autopilot mode prompted officials
                       to issue warnings.


                # ⚓ New York Times ☛ Meta_Calls_for_Industry_Effort_to_Label
                  A.I.-Generated_Content⠀⇛


                       The social network wants to promote standardized
                       labels to help detect artificially created photo,
                       video and audio material across its platforms.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Techdirt ☛ FCC_Takes_Aim_At_AI_Deepfake_Robocalls
                        After_Sloppy_Fake_Biden_Hoax⠀⇛


                             Last month you probably saw the story about
                             how somebody used a (sloppy) deepfake of Joe
                             Biden in a bid to try and trick voters into
                             staying home during the Presidential Primary.
                             It wasn’t particularly well done; nor was it
                             clear it reached all that many people or had
                             much of an actual impact.


                      # ⚓ YLE ☛ Digital_fraudsters_swiped_€44m_from_victims_in
                        Finland_last_year⠀⇛


                             Most victims were targeted in investment
                             schemes, which are often long-term scams.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Defence Web ☛ South_Africa’s_proposed_new_spying_law
                        is_open_for_comment_–_an_expert_points_out_its_flaws⠀⇛


                             In early 2021, the South African
                             Constitutional Court found that the country’s
                             State Security Agency, through its signals
                             intelligence agency, the National
                             Communication Centre, was conducting bulk
                             interception of electronic signals
                             unlawfully.


                      # ⚓ Reason ☛ San_Francisco_Police_Spent_193_Hours_Over_3
                        Months_Watching_Private_Surveillance_Footage⠀⇛


                             The surveillance yielded 49 arrests, of which
                             42 were for possession or sale of narcotics.


          o § Defence/Aggression⠀➾


                # ⚓ Pro Publica ☛ Supreme_Court_Hears_Case_on_Whether_Trump_Can
                  Run_for_President_Again⠀⇛


                       On Feb. 8, the Supreme Court will hear oral
                       arguments in Donald J. Trump v. Norma Anderson et
                       al, a case that could swing a presidential election
                       in a way not seen since Bush v. Gore a quarter-
                       century earlier.


                       The crux of Trump v. Anderson boils down to this:
                       Should a former commander in chief be disqualified
                       from seeking the presidency again if he engaged in
                       insurrection?


                # ⚓ The Strategist ☛ Green_barracks:_decarbonising_the_defence
                  estate⠀⇛


                       Climate change’s threat to national security has
                       been widely examined by security agencies,
                       researchers and thought leaders across the world.


                # ⚓ RFA ☛ Australian_writer_given_suspended_death_sentence
                  spied_for_Taiwan,_court_says⠀⇛


                       Experts say the heavy sentence, while rare, serves
                       as a warning to others.


                # ⚓ Hong Kong Free Press ☛ Australia_expresses_‘outrage’_after
                  China_hands_suspended_death_sentence_to_dissident_writer_Yang
                  Jun⠀⇛


                       Australia said Tuesday it had expressed “outrage”
                       to China over a suspended death sentence handed to
                       Chinese-Australian dissident writer Yang Jun. Yang
                       was sentenced to death on Monday with a two-year
                       suspended execution, and had all of his property
                       confiscated, the Chinese foreign ministry said.


                # ⚓ ADF ☛ RSF_Fighters_Plunder_Homes_and_Terrorize_Residents_in
                  Khartoum⠀⇛


                       For more than nine months, the paramilitary Rapid
                       Support Forces of Sudan have controlled large parts
                       of the capital, Khartoum. In that time, witnesses
                       say the militia’s fighters have plundered the city
                       and terrorized residents even as their leader
                       pledges to work toward peace.


                # ⚓ ADF ☛ SAF_Accused_of_Targeting_Civilians_Based_on
                  Ethnicity⠀⇛


                       As the civil war in Sudan raged into its ninth
                       month, the Sudanese Armed Forces faced allegations
                       of targeting civilians based on ethnicity.


                # ⚓ ADF ☛ Cabo_Delgado_Experiences_Fewer_Terror_Attacks,_But
                  Challenges_Remain⠀⇛


                       Counterinsurgency efforts in Mozambique’s Cabo
                       Delgado province have gained momentum since
                       international forces killed the leader of the Ahl
                       al-Sunna wal-Jama’a (ASWJ) extremist group in
                       August.


                # ⚓ YLE ☛ Defence_minister_Häkkänen_rows_back_on_plans_to_ban
                  reservists_from_resigning⠀⇛


                       Hundreds of people have resigned from the Finnish
                       Defence Forces' military reserve in the wake of the
                       minister's comments last week.


                # ⚓ France24 ☛ Turkish_police_shoot_dead_two_'terrorists'
                  during_attack_on_Istanbul_courthouse⠀⇛


                       Turkish police on Tuesday shot dead two assailants
                       from a leftist organisation, branded "terrorists"
                       by authorities, who attacked a security checkpoint
                       outside Istanbul's main court, killing one person
                       and injuring five, officials said.


                # ⚓ France24 ☛ US_Homeland_Security_chief_survives_House
                  impeachment_vote⠀⇛


                       Joe Biden's immigration chief, Alejandro Mayorkas,
                       narrowly escaped impeachment over the US border
                       crisis Tuesday, in a party-line vote dismissed by
                       Democrats as a political stunt ahead of a
                       presidential election expected to feature
                       immigration as a major issue.


                # ⚓ ADF ☛ SANDF_Troops_Face_Controversial,_Dangerous_DRC
                  Deployment⠀⇛


                       South African troops working with the Southern
                       African Development Community (SADC) have been
                       deployed to the conflict-ridden eastern Democratic
                       Republic of the Congo (DRC) since December, raising
                       concerns among some South African military
                       observers.


                # ⚓ New Yorker ☛ The_U.S._Confronts_Middle_Eastern_Militias_but
                  Not_Iran’s_Long_Game⠀⇛


                       Strikes against weapons depots and operations
                       centers in Iraq and Syria will not diminish Iran’s
                       determination to expel the U.S. from the Middle
                       East.


                # ⚓ New York Times ☛ Houthi_Attacks_and_U.S.-Led_Strikes_Dash
                  Hopes_for_Quick_Yemen_Peace_Deal⠀⇛


                       A U.N.-backed process to end Yemen’s nine-year
                       conflict appeared to be moving forward recently.
                       But then the war in Gaza began and tensions spilled
                       over.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ Latvia ☛ Urinating_Lithuanian_fined_for_paying
                        tribute_to_Putin⠀⇛


                             A criminal process against a Lithuanian
                             citizen, who urinated in the corridor of a
                             shopping center in Riga at the weekend and
                             glorified the war started by Russia, has seen
                             him fined EUR 7,000 within two days as a
                             result of an expedited procedure, the State
                             Police said February 6.


                      # ⚓ Meduza ☛ ‘Focus_on_the_apartment’s_potential’_A
                        Russian_propaganda_film_explores_the_‘unconventional
                        housing_market’_in_war-ravaged_Mariupol_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Documenting_every_step_and_sneeze’:_Former
                        Fox_News_host_Tucker_Carlson’s_Moscow_visit_has
                        Russia’s_media_in_a_frenzy_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_oil_refineries_see_drop_in_output,
                        partially_attributed_to_drone_attacks_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Boris_Nadezhdin’s_campaign_gets_Russian
                        election_authorities_to_accept_‘up_to_several_dozen’
                        signatures_previously_declared_invalid_due_to_typos_—
                        Meduza⠀⇛


                      # ⚓ RFERL ☛ Biden_Urges_Passage_Of_Ukraine_Aid,_Saying
                        Opposing_It_Plays_Into_Putin's_Hands⠀⇛


                             U.S. President Joe Biden on February 6 urged
                             Congress to pass a bipartisan immigration
                             bill that also includes aid for Ukraine as
                             lawmakers face political pressure from
                             Republican presidential front-runner Donald
                             Trump to scuttle it.


                      # ⚓ RFERL ☛ Former_Fox_News_Commentator_Tucker_Carlson
                        Says_He_Will_Interview_Putin⠀⇛


                             Former Fox News host and commentator Tucker
                             Carlson announced on February 6 that he has
                             been granted an interview with Russian
                             President Vladimir Putin.


                      # ⚓ Meduza ☛ Russian_inmate_whose_torture_led_to_prison
                        employees’_conviction_found_dead_in_cell_after_apparent
                        suicide_—_Meduza⠀⇛


          o § Environment⠀➾


                # ⚓ CS Monitor ☛ Pineapple_express?_Mudslides?_What’s_happening
                  in_California.⠀⇛


                       A pineapple express – a nickname for a long band of
                       water vapor over the Pacific Ocean – pummeled
                       Southern California with nearly half its annual
                       rainfall in two days. The atmospheric river is
                       causing deadly mudslides and overflowing rivers.


                # § Energy/Transportation⠀➾


                      # ⚓ Hackaday ☛ Retrotechtacular:_The_Master_Hands_Of_The
                        Early_Automotive_Industry⠀⇛


                             When motion pictures came along as a major
                             medium in the 1920s or so, it didn’t take
                             long for corporations to recognize their
                             power and start producing promotional pieces.
                             A lot of them are of the “march of progress”
                             genre, featuring swarms of workers happy in
                             their labors and creating the future with
                             their bare hands. If we’re being honest, a
                             lot of it is hard to watch, but “Master
                             Hands,” which shows the creation of cars in
                             the 1930s, is somehow more palatable, mostly
                             because it’s mercifully free of the flowery
                             narration that usually accompanies such
                             flicks.


                      # ⚓ ADF ☛ Chinese_Gold_Miners_Fuel_Insecurity_in
                        Nigeria⠀⇛


                             Illegal gold mining is a growing problem in
                             Nigeria that is benefiting terrorist groups,
                             causing violence and increasing pollution.
                             Residents of mining areas blame Chinese
                             nationals who set up and oversee mining and
                             refining operations. Tension continues to
                             rise around these pit mines.


                      # ⚓ New York Times ☛ Alaska_Airlines_737_May_Have_Left
                        Boeing_Factory_Missing_Bolts,_N.T.S.B._Says⠀⇛


                             A photo indicates that bolts in a fuselage
                             panel were removed at a Boeing factory and
                             not replaced, the National Transportation
                             Safety Board said.


                # § Wildlife/Nature⠀➾


                      # ⚓ New Yorker ☛ Will_Plants_Ever_Fertilize_Themselves?⠀⇛


                             Biologists aim to engineer crops that can eat
                             nitrogen straight from the air.


                      # ⚓ Science Alert ☛ Rise_in_Storm_Intensity_Prompts_Calls
                        For_a_Whole_New_Category_of_Hurricane⠀⇛


                             "The wolf is here."


          o § Finance⠀➾


                # ⚓ Silicon Angle ☛ Snap_shares_plunge_over_30%_on_revenue_miss
                  and_weak_guidance⠀⇛


                       Shares in Snap Inc. plunged by over 30% in late
                       trading today after the company fell short on
                       revenue and offered weak guidance for the quarter
                       ahead.


                # ⚓ Pro Publica ☛ Senate_Probe_Casts_Doubt_on_Harlan_Crow's
                  Yacht_Tax_Deductions⠀⇛


                       A key congressional committee is pressuring
                       billionaire Harlan Crow for answers after
                       investigators turned up additional evidence that he
                       misrepresented his yacht as a business to score a
                       tax break.


                # ⚓ The Kent Stater ☛ Wall_Street_is_worried_about_another
                  regional_banking_crisis⠀⇛


                       Wall Street is experiencing a case of déjà vu. It’s
                       been nearly a year since the collapse of three US
                       regional lenders left financial institutions and
                       regulators scrambling to prevent the spread of a
                       banking crisis. Today, investors are worried
                       they’re back on familiar territory.


                # ⚓ Federal News Network ☛ IRS_expects_to_collect_hundreds_of
                  billions_more_in_overdue_and_unpaid_taxes_thanks_to_new
                  funding⠀⇛


                       The IRS says it expects to collect hundreds of
                       billions of dollars more in overdue and unpaid
                       taxes than previously anticipated using funding
                       provided to the agency by the Democrats’ Inflation
                       Reduction Act. That's according to new analysis
                       released Tuesday by the Treasury Department and the
                       IRS. The report says tax revenues are expected to
                       increase by as much as $561 billion from 2024 to
                       2034, which is substantially more than previous
                       estimates. The Congressional Budget Office in 2022
                       estimated that tax revenues would increase by
                       $180.4 billion over the 2022 to 2031 period.


                # ⚓ Latvia ☛ Gambling_revenues_up_9%_last_year_in_Latvia⠀⇛


                       In 2023, the gambling industry revenues reached
                       288,633 million euros, up 9% from 2022, when
                       gambling venues were still closed in the first two
                       months of the year as a result of Covid-19 pandemic
                       restrictions, according to the Lotteries and
                       Gambling Supervisory Inspecorate's data on February
                       6.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Straits Times ☛ South_Korean_President_Yoon_set_to
                  speak_on_Dior_bag_uproar⠀⇛


                       He has not yet spoken publicly about a video that
                       reportedly showed his wife receiving a Christian
                       Dior bag.


                # ⚓ CS Monitor ☛ Despite_record_coal_use,_China_on_track_to
                  meet_green_energy_targets⠀⇛


                       China’s recent high levels of coal generation won’t
                       affect its goal of peaking emissions by 2030.
                       That’s because more energy production is coming
                       from renewables and the nation is shifting coal’s
                       role to a backup energy reserve.


                # ⚓ The Straits Times ☛ Beijing_calls_for_‘positive,_objective,
                  friendly’_China_policy_from_South_Korea⠀⇛


                       Both sides also exchanged views over the situation
                       on the Korean Peninsula.


                # ⚓ RFA ☛ Senate_confirms_Kurt_Campbell_as_No._2_US_diplomat⠀⇛


                       The White House’s ‘Asia czar’ is now the deputy to
                       Secretary of State Antony Blinken.


                # ⚓ New York Times ☛ What_King_Charles’s_Cancer_Diagnosis_Means
                  for_Princes_William_and_Harry⠀⇛


                       How life may change for the Prince of Wales and his
                       younger brother, Harry, who flew from Los Angeles
                       to visit their father.


                # ⚓ New York Times ☛ King_Charles’s_Push_for_Transparency_on
                  Cancer_Diagnosis_Raised_More_Questions⠀⇛


                       The king has let people know more about his health
                       than other monarchs, but a decision to keep private
                       the form of cancer he has is leading to speculation
                       in lieu of facts.


                # ⚓ Digital Music News ☛ Toby_Keith_Passes_Away_After_Battle
                  with_Cancer_—_Age_62⠀⇛


                       Country singer Toby Keith has passed away after a
                       battle with cancer. The “Red Solo Cup” singer was
                       62. A statement posted on his official website
                       reads, “Toby Keith passed peacefully last night on
                       February 5 surrounded by his family. He fought his
                       fight with grace and courage.


                # ⚓ University of Michigan ☛ Social_media_and_social
                  stratification⠀⇛


                       If you have a conversation with three new people
                       every day for 73 years, you will meet 80,000 people
                       throughout your lifetime — only 0.001% of the
                       world’s population. With the creation of popular
                       social control media platforms like Instagram,
                       TikTok, X (formerly known as Twitter) and more,
                       measurements of human interaction get increasingly
                       complicated.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Security Week ☛ Meta_Says_It_Will_Label_AI-Generated
                        Images_on_Facebook_(Farcebook)_and_Instagram⠀⇛


                             Facebook and Instagram users will start
                             seeing labels on AI-generated images that
                             appear on their social control media feeds,
                             as the tech industry aims to sort between
                             what’s real and not.


                      # ⚓ Scoop News Group ☛ White_House_ramping_up_efforts_to
                        combat_deepfakes⠀⇛


                             Cyber and national security advisor Anne
                             Neuberger says the White House is exploring
                             the use of watermarking to better identify
                             and disclose computer-generated images.


                      # ⚓ Silicon Angle ☛ New_Hampshire_AG_says_Texas_firm_was
                        behind_AI-generated_Joe_Biden_robocall [Ed: No, CG or
                        voice synthesis is not "artificial intelligence" and by
                        far predates this latest hype wave]⠀⇛


                             New Hampshire’s attorney general today named
                             the alleged sources of a mysterious deepfake
                             Joe Biden robocall last month that told
                             Democrats in the state not to vote in the
                             primary election, prompting more discussions
                             on the regulation of [CG].


                      # ⚓ Latvia ☛ Phone_scammers_reported_to_use_[CG]_voice_in
                        Latvia⠀⇛


                             Forms of phone scam are evolving. Fraudsters
                             with [CG] are now also able to provide calls
                             where the text of the conversation is
                             translated directly during the call,
                             according to mobile operator Bite, whose
                             employee recently faced this type of phone
                             call.


          o § Censorship/Free Speech⠀➾


                # ⚓ RFA ☛ China_jails_feminist_labor_activist_Li_Qiaochu_for
                  ‘subversion’⠀⇛


                       Fellow activists say Li was jailed for supporting
                       her partner, the jailed fellow dissident Xu
                       Zhiyong.


                # ⚓ Hong Kong Free Press ☛ Ex-student_leader_convicted_of
                  rioting_in_Hong_Kong_legislature_interrupted_by_judge_for
                  giving_‘political_opinions’⠀⇛


                       A former student leader convicted of rioting inside
                       the city’s legislature on the anniversary of Hong
                       Kong’s handover to China during the 2019 protests
                       was repeatedly interrupted by the judge for
                       “expressing political opinions.”


                # ⚓ Techdirt ☛ Fifth_Circuit:_Upon_Further_Review,_Fuck_The
                  First_Amendment⠀⇛


                       I’m not a religious man, but Jesus Fucking Christ.


                # ⚓ Meduza ☛ Navalny_sent_to_punitive_isolation_cell_for_26th
                  time_since_imprisonment_—_Meduza⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ New York Times ☛ Federal_Records_Show_Increasing_Use_of
                  Solitary_Confinement_for_Immigrants⠀⇛


                       A new report based on records from the Trump and
                       Biden years found the average length of solitary
                       detainment was longer than the duration the U.N.
                       says can constitute torture.


                # ⚓ JURIST ☛ Netherlands_police_crack_down_on_farmer_protests
                  disrupting_freeways⠀⇛


                       Dutch police stopped farmers’ protests across the
                       Netherlands on Monday regarding low prices for
                       produce and the EU’s Green Deal. The protests
                       disrupted traffic by blocking freeway exit roads
                       and setting fires. In a statement released on
                       Monday, the police in Gelderland highlighted the
                       health risks and environmental hazards posed by the
                       protests.


                # ⚓ JURIST ☛ US_federal_court_sentences_Illinois_man_to_five
                  years_in_prison_for_attempted_arson_of_a_reproductive
                  healthcare_clinic⠀⇛


                       US District Judge Colin S. Bruce sentenced Philip
                       Buyno to five years in prison in the Central
                       District of Illinois on Monday after he attempted
                       to commit arson against a future reproductive
                       healthcare center. Bruce also ordered Buyno to pay
                       $327,547 in restitution for the damages he caused.


                # ⚓ Stanford University ☛ Storms_knock_down_Blue_and_White
                  Tent⠀⇛


                       The Blue and White Tent was knocked down by storms
                       on Sunday. Organizers did not respond to questions
                       about plans to reassemble but during the three
                       months it stood at the center of White Plaza, its
                       organizers said they hoped to incentivize healthy
                       discourse on the Israel-Gaza war.


                # ⚓ Techdirt ☛ Senators_Ask_The_DOJ_To_End_Federal_Funding_For
                  Predictive_Policing_Programs⠀⇛


                       Predictive policing programs were supposed to make
                       police work smarter and more efficient. It was
                       supposed to trim down on hours wasted where a
                       police presence wasn’t needed and increase
                       enforcement in areas where crime was a problem.


                # ⚓ Hong Kong Free Press ☛ Veteran_Hong_Kong_activist_Koo_Sze-
                  yiu_to_face_verdict_over_planned_protest_against_‘unfair’
                  District_Council_race⠀⇛


                       Hong Kong veteran activist Koo Sze-yiu will face a
                       verdict under the sedition law next week over a
                       planned protest against what he called an “unfair”
                       District Council race.


                # ⚓ New York Times ☛ Columbia_Limited_On-Campus_Protests,_So
                  Students_Took_to_the_Streets⠀⇛


                       As Columbia and Barnard weigh how to protect free
                       speech and student safety, their protest rules have
                       forced some students off campus, where they have
                       clashed with the police.


                # ⚓ RFERL ☛ Iranian_Journalists_Detained_After_Security_Forces
                  Raid_Media_Outlet_Offices⠀⇛


                       Iranian security forces raided a building housing
                       the editorial office of the Fardaye Eghtesad media
                       outlet, detaining an unknown number of its
                       journalists for hours at their workplace in a sign
                       that a crackdown by authorities on free speech
                       continues.


                # ⚓ EDRI ☛ Automated_data_exchange_in_Prüm_II:_The_EU’s
                  securitisation_mindset_keeps_encroaching_on_our_fundamental
                  rights⠀⇛


                       The agreement on automated data exchange for police
                       cooperation, known as ‘Prüm II aligns with a
                       broader EU trend of laws prioritising national
                       security over human rights. The final text of this
                       regulation has insufficient fundamental rights
                       safeguards and could even encourage more member
                       states to adopt facial recognition technology. The
                       EU Parliament must reject the current Prüm II
                       Regulation in the upcoming plenary vote.


                # ⚓ YLE ☛ "No_need_to_hoard"_say_retailers_as_logistics_workers
                  announce_three-day_political_strike⠀⇛


                       The walkout from 14-16 February at 19 logistics
                       centres around the country could affect supermarket
                       supply chains.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Techdirt_Podcast_Episode_379:_Is_the_Internet
                  Killing_Culture?_(No._Don’t_Be_Stupid.)⠀⇛


                       A couple weeks ago, we released the 2024 edition of
                       our Sky Is Rising report about the state of the
                       entertainment industries. Last week, Mike and I
                       joined Corbin Barthold on Techfreedom’s Tech Policy
                       Podcast for a discussion about the report and, more
                       broadly, the state of culture in the internet era
                       and the conversations that surround it. You can
                       listen to the whole conversation here on this
                       week’s episode of the Techdirt Podcast.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Digital Music News ☛ SoundCloud_Taps_Trolley_to_Provide
                  Payouts_for_SoundCloud_for_Artists⠀⇛


                       SoundCloud taps Trolley to provide payouts for
                       their artist payments program. Music industry
                       payout platform Trolley has announced its selection
                       by SoundCloud to provide payouts for the streaming
                       platform’s SoundCloud for Artists program.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ JUVE ☛ “Thomas_Kühnen’s_retirement_brings_opportunity_for
                  renewal_in_Düsseldorf”⠀⇛


                       On the evening of 2 February, respected figures
                       from the German patent monopoly scene arrived at
                       the exclusive Düsseldorf Industrie-Club to pay
                       tribute to Thomas Kühnen. The highly respected but
                       controversial presiding judge of the 2nd Civil
                       Senate at the Düsseldorf Higher Regional Court has
                       now officially retired.


                # ⚓ Unified Patents ☛ $9,000_awarded_for_Emerging_Automotive
                  vehicle_patents_prior_art⠀⇛


                       Unified is pleased to announce PATROLL
                       crowdsourcing contest winners below totaling $9,000
                       in cash prizes. The patents are owned by Emerging
                       Automotive LLC. The patents generally relate to
                       user profiles for vehicles and e-Keys and have been
                       asserted against Toyota and Kia.


                       We would also like to thank the dozens of other
                       high-quality submissions that were made on this
                       patent. The ongoing contests are open to anyone,
                       and include tens of thousands of dollars in rewards
                       available for helping the industry to challenge NPE
                       patents of questionable validity by finding and
                       submitting prior art in the contests.


                # § Kangaroo Courts⠀➾


                      # ⚓ Kluwer Patent Blog ☛ Opt-out_challenges_in_the_UPC
                        [Ed: Illegal and unconstitutional. This is crimes of
                        the EPO, left unhandled by the EU, basically spilling
                        over to the EU, rendering it complicit.]⠀⇛


                             Opt-outs are dealt with in Part IV of the UPC
                             Agreement entitled “Transitional Provisions”.
                             The prevailing view is that these provisions
                             should be interpreted to mean that an opted-
                             out patent monopoly is no longer subject to
                             the jurisdiction of the UPC and the opt out
                             shall remain in place for the lifetime of the
                             patent.


                      # ⚓ Kluwer Patent Blog ☛ SPC_reform_progresses_to_plenary
                        vote_in_European_Parliament [Ed: They just blindly
                        approve whatever lobbyists push their way]⠀⇛


                             The SPC reform which is currently undergoing
                             the legislative procedure in the European
                             Union has taken a further decisive step
                             forward, as the European Parliament’s
                             Committee on Legal Affairs (JURI Committee)
                             has approved an amended version of the draft
                             text of the four new EU regulations on SPCs
                             for medicinal and plant protection
                             products...


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ Recommended_Reading:_Michael_P._Goodyear,
                  "Queer_Trademarks."⠀⇛


                       In his article, "Queer Trademarks," Michael P.
                       Goodyear, Acting Assistant Professor at New York
                       University School of Law and Fellow at the
                       Engelberg Center on Innovation Law Policy, provides
                       an enlightening analysis of the impact of Matal v.
                       Tam and Iancu v. Brunetti on the registration of
                       trademarks that refer to LGBTQ+ persons. With the
                       door opened to registration of slurs as trademarks,
                       what LGBTQ+-oriented marks have been registered?
                       Are they affirming in nature or the opposite? [The
                       article may be downloaded here, and it appears in
                       2024 U. Ill. L. Rev. 163 (Vol. 2024, No. 1)].


          o § Copyrights⠀➾


                # ⚓ Public Domain Review ☛ Never-again_Land:_J._M._Barrie's_My
                  Lady_Nicotine_(1896)⠀⇛


                       A genre-defying work by the creator of Peter Pan
                       about the pleasures of smoking.


                # ⚓ CS Monitor ☛ TikTok_and_a_major_label_are_in_a_standoff.
                  How_does_this_song_end?⠀⇛


                       TikTok videos featuring major artists’ music are
                       being muted after Universal Music Group terminated
                       its licensing deal on the platform. It’s part of a
                       larger conflict over fair compensation for
                       creators’ work – as well as questions about the use
                       of AI.


          o § Gemini* and Gopher⠀➾


                # § Personal/Opinions⠀➾


                      # ⚓ Birthday_2024⠀⇛


                             Happy fifth birthday to me! By which I mean
                             my fifth birthday spent as a man rather than
                             as a woman.


                             I normally don’t do this kind of post. Like,
                             being an adult and posting your birthday haul
                             on the internet feels... just, not the way I
                             wanna do things. But something about this
                             year was just Nice. My family only got me a
                             few things, but they’re all special to me.


                      # ⚓ I'm_busy⠀⇛


                             I don't know what happened in January, but
                             all of a sudden everyone wanted to do
                             everything all at once. I have been busy.


                             Busy feels weird. After a couple of years of
                             living like a mollusc stuck to glass, it
                             feels very strange to have and exert energy.
                             But I've already been writing about that.


                             I'm a lot better now at moving with the busy-
                             ness. Sometimes it's as simple as going to
                             the restroom and leaning against a hard wall
                             and closing my eyes. Other times it's saying
                             no to things, or limiting participation.


                      # ⚓ Weather_Station_Papers—API⠀⇛


                             For my final semester of college, I took a
                             special projects course which is essentially
                             a research class, but instead of the
                             professor telling me what to do, I go to the
                             professor with a project that I would like to
                             do. If they agree, they act as my mentor to
                             help me plan out and follow through with the
                             project.


                             I decided that I would like to finish my
                             weather station once and for all. At this
                             point, I have already finished the hardware
                             portion of the project (though there are some
                             issues I have yet to work out). My proposal
                             was to build a web server that would link
                             between the weather station hardware and the
                             end user.


                             [...]


                             Stations can be in locations where it is not
                             possible to make requests from outside the
                             local network. MQTT is a protocol that is
                             designed for IoT systems. MQTT clients may
                             publish/subscribe to endpoints. This allows
                             for stations to send weather updates to all
                             listening weather servers. Weather stations
                             would also be able to make requests to
                             specific stations if needed.


                      # ⚓ my_brains_incompatability_with_english⠀⇛


                             As a few of you may have worked out by now i
                             love to tell stories, sharing interesting
                             concepts is one of my favorite things to do,
                             and i have a lot of ideas for stories!


                             but last night i found myself coming to the
                             realisation that the reason i've struggled so
                             hard with writing those stories, and
                             similarly the reason i failed many of my
                             classes in school, is that my brain works in
                             the opposite way to english.


                      # ⚓ 🔤SpellBinding:_AEULQTI_Wordo:_BLOCS⠀⇛


                # § Politics and World Events⠀➾


                      # ⚓ “We_tried_polyamory_in_the_60s,_it_didn't_work”⠀⇛


                             A while ago i read a comment expressing the
                             sentiment expressed in the title. As someone
                             who's been doing consensual nonmonogamy (cnm)
                             in various forms - swinging, polyamory,
                             ‘relationship anarchy’, etc. - for well over
                             two decades, this made me bristle.


                             Regardless of whether or not there were
                             people in the 60s explicitly trying
                             ‘polyamory’, _per se_ - the Online
                             Etymological Dictionary says it was being
                             used “by 1972”[a] - there were certainly a
                             number of experiments in ‘consensual
                             nonmonogamy’ / ‘free love’ during that time.
                             They were also certainly not the first;
                             numerous such experiments have taken place
                             over the centuries, in various communities,
                             for various reasons.


                      # ⚓ The_Australian_activist_left_desperately_needs_an
                        infusion_of_class_politics⠀⇛


                             The Australian activist left will organise
                             protests and rallies regarding climate change
                             and things happening overseas. But what's it
                             doing about the housing crisis, about the
                             rate of homelessness, about migrants being
                             scapegoated for it all?


                # § Technology and Free Software⠀➾


                      # ⚓ Steam_Next_Fest_-_Day_2⠀⇛


                             It's day two out of seven in the Steam Next
                             Fest. I know I said I would write one review
                             per day but I also want to see if I can
                             squeeze more. It won't be as long as
                             yesterday's but I hope no one minds!


                             [...]


                             Other than the UI not being Deck-friendly,
                             this game evokes the familiarity with Hades,
                             but with an East Asian influence instead. The
                             only language available in full audio is
                             Simplified Chinese, as indicated on Steam so
                             I'm inclined to assume it's based on Chinese
                             legends and mythos. It's also nice to see
                             other cultures' wealth of stories and
                             characters being tapped for retelling. Of
                             course, I could just be very biased because I
                             am Chinese by birth.


                      # ⚓ gopherproxy.sh_fixed_(mostly)⠀⇛


                             I thought I'd post an update on my last phlog
                             entry from 13 Dec 2013... Better late than
                             never I suppose... The aforementioned
                             gopherproxy.sh script was fixed the next day
                             after I discovered it had stopped working.


                             It now uses lynx instead of squid, and seems
                             to actually be working better than squid did!
                             For instance, squid often choked badly on
                             multi- byte UTF-8 characters; lynx does not
                             suffer at all from this issue.


                      # ⚓ Hypermemetic_intersectional_normalcy⠀⇛


                             I am once again subposting a Lobste.rs
                             thread.


                             The other day, I saw some people discussing
                             an article on the subject of Elixir, where
                             the author said that they felt like when they
                             were present in the Elixir community, they
                             felt like they were surrounded by "tech
                             bros."


                             Now, in my experience Lobste.rs responds to
                             this sort of thing a lot better than Hacker
                             News. I wouldn't even want to see the replies
                             on Hacker News. Of course, in either case I
                             would expect them to have complicated
                             feelings about this because one way or the
                             other they are largely the people getting
                             labelled "tech bros." That sort of thing can
                             be hard to interrogate, I concede.


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




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