𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, October 27, 2021
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Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2021/10/27/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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QmSfTwYRE2mM7875hHQK9fmXEAAZS4i3r9frAmfJcCFGks
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Qmex86DPLV4yK5WC34kReVXbdEtRT7fvt7mBVzMTGbSCct


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

⦿ The EPO’s Overseer/Overseen Collusion — Part XXV: The Balkan League  -  Fresh Blood or Same Old, Same Old? | Techrights

⦿ Beatriz Busaniche Speaks Up in Defense of Richard Stallman | Techrights

⦿ ’Shaping the New Normal’ Survey at the EPO Got 5,554 EPO Staff to Participate, But It Was Controlled by Liars With an Agenda | Techrights

⦿ IRC Proceedings: Tuesday, October 26, 2021 | Techrights

⦿ Many of the National Delegations (or Delegates) in the EPO’s Administrative Council Have No Understanding of What They Vote on | Techrights

⦿ [Meme] EPO Presidential Surveys | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/10/27/balkan-league-summary/#comments
		http://techrights.org/2021/10/27/beatriz-busaniche-on-rms/#comments
		http://techrights.org/2021/10/27/better-epo-survey/#comments
		http://techrights.org/2021/10/27/irc-log-261021/#comments
		http://techrights.org/2021/10/27/political-patent-offices/#comments
		http://techrights.org/2021/10/27/presidential-surveys/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/10/27/murena-for-eos/#comments
		http://techrights.org/2021/10/27/xorg-server-21-1/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 63

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/balkan-league-summary/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/27/balkan-league-summary/

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Gemini_version_available_♊︎


✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_–_Fresh
Blood_or_Same_Old,_Same_Old?⠀✐


Posted in Europe, Patents at 5:06 am by Dr. Roy Schestowitz


Series parts:


   1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!
   2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous”
      Endorsement?
   3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes
   4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States
   5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja”
   6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch
      Courage
   7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity
   8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and
      Pusillanimous_Hibernia
   9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss
      Cheese
  10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the
      Controversial_Christian_Bock
  11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_–
      Battistelli’s_Swiss_Apprentice?
  12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection
  13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian
      Facilitators_–_Spain
  14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian
      Facilitators_–_Portugal
  15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria…
  16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the
      Austrian_Double-Dipper
  17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic
      Nordic_Bloc
  18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord
  19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States
  20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group
  21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The
      Doyen_and_His_“Protégée”
  22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_–
      North_Macedonia_and_Albania
  23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_–
      Bulgaria
  24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_–
      Romania
  25. YOU ARE HERE ☞ The Balkan League – Fresh Blood or Same Old, Same Old?
                    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_Balkan_gallery⦈_
  Some new faces on the EPO’s Administrative Council representing the Balkan
states that voted in favour of Battistelli’s “Strike Regulations” in June 2013.
Clockwise from top left: Goran Gerasimovski (MK), Marian Cătălin Burcescu (RO),
                Ledina Beqiraj (AL), and Vladya Borisova (BG).


Summary: We take stock of “captured states” that voted in favour of unlawful
“Strike Regulations”


In this part we conclude our whistle-stop tour of the “Balkan League” states
that helped to rubber-stamp Benoît_Battistelli‘s “Strike Regulations”.


As we have seen, there have been a lot of changes in those delegations since
2013.


“Insofar as they are prepared to swallow the sugar-coated “Kool-Aid” narrative
being spoon-fed to them by the spin-doctors of Team Campinos, they might not
even realise that there is a problem.”By a strange coincidence, the only
delegation which remains unchanged is the one representing Croatia, which is
still headed by Željko Topić’s “protégée” Ljiljana Kuterovac.


As far as the other delegations are concerned, it’s not clear to what extent
the new generation of representatives are aware of the damage caused by the
actions of their predecessors in supporting Battistelli’s “reign of terror” at
the EPO.


“It’s very clear that, in many of these countries, the appointment of the head
of the national “IP” office – who also acts as the head of delegation on the
EPO’s Administrative Council – is treated as a sinecure which is typically
handed out as a “reward” to some local party political opportunist.”Insofar as
they are prepared to swallow the sugar-coated “Kool-Aid” narrative being spoon-
fed to them by the spin-doctors of Team Campinos, they might not even realise
that there is a problem.


It’s very clear that, in many of these countries, the appointment of the head
of the national “IP” office – who also acts as the head of delegation on the
EPO’s Administrative Council – is treated as a sinecure which is typically
handed out as a “reward” to some local party political opportunist.


In the case of two of the new delegates pictured above, it can be said without
fear of contradiction that their appointments were overtly political in nature:


• the North Macedonian delegate Goran Gerasimovski who is a member of the
Macedonian SDSM; and
• the Romanian delegate Marian Cătălin Burcescu who is a member of the Romanian
PNL.


In the case of the two other delegates – Ledina Beqiraj from Albania and Vladya
Borisova from Bulgaria – there isn’t enough information available to indicate
whether or not their appointments might have been influenced by ulterior
political considerations.


“…it deserves to be pointed out that not all member states from the Balkan
region were prepared to kowtow before Battistelli.”In any event, it remains to
be seen whether the new representatives from the “Balkan League” states will
continue to play the role of “captured delegates”, meekly subservient to
Battistelli’s successor Campinos, or whether they will manage to take a
principled stand for justice and the rule of law at the EPO.


The voting record of these delegations during the Battistelli era, and
afterwards under Campinos, gives little cause for optimism in this regard.


The actions of these countries on the EPO’s Administrative Council tend to
confirm their reputation as "captured_states". However, it deserves to be
pointed out that not all member states from the Balkan region were prepared to
kowtow before Battistelli.


“In the next part we will stay in the general vicinity of the Balkan Peninsula
as we turn our attention to Greece and its neighbours, Cyprus and Turkey.”Two
of the successor states of the former Yugoslavia – namely, Slovenia and Serbia
– frequently took a critical stance towards the Corsican despot and his
nefarious machinations at the EPO. Both of these delegations withheld their
support during the vote on the “Strike Regulations” in June 2013.


However, before we take a closer look at the “abstentionists”, we will continue
and complete our examination of the remaining delegations that supported
Battistelli on that occasion.


In the next part we will stay in the general vicinity of the Balkan Peninsula
as we turn our attention to Greece and its neighbours, Cyprus and Turkey. █


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Gemini_version_available_♊︎


✐ Beatriz_Busaniche_Speaks_Up_in_Defense_of_Richard_Stallman⠀✐


Posted in Free/Libre_Software, FSF, GNU/Linux at 1:13 am by Guest Editorial
Team


Published two days ago in this_site


===============================================================================
Beatriz Busaniche sent us this comment in July 2021. She wrote it originally in
Spanish. Here are both the original text and our translation to English.


===============================================================================
⚓  Spanish (Original)⠀⇛


Soy Beatriz Busaniche, activista de Software Libre y Derechos Humanos de
Argentina desde hace 20 años. Escribo estas palabras porque me considero desde
hace mucho tiempo amiga de Richard Stallman, un hecho del que siempre me sentí
y me siento orgullosa. Richard se ha hospedado en mi casa muchas veces, hemos
compartido eventos, reuniones sociales, actividades políticas y públicas,
organicé muchísimas de sus conferencias en mi país. En todos estos años siempre
se ha comportado de forma totalmente respetuosa, cálida y generosa conmigo, mi
familia y mis amigos.


Richard hizo aportes inmensos al mundo de las tecnologías, sentó las bases de
la cultura del Software libre, un movimiento indispensable en los tiempos que
corren, nos ayudó a pensar críticamente lo que hacemos y cómo lo hacemos. Como
movimiento, le debemos mucho y debemos hacernos cargo de que nos hemos ocupado
poco de Richard como ser humano.


Quienes tenemos la suerte de conocerlo bastante, sabemos que es una persona
sensible, amorosa, con flaquezas y debilidades como cualquiera de nosotros, una
persona que igual que cualquiera de nosotros comete errores pero que es capaz
de cambiar de opinión frente a argumentos claros y razonables. Sabemos también
que es una persona con una lógica imbatible que no siempre aplica a las
cuestiones de la vida social.


Como feminista que soy, siempre he luchado por romper los estereotipos y los
procesos de normalización hegemónica. Siempre pensé que debíamos aprender a
integrar las minorías y las diferencias y sobre todo, luchar por la justicia y
los derechos para todas las personas.


No hemos sido justos con RMS en los últimos meses y me siento profundamente
avergonzada por no haber levantado mi voz en su defensa con más firmeza en
ocasiones anteriores.


Como bien dice Richard en su declaración del 12 de abril pasado[*], y como bien
sabemos todos los que hemos convivido con él en alguna instancia, su forma de
razonar y analizar es muy peculiar pero es algo que está más allá de lo que él
puede decidir. ¿De qué nos sirve llamarnos progresistas, feministas,
antifascistas si no somos capaces nosotros mismos de lidiar con la
neurodiversidad?


No voy a juzgar a quienes no quieren a RMS, cada quién construye las afinidades
y opiniones que quiere, pero arrojar piedras sobre RMS por su dificultad para
escapar de la literalidad es un acto de crueldad indigno de quienes creemos en
un mundo más justo y diverso. No cuenten conmigo para eso.


* RMS_addresses_the_free_software_community (Archived) ↑


⚓  English Translation⠀⇛


I am Beatriz Busaniche from Argentina, and I have been a free software and
human rights activist for 20 years. I’m writing because I am very proud to
consider myself a longtime friend of Richard Stallman. He has stayed in my home
many times. I have organized many of his conferences here in Argentina, and we
have shared events, social gatherings, and political and public activities. In
all these years Richard has always behaved in a totally respectful, warm, and
generous way to me, my family, and my friends.


Richard has made huge contributions to the world of technology. He laid the
foundation for the culture of free software, which has grown into a movement
that is crucial to our world today. He has helped us to think critically about
what we do and how we do it. Our movement is forever in his debt, and we must
acknowledge that we have not met our responsibility to appreciate Richard as a
human being.


Those of us who are lucky enough to be well acquainted with him know that he is
a sensitive, loving person, with weaknesses and imperfections like anyone. He
can make mistakes, just like any of us. Yet, he has an extraordinary capacity
for logical thinking, and is able to change his position when presented with
clear and reasonable arguments. Sometimes, however, he expresses his ideas in
an unusually direct way that may seem strange to some.


As a feminist, I have always worked to challenge stereotypes and over-
generalizations about people. I believe that we should be inclusive of those
with differences and, above all, fight for justice and the rights of all
people.


I feel that Richard has been treated unfairly in recent months, and I am deeply
ashamed for not having raised my voice in his defense more firmly before this.


In his statement of April 12, 2021[**], Richard admits—and those of us who know
him well will concur—that his way of reasoning and analyzing situations is very
idiosyncratic, an aspect of his personality beyond his control—an example of
what might be called neurodiversity. What is the point of calling ourselves
progressives, feminists, or anti-fascists, if we ourselves cannot deal with
someone who thinks and expresses himself differently?


I am not going to judge those who do not want to associate with Richard
Stallman, everyone is entitled to form their own opinion. But I think that
throwing stones at him for his tendency to speak logically and literally is an
act of cruelty unworthy of those of us who believe in a more just and diverse
world. In that, count me out.


** RMS_addresses_the_free_software_community (Archived) ↑



                    ䷩ 𝚕𝚒𝚗𝚎 405

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/better-epo-survey/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/27/better-epo-survey/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ ‘Shaping_the_New_Normal’_Survey_at_the_EPO_Got_5,554_EPO_Staff_to
Participate,_But_It_Was_Controlled_by_Liars_With_an_Agenda⠀✐


Posted in Europe, Patents at 9:13 am by Dr. Roy Schestowitz


The dictatorship hates independent surveys whose outcome it cannot control or
take out of context. Previously, staff representatives who ran a survey (not
controlled or ‘authorised’ by the king) got in serious trouble.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Another_survey?_Oh,_independent_survey..._Oy_vey⦈_


Summary: Last year’s EPO ‘study’ (hogwash about “quality” and other
unscientific_junk) was likely biased by virtue of autocrats controlling it and
exploiting it for nefarious agenda and brainwashing_of_national_delegates*. The
Staff Union of the EPO (SUEPO) has a new survey in the making.


OVER the years we saw many EPO surveys and SUEPO (union) surveys; with
dictators like Benoît_Battistelli and António_Campinos spying on all the staff
and flagrantly violating privacy laws (without any legal consequences) folks
can imagine what sort of answers staff gives to each; set aside the effect of
push_polling or loaded questions…


In any case, SUEPO is running a survey right now; we don’t want to disclose
URLs (that would interfere with the process), but someone has sent us a copy of
a paper from last week, which we’re reproducing below.


     22 October 2021
     su21030cp – 0.2.1


     Teleworking Survey


                       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇SUEPO survey⦈


     Reassessing the Telework preferences a year later


     Back in mid-2020, the Shaping the New Normal survey was conducted and
     with a participation rate of 86% it allowed for a quite large amount
     of 5554 staff members to be heard. Among the topics addressed by the
     survey there was future teleworking (e.g. different schemes,
     locations and durations, the relationship between long-term
     teleworking and expatriation benefits and the impact of extended
     teleworking and flexibility on the performance of daily tasks),
     working at the Office’s different sites and the future use of its
     buildings and premises. The different schemes were covered by 5
     different scenarios or personas.


     Now, over a year after Shaping the New Normal survey, it is important
     once again to launch a survey among staff to assess how the intended
     use of teleworking may have evolved after this one year pandemic
     period. This survey aims at assessing whether and how the proposed
     mid-term policy by the President would actually fit the wishes of
     staff.


     The survey contains solely 10 survey questions, chosen to mimic the
     questions asked in the Shaping the New Normal survey. The survey will
     be open for answers during 4 weeks.


     After the closure of this survey the results will be published to
     staff and the information used to argue and support the proposals
     within the working group.


     Take the SURVEY now! Thank you for considering your participation!


     SUEPO Central


     Staff Union of the European Patent Office (SUEPO)


As always, SUEPO surveys are very interesting as they reveal what staff really
thinks. Not what managers (politicians) want to show. The dictatorship of the
EPO just uses surveys for self-serving propaganda purposes, looking to justify
decisions already made regardless (before the surveys). █
_____
* They said the “Council expressed its keen interest in the presentation of the
analysis following the recent survey on “Shaping the new normal”.” But Office
management controlled it all. Under normal circumstances it might seem OK. But
they’re lying to the Council routinely.


⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣶⣾⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡃⠀⣶⡙⢿⡿⡿⠿⣿⡿⣿⣿⠟⠋⠉⠀⠀⢀⣀⣤⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣟⣷⢹⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⠀⢨⠻⡌⠃⠀⠀⣼⣷⡏⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣭⣿⣵⣿⣿⣼⣫⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠰⠘⠃⠀⠀⢠⡆⠛⣿⣧⠀⠀⠨⣻⣿⣿⣿⣿⣿⣿⡿⣿⣦⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣾⣿⣞⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⣀⢸⠇⠁⠀⠸⣿⠀⠀⠀⠉⠉⠉⠉⠀⣀⣀⣤⣍⠛⠣⢤⣤⣈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⡆⠙⠀⡀⠄⠸⣇⢿⣆⠀⠀⢤⡤⠶⡾⠟⣛⣻⣿⠟⣦⠀⠀⠀⠉⠙⠒⠤⣀⡈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠘⠁⢀⢠⡆⠃⠀⣤⣿⣾⣿⠀⠠⠐⠒⣚⡃⣨⣭⣿⣆⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⠋⢠⢿⠻⣿⠙⠩⡍⠛⣿⣿⡟⣿⡿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡄⣶⠸⠈⢀⣰⣾⣿⣿⣿⣿⡶⠶⠾⠛⠻⡏⣩⠭⢿⣶⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠮⣿⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠿⠷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⢁⣠⣼⣿⣿⣿⣿⡿⠙⣿⡇⠀⢀⠂⡏⡧⠤⠔⠾⣤⣼⣿⣿⣿⣿⣿⣿⣷⡆⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣇⠲⠾⣤⣿⡇⠀⣠⣤⣿⣛⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢫⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡈⢻⣿⡟⠁⠀⢠⡄⢰⣿⣿⣄⠹⠋⡋⡿⠀⣀⣨⣟⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⢸⣿⣶⡿⠰⣠⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠘⠻⠟⠀⠸⢻⣿⣶⣲⣾⡁⣾⣿⣿⣿⣆⠘⠿⡟⠚⣛⣉⡽⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⣿⠟⡞⠂⠃⠀⠀⠀⠀⠰⠿⢿⣏⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠉⠀⠈⠹⢿⣿⣯⠻⣾⣿⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⣿⣷⠏⠇⠀⠀⠀⠀⠀⠀⠀⠠⣴⣽⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠛⠛⠓⠀⠀⠀⠀⠙⠛⠃⠙⠛⠛⠛⢛⣗⠛⠛⠛⣻⣟⡛⠛⢛⡟⠛⠛⠋⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⢛⣿⣟⣿⠀⠀⠛⠃⣤⠀⠀⠪⣤⣶⡄⠚⠃⠀⠀⠉⠀⠈⠀⠀⢠⣤⢠⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣿⣿⣀⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠸⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢸⢸⠐⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢸⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⣿⠁⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⠀⠀⠀⠀⣿⠀⠀⢨⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣽⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠂⠀⠀⠀⢺⡿⠁⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠘⢸⡏⠀⠀⠀⠀⣿⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣾⣏⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⠀⠀⠀⢸⡸⢷⠀⠀⠀⠀⡏⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣤⣾⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠰⣤⣀⠀⣀⣤⠔⠀⢱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠈⣿⣿⡏⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣀⣿⣿⢫⣥⣭⡛⣭⣝⢫⣭⢛⣭⣭⣍⢠⣤⣤⣬⢩⣤⢠⣤⢠⣤⣤⡌⣭⣭⣭⡛⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⡇⣿⣿⣼⣿⢸⣿⢸⣿⠈⢹⣿⠉⢸⣿⣼⣿⢸⣿⣏⡁⣿⣏⣿⡇⣸⢹⡿⠋⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣼⣿⣿⣧⣿⡿⣿⣿⢸⣿⢸⣿⠀⢸⣿⠀⢸⣿⢻⣿⢸⣿⡟⠃⣿⡏⣿⡆⠁⠀⠁⠀⠠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠿⠟⠹⠿⠿⠇⠻⠿⡘⠿⠾⢟⣤⡸⠿⣀⠸⠿⠸⠿⠸⠿⠿⠇⠿⠇⠿⠇⠀⠀⠀⠀⢀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢋⣬⣭⡙⢩⣤⢩⣤⢀⣤⣭⣛⢻⣿⡟⣯⣄⣤⣤⣄⣤⡍⣩⡝⢋⣤⣄⡘⠃⠀⠀⠠⢻⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠁⡇⠘⠂⠀⠀
⠀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⣀⣀⣀⣾⣿⣿⡟⠀⢾⣿⡹⠟⢸⣿⢸⣿⢸⣿⣏⣿⡟⣿⡇⣿⡇⣿⣏⡉⢹⣧⣿⠃⠿⠇⣿⣧⠸⠿⠀⠠⢊⡞⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⣉⣩⣧⡔⢨⣝⢿⣷⢸⣿⢸⣿⢸⣿⡟⣿⡄⣿⣷⣿⠇⣿⡟⠃⡈⣿⡟⠀⣿⡷⣿⠏⠘⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⡇⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠸⠿⠾⠟⠘⠿⠾⠟⠸⠿⠇⠿⢇⠸⠿⠿⠀⠿⠿⠿⡀⠿⠇⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⠀
⠀⠉⠛⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠏⠋⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣾⣶⣿⣿⣰⣿⣶⣾⣶⣶⣿⣷⡖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠿⠇⠀⡀⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣾⣷⢸⣿⣷⠀⠀⣼⣿⣿⡇⢰⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣽⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⠀⠀⣿⣿⣿⡇⠀⢿⣿⣸⣿⣿⣿⠇⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣧⠛⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢈⠻
⠀⠀⠀⠀⠀⠼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⣼⣿⣿⣧⠀⢙⣿⣿⡇⠀⣸⣿⢻⣿⣿⣿⠀⠃⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣆⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠘⢿⣿⡗⠀⢹⣿⠧⣿⣿⣿⠀⠀⡙⢿⠀⠀⠀⢠⣶⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⡟⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢸⣿⡇⠀⠙⠿⠀⣿⡿⢻⠀⠀⣿⣍⠀⠀⢠⠿⠿⢿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⡄⣿⣷⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠓⠀⣿⣿⢰⠀⠀⣿⣿⣇⠀⠀⠀⠀⢠⣿⣀⣀⣀⣤⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⢯⠀⠐⢿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠛⠘⠀⠈⢿⣿⣿⡆⢸⣿⣿⡿⠿⠿⢿⣿⣿⣿⠀⠀⠀⢁⣾⣿⣿⣿⠰⣿⠋⠁⠀⠀⢸⣾⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⢠⠀⠀⢸⣿⡟⠛⠻⣿⢷⣦⠀⠀⠾⠟⠟⠀⠀⠀⠈⢨⢿⣿⣿⡿⠀⠉⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⡄⣿⣿⠈⠀⠀⠘⣿⠃⠀⠀⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡇⠀⠀⠀⠀⡿⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢶⠖⠀⠀⠀⠀⠀⠀⠀⠐⠟⠚⠋⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⣿⡇⢀⠀⠀⠘⠃⠀⠀⠀⡎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠟⣷⢼⠀⠀⢀⣠⣴⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⢠⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⠆⢤⣀⠀⠀⠀⠀⠀⠀⣀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣶⣶⡄⣶⢰⡆⠀⠀⣶⢰⣆⣶⢰⡶⣦⢰⡶⠆⣶⢶⣴⣶⠆⣶⣴⡆⣶⢶⣆⣶⡶⢰⣆⣶⠶⣶⠾⡋⣶⢶⡆⣶⣶⡖⣶⣶⣦⣶⣰⣶⣶⡶⢲⣦⡶⢹⣿⣿⡿⢱⡶⣦⢰⣦⡶⠀⣶⣰⣶⣶⡶⢲⣦⡶⠀⠀
⠀⢸⣿⣿⡇⣿⢿⡇⠀⠀⣿⢸⣿⣿⢸⡇⣿⢸⡿⠂⣿⠾⢻⣿⠃⣿⣿⡇⣿⢸⣿⣿⡟⢸⣿⣿⠀⣿⠘⠃⣙⢷⡆⣿⣿⡇⣿⣿⣯⢿⣿⡏⣿⡟⠈⣿⠃⠿⠿⠿⡇⢸⡇⣿⠈⣿⠇⠀⢿⣿⡇⣿⡟⠈⣿⠃⠀⠀
⠀⠈⠛⠛⠑⠛⠘⠃⠇⠀⠛⠘⠋⠛⠘⠛⠛⠘⠛⠃⠛⠀⠘⠛⠓⠛⠘⠃⣛⣛⣃⠛⢛⣘⡃⣛⣀⣛⣸⣧⣛⠚⣃⣛⠛⠃⠛⠛⠛⠘⠛⢃⠛⠛⣀⣛⣀⠛⢛⣛⣠⣘⠓⢛⣄⠛⠀⡆⠘⠛⠃⠛⠛⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣻⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣜⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣻⡁⡂⣁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⡟⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⡿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢟⠻⠟⡛⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣛⣛⣊⣋⣛⣻⣉⣛⣿⣿⣻⣯⣻⣹⣐⣢⠀⣋⣤⣘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣀⣀⠈⠉⠻⠋⠉⣀⣀⠈⠀⢺⣷⣤⣀⡀⠈⠁⣀⠘⠙⣿⠋⠁⣀⠈⠙⠋⠁⣀⣀⠈⠁⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⠆⠀⢩⣭⠉⠉⠀⡀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠿⠿⠿⠷⠀⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⠿⠆⠀⠀⠙⠛⠛⠋⠀⢀⣷⣝⠤⠙⠐⠃⠿⠄⠀⠛⠀⢀⣿⠀⠀⢠⣤⣤⣤⣤⠀⠀⠈⠛⠛⠛⠛⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⡟⠛⣶⣾⡟⠛⠻⢿⠀⢸⡟⠛⣿⣿⡟⠛⠻⢿⣿⣿⣿⣦⣤⡿⣿⡇⠀⠀⠴⠏⠀⠀⣶⣶⣾⡇⠉⠉⠋⣒⣒⡆⠀⠀⠶⠦⠀⠉⣿⣶⣦⣮⠉⠉⠈⠛⠒⣶⣷⣶⡶⢤⣴⡇⣿⣿⣿
⣿⣿⡇⣿⣿⢿⡏⠁⠈⠀⡀⠀⡀⠛⢿⠇⠀⠀⠈⠀⠀⠀⡀⠛⢿⡇⠀⠀⠀⠹⠣⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠟⠛⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛⠛⢿⡟⠀⠀⠀⠉⠀⠏⠙⣻⠀⠸⢿⡇⣿⣿⣿
⣿⣿⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣿⣿⣿
⣿⣿⡇⣿⠀⢀⡀⡀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⠠⠀⠀⠀⢀⢀⠀⠀⣿⠀⠀⠀⠀⢀⠀⡀⢀⠀⠠⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⢸⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⡷⠃⣠⣿⣿⣿⣿⣿⣿⠿⠄⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⣶⣾⣾⣿⠎⢿⣿⣶⣿⣾⣶⣶⡏⣤⣷⣶⣶⣾⣶⣿⣿⣿⠀⢀⣿⣿⣿⣶⣿⣷⡆⢐⣾⣿⣷⣿⣿⣿⣶⣤⠀⣿⣶⣶⣾⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⡿⠗⠀⠿⣿⣿⣿⣿⣿⡿⠓⠘⢿⣿⣿⣿⣿⣿⣏⢀⢠⣿⣿⣿⣿⣿⣿⠎⠛⢿⣿⣿⣿⣿⣿⣿⣿⢠⢰⣿⣿⣿⣿⣿⣯⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⡧⣾⢻⣿⣿⣿⣿⣿⣷⢘⣸⣿⣿⣿⣿⣿⣿⣗⡀⠀⣾⣿⣿⣿⣿⣿⣿⡾⢼⣿⣿⣿⣿⣿⣷⣶⠀⡀⠿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣾⢼⣿⣿⣿⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢇⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 591

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/irc-log-261021/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/27/irc-log-261021/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Tuesday,_October_26,_2021⠀✐


Posted in IRC_Logs at 2:28 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      261021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-261021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-261021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      261021.txt
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmaRadmLWmqAjP95ePsruoWEmr4qu54CojFhQM2SD6HgvA #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
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                                                 as plain/ASCII
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                                                 #boycottnovell-
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                                                 IRC log for
 QmUr1dfUe9JqHAUyM4PtweM2QiiT6GEayUmPLT4jSduRWY #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
                                                 #techbytes
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                                                 as plain/ASCII
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                                                 IRC log for
 QmPNvkzjCawfGrnSW7skhAEyYLNk7wRDQN4qkzMrYsTNb3 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): Qmex86DPLV4yK5WC34kReVXbdEtRT7fvt7mBVzMTGbSCct



                    ䷩ 𝚕𝚒𝚗𝚎 720

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/political-patent-offices/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/27/political-patent-offices/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Many_of_the_National_Delegations_(or_Delegates)_in_the_EPO’s_Administrative
Council_Have_No_Understanding_of_What_They_Vote_on⠀✐


Posted in Europe, Patents at 8:14 am by Dr. Roy Schestowitz


Video_download_link | md5sum f5d3b011ab2bcec45277ecbd8a2083bc


http://techrights.org/videos/misleading-delegates.webm


Summary: One must consider the possibility that ignorance or gullibility (which
lack of qualifications may entail) possibly became a contributing factor —
malice and bribery aside — in systemic failure of the EPO’s governance


THE 25th part of the series was published this morning (index below). We may
take a short recess and then continue; in the meantime we have this discussion
about what António_Campinos tells people in the EPO‘s Administrative Council as
well as the EC; based on the EPO’s site (the “news” section), he openly_tells
them_lies_about_the_UPC, which Benoît_Battistelli might still be planning to
preside over. They’ve long used this unconstitutional piece of trash (an
illegal coup) as an excuse for their staff-crushing ‘reforms’. The whole thing
is just insane. Earlier this week the EPO’s “news” section told a bunch of lies
about “quality” (more keyword-stuffing than actual information) and we’ve
already seen that many delegates lack background (educational and/or
experience) when it comes to matters of patents; many don’t understand the
sciences, either, as they’re basically political animals who compensate for a
lack of skills with a breadth of connections. The sooner the public understands
this, the better. The media sure is trying to keep the public in the dark on
these matters. Such media apathy is complicity in the coup — a takeover whose
end goal is to crush scientists for the financial benefit of law firms and
their largest clients (multinational monopolistic corporations). █


Series parts:


   1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!
   2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous”
      Endorsement?
   3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes
   4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States
   5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja”
   6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch
      Courage
   7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity
   8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and
      Pusillanimous_Hibernia
   9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss
      Cheese
  10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the
      Controversial_Christian_Bock
  11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_–
      Battistelli’s_Swiss_Apprentice?
  12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection
  13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian
      Facilitators_–_Spain
  14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian
      Facilitators_–_Portugal
  15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria…
  16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the
      Austrian_Double-Dipper
  17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic
      Nordic_Bloc
  18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord
  19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States
  20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group
  21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The
      Doyen_and_His_“Protégée”
  22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_–
      North_Macedonia_and_Albania
  23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_–
      Bulgaria
  24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_–
      Romania
  25. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_–
      Fresh_Blood_or_Same_Old,_Same_Old?

                    ䷩ 𝚕𝚒𝚗𝚎 814

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/presidential-surveys/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/27/presidential-surveys/

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Gemini_version_available_♊︎


✐ [Meme]_EPO_Presidential_Surveys⠀✐


Posted in Deception, Europe, Patents at 9:33 am by Dr. Roy Schestowitz


Who would have thought a survey organised by the regime would serve the regime?


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Obama_confusion:_See?_The_staff_whom_I_spied_on_while_they
participated_in_the_survey_are_happy⦈_


Summary: The 'social_democracy' of Benoît_Battistelli and António_Campinos as
demonstrated by a controlled survey (controlled by the subject of the survey,
EPO governance)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⢻⡏⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢿⣣⠀⠀⠃⠀⣙⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣹⣿⣿⣿⣿⣿⡟⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⢤⣾⣿⣿⣿⣿⣯⠉⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⣕⣿⣿⣿⠏⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢀⡿⠛⠛⠛⠛⢿⣿⣿⡿⠛⠛⠻⠿⢿⣿⣿⣿⣿⡿⣿⣿⣽⠛⠏⠁⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⠛⠀⠀⠀⢀⡃⢻⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠈⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣹⣼⠄⠀⡀⣠⣴⣾⣿⣿⣿⣧⣌⣉⣟⡲⣽⣿⣿⣿⢵⣿⣡⣿⣿⣿⣦⣄⣀⠘⠋⠀⢠⣺⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⢹⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⠙⠁⠈⠁⠀⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⢰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⠀⠚⠱⠀⠀⠈⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⢸⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣿⠃⠀⠀⠀⣴⣶⡀⢀⣭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡷⣾⣷⡀⠀⢸⣿⣧⢘⣿⣿⠋⠻⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣷⠀⢠⣤⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣧⣤⣴⣶⣷⣶⣶⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢻⣿⣷⣄⠀⣿⣿⣷⣿⣿⣷⡆⢡⣼⣿⣿
⣿⢻⡏⣿⣻⣿⠀⣾⣿⠇⢞⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢣⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠹⣿⣿⣦⣾⣿⣿⣾⠟⣿⣇⠀⣿⣿⣿
⣿⠸⣿⣿⣿⣿⣴⣿⣿⠀⣼⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢻⣿⣿⣿⣿⣿⣿⣿⠿⠟⢣⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣦⡈⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⠛⢦⡀⠀⠻⠋⣿⣿⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣉⠉⠉⠉⣉⣡⣤⢶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⣽⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡶⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢻⣿⣿⣿⣶⣿⣿⣿⣿⠇⠀⠀⠀⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠐⠂⢼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⠤⡆⢀⣤⣤⣴⣦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣀⣀⣀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⣼⠀⠿⢲⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⣿⣄⣀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⣿⣿⣿⣿⢛⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣽⣻⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣀⠀⠉⠻⣟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠁⠐⣙⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠸⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⡿⠟⣩⣿⣿⣿⣿⣿⠏⠁⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣏⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣇⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢺⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡙⣿⣿⣿⠏⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠃⢠⡿⠛⠛⠛⠛⢿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⠟⠀⠀⠀⠀⠁⢻⣿⡟⠀⠀⠀⣿⣿
⠈⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣌⣹⣼⠀⠀⣀⣠⣴⣾⣿⣿⣿⣧⣄⣉⣟⡲⣽⣿⣿⣿⣹⣿⣡⣿⣶⣿⣶⣄⣀⠘⠋⠀⠀⢘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠜⠋⠁⠀⠀⠁⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⢀⣷⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢙⡙⠖⠀⠀⠀⢨⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢃⠀⠀⢠⣶⡄⠀⣠⣭⢽⣟⣸⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣷⡄⠀⠘⣿⣿⡀⣿⣿⡏⠹⠛⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⡆⢠⣤⣄⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⡧⣤⣴⣶⣷⣶⣶⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⠻⣿⣿⣦⠀⢻⣿⣷⣿⣿⣿⣿⡆⠁⣼⣿⣿
⣾⢫⣿⣿⣘⣿⡇⢸⣿⡏⡬⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢣⣝⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡈⣿⣿⣷⣬⣿⣿⣷⣿⢻⣿⣧⠈⣿⣿⣿
⣿⠧⣿⣿⣿⣿⣧⣿⣿⠇⢠⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⢣⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠛⣧⡀⠀⠹⠏⣿⣿⣿⣦⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣉⠉⠉⠉⣉⣡⣤⢶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⢹⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡾⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⣾⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣠⣤⣴⣶⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠻⠋⣁⣀⣀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⣸⠀⠿⢓⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⣿⣄⣀⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⣿⣿⣿⢻⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣛⣻⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⢻⡿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠁⠐⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠸⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⡿⠟⣹⣿⣿⣿⣿⣿⠟⠀⣻⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣯⠉⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⣭⣿⣿⣿⠏⠀⠀⣿⣿
⡀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠃⢀⠿⠛⠛⠛⠛⢿⣿⣿⡿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠋⠁⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⠀⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿
⠘⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣹⣼⠄⠀⠀⣠⣴⣾⣿⣿⣿⣧⣄⣉⣗⠲⣽⣿⣿⣿⣹⣿⣡⣿⣿⣿⣶⣄⣀⠘⠋⠀⠠⢺⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠸⠋⠁⠈⠉⠉⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢿⠉⡟⠉⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣸⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠨⠀⠀⠁⠀⠀⠀⢰⢿⣿⣿⢁⠀⠀⣤⣶⡀⠀⣤⣭⢿⡿⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⡀⠀⢸⣿⣧⠀⣿⣿⡄⠙⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠀⣤⣔⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡧⣤⣴⣶⣷⣶⣦⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⢻⣿⣷⣄⠀⢿⣿⣷⣿⣿⣿⣿⡆⢡⣼⣿⣿
⣷⠏⣿⣿⣞⣿⡇⢰⣿⡿⢹⣻⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢳⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠙⣿⣿⣦⣸⣿⣿⣿⡿⢻⣿⣇⠉⣿⣿⣿
⣿⡇⣿⣿⣿⣿⣧⣾⣿⡇⢀⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣧⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣧⡀⠉⠹⠟⣽⣿⣿⣦⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣉⠉⠉⠉⡉⣡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⣹⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⡾⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⣽⣿⣿⣷⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠈⠂⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⣠⣤⣤⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠟⠋⣀⣄⣀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣸⠀⠿⢷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⣿⣄⣀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣿⣿⣿⣿⣻⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣛⣻⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣀⠀⠉⢻⡿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠃⠀⣹⢿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢨⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣴⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣻⣿⣿⣿⣿⣿⠏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣀⣾⣿⣿⣿⣿⣟⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢽⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⣶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡭⣿⣿⣿⡏⠀⠀⣿⣿
⡀⢰⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡛⠙⠁⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡿⠀⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿
⠘⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣌⣹⣼⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣀⢐⣖⠲⣽⣿⣿⣿⣽⣿⣡⣿⣾⣿⣦⣄⣀⠘⠃⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠜⠛⠁⠀⠀⠁⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⠀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢋⠞⢿⠋⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠀⠀⠀⠀⠀⠀⢘⢿⣿⡿⠁⠀⢀⣴⣦⠀⢀⣤⡌⠿⣿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣆⠀⠀⢿⣿⣆⠘⣿⣿⡀⠋⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠀⣤⣄⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣧⣤⣤⣶⣿⣶⣦⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⣿⣧⡀⠘⣿⣿⣶⣿⣿⣿⣿⡆⢡⣼⣿⣿
⣷⡟⣿⣿⣇⣻⡇⢀⣿⣿⠉⣟⣻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢣⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡄⢿⣿⣿⣦⣹⣿⣿⣿⡿⣿⣿⣇⠈⣿⣿⣿
⣿⡇⣿⣿⣿⣿⣧⣾⣿⡇⢀⣾⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢧⡀⠉⠹⠿⢹⣿⣿⣧⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠉⠀⣽⣿⣿⣿⣿
⠀⠉⠉⠀⠀⠀⠀⢙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣽⣿⣿⣯⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠒⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠈⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣤⣤⣴⣦⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⣀⣀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢰⠁⠿⢣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣄⣀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢿⣿⣿⣿⣿⣻⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣻⣿⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣀⠀⠈⢻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠃⠀⣹⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⠿⠟⣻⣿⣿⣿⣿⣿⠟⠀⢿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⣢⣾⣿⣿⣿⣿⣟⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⢀⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣭⠈⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡌⣿⣿⣿⡏⠀⠀⣿⣿
⡀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣽⢿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠿⠀⠀⠀⠀⠃⢻⣿⡿⠀⠀⠀⣿⣿
⠘⣶⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣌⣹⣼⠀⠀⠀⣠⣴⣾⣿⣿⣿⣆⣀⢐⣖⠲⣽⣿⣿⣿⢽⣿⣡⣿⣷⣿⣶⣄⣀⠘⠋⠀⠀⣬⣿⣿⣿⡯⠃⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠴⠟⠉⠀⠁⠉⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣟⣀⢀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢹⡻⠏⠂⠀⠀⠀⢽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⢼⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠀⠀⠀⠀⠀⠀⡠⣿⣿⢿⣃⠀⢠⣶⡆⠀⢠⣤⡍⠿⣿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣄⠀⠘⣿⣿⡄⢸⣿⣧⢀⠹⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⠀⣤⣄⢺⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣧⣄⣤⣶⣿⣶⣦⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠞⢿⣿⣦⡀⠸⣿⣿⣶⣿⣿⣿⣿⡆⢡⣼⣿⣿
⣿⡟⣽⣿⣇⣻⡇⢀⣿⣿⢹⣿⣛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢣⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣐⢿⣿⣿⣄⣿⣿⣿⣾⠿⣿⣿⣇⠉⣿⣿⣿
⣿⡇⢼⣿⣿⣿⣧⣼⣿⡏⢀⣿⣿⡟⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣷⡄⠉⠹⠿⢹⣿⣿⣧⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⢡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣿⣿⣷⣿⣿⣿⣿⣿⣿⠇⠉⠁⣹⣿⣿⣿⣿
⠀⠘⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⡼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣾⣯⣿⣿⣿⡏⠀⠀⠀⠈⠉⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠂⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣤⣤⣠⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⣀⣄⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢰⠁⠿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣄⣀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢿⣿⣿⣿⣿⣻⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣻⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠁⢻⣟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠃⠐⣹⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠹⠿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠐⣠⣾⣿⣿⣿⣿⣯⡁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⣶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡼⣿⣿⣿⡏⠀⠈⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠃⢠⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⠙⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣿⡿⠀⠀⠀⠀⡃⢻⣿⡟⠀⠀⠈⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣌⣽⣼⠄⠀⠀⣠⣴⣾⣿⣿⣿⣆⡀⢐⣒⠲⣽⣿⣿⣿⣹⣿⣩⣿⣿⣿⣷⣄⣀⠘⠃⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠸⠟⠉⠀⠀⠉⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣹⡹⡿⠓⠀⠀⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠌⠀⠀⠀⠀⠀⠀⢠⣻⣿⡿⢣⣶⣆⠀⢀⣴⣦⠀⠘⠿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣾⣏⠋⠘⣿⣿⣆⠈⣿⣿⡄⣀⠀⠟⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢸⣿⡇⢀⣾⣟⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⣧⣤⣤⣶⣿⣶⣤⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣿⣷⣄⠹⣿⣿⣧⣾⣿⣿⣿⣿⣾⡆⢡⣼⣿⣿
⣿⣿⣿⢻⣿⣷⣜⣿⡇⢸⣿⣿⣿⢟⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢃⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠹⣿⣿⣷⣼⣿⣿⣿⣽⠟⣿⣿⣿⣇⠁⣿⣿⣿
⣿⣿⣿⠰⣿⣿⣿⣿⣣⣿⣿⡏⣹⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿
⠛⢿⣿⠄⠈⠉⠻⠏⣿⣿⣿⣄⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠁⣹⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣯⣭⣿⣿⣿⡿⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠲⢀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠯⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣬⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⣄⣠⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠻⠋⢀⣀⣀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⡞⠸⠷⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡎⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢸⣷⣀⡰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⡟⣷⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣀⠀⠉⢻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠃⠐⣹⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⠿⠟⣹⣿⣿⣿⣿⣿⠏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⣢⣾⣿⣿⣿⣿⣏⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠆⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢺⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⣶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠗⠛⠀⠀⡭⣿⣿⣿⠏⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠃⢀⠿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠟⠀⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣌⣽⣼⠄⠀⠀⣠⣴⣾⣿⣿⣿⣆⡀⢐⣒⠢⣽⣿⣿⣿⣽⣿⣡⣿⣿⣿⣶⣄⣀⠘⠃⠀⢀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⡰⠋⠁⠀⠀⠉⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⠀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢫⡚⡯⠁⠀⠀⠀⢘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣧⡄⠀⣴⣶⠀⠀⠀⠘⠿⡿⣞⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡼⢿⣿⣿⣿⡄⢿⣿⣧⠀⠀⠀⠀⡛⠋⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣧⣤⣤⣶⣿⣶⣤⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⢻⣿⣿⣶⣿⣿⣷⠀⣾⣿⣶⡆⢁⣼⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢣⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣇⠈⣿⣿⣿
⣿⣿⣿⣷⠱⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⡿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠾⠄⠀⠈⠛⠋⣿⣿⣿⣁⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠉⠁⣽⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠀⠀⣀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣯⣭⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣴⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣔⡀⣤⣤⣤⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠟⠋⢀⣀⣀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣰⠁⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⣿⣿⣿⣿⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣙⣿⣿⣿⣽⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣀⠀⠈⢹⡏⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠁⠀⡝⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠸⠿⠟⣩⣿⣿⣿⣿⣿⠋⠁⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣇⠀⠀⣿⣿
⠀⠀⢀⣿⣧⠀⠀⠀⢼⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⡿⠷⠛⠀⠀⠁⣼⣿⣿⠏⠀⠀⣿⣿
⡀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠙⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠗⠀⠀⠀⠀⡀⢻⣿⡟⠀⠀⠀⣿⣿
⠈⣾⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣌⣽⣼⠀⠀⠀⣠⣴⣾⣿⣿⣿⣆⡀⢐⣖⠢⣽⣿⣿⣿⣹⣿⣡⣽⣿⣿⣧⣄⣀⠘⠂⠀⢀⠨⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⢹⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⠋⠁⠀⠀⠁⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣾⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⠀⣷⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢏⠨⠿⠉⠀⠀⠀⢈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠈⠟⠟⣘⣷⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⣠⣤⣤⣻⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠟⠋⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⡧⣤⣴⣶⣿⣶⣤⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⡀⠀⠀⣿⣿⣷⡀⠃⣴⣿⣿
⣿⣿⣿⡿⣿⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢃⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⡷⣣⠀⠘⠻⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠾⣿⣿⣿⣷⣿⣿⣿
⠛⣿⣿⠾⠕⠀⠀⠀⠀⣿⠛⣿⣿⣿⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⣽⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⠀⢈⣿⣷⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⣴⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣠⣤⣤⣤⣤⣄⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠻⠋⠁⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣿⣿⣿⣿⢿⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣻⣿⣿⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠀⢛⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⣣⠀⠀⠁⠐⣹⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠸⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢸⡿⠛⣹⣿⣿⣿⣿⣿⡟⠀⣺⡏⢹⠙⡏⣿⡉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠈⣂⣼⣿⣿⣿⣿⣏⡁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣇⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⣿⡷⠛⠀⠀⡀⣿⣿⣿⠏⠀⠈⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⡿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣽⣴⠄⠀⠀⣠⣴⣼⣿⣿⣿⣆⡀⢐⣒⠢⣽⣿⣿⣿⢱⣟⣡⣽⣶⣿⣶⣄⣀⠘⠃⠀⠀⠘⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠜⠉⠁⠈⠀⠙⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡷⠋⠀⠀⢰⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢙⠈⠃⠁⠀⠀⠀⡼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠘⠟⡿⣺⣿⣾⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⢀⣠⣤⣤⣠⣀⣨⣿⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠠⣼⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣤⣤⡀⠀⠀⢻⢿⡧⣄⣤⣶⣷⣶⣤⣬⣽⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡆⠀⠀⠀⠀⠀⠀⣾⣿⣾⡆⢁⣼⣿⣿
⣿⣿⣿⡿⣟⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠘⣌⢣⣙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⠈⣿⣿⣿
⣷⣿⣿⢦⡟⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣶⣶⡄⠀⠀⠀⠈⡀⠿⢻⣿⣿⣿⣿⣿⣿⠿⠟⢁⣾⢷⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣿⣿⣿
⠛⣿⡿⠓⠄⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⢡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿
⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣴⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⣴⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣶⣦⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣧⣤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠋⠁⠈⢀⣤⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣾⣿⣿⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣙⣿⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠀⠙⡋⠻⣿⣿⣿⠾⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢧⣢⠀⠀⠁⠀⡘⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⢶⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠘⠿⠛⢉⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣌⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⠸⣿⣿⣿⡇⠀⠀⣽⣿
⠀⠀⠀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣴⣿⣿⠇⠀⠀⣿⣿
⠀⠠⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣸⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⢿⣿
⠀⣴⣿⣿⣿⠀⠀⠀⠀⣫⣷⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⣱⣴⠀⠀⠀⣠⣠⣼⣿⣿⣷⣆⡀⢒⡒⠬⣿⣿⣿⣿⠱⣝⣡⣼⣤⣶⣦⣄⡀⠐⠀⠀⠀⢈⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢻⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣏⣿⣿⣷⠋⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⠀⠀⠀⣵⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠁⠀⠀⠀⠀⠀⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⢐⡦⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣉⣻⢟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡕⢀⣷⣝⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⢻⣿⣿⣿⣿⡟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠅⢼⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣤⣬⣿⣶⣤⣭⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠢⠄⠀⠀⠀⠀⠀⠀⣰⣷⣶⡀⠁⢴⣿⣿
⣿⣿⣿⠟⡛⠀⠀⠀⠀⠀⠀⢽⣟⢻⢿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠀⠀⠀⠀⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢾⣿⣿
⣷⣿⣿⠄⠃⠀⠀⠀⠀⠀⠀⠼⠙⠀⠐⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⣾⣷⣄⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿
⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠿⠟⠉⠉⣁⣤⢴⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣛⣉⣿⣿⣿⣶⣤⣚⠺⢯⣷⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣋⠀⠀⠀⠈⠻⣿⣿⣿⣴⠿⠟⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⣤⣼⣿⣿⠁⠐⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠀⠛⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠈⢧⣣⠀⠀⠁⠀⠘⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠐⣶⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠘⠿⠛⣋⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠐⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⠸⣿⣿⣿⡇⠀⠀⣻⣿
⠀⠀⢀⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣥⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠷⠛⠀⠀⠀⢹⣿⣿⠏⠀⠀⣿⣿
⠀⠰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⢀⡿⠛⠛⠛⠻⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣻⣿⠇⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄⣹⣼⠀⠀⠀⣠⣠⣼⣿⣿⣷⣆⡀⢒⡒⠬⣿⣿⣿⣿⢱⣟⣡⣽⣤⣶⣦⣄⡀⠐⠂⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠁⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣏⢿⣿⢿⠊⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⠀⠀⣷⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠩⠀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣦⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣉⣻⢿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⢀⣷⣜⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⢻⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡤⢼⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣡⣤⣤⣬⣷⣶⣤⣭⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢋⠂⠀⠀⠀⠀⠀⠀⢸⣷⣶⡆⠁⣴⣿⣿
⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⢀⣿⣿⢻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢸⠅⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢿⣿⣿
⣿⣿⣿⠀⠑⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢁⣾⣷⣄⣿⣿⣿⣷⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠂⠄⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿
⠛⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣭⣽⣿⣿⣅⣤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠈⠻⣿⡏⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⠏⠀⠀⢠⣤⣿⣷⠀⠁⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⢀⣙⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣀⠀⠀⠙⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⣢⠀⠀⠃⠐⡩⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣴⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⡿⠛⣹⣿⣿⣿⣿⣿⠏⠀⢻⡏⢹⠙⡏⣿⣉⢉⡏⢹⠹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⢠⣼⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡿⢸⡇⢠⠘⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣇⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢼⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠟⠒⠓⠓⠚⠲⢶⣿⣷⣾⣿⠗⠛⠀⠀⡀⣿⣿⣿⠏⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢠⠿⠛⠛⠛⠻⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿
⠀⣴⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡈⣽⣼⠀⠀⠀⣤⣠⣼⣿⣿⣷⣆⡀⢒⡒⠬⣿⣿⣿⣿⣹⣟⣡⣽⣵⣿⣦⣄⣀⠘⠃⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⠋⠁⠀⠀⠁⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣿⣿⣷⠋⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⠀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢉⠨⠍⠀⠀⠀⠈⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⢘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣉⡻⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠟⣟⢐⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣁⣀⣤⣬⣷⣶⣬⣭⣹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⢯⡇⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠁⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⡪⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡹⢽⡏⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⠈⢿⣿⣿
⣷⣿⣿⢆⢛⠀⠀⠀⠀⠀⠉⢿⠋⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⣶⠆⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣷⣿⣿⣿
⠛⢿⣿⠚⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⢠⠀⢀⣽⣜⣅⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⣹⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠁⠙⠻⠫⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡄⠀⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠁⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⣦⣴⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠋⠙⢿⣿⣿⣿⣿⣿⣿⣷⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠈⠻⡿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣢⠀⠀⠋⠀⣭⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠚⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⡿⠟⣹⣿⣿⣿⣿⣿⡟⠀⢿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣏⠉⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡇⠀⠀⣿⣿
⠀⠀⢀⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣗⢲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⠏⠀⠀⣿⣿
⠀⢠⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⢠⠿⠛⠛⠛⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⢟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿
⠈⣾⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⡀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣄⣽⣼⠀⠀⠀⣤⣰⣾⣿⣿⣷⣂⠐⢒⠲⢭⣿⣿⣿⣿⣩⣿⣉⣽⣾⣿⣶⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠐⠛⠉⠁⠀⠈⠸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⡀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢩⠋⠯⠩⠀⠀⠀⡸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣙⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡄⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠨⠻⡿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⠉⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⣻⣿⣿⣿⣿⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣀⣠⣴⣿⣷⣤⣭⣙⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⣾⣿⣷⡆⢁⣴⣿⣿
⣿⣿⣿⡿⣯⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⡂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⡇⣯⠀⠀⠀⠀⠀⠈⢟⢛⠏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡸⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣠⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣎⣯⣼⡅⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠿⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣈⠉⠉⠉⠛⢉⣡⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡀⢂⣿⣯⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣴⣻⠿⣿⣷⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣋⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠙⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠈⠉⠉⠉⠻⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣽⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣄⠁⠙⢻⣿⢿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣿⣣⠀⠈⠛⢹⣿⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠺⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⣻⡿⢿⣻⣿⣿⣿⣿⣿⡿⠇⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠈⣶⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠠⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠇⢰⢸⠅⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣏⠀⢀⣿⣿
⠀⠀⣄⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⠾⣾⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣷⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⣿⣿⣿⣿⡏⠀⠀⣿⣿
⣀⢰⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣃⢰⠿⠛⠛⠛⠿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠐⠃⢿⣿⡿⠀⠀⠈⣿⣿
⢸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⢀⣀⣀⣤⣤⣤⣽⣾⠄⠘⠓⣲⣷⣿⣿⣿⣷⣒⠲⢶⣦⣽⣿⣿⣿⣿⣹⣿⣋⣿⣿⣿⣷⣤⣀⠘⠛⠀⢄⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⠺⠻⠙⠛⠉⠋⠛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣠⣀⣀⢴⣿⣿
⣰⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢻⣿⣿⠿⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣻⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡽⠉⠹⠧⠀⠀⠀⡽⣿⣿⣿⣯⣇⠂⠀⠀⠀⠀⠀⡻⢿⣿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣀⡿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣤⣤⣶⣿⣷⣬⣭⣟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⣽⣿⣿⣷⠉⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢹⣿⢻⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢛⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣉⠉⠉⠛⠛⣉⣡⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠁⠉⠁⣿⣿⣿⣿⣿
⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣴⣿⠿⢿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣋⠀⠀⠀⢈⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣄⠁⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠿⠿⣿⣿
⠘⢿⣣⠀⠀⠛⢑⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠻⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢻⡿⠟⣻⣿⣿⣿⣿⣿⡿⠃⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠋⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠘⣶⣾⣿⣿⣿⣿⣯⡉⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠈⠓⠚⠾⢶⣿⣷⣾⣷⡾⢾⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⠶⢾⣾⣷⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡿⣿⣿⣿⡏⠀⠈⣿⣿
⣄⢰⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⡇⠉⢉⠉⠉⢻⣿⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣝⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠃⠀⠀⠀⠇⢻⣿⡿⠀⠀⠈⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠊⠀⠀⠀⣀⣀⣤⣤⣤⣤⣼⢀⣀⣰⣿⣿⣿⣿⣿⣏⣘⣛⡶⢮⣽⣿⣿⣿⣿⢻⣿⠿⢃⣾⣿⣷⣤⣀⠘⠛⠀⢤⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⢹⣿⡇⠀⠀⠀⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣐⠺⠯⠛⠉⠋⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣱⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣸⣿⣀⣀⣀⢰⣿⣿
⣠⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣼⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⠃⠙⠇⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠺⢿⡿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⠟⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣶⣿⣿⣿⣶⣦⣭⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⢨⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠈⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢹⣿⢿⡿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣁⣴⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢹⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⢿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⠈⠉⣉⣡⣤⣬⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⣿⣶⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠙⠁⣽⣿⣿⣿⣿
⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⢈⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣽⣟⣛⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⢠⣔⠲⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠉⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢾⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣄⠁⠩⢿⣿⣿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣿⣣⠀⠀⠛⢙⣿⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠿⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢻⡿⢿⣻⣿⣿⣿⣿⣿⡿⠇⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠺⣷⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⡄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣇⠀⠀⣿⣿
⠀⠀⣄⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⢺⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⡶⠾⣾⣷⡶⠟⠖⠓⠓⠚⢶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡿⣿⣿⣿⡏⠀⠀⣿⣿
⣄⢰⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣿⠀⠠⡀⢈⣙⣿⣿⣟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠀⣯⡉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⡏⢿⣿⡿⠀⠀⠨⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠚⠀⠀⢀⣀⣠⣤⣤⣤⣤⣴⣀⣤⣴⣿⣷⣿⣿⣿⣯⣍⣙⡷⠦⣽⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⣷⣤⣀⠘⠋⠀⢚⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⣿⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⢻⠿⠛⠉⠉⠋⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣶⣾⣿⣿⣿⣿⣿⡏⠀⠀⢱⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣠⣀⡀⢰⣿⣿
⣠⣿⣿⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣾⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠏⠉⠋⠀⠀⠀⠿⣿⣿⣿⣿⡗⠁⠀⠀⠀⠀⠀⢻⢿⡿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠐⢽⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⠿⠋⠀⠇⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣈⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣾⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢉⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢾⣿⢿⡿⠻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣡⣴⣿⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡆⢿⣿⣿⣿⣿⣋⠄⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⠀⣉⣡⣤⣤⣬⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿
⠀⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠈⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣛⠿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⡲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠈⣿⠀⠀⠉⠙⠋⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣄⠁⠈⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣿⣣⠀⠀⠛⢐⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠺⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⡀⠀⠀⢻⡿⠟⣻⣿⣿⣿⣿⣿⡿⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠈⣶⣾⣿⣿⣿⣿⣿⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⡅⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣄⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⢺⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⡶⠾⣾⣶⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⢟⣿⣿⣿⡏⠀⠀⣿⣿
⣀⢰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠻⠀⠠⡀⢈⣙⣿⣿⣟⡛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡯⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠃⠀⠀⠀⠂⢻⣿⡿⠀⠀⠈⣿⣿
⠈⣾⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣁⣤⣴⣿⣷⣿⣿⣿⣯⣍⣙⡷⠶⣽⣿⣿⣿⣿⢿⣿⣿⠟⢰⣿⣷⣄⣀⠘⠛⠀⠄⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠁⢺⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣐⠚⠟⠉⠉⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣶⣿⣿⣿⣿⣿⡏⠀⠀⢑⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀⢠⣿⣿
⣠⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣋⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠃⠐⠇⠀⠀⠀⠻⣿⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⢺⠿⡿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠛⠛⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⡿⠛⠀⠇⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⣘⠀⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣾⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢩⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣹⣿⣿⣇⠈⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠘⣿⠻⠟⠸⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡿⠿⢟⣁⣴⣿⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢘⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⢿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⠀⢉⣡⣤⣤⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣳⣴⣳⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿
⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠈⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣛⠿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⡲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠋⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣄⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣿⣣⠀⠀⠛⢙⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠻⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⡀⠀⠀⢽⡿⢿⣻⣿⣿⣿⣿⣿⡿⠂⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣙⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠈⣶⣾⣿⣿⣿⣿⣯⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⢞⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠺⢾⣶⡶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⠿⣿⣿⣿⡏⠀⠀⣿⣿
⣄⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠀⠀⠄⢀⣙⣿⣿⣿⡛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠈⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠇⢿⣿⡿⠀⠀⠈⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣤⣤⣿⣷⣿⣿⣿⣿⣍⣉⣟⠶⣽⣿⣿⣿⣿⣿⣿⣿⠿⢀⣿⣷⣄⣀⠘⠛⠀⢄⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⢾⣿⡇⠀⠀⠀⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣐⠚⠛⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣾⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣀⣀⣀⢠⣿⣿
⣠⣿⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⠀⠀⠀⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣷⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠉⠨⠀⠀⠀⣯⢿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⢙⢿⡿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⣻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⠟⠁⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣨⠀⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣿⣿⣿⣿⣷⣶⣮⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⠉⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢸⣿⢻⠟⠽⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⡿⠿⢟⣡⣼⣿⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢺⣽⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⢿⡯⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⡀⣈⣡⣤⣤⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣶⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿
⠀⠹⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣋⡀⠀⠀⠀⣙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣟⣛⡻⢿⣿⣿⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢀⣲⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢾⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣄⠁⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣿⣣⠀⠀⠛⢑⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠻⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⡀⠀⠀⢻⡿⠟⣻⣿⣿⣿⣿⣿⡿⠂⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠘⣶⣿⣿⣿⣿⣿⣯⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⡀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⢀⣿⣿
⠀⠀⣀⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⠞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⢾⣷⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⢿⣿⣿⣿⡏⠀⠀⣿⣿
⡄⢰⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠟⠿⠃⠀⠄⢀⣙⣿⣿⣿⡛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠘⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⠃⠀⠀⠀⠃⢻⣿⡿⠀⠀⠈⣿⣿
⠘⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠃⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣂⣤⣤⣿⣷⣿⣿⣿⣿⣍⣉⣟⠶⣽⣿⣿⣿⣿⡟⣿⣿⡿⢀⣿⣷⣄⣀⠘⠛⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⡐⠘⠛⠋⠙⠈⠋⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡏⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⣀⣰⣿⣿
⣠⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠏⠋⠏⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⢿⡿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⣻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⠟⠁⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⢀⡯⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢩⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⠉⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⢻⠿⠻⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⡿⠿⣟⣡⣼⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢻⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⣈⣡⣤⣤⣼⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣜⣷⣦⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠉⠙⠁⣿⣿⣿⣿⣿
⠀⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣋⡀⠀⠀⠀⣙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣟⣛⡻⢿⣿⣿⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢠⣒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⠉⠉⠉⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣄⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠛⢘⣽⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠻⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢿⡿⠿⣻⣿⣿⣿⣿⣿⡿⠇⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠘⣶⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣄⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⠉⠁⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⠞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢾⣶⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡻⣿⣿⣿⡏⠀⠀⣿⣿
⣄⢰⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠟⠿⠃⠀⠄⢀⣉⣿⣿⣿⣋⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡆⠈⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠇⢻⣿⡿⠀⠀⠘⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣆⣤⣴⣿⣿⣿⣿⣿⣿⣬⣉⣟⡲⣽⣿⣿⣿⣿⡟⣿⣿⠿⠀⣿⣷⣤⣀⠘⠛⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⣺⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠐⡸⠟⠉⠉⠉⠋⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⡀⢰⣿⣿
⣰⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠉⠂⠀⠀⠀⠿⣿⣿⣿⡟⡗⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⢉⣛⣿⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡀⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣻⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢫⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣸⣿⣿⣾⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠉⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢹⣿⣛⠿⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢟⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠻⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⢿⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣷⣤⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣽⣿⣿⣿⣿
⠀⠙⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣿⣣⠀⠀⠃⢐⣽⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠺⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⡀⠀⠀⢹⡿⠟⣹⣿⣿⣿⣿⣿⠟⠀⢿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⢴⣾⣿⣿⣿⣿⣯⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣇⠀⠀⣿⣿
⠀⠀⣀⣿⣷⠀⠀⠀⢺⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⡞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢺⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⣿⣿⣿⣿⡏⠀⠀⣿⣿
⡀⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠻⠁⠀⠄⢀⣉⣿⣿⣿⡋⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠈⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠃⠀⠀⠀⠃⢻⣿⡟⠀⠀⠈⣿⣿
⠘⣾⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣤⣴⣿⣷⣿⣿⣿⣿⣤⣉⣟⡲⣽⣿⣿⣿⣿⡿⣿⣿⡿⠀⣿⣶⣄⣀⠘⠋⠀⠀⢾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⠋⠁⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠏⠀⠀⢈⣾⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡯⣿⡟⠀⠀⠀⢾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠀⠀⠀⠀⠝⣿⣿⣿⠓⡄⠀⠀⠀⠀⠀⠀⠘⠿⡿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢉⣻⣿⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⠻⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢻⡿⠀⠀⠀⠀⠀⠀⣽⣿⣿⡆⢉⣼⣿⣿
⣿⣿⣿⡟⣿⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢠⢼⣿⣖⣾⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣟⠈⣿⣿⣿
⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢸⣿⠫⠯⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢼⣿⣿⣿⠇⠀⠀⠀⢀⡀⠈⣨⡿⣾⡟⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠿⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠀⠀⢀⠀⠀⣱⣤⢸⣿⣹⣻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣹⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠙⠿⠾⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣄⠀⠈⢻⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢿⣢⠀⠀⠁⠀⣘⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠐⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢹⠿⠟⣩⣿⣿⣿⣿⣿⠇⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣍⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⢀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣯⠈⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢚⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⠁⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠠⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⢀⣈⣻⣿⣿⣉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣹⣿⠟⠀⠀⠀⠀⠂⢹⣿⡿⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⢛⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⠠⣤⣤⣄⣤⣄⣤⣴⣾⣿⣿⣿⣿⣿⣤⣉⣝⡲⢾⣿⣿⣿⣿⡟⣿⣿⡿⠃⣴⣦⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠋⠀⠀⠀⠀⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣶⣶⣿⣿⣿⣾⠏⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⢀⡀⡀⠀⣷⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡇⠁⠉⠀⠀⠀⠘⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢹⣽⣿⡿⣦⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠈⠿⡿⣸⣷⣟⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡽⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠋⢉⣛⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡡⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠛⢻⡅⠀⠀⠀⠀⠀⠀⣺⣿⣷⡆⢉⣴⣿⣿
⣿⣿⣿⡟⣯⠀⠀⠀⠀⠈⠩⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣴⡆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣦⣀⠈⠹⣿⣿⣷⡄⠀⠀⠀⣈⣼⣷⣀⡜⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⣣⣫⠀⠀⠀⠀⠀⠈⣟⠉⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡟⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢻⣅⣴⣿⣗⣆⣻⣿⣿⣿⣷⣄⢹⣿⣿⣿⡀⠀⣼⣿⣿⣿⢛⡁⠀⠀⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⢼⣯⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣤⣼⣿⣿⣿⠀⣜⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⠀⠀⢵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠟⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠀⣴⣾⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⡇⠀⠀⠀⣶⣶⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⡟⠉⢉⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠘⣿⣿⣿⡏⠉⣄⢀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠁⢆⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣧⣤⣠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠐⢷⣡⣽⣿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠈⠹⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⣣⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠒⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢸⠿⠟⣻⣿⣿⣿⣿⣿⠏⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣷⠀⠀⠀⢨⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡾⠶⠶⠿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⠚⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠰⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠻⠇⠀⠀⠀⢀⢹⣿⣿⣋⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣻⣿⠟⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿
⠘⣶⣿⣿⣿⠀⠀⠀⠀⣉⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣠⣴⣴⣾⣿⣿⣿⣿⣿⣦⣌⣭⣓⢾⣿⣿⣿⣿⡿⣿⣿⡿⠃⣰⣦⣄⣀⠘⠃⠀⠀⠨⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠒⠛⠁⠁⠀⠉⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⡀⢀⣿⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⠇⠂⠀⠀⠀⠠⢿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢘⣽⣿⣿⣯⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣥⣽⡟⠝⠀⠀⠀⠀⠀⠀⠀⠘⠽⣿⣹⣿⣾⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢉⣙⣟⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣋⡀⠀⠀⠀⢀⣀⣄⡀⠠⣿⡁⢐⠄⠀⠀⠀⠀⠀⠀⢀⠀⠑⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢯⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢻⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠈⢿⣿⣿⣦⡀⠀⠸⣿⣿⣷⠀⠿⠳⢢⡄⠀⠀⠀⠀⠀⠀⣸⣿⣷⡆⠉⣴⣿⣿
⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠈⣿⣟⣿⣿⣿⣓⠀⠀⢰⣶⣿⠷⣶⣶⡆⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣵⡆⠀⠀⠀⣀⣀⡹⣿⣿⣷⣄⠀⠘⣿⣿⣧⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⠁⣿⣿⣿
⣿⣿⣿⣇⣽⠀⠀⢠⣴⣶⣦⡛⠻⠻⠿⣿⣿⠃⠀⣸⣿⡋⢠⣿⠏⠀⣤⣤⠀⠀⠙⠛⠛⠿⣿⡿⠿⠟⠛⢛⣤⣴⣿⣟⣄⠀⠀⠀⢿⣿⣿⣽⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⣴⣾⣿⣿⠇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠇⡍⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⣹⡆⠀⣸⣿⣿⣿⣿⣿⠃⣼⣿⠟⠀⠀⠀⣶⣤⣀⢀⣀⣤⣤⣤⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣵⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠙⠁⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⠉⢹⣶⣿⣿⢿⣿⣿⣯⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢷⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠀⠈⣿⣿⣄⣤⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⠛⢛⠁⠘⡂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⣀⣀⡄⠐⠂⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣥⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣄⠀⠀⢠⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣯⡾⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣄⠀⠈⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⣣⠀⠀⠃⠀⡜⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠲⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⢾⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡾⠶⠶⠿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡾⠚⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠌⣿⣿⣿⡏⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠇⠀⠀⢀⣠⢽⣿⣿⣍⡉⣉⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⠟⠂⠀⠀⠀⠂⢹⣿⡟⠀⠀⠐⣿⣿
⠰⣾⣿⣿⣿⠀⠀⠀⠠⢻⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⡤⣤⣤⣄⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣤⣭⣙⣺⣿⣿⣿⣿⡿⣿⣿⡿⠃⣰⣶⣄⣀⠘⠓⠀⠀⢹⣿⣿⣿⣯⠂⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠴⠙⠉⠈⠈⠁⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⡏⠢⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢺⣽⣿⣿⣯⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡀⣬⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⡿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢀⣬⣻⣟⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠟⠋⣀⣀⡀⠀⠀⠀⠀⠈⠉⣿⠗⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⢸⣿⣿⣧⢙⢻⣀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡆⢉⣴⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⡓⢀⣠⣤⢀⣤⣤⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣵⡆⠀⠀⠀⠀⠀⣀⣀⠹⣿⣿⣦⡀⠀⠙⣿⣿⡄⠨⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⣧⣏⠀⣀⣀⡀⠀⢮⣽⣿⣿⣿⠉⠁⢸⣿⠋⢸⣿⡟⠀⣠⣄⠀⠀⠀⠀⠉⠛⠛⠿⣿⡿⠿⠛⠛⢻⣦⣴⣿⣟⣤⠀⠀⠀⠀⠘⢿⣿⣷⣽⣿⣿⣿⡄⠀⣿⣿⣿⡄⢄⣠⣶⣶⣶⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⢻⡏⠘⢿⣿⣿⣦⡉⠁⠈⠛⡇⠀⢠⣿⣶⢤⣾⣿⠁⣼⣿⡏⠀⠀⠀⠀⠀⣷⣦⣀⣀⣠⣤⣤⣴⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢶⣾⣿⣿⠛⠁⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠙⠃⠀⠁⠀⠀⠉⠻⣿⣿⣦⡄⠰⢷⣠⣿⣿⡿⣿⣿⡏⣰⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠀⠀⠋⠉⡏⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣼⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⢶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡧⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣯⣭⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡚⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠉⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡜⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣆⠀⠀⠐⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣻⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠼⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⢾⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⢲⣾⣿⣿⣿⣿⣍⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⠀⣿⣷⠀⠀⠀⢺⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⣾⠶⠶⠿⠷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡞⠞⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡈⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠋⠀⠐⢀⣤⣼⣿⣿⣧⡄⢈⣉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠂⠀⠀⠀⠂⢹⣿⡟⠀⠀⠈⣿⣿
⠘⣶⣿⣿⣿⠀⠀⠀⠀⡻⣻⣿⣿⣿⣧⠀⠀⠒⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣴⣭⣳⣿⣿⣿⣿⡿⣿⣿⡿⠃⢰⣦⣄⣀⠘⠃⠀⠀⢼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠒⠙⠁⠁⠀⠈⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⡝⠎⠀⠀⠀⠀⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⡿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢨⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣤⣿⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡟⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠑⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡀⠀⠀⠀⣠⣤⡚⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⢉⣰⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣟⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠑⣿⣿⣿
⣿⣿⣿⣦⡏⠀⠀⠀⠀⠀⠨⣿⣿⠿⠿⠙⢱⣿⠷⢰⣿⡷⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠟⠛⠛⢫⣦⣴⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⣾⣷⣆⠹⣿⣿⣧⡀⠸⣿⣿⣇⠀⠀⢀⣠⣤⣄⠺⣿⣿⣿⣿⣿⣿⣿
⠛⣿⡿⠯⡷⣿⣿⣦⡀⠀⠈⠙⠿⣧⠀⢀⣞⣫⠀⣼⣿⠃⣰⣿⡇⠀⠀⠀⠀⠀⠈⣿⣦⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣽⣿⣿⣷⢠⣿⣿⣿⠀⣴⣿⣿⠟⠋⠀⠈⠁⣹⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠈⠙⢿⣿⣶⣤⡀⢀⣷⠀⣼⣿⡿⣼⣿⡏⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠃⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡇⠀⠉⠷⠘⠿⠃⣿⣿⡱⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠈⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⢸⣿⣸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⢶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣽⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠿⠿⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣕⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⣿⣿⣟⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡈⢽⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⡡⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠬⢿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⠹⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠲⢯⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣻⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢭⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠀⣄⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⣾⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡾⠞⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⠝⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⢀⣤⢼⣿⣿⣧⡄⢈⣉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⣿⠟⠀⠀⠀⠀⠂⢻⣿⡟⠀⠀⠀⣿⣿
⠰⣾⣿⣿⣿⠀⠀⠀⠠⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣴⣭⣳⣿⣿⣿⣿⣿⣻⣿⡿⠇⢰⣶⣄⣀⠘⠃⠀⠀⢚⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⢹⣿⣿⣿⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⡄⠀⢀⠒⠋⠁⠈⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣻⠏⠀⠀⢠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣟⡙⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⠋⠀⠀⠀⠀⠀⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢼⣽⣿⣻⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠶⣿⣿⢃⠂⠀⠀⠀⠀⠀⠀⠰⠊⣿⣹⣿⣼⣿⣿
⣿⣿⣿⣿⣟⠀⠀⠀⠀⢈⣟⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣬⣿⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡩⢿⢋⠤⠅⠀⠀⠀⠀⠀⠀⠀⢀⠋⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⢛⣻⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⡀⠀⠀⠀⣢⣤⡛⠢⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠉⣴⣿⣿
⣿⣿⣿⡟⣿⠀⠀⠀⠀⠈⢰⣿⡿⣿⣿⣿⡗⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠐⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠁⣿⣿⣿
⣿⣿⣿⣦⣿⠀⡀⠀⠀⠀⢾⣟⣟⣻⠻⠛⠃⣿⡿⠂⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⢈⠉⠙⠻⠿⠿⠟⠛⠛⢻⣦⣴⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⢻⣿⣿⣦⡀⢹⣿⣿⣆⠀⠀⢀⣤⣤⡄⡾⢿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⠫⡗⠺⣿⣷⣆⠀⠈⠁⠻⣿⠆⠀⣼⣭⡄⣴⣿⡇⢠⣿⡿⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⣷⢠⣿⣿⡿⢀⣼⣿⣿⠟⠁⠀⠉⠁⣽⣿⣿⣿⣿
⠀⠙⠃⠀⠁⠀⠈⠻⣿⣿⣦⡄⠀⣹⡀⣸⣿⣿⢵⣿⡿⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠃⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠈⠸⠈⠻⠃⢸⢿⡧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣿⣶⣵⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣽⣿⣿⣿⣿⣿⡟⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠛⠻⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡘⣿⣿⣭⣽⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣈⠻⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣯⣡⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠈⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡌⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠒⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⡠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣄⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⣾⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡞⠞⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠌⣿⣿⣿⡇⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠋⠀⠐⢀⣤⣼⣿⣿⣧⠄⢈⣉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣟⣻⣿⠟⠃⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿
⠘⣾⣿⣿⣿⠀⠀⠀⠀⢻⣻⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣴⣭⣳⣿⣿⣿⣿⣿⣿⣿⡿⠇⢰⣦⣄⣀⠘⠃⠀⠠⢘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⢀⠂⠛⠉⠁⠈⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣶⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⡅⠀⠀⠀⠀⠀⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣥⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠺⣿⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣤⣿⣭⣍⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢇⢔⡀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠋⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣫⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⣠⣌⠙⡂⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠋⣴⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⢽⣿⣟⢿⣿⣿⡳⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠸⣿⣿⣧⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⣷⣿⠀⡀⠀⠀⠀⢶⣟⣿⣛⠻⠋⠓⣿⡟⠃⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠛⠻⠿⠿⠟⠛⠛⢻⣦⣴⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⢻⣿⣿⣆⡀⢻⣿⣿⡆⠀⠀⣀⣤⣤⡀⣺⣿⣿⣿⣿⣾⣿⣿
⠛⣿⣿⢣⠛⠺⣿⣷⣦⡀⠈⠁⠻⣿⠂⠀⣼⣭⡆⣴⣿⡇⢠⣿⡿⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣻⣿⣿⣷⢰⣿⣿⣿⢀⣾⣿⣿⠟⠁⠀⠈⠁⣹⣿⣿⣿⣿
⠀⠛⠃⠀⠀⠀⠈⠻⣿⣿⣦⡄⠀⣹⡀⣸⣿⣿⢵⣿⡿⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠀⠼⠘⠛⠃⢸⢿⡇⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⣿⣤⣧⣮⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣽⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣭⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡜⣿⣿⣯⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣈⠹⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣯⣣⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠼⣿⣿⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠈⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣣⠀⠀⠋⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠂⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢰⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠘⣤⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢪⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⣾⠶⠶⠿⠷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⠞⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⠈⣽⣿⣿⡇⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠇⠀⠐⢀⣤⣼⣿⣿⣧⠄⢈⣉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠂⢻⣿⡟⠀⠀⠀⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣴⣭⣳⣿⣿⣿⣿⣿⣿⣿⡿⠇⢰⣦⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⢀⠢⠛⠉⠀⠀⠁⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⠕⠠⠀⠀⠀⠀⣽⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠅⠀⠀⠀⠀⠀⠀⠘⠫⣿⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⢿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣤⣿⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢇⠝⠄⠀⠀⠀⠀⠀⠀⢀⠀⠙⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣷⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⢀⣤⣅⠑⣀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡆⠉⣴⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⢙⣾⣿⣻⣿⣿⡃⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⢾⣿⣿⡆⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⣷⣿⢀⣀⠀⠀⠀⠽⣿⣯⣟⠿⠛⢻⣿⠛⢰⣿⡿⠀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠙⠻⠿⠿⠟⠛⠛⢻⣶⣼⣿⣟⣤⠀⠀⠀⠀⠀⠀⢀⣶⣤⡘⢿⣿⣷⣄⠈⣻⣿⣿⡄⠀⠀⣠⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠻⠓⠻⣿⣷⣆⠀⠈⠁⠟⣿⠀⢠⣯⣽⢀⣾⣿⠁⣼⣿⡇⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣮⣿⣿⣿⣶⢾⣿⣿⡇⣠⣾⣿⡿⠋⠀⠀⠈⠁⣿⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠈⠻⣿⣷⣦⡄⠀⣿⠀⣾⣿⡿⣾⣿⡏⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⢿⣿⣿⣿⣿⣶⣷⣿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⠀⠀⠟⠙⠟⠁⣿⣿⣴⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣀⣨⣿⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣥⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⣿⣿⣭⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣔⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣈⠻⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⡡⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⣿⣿⢟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠈⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡜⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠸⡿⠟⣛⣿⣿⣿⣿⣿⡗⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⢀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡾⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠞⠞⣶⡶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢇⠀⠐⢀⣤⣼⣿⣿⣧⠄⢈⣉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⠟⠂⠀⠀⠀⠂⢹⣿⡟⠀⠀⠀⣿⣿
⠰⣾⣿⣿⣿⠀⠀⠀⠐⢙⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣶⣭⣳⣿⣿⣿⣿⣿⣻⣿⡿⠃⢰⣦⣄⣀⠈⠂⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠐⠛⠁⠁⠀⠁⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡗⠕⠐⠀⠀⠀⠀⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⣬⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢸⣷⣽⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣬⣽⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⢀⣤⡄⠉⡠⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠋⣴⣿⣿
⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣻⣿⣿⢇⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣵⡎⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⡷⢟⢀⣀⠀⠀⠀⠰⣿⣽⡟⠿⠙⣻⣿⠛⢸⣿⡟⠀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠙⠻⠿⠿⠟⠛⠛⢹⣶⣶⣿⣟⣄⠀⠀⠀⠀⠀⠀⢠⣶⣤⡘⣿⣿⣷⣀⠈⣿⣿⣿⠄⠀⢀⣠⣤⣤⠀⢾⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠋⠇⠻⣿⣷⣆⠀⠀⠈⠛⡿⠀⢠⣯⣽⢠⣾⣿⠁⣼⣿⠇⠀⠀⠀⠀⠀⠈⣿⣶⣤⣠⣤⣴⣴⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⣿⣿⣿⡾⣿⣿⣿⡇⣠⣿⣿⠟⠋⠀⠀⠈⠁⣽⣿⣿⣿⣿
⠀⠛⠃⠀⠀⠀⠈⠻⣿⣿⣦⡄⠈⣿⠀⣿⣿⡏⣾⣿⡇⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⠀⠀⠗⠙⠟⠀⣿⣿⢼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡀⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⣸⣧⣮⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⣿⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠛⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣥⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⣿⣿⣭⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣔⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣈⠻⣿⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⡱⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢩⣾⣿⢟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⢻⡿⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⣂⠀⠀⠃⢀⣬⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠚⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⠻⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠠⢢⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⡞⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢺⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿
⢀⢰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠃⠀⠀⣠⣴⣿⣿⣿⣥⠄⣉⣙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⣿⡟⠂⠀⠀⠀⠁⢻⣿⡿⠀⠀⠀⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⠐⠿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣮⣭⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⣼⣶⣄⣀⠘⠃⠀⠀⢺⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠐⣴⣿⣿⣿⣿⣿⣷⡄⠀⢀⠖⠛⠉⠁⠀⠀⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⠿⠋⠀⠀⢨⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣀⢀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⡟⠷⠀⠀⠀⠀⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠉⠘⠀⠀⠀⠀⢦⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠸⠻⠿⣸⣷⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⢀⣬⣿⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠍⡍⠄⠀⠀⠀⠀⠀⠀⢠⠀⡙⠯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣲⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⣀⣁⠉⠀⣂⠀⠀⠀⠀⠀⠀⣽⣿⣿⡎⠋⣼⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⢪⣿⣿⢿⣿⣿⡟⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣵⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠨⣿⣿⣧⠂⠄⠀⠀⠀⠀⠀⠀⣹⣿⣿⣏⠀⣿⣿⣿
⣿⣿⣿⣗⣏⠀⣀⡀⠀⠀⠣⣿⣻⣟⠿⠛⢻⣿⡿⢀⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠛⢻⣶⣼⣿⣟⡄⠀⠀⠀⠀⠀⠀⢠⣤⡀⢻⣿⣿⣆⡀⢻⣿⣿⣆⠀⠀⣀⣤⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠣⡇⠘⢿⣿⣦⡀⠉⠉⠻⣻⠀⢀⣾⣭⡆⣬⣿⠃⣰⣿⡇⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣻⣿⣿⣷⣉⣿⣿⣿⢄⣼⣿⡿⠋⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿
⠀⠊⠁⠀⠁⠀⠀⠹⣿⣿⣦⡄⡀⣽⡀⣾⣿⡿⣼⣿⡟⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠯⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡹⣿⣿⣯⣿⣿⣿⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠈⠟⠙⠟⠃⡿⢿⡡⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣿⣬⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣴⣮⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⠿⠿⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⢣⡈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣘⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡉⢽⣿⣿⣿⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢽⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣭⣡⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣠⣿⣿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⢂⠀⠀⠃⠀⣌⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠺⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢹⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠘⢠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠀⡀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⡞⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢺⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠇⠀⠀⣠⣴⣿⣿⣿⣥⠄⣉⣙⡛⢿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠐⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⣿⠟⠃⠀⠀⠀⠂⢻⣿⡟⠀⠀⠀⣿⣿
⠸⣾⣿⣿⣿⠀⠀⠀⢐⠿⢿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣮⣭⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⣼⣦⣄⣀⠘⠃⠀⠀⢪⣿⣿⣿⣟⠁⠀⠀⠀⠈⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣷⡄⠀⢄⠆⠛⠉⠁⠈⠈⠙⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⢿⠏⠀⠀⢀⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⡏⠾⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿
⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠐⠈⠀⠀⠀⡠⣧⣽⣿⠛⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣻⢿⣿⣿⣿⣿⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⢀⣬⣿⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢏⠌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣾⣾⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⣀⣀⠉⠛⣆⠀⠀⠀⠀⠀⠀⣹⣿⣿⡆⢉⣴⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡟⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣵⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣇⠁⣿⣿⣿
⣿⣿⣿⣗⣟⠀⣀⡀⠀⠀⢨⣿⣻⣟⠿⠟⢻⣿⡿⢀⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠟⠛⠛⢻⣶⣾⣿⣟⡄⠀⠀⠀⠀⠀⠀⢠⣤⡀⢻⣿⣿⣆⠀⢹⣿⣿⣆⠀⠀⣀⣤⣤⡀⠀⢽⣿⣿⣿⣿⣿⣿⣿
⠛⣿⡿⢣⡇⠘⢿⣿⣦⡀⠉⠉⠻⣻⠀⢀⣾⣭⡆⣬⣿⠃⣰⣿⡇⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣻⣿⣿⣷⣈⣿⣿⣿⢄⣼⣿⡿⠋⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠀⠹⢿⣿⣦⡄⡀⣽⡀⣾⣿⡿⣼⣿⡟⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠯⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡹⣿⣿⣯⣿⣿⣿⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠀⠟⠘⠟⠃⡿⢿⡡⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⣀⣀⣿⣾⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⠿⠿⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⢧⡈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣅⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣘⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡁⢿⣿⣿⣾⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣭⣩⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⣡⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⠻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣯⢂⠀⠀⠃⢀⡌⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠒⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⠸⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣾⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠈⣤⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣏⠀⠀⣿⣿
⠀⠀⣀⣿⣇⠀⠀⠀⢽⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⡞⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠺⢺⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠠⣾⣿⣿⡏⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠇⠀⠀⣠⣴⣿⣿⣿⣥⠄⣉⣙⡛⢿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠈⠁⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⠿⠂⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿
⠐⣾⣿⣿⣿⠀⠀⠀⠀⢛⢿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣮⣭⣿⣿⣿⣿⣿⣟⣿⣿⡿⠁⣼⣦⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠂⠫⠉⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⠏⠀⠀⢘⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠯⢟⠓⠀⠀⠀⠀⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿
⣼⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠀⠀⠀⠈⢢⣿⣟⠂⠃⠀⠀⠀⠀⠀⠀⠘⠻⡿⣹⣿⣟⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⢀⣬⣿⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠋⢴⠄⠀⠀⠀⠀⠀⠀⢀⠀⠁⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣢⡂⠈⠉⠤⠀⠀⠀⠀⠀⠀⣸⣿⣷⡆⠉⣴⣿⣿
⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⠷⣿⣿⣿⣿⣿⡗⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣵⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⢸⣿⣿⡆⠀⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿
⣿⣿⣿⣧⣿⠀⣀⡀⠀⠀⠻⣿⣛⣛⠿⠏⢹⣿⡿⠇⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠛⢹⣷⣼⣿⣟⡄⠀⠀⠀⠀⠀⠀⣠⣤⡈⢿⣿⣷⣄⠀⣻⣿⣿⡄⠀⠀⣠⣤⣤⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⠻⡟⠈⢿⣿⣷⡄⠁⠉⠻⢿⠇⠀⣼⣭⡇⣼⣿⡏⢠⣿⡟⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣮⣻⣿⣿⣧⢹⣿⣿⣿⢠⣾⣿⡿⠋⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿
⠀⠛⠃⠀⠁⠀⠀⠙⢿⣿⣶⡄⡀⣽⡀⣸⣿⣿⣱⣿⡿⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠯⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣹⣿⣿⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠈⠼⠘⠿⠃⡿⠿⡃⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣻⣿⣷⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣀⣀⣿⣲⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣴⣮⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣻⣿⣿⣿⣿⣿⡿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠈⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡘⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡈⢿⣿⣿⣿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣽⣩⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⣨⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣯⢆⠀⠀⠃⠀⡝⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢸⣿⠟⣋⣿⣿⣿⣿⣿⡟⠀⣽⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠀⣠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠀⣀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡞⠶⠶⠿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠺⢺⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⡀⣿⣿⣿⡏⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠇⠀⠂⣠⣤⣿⣿⣿⣥⢈⣉⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣟⣻⣿⠛⠁⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿
⠠⣾⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣦⣤⣮⣝⣺⣿⣿⣿⣿⡟⣿⣿⡿⠀⣴⣦⣄⣀⠐⠒⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣼⣿⣿⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠛⠉⠀⠀⠁⠉⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⣀⠀⠀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠟⢻⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿
⣼⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣱⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣃⢀⣬⣿⣭⣙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠑⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢭⣻⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⢀⣀⡠⠂⠀⡠⠀⠀⠀⠀⠀⠀⣺⣾⣷⡖⠋⣸⣿⣿
⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢩⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⣵⠏⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⣿⣿⣿⡂⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠑⣿⣿⣿
⣿⣿⣿⣧⣿⠀⣀⣀⠀⠀⢸⣽⣟⣚⡟⠍⠓⣿⣿⠇⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠛⢹⣶⣶⣿⣟⡄⠀⠀⠀⠀⠀⠀⣠⣀⠙⣿⣿⣧⡀⠸⣿⣿⣷⠀⠀⢀⣤⣶⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⢏⡛⠀⠻⣿⣷⣄⠈⠉⠹⢿⡇⠀⣼⣭⡅⣠⣿⡟⢀⣿⡿⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣷⣌⢿⣿⣿⣦⣿⣿⣿⡷⣰⣿⣿⠟⠁⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⠈⢿⣿⣷⣤⣀⣹⡇⣰⣿⣿⣱⣿⣿⢁⣾⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠈⠽⠙⠻⠋⠺⢿⡇⢾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢰⢀⢀⣶⣴⣇⣝⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣤⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⡿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠻⠿⠿⠊⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠈⡅⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣕⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠸⣿⣿⣗⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣺⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡉⢿⣿⣿⣿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣝⣫⠎⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣼⣿⣿⢻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢷⣀⠀⠉⠻⣿⡿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⣯⢆⠀⠀⠓⢐⡝⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠋⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢽⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠈⣤⣾⣿⣿⣿⣿⣏⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠀⡀⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⡞⣶⣶⡿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢾⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡘⣿⣿⣿⡏⠀⠀⣿⣿
⠀⢠⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⡁⠀⠀⣄⣀⣬⣿⣿⣿⣍⣉⣉⡛⠿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠁⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡟⠀⠀⠀⠀⠁⢻⣿⡟⠀⠀⠐⣿⣿
⢸⣾⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣻⣠⣤⣴⣶⣾⣿⣿⣿⣿⣶⣬⣍⣛⣾⣿⣿⣿⣿⣿⣿⡿⠀⣶⣦⣄⣀⠘⠂⠀⠀⢸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⠰⠛⠉⠁⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢠⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠏⡯⠯⠀⠀⠀⠀⣿⣿⣿⡿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣘⣿⣿
⣼⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠻⣿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⢿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠉⣙⣟⣛⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡃⢳⠀⠀⠀⠀⠀⠀⠀⢸⢀⠹⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⣈⣐⢶⠃⠌⡀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡖⠋⣼⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⡖⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⣿⣿⣧⠂⠲⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠉⣿⣿⣿
⣿⣿⣿⣷⣿⠀⢀⣀⠀⠀⣶⣿⣿⣛⡟⠟⠋⣿⣿⡇⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢈⠙⠛⠛⠿⣿⡿⠿⠟⠻⣷⣶⣿⡿⡄⠀⠀⠀⠀⠀⠀⣀⡀⠻⣿⣿⣦⡀⢸⣿⣿⣧⠂⠀⢀⣤⣦⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⢿⡟⠀⠹⣿⣿⣆⠁⠉⠹⢿⡇⠀⣰⣽⡏⢠⣿⡿⢀⣾⣿⠀⠀⠀⠀⠀⠘⣿⣶⣄⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⣙⣿⣿⣿⡦⣿⣿⣿⡇⣴⣿⣿⠟⠀⠀⠀⠀⠙⠉⣿⣿⣿⣿⣿
⠀⠙⠋⠀⠁⠀⠀⠈⢻⣿⣷⣤⣀⣸⡇⢰⣿⣿⣣⣿⣿⠃⣼⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠈⢹⠞⠻⠟⢸⢿⣏⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⡁⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⡈⣲⣡⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡗⠀⠀⠠⣤⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣻⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠸⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣕⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⣗⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣺⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠉⣿⣿⣿⣽⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣟⣋⠜⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣬⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠉⢻⡟⢿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⣯⢆⠀⠀⠃⠀⣜⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠊⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢸⣿⠟⣫⣿⣿⣿⣿⣿⡗⠀⣺⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠀⣀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿
⠀⠀⣀⣿⣇⠀⠀⠀⢲⣿⣿⣿⣿⣭⠁⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⠞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⣾⣶⠶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡈⣿⣿⣿⡇⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣻⠀⣿⠋⣠⣤⣤⣈⣽⣿⣿⣿⣉⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⣺⣿⠏⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⣿⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣠⣀⣿⣷⣿⣧⣭⣭⣭⣭⣿⣿⣿⣿⣿⣽⣛⣛⣳⣿⣿⣿⣿⣽⠟⢁⣦⣤⣄⣀⠘⠐⠀⠀⢘⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠐⠛⠉⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⡀⠀⠀⣽⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠋⠇⠀⠀⠀⠀⠀⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⢫⣿⣿⣷⣧⢘⣿⣿
⣼⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢼⣽⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⣛⣿⣛⡻⠿⢿⣿⣿⣿⣿⣿⣿⠏⠿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠠⠀⠀⠀⠀⠀⠀⠀⢀⢀⠩⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⣀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⡆⠋⣼⣿⣿
⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡍⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⢸⣿⣿⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠘⣿⣿⣿
⣿⣿⣿⣯⣿⠀⢀⣀⡀⠀⢪⣽⣿⣒⡟⠻⠋⣾⣿⡇⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣮⡙⠿⠿⠿⣿⣿⣿⠿⠿⣏⣵⡿⡅⠀⠀⠀⠀⠀⠀⣀⡈⢻⣿⣿⣄⡁⢿⣿⣿⣷⠀⠀⣀⣤⣤⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⠟⠛⠀⠙⣿⣿⣆⠈⠉⠙⢿⡇⠀⢰⣿⣿⢠⣿⡿⠁⣼⣿⠀⠀⠀⠀⠀⠸⣿⣿⣶⣄⡀⠀⣀⣤⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⡻⣿⣿⣿⡾⣿⣿⣿⡧⣴⣿⣿⠏⠀⠀⠀⠀⠘⠁⣽⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠀⠀⠈⠻⣿⣷⣤⣂⣸⡇⢠⣿⣿⣇⣾⣿⠇⣼⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⢹⠞⢿⠟⢸⢿⣟⢼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡁⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣤⣤⣀⡈⣲⣽⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡗⠀⠀⠠⣤⣬⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣞⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⠿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠸⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣕⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠛⠛⠃⠈⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣗⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣾⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠉⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣟⣋⠜⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢐⣮⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠉⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⣯⢆⠀⠀⠃⠀⡜⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠈⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⠰⡿⠛⣋⣿⣿⣿⣿⣿⡇⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣉⠁⠀⠀⢸⡇⢸⢠⠀⣿⡗⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠓⠚⢺⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠷⠋⠀⠀⡈⣾⣿⣿⡇⠀⠀⣿⣿
⠀⢰⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⠿⣛⣋⡉⣉⣿⣿⣿⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⠳⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿
⠨⣾⣿⣿⣿⠀⠀⠀⠀⡽⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⡀⣠⣤⣀⣀⣴⣶⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣿⣿⣿⣿⣷⣆⣠⣦⣦⣄⣀⠘⠐⠀⠀⠐⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⣹⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠚⠁⠀⠀⠉⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣳⠇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⡀⠀⠀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⠱⠂⠀⠀⠀⠀⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣧⣈⣿⣿
⣼⣿⣿⣿⣿⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⣹⣷⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣟⡿⣿⣿⣿⣿⣿⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢟⣿⣿⣿⣿
⣷⣿⣿⣿⣿⠀⠀⠀⠀⠐⣒⣽⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣷⣴⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢺⣶⣶⡆⠉⣸⣿⣿
⣿⣿⣿⡿⣏⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⣿⣿⣦⡀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠘⣿⣿⣿
⣿⣿⣿⣇⢿⠀⠀⢀⣀⠀⠰⡿⣟⢞⣽⠓⠃⠀⣰⣿⡆⢰⣶⡄⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣍⡛⠻⢿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠈⠻⣿⣿⣄⠀⠘⣿⣿⣧⡀⠀⠀⣠⣤⡄⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿
⠛⣿⣿⠗⡏⠀⠀⠹⣿⣿⣌⠁⠀⠸⡿⡇⠀⢠⣟⣯⢀⣿⡿⠁⣴⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⣀⡀⠉⠉⠀⠀⠀⠀⠀⢿⣿⣦⡙⣿⣿⣷⣄⢿⣿⣿⣧⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠁⣽⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⣺⡇⢠⣿⣿⢇⣾⣿⠃⣼⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠯⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣎⢿⣿⣿⣸⣿⣾⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠀⠈⣱⠸⠿⠟⢼⣿⠏⣼⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⡁⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣠⠀⠁⣼⢧⡏⠛⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⣤⣦⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⣯⢟⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⢿⣿⣟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢀⢛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⢙⣿⣿⣿⡟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣝⡛⣣⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢊⣹⣿⡿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠉⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⢂⠀⠀⠃⢐⡜⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠘⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣷⠀⠀⠀⠸⡿⠛⣻⣿⣿⣿⣿⣿⡇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠈⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠓⠚⠚⢲⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⡿⠷⠛⠀⠀⠀⣽⣿⣿⡇⠀⠀⣿⣿
⠀⠰⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣻⣿⣿⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⠇⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⣟⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡀⡀⣠⣄⣀⠀⢀⣤⣤⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣋⣹⣿⣿⣿⣷⣀⣤⣤⣄⡀⠘⠀⠀⠀⢘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⣻⣾⣿⣿⣿⣿⣗⡀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠻⠏⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⢀⣀⠀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⠩⠹⠀⠀⠀⠐⢻⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠨⣽⣿⣟⣧⣘⣿⣿
⣼⣿⣿⣿⣏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠸⠫⢟⢩⣷⣽⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⡿⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⠟⣿⣿⣿⣿
⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⡉⣩⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣴⣾⣿⣶⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⠉⣼⣿⣿
⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⣿⣟⣻⣿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⣿⣿⣦⠀⠀⠀⣾⣿⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠘⣿⣿⣿
⣿⣿⣿⡶⢾⠀⠀⢀⣀⡀⣄⣿⣷⡴⠽⠛⠓⠀⢠⣶⣦⢠⣶⡄⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣷⣄⠀⠙⣿⣿⣆⠀⠀⠀⣠⣤⡄⠀⠀⠀⠸⣿⣿⣿⣷⣿⣿⣿
⠛⣿⣿⠣⡏⠀⠀⠘⣿⣿⣆⠁⠀⠰⣿⡧⠀⢀⣟⣟⠀⢼⣿⠃⣰⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣅⣀⠀⠈⠉⠉⠉⠀⠀⣿⣿⣦⡹⣿⣿⣷⡄⣻⣿⣿⣧⢠⣾⣿⡿⠁⠀⠀⠀⠀⠈⠁⣽⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠆⢐⡇⢀⣾⣿⡏⣼⣿⠇⣰⣿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣎⢿⣿⣿⢸⣿⣿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠈⠈⢳⠼⢿⠟⢸⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣁⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣟⢿⣿⣾⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⢀⠀⠀⣨⢫⠈⠻⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢤⣦⣽⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣯⢟⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⢷⣿⣾⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣿⣿⣽⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢛⣿⣿⣿⡛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣯⣝⡛⢣⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢊⣙⣿⡿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢧⣀⠀⠉⠹⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡀⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠈⣭⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣷⠀⠀⠀⢠⡿⠛⣫⣿⣿⣿⣿⣿⠇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢐⣾⣿⣿⣿⣍⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠓⠚⠒⠒⢶⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⣿⠗⠋⠀⠀⠀⢼⣿⣷⠇⠀⠀⣿⣿
⠀⠠⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣻⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣐⡏⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⣹⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⣠⣬⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⣁⣾⣿⣿⣯⢀⣤⡄⠀⠐⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣗⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠁⠀⠀⠀⣺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⠀⡀⠀⢀⣿⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠀⠀⠀⢻⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠈⣽⣿⠚⣦⢈⣿⣿
⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣙⣿⡅⠀⠀⠀⠀⠀⠀⢘⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢀⣷⣟⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣛⢻⣿⣿⣿⣿⡿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢛⣿⣿⣿⣿
⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⣰⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣶⣶⣶⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⠆⠉⣼⣿⣿
⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⢁⣿⣻⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⡀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿
⣿⣿⣿⠇⣣⠀⠀⠀⣀⡀⠌⡌⣶⡮⠯⠓⠁⠀⠀⣴⣶⠀⣤⣤⠀⠀⠀⠀⠀⠀⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣿⣿⠿⠈⠻⣿⣿⣆⠀⠘⢿⣿⣇⠀⠀⠀⣠⣤⡄⠀⠀⠀⠸⢿⣿⣿⣿⣼⣿⣿
⠙⣿⣿⠇⠏⠀⠀⠘⢿⣿⣧⠁⠀⠀⣿⣷⠀⠀⣜⢿⡃⡰⣿⡟⢠⣶⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣟⣛⣃⠀⠈⠉⠉⠉⠀⢿⣿⣦⡙⣿⣿⣷⡄⢿⣿⣿⣧⢠⣾⣿⡿⠁⠀⠀⠀⠀⠘⠁⢹⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⣻⠀⣼⣿⡿⣰⣿⡿⢀⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣎⢿⣿⣿⣸⣿⣾⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡌⠈⠻⡄⠿⠿⢣⣿⣿⢡⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣅⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣏⢿⣿⣮⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⡀⠀⢀⢓⡈⠛⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⢰⣶⣼⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣯⢿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠵⢧⣾⣿⠳⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⣿⣿⠭⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠙⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣮⣝⡻⢋⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢊⣙⣿⡿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢷⣀⠀⠉⠹⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣭⣾⣿⣤⣤⣧⣼⣿⣬⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣷⠀⠀⠀⠰⡿⠟⣉⣿⣿⣿⣿⣿⠃⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣅⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⡇⠀⠀⠀⠰⣿⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠗⠚⠚⠒⠒⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣼⣿⣷⡇⠀⠀⣿⣿
⠀⠠⣾⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⣼⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠛⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⡀⠀⠀⢀⣴⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⢀⣾⣿⣿⡄⢀⣀⡀⠐⠂⠀⠀⠘⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠁⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠷⠉⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⢀⣵⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠐⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣽⣽⢓⣧⠈⣿⣿
⣼⣿⣿⣿⣏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⡿⠁⠀⠀⠀⠀⠀⠨⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠿⢨⣧⣟⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡾⣻⣿⣿⣿⣿⡿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠬⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠩⢛⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠊⢘⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣶⣶⣶⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⠉⣼⣿⣿
⣿⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣾⢟⢿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠐⣿⣿⣿
⡾⣿⣿⠴⢟⠀⠀⠀⣀⣀⠠⠈⣶⡾⠫⠓⠁⠀⠀⣴⣶⡄⣤⣤⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⣿⣿⣿⣿⣿⡿⡇⠙⣿⣿⣦⡀⠈⢻⣿⣷⡀⠀⠀⣠⣤⣄⠀⠀⠀⠸⢿⣿⣿⣷⣾⣿⣿
⠛⣿⣿⠗⠆⠀⠀⠀⢻⣿⣷⡁⠀⠀⢾⣿⠄⠀⣰⠿⡇⠠⣿⡟⢀⣴⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣛⣛⠂⠀⠉⠉⠉⠁⠻⣿⣷⣌⢿⣿⣿⣦⠘⣿⣿⣷⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⡀⠀⣺⠀⣰⣿⡿⢡⣿⣿⢁⣾⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⢹⣿⣿⡇⣿⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠙⡦⠿⡻⠃⣿⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣥⡀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡻⣿⣷⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⢀⡓⣈⡛⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠰⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣷⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠳⢦⣾⣷⡃⢶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⡭⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠙⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣮⣝⡛⢋⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣉⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢷⣀⠀⠉⠹⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠾⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡈⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣷⡆⠀⠀⠀⣽⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⡿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⢠⠿⠟⣋⣿⣿⣿⣿⣿⠏⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⣿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢑⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡗⠚⠒⠒⠒⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠗⠋⠀⠀⠀⢽⣿⣿⡇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣸⣏⢻⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⢿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⡙⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⠀⡀⠀⠀⠀⣤⣶⣯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣗⠀⣴⣿⣿⡄⢀⣄⣀⠐⠂⠀⠀⢐⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠯⠁⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⢀⡀⠀⠀⣽⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁⠀⠀⠀⠀⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢈⣽⣿⠯⣦⢈⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⠁⠀⠀⠀⠀⠀⠐⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠟⢁⣿⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠺⠻⣿⣿⣿⣿⡿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢛⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⢢⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣴⣶⣶⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣶⠆⠉⣸⣿⣿
⣿⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⣾⣛⢻⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣷⣄⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠐⣾⣿⣿
⡿⣿⣿⡄⠍⠀⠀⠀⣀⣀⠀⢊⢷⠼⠋⠅⠀⠀⠀⣴⣶⡄⣤⣤⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⣿⣿⣿⣿⣿⣿⣇⠘⢿⣿⣧⡀⠀⢻⣿⣿⡀⠀⠀⣠⣤⣤⠀⠀⠀⠰⢿⣿⣿⣿⣾⣿⣿
⠛⣿⣿⠇⠅⠀⠀⠀⢻⣿⣷⡀⠀⠀⢾⣿⠄⠀⣰⠿⡇⠠⣿⡟⢀⣴⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣛⣛⠂⠀⠉⠉⠉⠉⠸⣿⣷⣌⢻⣿⣿⣦⠘⣿⣿⣿⢀⣾⣿⡿⠋⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⣀⠀⣺⠀⣰⣿⡿⢡⣿⣿⢁⣾⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡹⣿⣿⣇⣿⣽⣿⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠙⡦⠿⡿⠇⣿⣿⢃⣾⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣥⡀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷⡹⣿⣷⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⢀⡕⣈⠛⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣾⣿⡋⢶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⢛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣭⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠉⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣯⣟⡛⢋⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣍⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢧⣀⠀⠈⠩⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡘⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣷⡆⠀⠀⠀⣭⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣷⠀⠀⠀⠠⡿⠟⣋⣿⣿⣿⣿⣿⠉⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⠸⣿⣿
⠀⠀⠘⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⡅⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡇⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠐⣾⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣼⣿⣷⡇⠀⠀⣿⣿
⠀⠠⣾⣿⣿⠀⠀⠀⠐⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⡍⢸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠨⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⣠⣶⣶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⡂⢠⣶⣿⣧⠀⣀⡀⠐⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠅⠂⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⢀⣽⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠨⣽⣽⡻⣦⠈⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠏⠀⠀⠀⠀⠀⠘⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠿⢑⣷⣽⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠼⢻⣿⣿⣿⣿⡿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⣿⣿⣿⣿
⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⢡⣬⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡆⠊⣼⣿⣿
⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠐⣾⢻⢻⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠐⣿⣿⣿
⡾⣿⣿⠀⠜⠀⠀⠀⣀⣀⠀⠘⣾⠦⠭⠃⠁⠀⠀⣠⣶⡄⣠⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⣇⠙⢿⣿⣧⡀⠀⢛⣿⣿⡄⠀⠀⣠⣤⣤⠀⠀⠀⠨⣿⣿⣿⣿⣼⣿⣿
⠛⣿⣿⠃⠃⠀⠀⠀⠻⣿⣷⡄⠀⠀⢸⣷⡆⠀⣰⠿⠏⠁⣿⡿⠁⣤⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣛⣛⡛⠒⠀⠉⠛⠛⠋⠻⣿⣷⣌⢻⣿⣿⣦⠈⣿⣿⣿⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣠⠀⢺⠁⢰⣿⣿⢣⣾⣿⠁⣼⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡹⣿⣿⣇⣿⣯⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠁⠙⣤⠞⣿⡏⣿⣿⠇⣼⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣥⡀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡹⣿⣷⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⡀⠀⠉⡙⢂⠛⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣮⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠥⣦⣾⣷⡻⢶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿⣿⠥⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠙⣿⣿⣟⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣯⣝⡻⢇⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣍⣿⡿⣻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢷⣀⠀⠈⠩⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡘⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣷⡆⠀⠀⠀⣥⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣷⠀⠀⠀⠠⡿⠟⣉⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⠀⣿⣿⣿⣾⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⢀⣺⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⡇⠀⠀⠀⢐⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⠻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣽⣿⣿⠇⠀⠀⣿⣿
⠀⠠⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⣏⢸⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⣿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠘⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⡂⢀⣶⣿⣧⠀⣀⠀⠐⠂⠀⠀⠐⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣽⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠁⠃⠀⠀⠀⣬⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣟⢀⡀⠀⠀⣼⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⣿⣽⠛⣧⠈⣿⣿
⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠟⠀⠀⠀⠀⠀⠀⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠟⢁⣷⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⡟⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠛⣿⣿⣿⣿
⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣶⠂⠉⣼⣿⣿
⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⢿⢛⣻⣿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣇⠐⣿⣿⣿
⡿⣿⣿⠀⢝⠀⠀⠀⢀⣀⡀⢉⢲⠼⠽⠑⠁⠀⠀⢠⣴⡄⢠⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣦⡀⠈⢻⣿⣧⡀⠀⠀⣠⣤⣄⠀⠀⠀⠸⢿⣿⣿⣷⣼⣿⣿
⠛⣿⣿⠇⠆⠀⠀⠀⠹⣿⣿⡄⠀⠀⢰⣿⡆⠀⢠⠿⠏⠁⣽⣿⠁⣤⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣛⣛⡛⠒⠀⠉⠛⠛⠛⢿⣿⣦⣜⢿⣿⣿⣄⠈⣿⣿⣷⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⢐⠁⢠⣿⣿⢃⣾⣿⠃⣼⣿⠏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢻⣿⣿⡆⣿⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡇⠀⠙⣧⠻⣿⡏⣾⣿⠏⣼⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣥⡀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⡙⢂⠛⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣮⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠧⣤⣴⣧⡋⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢀⠛⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⣿⣿⠥⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠙⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡛⢟⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣍⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢷⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡌⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣡⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣷⠀⠀⠀⢀⡿⠟⣋⣿⢗⣿⣿⣿⠅⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⠸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⠃⠀⠀⣿⣿
⠀⠀⡀⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⠻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠀⣬⣿⣷⠇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠐⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣏⢸⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⢿⣿
⠠⣾⣿⣿⣿⠀⠀⠀⠀⠹⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⠀⠀⢠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣶⡆⢀⣶⣿⣧⠀⡀⠀⠐⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⢾⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⣸⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⠰⠋⠀⠀⠀⣦⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⢸⣟⡀⠀⠀⠀⢼⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢹⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⡿⣽⡲⣤⢘⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠟⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠸⢠⣷⣙⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠒⣿⣿⣿⣿
⣷⣽⣿⣿⡗⠀⠀⠀⠀⠀⢆⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠆⠉⣰⣿⣿
⣯⣿⣿⠟⠅⠀⠀⠀⠀⠀⠀⣾⢹⢹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠐⣿⣿⣿
⣿⣿⣿⠀⢪⠀⠀⠀⢀⣀⡠⢋⣶⠒⠭⠀⠁⠀⠀⢠⣴⡄⢠⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⡗⠙⣿⣿⣦⡀⠈⢻⣿⣧⡀⠀⠀⣠⣤⣄⠀⠀⠀⠈⣿⣿⣿⣷⣾⣿⣿
⠙⣿⡿⠞⠈⠀⠀⠀⠙⣿⣿⣄⠀⠀⢰⣿⡆⠀⢠⠿⠏⠁⣿⣿⠁⣤⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣛⣛⡛⠒⠀⠉⠛⠛⠋⢿⣿⣦⣜⢿⣿⣿⣆⠨⣿⣿⣧⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠐⠁⢠⣿⣿⢇⣾⣿⠇⣼⣿⠏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢻⣿⣿⡆⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠙⣧⠚⣿⡏⣾⣿⠏⣼⣿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣥⡀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡙⢂⠻⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣮⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠧⣤⣴⣧⡋⠴⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢀⢛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⡯⠥⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡛⠓⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿
⢧⣀⠀⠉⠻⡏⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⢂⠀⠀⠃⠀⡈⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣷⡆⠀⠀⠀⣣⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣷⠀⠀⠀⠰⠿⠟⣫⣿⣽⣿⣿⣿⠇⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⠸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⡉⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⡿⣿⡿⡏⠀⠀⣿⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⢷⡾⡟⠗⠋⠀⠀⠀⢻⣿⣷⠇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⢿⠃⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⢸⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⡂⢀⣶⣿⣧⠀⣀⠀⠐⠂⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡺⠽⠃⠀⠀⠀⣬⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⠀⢼⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡷⣤⠘⣿⣿
⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠟⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢡⣧⣝⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠸⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠂⠉⣴⣿⣿
⣿⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⣿⠫⢹⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠐⣿⣿⣿
⣿⣿⣿⡂⠿⠀⠀⠀⢀⣀⡠⠉⢳⠶⠩⠄⠁⠀⠀⢠⣴⣄⢠⣤⡀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠿⣿⣿⣿⣿⣿⣿⡷⠙⣿⣿⣦⡀⠈⢻⣿⣧⠀⠀⠀⣠⣤⣄⠀⠀⠀⠈⣿⣿⣿⣷⣾⣿⣿
⠛⣿⡿⠇⠈⠀⠀⠀⠘⣿⣿⣆⠀⠀⢰⣿⡆⠀⢠⡻⢿⠁⣼⣿⠃⣠⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣟⣛⣛⠒⠀⠉⠛⠛⠋⢿⣿⣦⣜⢿⣿⣿⣆⠸⣿⣿⣷⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠰⡇⢠⣿⣿⠇⣾⣾⠇⣰⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢹⣿⣿⡆⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠘⣣⠚⣿⡟⣸⣿⠏⣴⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠂⠛⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠇⣤⣴⣧⡇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡹⣿⣯⠥⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢻⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡻⠓⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠀⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢷⣀⠀⠉⠹⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡈⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣷⡆⠀⠀⠀⣥⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣷⠀⠀⠀⢀⡿⠟⣫⣿⣿⣿⣿⣿⠁⠀⣼⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⡃⠀⠀⣿⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠠⢿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠚⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⠟⠗⠋⠀⠀⠁⣽⣿⣷⡇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢴⡋⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠘⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡀⠀⠀⠀⣠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡂⢀⣶⣿⣧⠀⡀⠀⠐⠀⠀⠀⠀⣿⣿⣯⠂⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣾⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠁⠉⠀⠀⠀⣜⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⠀⢼⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⡗⣦⡘⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠟⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠸⠀⣧⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠚⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠂⠉⢴⣿⣿
⣮⣿⣿⠛⠇⠀⠀⠀⠀⠀⠀⣾⠝⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠐⣿⣿⣿
⠾⣿⣿⠀⠻⠀⠀⠀⢀⣀⣀⢹⡅⠌⠍⠂⠁⠀⠀⢠⣤⣤⢀⣤⡀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⠿⣿⣿⣿⣿⣿⣿⡷⠙⣿⣿⣦⡀⠀⢻⣿⣧⡀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿
⠙⣿⡿⠃⠁⠀⠀⠀⠘⢿⣿⣆⠀⠀⠰⣿⣦⠀⢀⡾⢿⠁⣼⣿⠇⣠⣤⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣟⣛⣛⠓⠀⠉⠛⠛⠋⢿⣿⣷⣜⢿⣿⣿⣆⠈⣿⣿⣧⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⠀⠠⡇⢀⣾⣿⡏⣼⣾⠏⣰⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣧⢹⣿⣿⡆⣿⣽⣽⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠙⢣⠘⣿⡿⣸⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣧⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣻⣿⣷⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⡉⠂⠙⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣤⣴⣧⡏⠄⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣯⠥⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢿⣿⣟⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡛⠟⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿
⢷⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⠿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡈⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣭⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⢰⡿⠟⣉⣽⢳⣿⣿⣿⠁⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⠸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⢾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⡃⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠠⣾⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠚⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠈⣸⣿⣷⡏⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠘⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣍⢙⣿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿
⠠⣾⣿⣿⣿⠀⠀⠀⠀⠸⢿⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⣠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⡆⢠⣾⣿⣧⠀⣀⠀⠐⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢾⣿
⠀⢹⣿⣿⣿⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠈⠀⠀⢰⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠑⠉⠀⠀⠀⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣟⣀⠀⠀⠀⣼⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢹⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⡑⣤⠈⣿⣿
⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠛⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡘⠀⣷⣟⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠟⠃⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠛⣿⣿⣿⣿
⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣤⣬⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠆⠁⢴⣿⣿
⣯⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⣾⠟⢹⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠐⢿⣿⣿
⣾⣿⣿⠀⢫⠀⠀⠀⢀⣤⣄⠚⡤⠶⠛⠂⠁⠀⠀⢀⣴⣦⢀⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⣦⡀⠀⢹⣿⣧⡀⠀⢀⣠⣶⣆⠀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿
⠛⢿⡿⠂⡈⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣿⣷⠀⢀⡾⢿⠁⢼⣿⠇⣠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣛⣛⠓⠀⠉⠉⠙⠉⠻⣿⣷⣌⢿⣿⣿⣆⠈⣿⣿⣷⢠⣾⣿⡿⠁⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⡇⢀⣾⣿⡏⣼⣾⠏⣰⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠹⣿⣿⣆⣿⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠙⢣⠘⣽⡿⢸⣿⡟⣰⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⡹⣿⣷⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠂⠛⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢷⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⣤⣴⣧⡏⠤⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⠋⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⠥⢴⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢻⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣮⣽⡛⠟⡜⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⢧⣀⠀⠈⠙⡛⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡄⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢡⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢻⣿⠀⠀⠀⠠⠿⠟⣉⣿⣯⣽⣿⣿⠇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⡍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⡿⡃⠀⠀⣻⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣅⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡟⠗⠋⠀⠀⠀⣴⣿⣷⠇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢰⡍⡸⢿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠘⢛⣫⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣀⠀⠀⠀⣴⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⡂⢠⣾⣿⣧⠀⣀⡀⠐⠀⠀⠀⠀⣼⣷⣷⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢼⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⠨⠁⠀⠀⠀⢠⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⢴⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⠰⣤⠈⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠐⢽⡷⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠛⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣤⣝⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠟⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠟⣿⣿⣿⣿
⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠁⢘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣴⣬⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⠂⠁⢰⣿⣿
⣧⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⢞⠉⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡃⠐⣿⣿⣿
⣿⣿⣿⠀⢫⠀⠀⠀⢀⣤⣄⢊⠤⠔⠜⠀⠀⠀⠀⢀⣴⣦⢀⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣦⡀⠈⢻⣿⣧⡀⠀⢀⣠⣶⣆⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿
⠛⢿⡿⠃⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣿⣷⠀⢀⡾⢿⠁⢼⣿⠇⣠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣛⣛⠓⠀⠈⠉⠙⠋⠻⣿⣷⣌⢿⣿⣿⣆⠨⣿⣿⣷⢠⣾⣿⡿⠁⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠄⠀⡇⢀⣾⣿⡏⣼⣿⡏⣰⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠹⣿⣿⣇⣿⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠀⠘⢣⠘⢿⡿⢸⣿⡟⣰⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣹⣿⣷⡻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠂⠉⠂⠛⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠇⣤⣴⣷⡏⠤⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⠥⢴⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⣻⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣮⣽⡛⠟⡜⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠐⢫⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠠⠿⠛⣩⣿⣿⣿⣿⣿⠇⠀⣼⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠚⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠁⣾⣿⣷⠇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣿⠁⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿
⠈⣾⣿⣿⣿⠀⠀⠀⠀⢼⣽⣿⣿⣿⣦⠀⠀⠃⠀⠀⠀⡀⢀⠠⢄⣀⡀⠀⠀⣴⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣅⣰⣿⣿⣿⡄⢀⣀⠀⠐⠀⠀⠀⢒⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⢹⣿⣿⣿⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣷⡀⠀⠀⠈⠈⠀⠀⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⠔⠃⠀⠀⠀⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣾⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠀⠀⠀⠀⠀⠺⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡼⣽⢤⣦⢘⣿⣿
⣼⣿⣿⣿⡯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⢻⡍⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡘⢀⣷⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⡟⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⣿⣿⣿⣿
⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣄⣤⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠄⠁⣸⣿⣿
⣿⣿⣿⠟⡯⠀⠀⠀⠀⠀⠀⣾⢭⢹⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣷⣄⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠐⣽⣿⣿
⣾⣿⣿⡆⣿⠀⠀⠀⢀⣤⣄⠛⠧⠞⠛⠂⠉⠀⠀⠀⣤⣤⠀⣤⣄⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⣿⣿⣿⣿⣿⣟⣤⣄⠙⣿⣿⣦⡀⠈⣿⣿⣧⠀⠀⣀⣴⣶⡆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠙⣿⡿⠃⠈⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⣾⣷⠀⠀⡼⠿⠉⢰⣿⡏⢠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣍⣉⠀⠈⠉⠉⠁⠀⠈⠻⣿⣷⣜⢿⣿⣿⣆⢸⣿⢿⡧⣰⣿⣿⠏⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿
⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠄⠀⡎⠀⣾⣿⡟⣰⣷⡟⢠⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣧⢻⣿⣿⣸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠈⠈⢣⡜⢻⣿⢱⣿⡿⣠⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢻⣿⣿⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢉⠃⠙⠿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣫⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠌⣤⣴⣷⡾⠅⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⣿⣿⠭⣴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠙⢿⣿⣟⠛⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣮⣿⡛⢟⠜⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣠⣽⣿⣻⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢧⣀⠀⠉⠙⡋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠶⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡀⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢣⣶⣿⣤⣤⣧⣼⣿⣬⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠸⠿⠛⣉⣿⡿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠃⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⡍⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⡿⡃⠀⠀⣿⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠁⣼⣿⣷⠇⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠛⠛⢛⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⢺⣿⠃⠀⠀⠀⠀⠁⢸⣿⡟⠀⠀⠀⢻⣿
⠠⣶⣿⣿⣿⠀⠀⠀⠀⢘⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢀⡠⠀⢀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣷⠄⢀⣀⡀⠐⠀⠀⠀⠘⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣼⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢱⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠺⡿⠑⠃⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣴⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠆⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⡾⣦⢘⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⢻⡇⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢘⣧⣝⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⣿⣿⣿⣿
⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠢⢸⣿⣿⣿⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠄⠀⠀⠰⣿⣿⣷⡄⠀⠀⣤⣶⣆⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⣰⣿⣿
⣷⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⢸⠻⢹⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣀⡈⢻⣿⣿⣆⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠰⣿⣿⣃⠐⣿⣿⣿
⡿⣿⣿⠦⡏⠀⢀⣀⣀⠀⣴⠜⠲⠌⠋⠉⠁⠀⣰⣶⡆⣰⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣝⣛⠿⠿⣿⣿⣿⣿⣿⠟⠀⠀⢾⣿⣿⣬⣿⣿⣿⣦⠀⣻⣿⣧⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠙⢿⡿⠓⠂⠀⠈⢿⣿⣿⡀⠀⠀⠸⣿⡇⠀⣠⡻⡏⢀⣿⡿⢡⣶⣦⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣢⣾⣿⣿⠋⠀⠈⠀⢹⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣿⣄⣀⠀⠐⠁⢰⣿⣿⢣⣿⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡟⠁⠙⡶⠻⠿⠟⢿⣿⠫⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈⡁⠉⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠐⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠤⠼⣷⡇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⣒⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣄⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠐⣿⣿⣏⡉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⣿⣿⣿⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣭⣛⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣐⣲⣿⣫⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠀⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿
⢳⣀⠀⠈⠙⡋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢯⣢⠀⠀⠃⠀⡈⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢡⣼⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠨⠿⠟⣉⣿⣻⣿⣿⣿⠇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣽⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⡌⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣹⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⠶⠛⠒⠓⠓⠚⠲⠶⢿⣷⣾⡟⠗⠋⠀⠀⠀⣾⣿⣷⠇⠀⠀⣿⣿
⠀⢠⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠹⢹⣽⣿⣿⣆⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⢠⣾⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣀⣾⣿⣿⡆⠀⣀⡀⠐⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢹⣿
⠀⢹⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠻⠀⠁⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣼⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠀⠀⠀⠀⠻⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⡦⣤⠈⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣙⡯⠁⠀⠀⠀⠀⠀⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢠⣷⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠈⣿⣿⣿⣿
⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⢘⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠸⣿⣿⡆⠀⢠⣾⣷⠀⠁⢴⣿⣿
⣿⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣾⠟⢹⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⣶⣿⣷⣌⣿⣿⣿⣆⠀⢹⣿⣧⠀⢸⣿⠿⡃⠐⣿⣿⣿
⣿⣿⣿⣤⣻⠀⠀⠀⠀⠀⠰⠌⠵⠓⢺⣾⡷⣼⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⡛⠿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡆⣠⣿⣿⣿⣿⣼⣿⣿
⠙⣿⡿⢿⣿⣿⣦⠀⠀⠘⣿⣷⠀⢀⣾⣃⢀⣾⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⠟⢹⣿⣿⣿⣿
⠀⠈⠁⠀⠉⠻⣿⣷⣤⣀⠀⠁⠀⣾⣿⣏⣾⣿⣏⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠈⠹⠶⠛⠿⠝⠿⣿⠺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣶⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠐⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠒⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⣐⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢲⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⠿⢤⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢠⣿⣧⣄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⣤⣽⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣥⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿
⢳⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠈⢧⣣⠀⠀⠁⠀⡈⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢳⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠐⠿⠛⣉⣿⣟⣿⣿⣿⠋⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠅⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⡿⡃⠀⠀⣹⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣅⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠚⠒⠲⢿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠁⣼⣿⣷⠇⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠚⠻⣿⣿⣿⣇⠀⠀⠂⠀⠀⠀⠀⢀⢀⣄⣀⣠⠀⠀⢠⣾⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣀⣼⣿⣿⣤⢀⣀⣀⠐⠀⠀⠀⠈⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢻⠰⠃⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣺⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⣽⡳⣦⠘⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡙⡿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢀⣧⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣀⡀⠛⣿⣿⣿⣿
⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⢻⣿⣧⡀⠀⢸⣿⣿⡆⠀⢴⣿⣿
⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⢾⢻⢻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠈⢿⣿⣷⡀⢘⣿⣿⣦⡐⣿⡿⣿
⣾⣿⣿⣔⣗⠀⠀⠀⠀⠀⢰⠌⣒⣘⠛⣩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣛⡛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⣷⡌⣿⣿⣷⢀⣿⣿⣿⣿⣾⣿⣿
⠙⣿⣿⣿⡻⠀⠀⢀⣀⡀⠀⠀⣿⠟⠀⣿⡿⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿
⠀⠙⠿⣿⣿⣦⡀⠘⠟⡇⠀⣾⣽⡇⣴⣿⡇⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⣿⣿
⠀⠀⠀⠀⠙⢿⣿⠀⠨⠶⡆⠿⣿⢳⣿⣿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠉⠀⠉⠛⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⠀⠀⠐⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⣴⣧⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⢿⡀⢀⣲⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⣿⣿⣽⣾⡿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣞⣭⣤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠼⣶⣿⢟⣿⣶⣤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣽⣟⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢧⣀⠀⠈⠩⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣣⠀⠀⠁⠀⡀⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣡⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠠⠿⠛⣉⣻⢭⣽⣿⣿⠊⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⡉⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⡿⡃⠀⠀⣽⣿
⠀⠀⡀⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣄⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠲⢿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⢷⣾⠟⠗⠋⠀⠀⠁⢼⣿⣷⠇⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠐⢾⣿⣯⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠛⠛⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⡋⠸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢻⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠼⠻⣽⣿⣿⣆⠀⠀⠃⠀⠀⠀⠀⣀⣀⡤⢀⠀⠀⠀⢠⣾⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣦⢀⣀⡀⠐⠁⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣺⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢰⣾⣯⣿⣿⣿⣷⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⠙⠃⠀⠀⠀⣼⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣴⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠹⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡶⣤⠈⣿⣿
⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡙⡯⠁⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣧⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠀⠀⠀⠀⠘⠉⣾⣿⣿⣿
⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣿⣿⡄⠀⠀⣾⣿⣧⠀⢰⣿⣿
⣧⣿⣿⠛⡧⠀⠀⠀⠀⠀⠀⣞⠛⢻⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠸⣿⣿⣆⠀⣿⣿⣿⢈⢿⣿⣿
⡞⣿⣿⣴⣇⠀⠀⠀⠀⠀⠠⡍⠒⣐⠛⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣙⣛⠻⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣆⢹⣿⣿⡆⢻⣿⣿⣿⣽⣿⣿
⠙⣫⣿⣯⣇⠀⠀⠀⣀⡀⠀⠀⢸⡿⠃⢸⣿⠇⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣿⣿⡏⣿⣿⣧⣿⣿⣋⣿⣿⣿⣿
⠀⠉⠻⣿⣿⣦⣀⠀⠿⢿⠀⢠⣬⣭⢠⣾⡿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠋⠉⣾⣿
⠀⠀⠀⠀⠙⢿⣿⡇⠀⠽⣦⠹⣿⡇⣾⣿⠇⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠁⠉⠛⠂⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣾⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⢿⠀⠀⣒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣾⣿⣴⣼⣿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣸⣍⣁⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣷⣾⡿⣻⣷⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣭⣟⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⢀⢴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿
⢳⣀⠀⠈⠉⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⠿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠈⢧⣣⠀⠀⠁⢀⠌⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡇⠀⠀⠀⣡⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠀⠿⠟⣉⣿⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⡿⡅⠀⠀⣹⣿
⠀⠀⢀⣿⣧⠀⠀⠀⠀⣽⣿⣿⣿⣍⠀⠀⠀⠀⠀⠓⠚⠚⠶⢿⣷⣾⢷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣸⣿⣿⠇⠀⠀⣿⣿
⠀⠐⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⣸⣟⣸⢿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢿⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⠩⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⣾⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⣿⣿⣧⠀⣀⢀⠈⠂⠀⠀⠀⣺⣿⣿⡍⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⣾⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠐⠁⠀⠀⠀⣤⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣽⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡼⢼⠯⣤⠀⣿⣿
⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣫⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢀⣯⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⣾⣿⡆⠁⣰⣿⣿
⣿⣿⣿⠟⡆⠀⠀⠀⠀⠀⠀⣸⢻⢹⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣆⠀⢻⣿⣷⡀⠀⣿⣿⣷⠀⢿⣿⣿
⡾⢿⣿⣂⢷⠀⠀⠀⠀⠀⢦⡮⠎⠌⢛⡁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣛⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿⣷⡄⢿⣿⣿⡄⣿⣿⣿⣿⣼⣿⣿
⠈⠿⢿⣷⣶⣄⠀⠀⠀⢀⣀⠀⠀⠠⣿⠟⢀⣿⡿⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⣭⣍⡉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⣿⡼⣿⣿⣇⣿⣿⣋⣿⣿⣿⣿
⠀⠀⠁⠙⢿⣿⣷⣄⠀⠹⢿⠇⢀⣮⣭⠃⣶⣿⠃⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠉⠙⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⡿⠛⠉⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣟⠀⢨⢦⠸⣿⡿⢰⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣍⣽⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠁⠈⠛⠃⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⠀⢀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠺⠄⠁⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣼⣷⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣔⣏⣉⣉⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⣿⡿⣻⣷⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣮⣭⡋⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣾⣿⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣿
⢳⣀⠀⠈⠫⠏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠈⢧⣡⠀⠀⠁⢀⡌⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣇⠀⠀⠈⣥⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠨⠿⠏⣉⣿⣯⣿⣿⣿⠀⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡅⠈⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⡿⡃⠀⠀⣹⣿
⠀⠀⢀⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠒⢿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠚⠀⠀⠀⢸⣿⣿⠇⠀⠀⣿⣿
⠀⢐⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢐⣟⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢿⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠄⢀⣀⡀⠀⠀⠀⣴⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣄⣠⣿⣿⣧⠀⣀⢀⠈⠀⠀⠀⠀⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣾⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⠀⠃⠀⠀⠀⢴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⣽⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⡼⢾⢣⣤⢀⣿⣿
⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⢻⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⢀⣧⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠂⢠⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣶⣷⡶⠂⠀⢰⣿⣿
⣿⣿⣿⠽⣇⠀⠀⠀⠀⠀⠀⢸⠻⢻⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣄⠀⢿⣿⣧⠀⠀⣿⣿⣿⡀⠀⣿⣿⣿
⡿⣿⣿⣶⣿⠀⠀⠀⠀⠀⢶⡪⠄⠶⠛⢁⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣍⣛⠻⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡈⢿⣿⣷⡀⣿⣿⣿⣿⣽⣾⣿⣿
⠙⢻⡿⣻⣷⣦⡀⠀⠀⠀⣀⣀⠀⠀⢸⣿⠟⢰⣿⡟⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣭⣍⡉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡻⣿⣿⡸⣿⣿⣇⣿⣿⢏⣿⣿⣿⣿⣿
⠀⠁⠀⠈⠛⢿⣿⣦⣀⠀⠻⢻⠀⢠⣯⣽⢀⣾⣿⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠉⠙⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣿⣿⣷⢿⣿⣿⣿⣿⣿⠟⠉⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠰⣤⡸⣿⡏⣾⣿⠇⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠁⠙⠛⠊⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⢀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢠⣦⡄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠣⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣦⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⣙⣉⣉⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣽⣯⣿⢟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣭⣛⢋⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣿⣷⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿
⢳⣀⠀⠈⠹⡍⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠈⢧⡣⠀⠀⠀⠀⠌⠽⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡇⠀⠀⠀⣡⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠈⠿⠛⣉⣿⡿⣿⣿⣿⠀⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⣺⣿⣿⣿⣿⡅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡅⠀⠀⣹⣿
⠀⠀⢀⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣅⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⢷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠓⠛⠀⠀⠀⢸⣿⣿⠇⠀⠀⣻⣿
⠀⢐⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢰⣟⣸⢿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿
⠀⣶⣿⣿⣿⠀⠀⠀⠀⠈⠙⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⣾⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣄⣰⣿⣿⣧⠀⣀⣀⠀⠀⠀⠀⠰⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⢾⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⠂⠁⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣴⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼⣴⠠⣦⠀⣿⣿
⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⣻⠉⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⢠⣧⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿
⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⢰⣶⣦⣶⠂⠀⢰⣿⣿
⣾⣿⣿⡝⡇⠀⠀⠀⠀⠀⠀⢸⠛⢹⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⠀⢹⣿⣷⡄⠀⢸⣿⣿⣏⡀⠀⣿⣿⣿
⡾⣿⣿⣶⡵⠀⠀⠀⠀⠀⢄⡎⠸⠞⠒⢁⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡛⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⢻⣿⣿⣄⢸⣿⣿⣿⣿⣶⣿⣿⣿
⠉⠻⠿⣻⣷⣦⡄⠀⠀⠀⣀⣀⠀⠀⢰⣿⠛⢰⣿⡟⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣭⣍⡉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣟⢿⣿⡇⣿⣿⣿⣸⣿⠟⣹⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠛⢿⣿⣦⣀⠀⠻⢻⠀⢠⣧⣽⢀⣾⣿⠁⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠉⠙⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⡾⣿⣿⣿⣿⣻⠿⠋⠁⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠸⣤⡸⣿⡏⣼⣿⠏⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠁⠙⠛⠂⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⣦⡄⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⠧⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣧⣆⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⣝⣉⣉⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣿⣽⣿⢻⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣭⣛⠓⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⣿⣿⣵⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿
⢳⣀⠀⠈⠙⡋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠈⢧⡡⠀⠀⠁⠀⠌⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⣇⠀⠀⠀⢠⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠈⠿⠛⣉⣿⣿⣿⣿⣿⠁⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡟⡅⠀⠀⣹⣿
⠀⠀⢀⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣅⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⢷⠚⠒⠒⠲⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠓⠊⠀⠀⠀⣸⣿⣿⠇⠀⠀⣻⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢠⣟⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⠀⢄⣀⡀⠀⠀⢠⣾⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣾⣿⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⣺⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢾⠀⠀⠀⠀⠀⣰⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣺⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⠁⣤⢀⣿⣿
⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠙⡏⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⢠⣿⣽⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⢠⣶⣦⣴⣶⠀⠀⢰⣿⣿
⣿⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⣼⡏⠻⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⢹⣿⣷⡄⠀⢸⣿⣿⣟⣟⡅⢀⣿⣿⣿
⡾⣿⣿⣶⡭⠀⠀⠀⠀⠀⢴⡖⠠⠖⠛⢁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣟⡛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⢻⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠙⠿⡿⣳⣶⣤⡀⠀⠀⠀⣀⡀⠀⠀⢸⡿⠇⣸⣿⡇⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⡁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⢿⣿⣧⢿⣿⣿⢠⣿⣿⢻⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠻⡻⠀⢰⣯⣽⢠⣮⡿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠉⠙⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠟⠁⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⡤⡄⣿⣿⠇⣾⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠀⠙⠛⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣦⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠧⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣤⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢘⣉⣉⣉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⣝⣿⡿⣯⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣽⡛⢋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣭⣿⣯⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿
⢳⣀⠀⠈⠙⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣣⠀⠀⠀⠀⠈⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣁⣻⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣾⣿⣿⣽⠁⢸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⢾⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡅⠀⠀⣹⣿
⠀⠀⢀⣿⣇⠀⠀⠀⠀⣼⣿⣿⣿⡁⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⣷⠚⠒⠒⠲⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⢟⢷⣾⡿⠗⠛⠀⠀⠀⣠⣿⣿⠇⠀⠀⣻⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⢿⠃⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⢿⣿
⠀⣬⣿⣿⣿⠀⠀⠀⠀⠈⠹⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⢀⡠⠀⠀⢠⣾⣿⣗⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣀⣼⣿⣿⣤⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⣺⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠸⠀⠀⠀⠀⠀⣀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣼⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⣄⠀⣿⣿
⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣧⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⢀⣤⣄⠀⣺⣷⠂⠀⢰⣿⣿
⣿⣿⣿⠟⡏⠀⠀⠀⠀⠀⠀⢰⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠹⣿⣷⡄⠀⠘⣿⣿⡆⢻⣿⡅⠀⣿⣿⣿
⠾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠠⡄⠀⠾⠈⣐⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣟⡻⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⢹⣿⣿⣄⠀⣿⣿⣿⢿⣻⣿⣷⣭⣿⣿
⠙⣻⡟⣻⣷⣦⡀⠀⠀⢀⣀⡀⠀⠀⣼⡿⠃⣸⣿⠇⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⡁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣧⢻⣿⣿⡄⣼⣿⡟⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠟⡟⠀⣰⣭⡕⢰⣿⡏⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣎⣿⣿⣧⣿⣿⣾⡿⠛⠁⠁⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁⠀⡦⡄⣿⣿⠣⣿⣿⢡⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠉⠈⠛⠓⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠐⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠆⠈⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣄⡀⢀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣛⣋⣉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣝⣻⣷⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣮⣝⡛⢋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣛⣿⣋⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣑⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿
⢳⣀⠀⠈⠙⠋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣣⠀⠀⠀⢀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣉⣻⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣾⣿⣿⣽⠁⠸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⢾⣿⣿⣿⣿⡀⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡁⠀⠀⣹⣿
⠀⠀⢀⣿⣇⠀⠀⠀⠀⢾⣿⣿⣿⣅⠀⠀⠀⠀⠀⠓⠚⠚⠲⢿⣷⣾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⢿⢷⣾⡿⠓⠛⠀⠀⠀⢸⣿⣿⠇⠀⠀⣻⣿
⠀⠰⣾⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⢿⠃⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⢿⣿
⠀⣬⣿⣿⣿⠀⠀⠀⠀⠈⢹⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⠠⠀⠀⢠⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻⣯⣀⣼⣿⣿⣤⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠉⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⢺⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢀⣾⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠹⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢨⣏⣀⠀⠀⠀⣰⣿
⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡘⢹⠁⣤⠀⣿⣿
⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠙⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣧⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⢀⣤⣄⠀⣼⣶⠂⠀⢰⣿⣿
⣯⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⢰⠉⢙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣿⣷⡀⠀⠸⣿⣿⣌⣿⣞⡁⠀⢾⣿⣿
⡾⣿⣿⣶⣢⠀⠀⠀⠀⠀⠠⡅⠚⠸⠚⣃⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⡻⠿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⢻⣿⣿⡄⠀⣿⣿⣷⠽⣻⣽⣷⣬⣿⣿
⠙⡿⡟⣻⣶⣦⡀⠀⠀⠀⣀⣀⠀⠀⣸⡿⠃⢸⣿⡇⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣦⢻⣿⣿⡀⣼⣿⡿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠙⢿⣿⣦⡀⠀⠛⠻⠀⢰⣯⡽⢰⣮⡿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣿⣿⣞⣿⣿⣧⣿⣷⣾⡿⠛⠁⠁⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠤⡄⣿⣿⠇⣿⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠉⠀⠙⠛⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠘⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⢦⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡀⣠⣴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣋⣈⣙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣽⣻⣷⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣬⣽⡛⢛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣈⣻⣿⣋⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿
⢣⣀⠀⠈⠩⡏⠻⢿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣣⠀⠀⠀⢀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣉⣻⣿⣿⣿⣿⠀⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢉⡇⠀⢀⣾⣿⣿⣼⠁⠸⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⢶⣿⣿⣿⣿⡅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡃⠀⠀⣹⣿
⠀⠀⢀⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠓⠚⠚⠒⠿⣷⡾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⢿⢷⣾⡟⠗⠛⠀⠀⠀⣠⣿⣿⠇⠀⠀⣻⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⢿⠁⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⢿⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⠹⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢀⠠⠀⠀⢠⣾⣿⣗⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣧⣀⣼⣿⣿⣥⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠂⠀⠀⠀⢺⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠿⠀⠁⠀⠀⠀⢀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⢐⣏⣀⠀⠀⠀⣴⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⠠⣄⠀⣿⣿
⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⡯⠁⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⣥⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠋⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⢀⣤⣄⠀⣴⣷⠂⠀⢰⣿⣿
⣿⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⢰⠛⢙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣿⣷⡀⠀⠸⣿⣿⡌⣿⣿⡃⠀⣾⣿⣿
⡾⣿⣿⣿⣥⠀⠀⠀⠀⠀⠠⡄⠀⠰⠋⣁⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⢻⣿⣿⡄⠀⣿⣿⣷⠾⣻⣿⣷⣬⣿⣿
⠙⢟⡿⣻⣷⣦⣄⠀⠀⠀⣠⣀⠀⠀⢸⡿⠛⢸⣿⡏⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣦⢻⣿⣿⡀⣽⣿⡿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣧⣄⠀⠛⢻⠀⢠⣯⣭⢠⣮⣿⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⣿⣿⣎⣿⣿⣧⣿⣷⣾⡿⠛⠁⠁⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠴⡄⠿⣿⡇⣾⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠀⠙⠛⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⣮⠈⠀⢠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⡀⣠⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣇⣊⣉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢝⣻⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣝⡛⠛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣈⣻⣿⣋⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿
⢳⣀⠀⠈⠛⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣢⠀⠀⠁⠀⠈⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣁⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣉⣿⣏⣽⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠁⠸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣁⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⠸⡯⣿⡿⡇⠀⠀⣹⣿
⠀⠀⢀⣿⣇⠀⠀⠀⠀⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠒⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⢹⣿⣿⠇⠀⠀⣻⣿
⠀⠰⣾⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣝⡼⢻⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢿⣿
⠀⣾⣿⣿⣿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⡠⠀⠀⢀⣾⣿⣟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣀⣼⣿⣿⣧⠀⣀⠀⠀⠀⠀⠀⠈⣾⣿⣿⠍⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⣾⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠽⠀⠂⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣽⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠸⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠜⢽⠡⣤⢀⣿⣿
⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⢠⣷⣜⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⢀⣤⡄⠀⣴⣶⠂⠀⢸⣿⣿
⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⣿⠍⡻⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢀⣤⣄⠈⢻⣿⣷⡀⠀⢸⣿⣿⠘⢿⣿⡇⠈⣿⣿⣿
⡿⣿⣿⣦⡗⠀⠀⠀⠀⠀⠠⣥⠓⠼⠉⢑⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⢻⣿⣷⡄⠀⣿⣿⣧⢿⣿⣿⣷⣽⣿⣿
⠉⠻⡟⡻⣶⣶⣄⠀⠀⠀⣀⣀⠀⠀⢰⣿⠛⢰⣿⡟⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⢿⣿⣿⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠁⠀⠙⠿⣿⣷⣄⠀⠻⢻⠀⢠⣯⣥⢀⣮⣿⠁⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⣿⣿⣾⣿⣿⣧⣿⣷⣾⡿⠋⠀⠁⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⡇⠀⠸⣤⡾⣿⡏⣾⣿⠏⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠈⠁⠙⠻⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣧⡄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢦⠁⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⠀⢠⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢐⣇⣛⡉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣝⣻⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣬⣽⡛⠛⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⣿⣿
⢳⣀⠀⠈⠹⡏⠛⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣢⠀⠀⠀⠀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠈⠿⠛⣉⣿⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠁⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⡀⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡇⠀⠀⣽⣿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣁⠀⠀⠀⠀⠈⠓⠚⠚⠒⢿⣷⣾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⢷⣾⡿⠗⠛⠀⠀⠀⣸⣿⣿⠇⠀⠀⣿⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢀⣟⣸⢿⠃⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⢿⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⢹⣽⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠠⠀⠀⢀⣾⣿⡗⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣀⣼⣿⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⣺⣿
⠀⣹⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠿⠀⠁⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⣸⣿
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⣤⠀⣿⣿
⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣧⣜⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠀⠀⢀⣤⡄⠀⣴⣶⠀⠀⢰⣿⣿
⣾⣿⣿⠋⡇⠀⠀⠀⠀⠀⠀⢰⢋⠛⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣀⠈⢻⣿⣧⡀⠀⢸⣿⣿⠀⣿⣿⡆⠀⣾⣿⣿
⡾⣿⣿⣮⣇⠀⠀⠀⠀⠀⠠⡄⠒⠢⠋⢐⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡈⢿⣿⣷⡀⠀⣿⣿⣇⢯⣯⣿⣧⣼⣿⣿
⠙⣟⡟⡫⣷⣶⣄⠀⠀⠀⣁⣀⠀⠀⢠⣿⠟⢠⣿⡿⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣝⣙⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣎⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⠀⠙⠿⣿⣷⣄⠀⠸⢛⠃⢀⣦⣭⠀⣮⣿⠁⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠋⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣶⣾⠿⠋⠀⠁⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠿⣿⡇⠀⠸⣤⠸⣿⡏⣼⣿⡏⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣷⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠋⠀⠘⠁⠙⠻⠌⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⡄⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⢶⠁⠀⢤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣤⡀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢘⣛⡛⠉⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣙⣿⣿⢿⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣬⣝⡛⠓⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣐⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿
⢳⣀⠀⠈⠩⡍⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿
⠘⢧⣢⠀⠀⠁⠀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⢠⣴⣿⣤⣤⣧⣼⣿⣬⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠀⠟⠛⣉⣿⣯⣿⣿⣿⠈⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢉⡇⠀⢀⣽⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⢻⣿⡿⠇⠀⠀⣹⣿
⠀⠀⢀⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣅⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⣷⠚⠒⠒⠒⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠚⠀⠀⠀⢸⣿⣿⠇⠀⠀⣻⣿
⠀⢰⣾⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡞⣸⢧⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⢹⣼⣿⣿⣤⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⢀⡠⠀⠀⢀⣾⣿⣗⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣀⣴⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠉⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠾⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⠈⠁⠀⠀⠀⢀⣾⢿⢷⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⣸⣿
⢠⣿⣿⣿⡯⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⣤⠀⣿⣿
⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣫⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⣧⣜⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣆⠀⠀⠀⢠⣤⡀⠀⣴⣶⠂⠀⢰⣿⣿
⣾⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⢰⢛⠹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⢿⣿⣦⠀⠀⢹⣿⣷⠀⢽⣿⡁⠀⣿⣿⣿
⡾⣿⣿⣶⡇⠀⠀⠀⠀⠀⠠⡌⠃⠠⠂⢑⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡈⣿⣿⣷⡀⠸⣿⣿⡆⢮⣿⣿⣧⣸⣿⣿
⠉⣿⡟⡛⣷⣶⣄⠀⠀⠀⣁⣀⠀⠀⢠⣿⠟⢰⣿⡿⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣝⣙⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣎⣿⣿⣷⢀⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠸⢻⠃⢀⣯⣭⠀⣮⣿⠁⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡝⣿⣿⣼⣿⣿⣾⣿⣶⣼⠟⠋⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠿⣿⡏⠀⠸⣤⠸⣿⡏⣼⣿⡏⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠋⠀⠘⠁⠙⠻⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢦⠁⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣠⢀⣠⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢈⣎⣛⣋⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⣙⣿⣿⢿⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣬⣝⡙⠛⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢷⣀⠀⠈⠩⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⠿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿
⠈⢧⣢⠀⠀⠁⠀⡌⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿
⠀⠀⣿⡆⠀⠀⠀⣠⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿
⠀⠀⢹⣿⠀⠀⠀⠨⠿⠛⣉⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠃⢸⣿⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⡃⠀⠀⣹⣿
⠀⠀⡀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣍⠀⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠒⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠓⠊⠀⠀⠀⢰⣿⣿⠇⠀⠀⣻⣿
⠀⢐⣾⣿⣿⠀⠀⠀⠈⢽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣟⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⣿
⠀⣼⣿⣿⣿⠀⠀⠀⠀⠸⢛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⠠⢤⣀⡀⠀⠀⢀⣾⣿⣟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⢀⣼⣿⣿⣧⠀⣀⡀⠐⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣺⣿
⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣻⡰⠁⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⢀⣽⣿
⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⡼⢼⠡⣤⡐⣿⣿
⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣿⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣷⣼⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠢⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⢠⣤⡀⠀⣴⣶⠂⠁⢰⣿⣿
⣾⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣺⠻⢻⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⢿⣿⣧⠀⠀⢸⣿⣷⢈⢽⣿⡀⠀⣿⣿⣿
⣿⣿⣿⣶⡷⠀⠀⠀⠀⠀⠰⠭⠀⠾⠉⢉⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡈⢿⣿⣷⡀⠸⣿⣿⡆⢞⣿⣿⣯⣹⣿⣿
⠙⣿⣿⡟⣷⣶⣤⠀⠀⠀⢀⣀⠀⠀⢠⣿⠿⢠⣿⣿⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣙⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣎⣿⣿⣷⢀⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠘⢛⠇⢀⣮⣭⠄⣮⣿⠇⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡽⣿⣿⣼⣿⣿⣾⣿⣶⣾⠿⠋⠈⠁⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⢠⢤⠸⣿⡿⢸⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⢿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠘⠁⠙⠛⠄⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
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                    ䷩ 𝚕𝚒𝚗𝚎 2610

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/10/2021:_Murena_for_/e/_and_Red_Hat_Condemned_for_Its_Nationalism/
Racism⠀✐


Posted in News_Roundup at 11:40 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o ⚓ Top_10_free_cloud_services_for_Linux⠀⇛


                 Cloud service refers to data storage away from users’
                 local systems and across the span of dedicated servers
                 meant for this. It is an alternative way of storing data
                 online instead of your local machines. At its earliest,
                 in 1983, CompuServe provided 128 KB of disk space that
                 could be used for files storage to its users. This proved
                 to be crucial despite not being enough.


                 In today’s world, the storage field is under active
                 development because of potential threats such as loss of
                 data/information, data hacking or masquerading, and other
                 attacks. However, many companies have come forward with
                 their solutions to Cloud storage and data privacy,
                 strengthening and stabilizing their future.


                 While using any cloud service, note that you cannot
                 upload your data without an internet connection.
                 Furthermore, you will still need an internet connection
                 to either modify or share documents, presentations,
                 spreadsheets, images, audio, video e.t.c with others.
                 Cloud is virtual and provides services to end-users in
                 storage, hosting of apps, or virtualizing any physical
                 space. In today’s world, cloud computing is used by small
                 and large organizations for data storage.


                 There are three main types of services associated with
                 the cloud, namely, SaaS (Software as a Service) that
                 allows users to access other publicly available clouds of
                 large organizations for storing their data, for instance,
                 Gmail, PaaS (Platform as a Service) for hosting of
                 applications or software on other public clouds, for
                 example, Google App Engine which hosts apps of users,
                 laaS (infrastructure as a Service) for virtualizing any
                 physical machine and availing it to customers to make
                 them get the feel of a real machine.


          o § Desktop/Laptop⠀➾


                # ⚓ Star_Labs_Releases_Coreboot_7_Open-Source_Firmware_for_Its
                  Linux_Laptops_with_New_Features⠀⇛


                       Based on the upstream Coreboot 4.14 release, Star
                       Labs’ Coreboot 7 open-source firmware is now
                       available for the StarBook Mk V, Star LabTop Mk
                       III, and Star LabTop Mk IV Linux notebooks, along
                       with an updated Coreboot Configurator utility.


                       This release comes about three months after
                       Coreboot 6 and brings several new features,
                       including a new option to set the maximum charge
                       level as 60, 80, or 100 percent, as well as a new
                       option to set the fan curve as Aggressive, Normal,
                       or Quiet.


          o § Audiocasts/Shows⠀➾


                # ⚓ Linux_Action_News_212⠀⇛


                       Major performance milestones are being hit with new
                       code inbound for Linux, Plasma and GNOME desktops
                       are set to run Wayland on NVIDIA’s binary driver,
                       and why the SFC’s new GPL fight could have
                       implications for you.


                # ⚓ mintcast_372.5_–_The_Tablet_Chronicles⠀⇛


                       1:22 Linux Innards
                       36:00 Vibrations from the Ether
                       52:41 Announcements & Outro


                       In our Innards section, tablets


                       And finally, the feedback and a couple of
                       suggestions


                # ⚓ Video_Editing_with_Linux:_The_Most_Important_Part_of_a
                  Video⠀⇛


                       Next in our video editing series for the Librem 14,
                       Gardiner Bryant explains why audio is critical in
                       video production, capturing good sound, and post-
                       processing using Audacity, an open source sound
                       editing solution. This video will help those
                       looking to level up their audio and overall
                       production.


                # ⚓ Starlink’s_Linux_Secrets_|_LINUX_Unplugged_429⠀⇛


                       We attempt a live production over Starlink, and dig
                       into the secrets of this giant Linux network in
                       space.


          o § Kernel Space⠀➾


                # ⚓ Linux_5.14.15⠀⇛


                       I'm announcing the release of the 5.14.15 kernel.

                       All users of the 5.14 kernel series must upgrade.

                       The updated 5.14.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.14.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,

                       greg k-h
                # ⚓ Linux_5.10.76⠀⇛


                # ⚓ Linux_5.4.156⠀⇛


                # ⚓ Linux_4.19.214⠀⇛


                # ⚓ Linux_4.14.253⠀⇛


                # ⚓ Linux_4.9.288⠀⇛


                # ⚓ Linux_4.4.290⠀⇛


          o § Benchmarks⠀➾


                # ⚓ Intel_Announces_12th_Gen_Core_“Alder_Lake”_CPUs,_Linux
                  Tests_Forthcoming⠀⇛


                       Intel is using their inaugural Intel Innovation
                       virtual event today to formally announce the
                       highly-anticipated 12th Gen Core “Alder Lake”
                       processors. These first desktop processors built on
                       their “Intel 7″ process and employ a hybrid
                       architecture will be available in retail channels
                       next week. Today we can talk more about Alder Lake
                       specifications and features while our Linux
                       performance benchmarks and support analysis will
                       come once the Alder Lake review embargo expires
                       next week.


                       While there have been many Alder Lake leaks in
                       recent weeks/months and a number of features
                       disclosed back during Architecture Day, today marks
                       the official unveil for the next-gen Intel Core
                       processors. This is a very exciting transition as
                       they have now shifted to their Intel 7
                       manufacturing process, the hybrid architecture
                       provides a combination of high performance and low
                       power cores depending upon needs, and Intel is at
                       the forefront now in delivering DDR5 memory and
                       PCIe 5.0 to the masses. When it comes to
                       performance, Intel claims Alder Lake can deliver up
                       to two times the performance of prior generation
                       processors for content creation workloads.
                       Meanwhile when it comes to the generational
                       performance uplift for the P (Performance) cores
                       it’s said to be around 19%.


          o § Applications⠀➾


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Microsoft
                  Dynamics_365⠀⇛


                       Microsoft’s stance for decades was that community
                       creation and sharing of communal code (later to be
                       known as free and open source software) represented
                       a direct attack on their business. Their battle
                       with Linux stretches back many years. Back in 2001,
                       former Microsoft CEO Steve Ballmer famously
                       tarnished Linux “a cancer that attaches itself in
                       an intellectual property sense to everything it
                       touches”. Microsoft also initiated its “Get the
                       Facts” marketing campaign from mid-2003, which
                       specifically criticized Linux server usage, total
                       cost of ownership, security, indemnification and
                       reliability. The campaign was widely criticized for
                       spreading misinformation.


                       However, in recent years, there has been a partial
                       shift by Microsoft to embrace the open source
                       software paradigm. For example, some of their code
                       is open sourced. Examples include Visual Studio
                       Code, .NET Framework, Atom, and PowerShell. They
                       have also made investments in Linux development,
                       server technology and organizations including the
                       Linux Foundation and Open Source Initiative. They
                       have made acquisitions such as Xamarin to help
                       mobile app development, and GitHub a hugely popular
                       code repository for open source developers. And
                       they have partnered with Canonical, the developers
                       of the popular Ubuntu distro. But many developers
                       remain hugely sceptical about Microsoft and their
                       apparent shift to embrace open source.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_MelonDS_on_a_Chromebook_–_Updated_Tutorial⠀⇛


                       This tutorial will only work on Chromebooks with an
                       Intel or AMD CPU (with Linux Apps Support) and not
                       those with an ARM64 architecture CPU.


                # ⚓ How_to_Clean_Up_Flatpak_Apps_to_Clear_Disk_Space⠀⇛


                       Here’s how to clean up Flatpak apps to reclaim your
                       precious disk space. Follow along.


                       Flatpak (like Snap) packages runs in sandbox mode.
                       By design, it takes a considerable amount of disk
                       space for an individual application, even if it is
                       a smaller one. For example, a simple Test editor or
                       a basic image annotator application can take up
                       more than 100+ MB of storage space.


                       It’s how Flatpak, or even Snap operates
                       fundamentally. It pulls all dependencies for an app
                       and runs independently. The advantage of this
                       design is – you do not need to worry about
                       dependencies, updates. All you need to do is
                       install and run. On the contrary, it takes up huge
                       amount of disk space.


                       And if you are running Ubuntu, elementary OS or any
                       distribution for longer period, you would be
                       surprised that over time, Flatpak keeps on taking
                       up more space.


                       Hence, in this guide, we will give you some
                       commands which you can run it by yourself to clean
                       up flatpak apps.


                # ⚓ How_To_Install_Fail2Ban_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Fail2Ban on Debian 11. For those of you who didn’t
                       know, Fail2Ban is an intrusion prevention framework
                       written in the Python programming language. This
                       service will help prevent unwanted logins by
                       banning nefarious IP addresses from gaining access
                       to your server. Whereas, other basic functions are
                       monitor log files, searches for predefined
                       patterns, and temporarily block IP addresses.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you through the step-by-
                       step installation of Fail2Ban on a Debian 11
                       (Bullseye).


                # ⚓ How_eBPF_Streamlines_the_Service_Mesh [Ed: Disclosure at
                  the bottom reminds people that Linux Foundation is basically
                  buying such articles]⠀⇛


                       There are several service mesh products and
                       projects today, promising simplified connectivity
                       between application microservices, while at the
                       same time offering additional capabilities like
                       secured connections, observability, and traffic
                       management. But as we’ve seen repeatedly over the
                       last few years, the excitement about service mesh
                       has been tempered by practical concerns about
                       additional complexity and overhead. Let’s explore
                       how eBPF allows us to streamline the service mesh,
                       making the service mesh data plane more efficient
                       and easier to deploy.


                # ⚓ How_to_Create_File-Sharing_with_ONLYOFFICE_Docs_and
                  Seafile⠀⇛


                       File sharing, as the act of distributing and
                       providing access to different types of files over
                       the Internet, has become something that everyone is
                       familiar with. The fast development of file-sharing
                       services makes it extremely easy for us to share
                       whatever we need with friends, family, or co-
                       workers. For example, a couple of clicks is enough
                       to instantly share a funny video or picture with
                       someone who is halfway around the world.


                       One of the most popular services for file sharing
                       and synchronization is Seafile. In this article,
                       you will learn how to integrate Seafile with
                       ONLYOFFICE Docs to create a collaborative file-
                       sharing environment on Linux.


                # ⚓ How_to_Delete_One_or_More_Lines_in_Vi_and_Vim⠀⇛


                       Editing text files directly from the Linux terminal
                       can be tough, especially if you’re using a
                       complicated text editor like Vi or Vim. Beginner
                       users have a tough time wrapping their heads around
                       command-line text editors and often find it hard to
                       memorize the key bindings used to perform basic
                       operations.


                       Even deleting lines in Vi and Vim can be a nerve-
                       wracking job for newcomers. But using a rudimentary
                       tool like a text editor doesn’t have to be so hard.


                       Here’s how you can remove one or more lines from a
                       text file using Vi and Vim.


                # ⚓ How_to_Install_Firefox_93_in_Linux_Desktop⠀⇛


                       Firefox 93 officially released for all major OS
                       e.g. Linux, Mac OSX, Windows, and Android. The
                       binary package is now available for download for
                       Linux (POSIX) systems, grab the desired one, and
                       enjoy browsing with new features added to it.


                # ⚓ How_to_Install_OpenNMS_Network_Monitoring_Solution_on
                  Debian_11⠀⇛


                       OpenNMS is a free and open-source Open Network
                       Management System written in Java. It is a network
                       monitoring application that gathers critical
                       information from local and network hosts using the
                       SNPM protocol. It can be installed on Linux and
                       Windows operating systems and provides a web-based
                       interface to monitor network traffics through a web
                       browser. It offers a rich set of features
                       including, Provisioning, Service Monitoring, Event
                       Management, Charting support and Performance
                       Measurement.


                       In this post, we will show you how to install
                       OpenNMS on Debian 11.


                # ⚓ How_to_Install_Zabbix_Monitoring_Tool_on_Debian_11/10⠀⇛


                       Zabbix is a free, open-source, popular, and
                       feature-rich IT infrastructure monitoring software
                       developed using PHP language. It is used to monitor
                       networks, servers, applications, services as well
                       as cloud resources. It also supports the monitoring
                       of storage devices, databases, virtual machines,
                       telephony, IT security resources, and much more.


                # ⚓ How_to_Install_Zabbix_on_RHEL/CentOS_and_Debian/Ubuntu⠀⇛


                       Zabbix is an Open Source, high-level enterprise
                       software designed to monitor and keep track of
                       networks, servers, and applications in real-time.
                       Build in a server-client model, Zabbix can collect
                       different types of data that are used to create
                       historical graphics and output performance or load
                       trends of the monitored targets.


                       The server has the ability to check standard
                       networking services (HTTP, FTP, SMTP, IMAP, etc)
                       without the need to install extra software on the
                       monitored hosts.


                # ⚓ How_to_Reset_Forgotten_Root_Password_in_Ubuntu⠀⇛


                       User roles on a Linux operating system are
                       hierarchy-based. The root user sits on the iron
                       throne and is able to control the actions of all
                       other users. It is the administrative/
                       authentication power of this root user that
                       controls the actions of any other user with access
                       to the Linux system.


                # ⚓ How_to_Set_Date_and_Time_on_Rocky_Linux_8_Desktop_and
                  Server⠀⇛


                       Here are the two ways to set a date and time on
                       Rocky Linux 8 or AlmaLinux using the command
                       terminal and graphical user interface.


                       There are many processes on the Linux operating
                       system that requires the correct system date and
                       time. Also, to update the system properly and other
                       processes like cronjobs we must need the up-to-date
                       time & date. However, Linux or any other OS
                       automatically syncs the system time from the
                       server, in case not or you want to change the
                       timezone manually then let’s explore how to do
                       that.


                # ⚓ How_to_install_PostgreSQL_on_Debian_11?⠀⇛


                       PostgreSQL is one of the best open source solutions
                       for relational database management. So, many
                       developers use it as an alternative to MariaDB or
                       proprietary solutions like Oracle. That’s why,
                       today in this post, you will learn how to install
                       PostgreSQL on Debian 11 quickly and easily.


                # ⚓ How_to_install_complete_Kali_Linux_on_USB_drive_|_FOSS
                  Linux⠀⇛


                       Kali Linux, previously known as BackTrack Linux, is
                       a Debian-based open-source Linux distribution
                       designed for advanced penetration testing and
                       security auditing. This operating system has many
                       tools for diverse information security
                       undertakings, including penetration testing,
                       reverse engineering, security research, and
                       computer forensics.


                       Kali Linux is a multi-platform elucidation that
                       information security pros and hobbyists can use for
                       free. It is designed to satisfy the needs of
                       penetration testing and security auditing
                       professionals.


                # ⚓ Installing_NFS_Server_and_NFS_Client_on_Ubuntu_20.04_–
                  ByteXD⠀⇛


                       NFS server is also known as Network File System
                       server, was developed by Sun Microsystems in 1984.
                       NFS was designed to share files and folders between
                       Linux/Unix systems. After its initial success, NFS
                       version 2 became public, and then everyone could
                       use this to exchange files.


                       It is a distributed file system protocol that
                       allows the client computer to access files over the
                       network. The server requires to validate the client
                       computer, and then after successful validation,
                       files and folders are shared amongst each other.
                       However, the data is not encrypted.


                       Because NFS transfers are not encrypted, it’s not
                       recommended to be used over the internet.


                       NFS server allows you to mount your local files
                       over a network and remote hosts, to interact with
                       them as they are both mounted locally on the same
                       system. NFS serves the same purpose as SMB(Server
                       Message Block), but it is faster as compared with
                       SMB.


                       Currently, there are three NFS protocol versions:
                       NFSv2, NFSv3, NFSv4.


          o § Games⠀➾


                # ⚓ Google’s_Stadia_Pivots_To_Being_Some_White_Label_Game
                  Streaming_Platform_For_Others_To_Use⠀⇛


                       The saga of Google’s Stadia product has been long,
                       winding, and mostly disappointing. The initial
                       launch of Google’s platform, billed as a Netflix-
                       style video game streaming service, was
                       underwhelming and plagued with Obamacare-like
                       rollout issues, failed promises, underperforming
                       adoption rates, and a paltry catalogue of games on
                       the platform. Other than that, the launch of Stadia
                       went off without a hitch.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE_Connect_Arrives_for_iPhone,_At_last._Here’s_How
                        to_Try.⠀⇛


                             Long awaited KDE Connect is now available for
                             iPhone (iOS >= 15). Here are the details.


                      # ⚓ KDE:_Multi-Axes_Made_Easy⠀⇛


                             Today we want to introduce the last of the
                             new features we are implementing into the 2.9
                             release which we have recently finalized.


                             To demo this new feature, let’s use an
                             example contributed by one of our users. This
                             example is based upon the measurement data
                             from a solar cell. The so-called “incident
                             photon to current efficiency” (IPCE) tells us
                             how many incoming photons are converted into
                             free electrons in the cell. This conversion
                             efficiency, together with the generated
                             current and their dependency on the
                             wavelength of the incoming light, are the
                             usual subjects of studies and optimizations
                             for solar cells.


                             Consider the example where we want to plot
                             the IPCE and the current density in the same
                             plot and to see their behavior as a function
                             of the wavelength. Your first idea may be to
                             just lay out the curves for the plot like
                             this…


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ On_Free_Software,_Red_Hat,_and_Iran [Ed: Context
                        here]⠀⇛


                             I was visiting the Fedora Council ticket
                             tracker when I noticed this ticket up for
                             discussion. The ticket’s purpose is minor and
                             appears inconsequential. It involves adding
                             some legal text to the Fedora Accounts
                             system. The change is related to Export
                             Administration Regulations (the “EAR”) as
                             maintained by the United States Department of
                             Commerce. And the change is not actually a
                             change, but a clarification of a policy that
                             has always been in effect.


                             I am opposed to the impact of Export
                             Administration Regulations by the United
                             States as it pertains to free and open source
                             software. I am a strong believer that the
                             impact of these regulations are most harmful
                             to all free & open source software
                             communities at an individual, human level.
                             When I saw this discussion at the Fedora
                             Council level, it offered me an opportunity
                             to reflect on my own feelings about these
                             regulations, and also to share an opinion on
                             how I believe Fedora Linux could truly live
                             up to its certification as a Digital Public
                             Good to ensure a more equitable world.


                             [...]


                             Firstly, it creates confusion, doubt, and
                             feelings of ill intent. These laws and
                             regulations are meant to impact governments
                             and nation-states. In a Free & Open Source
                             community such as ours, these regulations
                             impact individual people. Not governments or
                             nation-states. As an example, a Fedora
                             community member, Ahmad Haghighi, was
                             recently permanently removed from the Fedora
                             Community. In a few quick clicks, Ahmad’s
                             legacy in the project was erased. As a
                             precedent, even if someone’s contributions
                             were not “supposed” to be accepted in the
                             first place, it does not sit well with me
                             that any one person’s legacy of contributions
                             can so easily be removed from project
                             records.


                             Secondly, it challenges the vision and
                             foundations of the Fedora Project.
                             Particularly our vision statement and the
                             Friends Foundation. When I contribute to the
                             Fedora Project, I do not see people as a
                             citizen of this-country or that-country. I
                             see them as my peers and fellow Fedorans,
                             helping meet that shared vision of creating
                             “a world where everyone benefits from free
                             and open source software built by inclusive,
                             welcoming, and open-minded communities.” As
                             an American citizen, I know my country makes
                             such discriminations about large groups of
                             people based only on their nationality, but
                             as a contributor to Free & Open Source
                             communities, I see people by their individual
                             character and intention to be a part of our
                             shared vision. But how can we truly aspire to
                             this vision if we are consciously making
                             deliberate exclusions, even if they make
                             little to no sense in our own context? This
                             geographic restriction policy sits in
                             contrast to the vision and purpose we spell
                             out “on paper”.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Nine_Raspberry_Pis_power_this_entire_office⠀⇛


                             Monterail decided they needed a bigger
                             office, and they wanted that office to be
                             smarter, so they turned to Raspberry Pi to
                             make it happen.


                             It was a real leap of faith because the team
                             couldn’t find a similar Raspberry Pi project
                             quite this big, so they didn’t have much to
                             go on. Spoiler: their courage paid off.


                      # ⚓ How_I_made_an_automated_Jack-o’-lantern_with_a
                        Raspberry_Pi_|_Opensource.com⠀⇛


                             It’s almost Halloween, one of my favorite
                             days and party times. This year, I decided to
                             (pumpkin) spice up some of my decorations
                             with automated motion sensing. This
                             spooktacular article shows you how I made
                             them, step by step, from building and wiring
                             to coding. This is not your average weekend
                             project—it takes a lot of supplies and
                             building time. But it’s a fun way to play
                             around with Raspberry Pi and get in the
                             spirit of this haunting holiday.


                      # ⚓ Engaging_Black_students_in_computing_at_UK_schools_—
                        interview_with_Joe_Arday⠀⇛


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Moto_G100_Android_Smartphone_returns_to_all-time_low
                        with_$100_discount_to_$500_–_9to5Toys⠀⇛


                      # ⚓ How_To_Take_A_Scrolling_Screenshot_On_Android_12⠀⇛


                      # ⚓ Android_12_release_roadmap_for_the_ASUS_Zenfone_7,
                        Zenfone_8_and_ROG_Phone_series_announced_|_Nasi_Lemak
                        Tech⠀⇛


                      # ⚓ Infinix_Smart_6_launched_with_UNISOC_SoC,_5000mAh
                        battery,_and_Android_11_GO_Edition⠀⇛


                      # ⚓ Infinix_Smart_6_With_Dual_Rear_Cameras,_Android_11_
                        (Go_Edition)_Launched:_Price,_Specifications_|
                        Technology_News⠀⇛


                      # ⚓ Pikmin_Bloom,_the_latest_from_Niantic,_to_begin
                        rolling_out_to_Android_users_today_|_Android_Central⠀⇛


                      # ⚓ How_to_Use_Android_Recovery_Mode_|_WIRED⠀⇛


                      # ⚓ PUBG_Mobile_1.7_beta_latest_APK:_Direct_download_link
                        for_Android_devices⠀⇛


                      # ⚓ Want_to_Remove_Unnecessary_Files_on_Your_Android
                        Phone?_5_Options_You_Must_Try⠀⇛


                      # ⚓ Android_Auto_has_a_hidden_Easter_egg_that’s_never
                        gonna_give_you_up⠀⇛


                      # ⚓ How_to_Get_Android_12_Widgets_on_Any_Phone_Right_Now_
                        (2021)_|_Beebom⠀⇛


                      # ⚓ Infinix_Smart_6_with_Android_11_Go_Edition,_5,000mAh
                        battery_launched:_price,_specifications_–_Pricebaba.com
                        Daily⠀⇛


                      # ⚓ Motorola_Android_11_update:_List_of_eligible_devices
                        &_release_date⠀⇛


                      # ⚓ Kodak_CA_Pro_Android_TV_Series_With_40W_Sound_Output
                        Launched_in_India,_Available_via_Flipkart_|_Technology
                        News⠀⇛


                      # ⚓ Samsung_Galaxy_Buds_2_review:_Solid_earbuds_for
                        Android_–_SoundGuys⠀⇛


                      # ⚓ LumaFusion_set_to_come_to_Android_and_Chrome_OS_–
                        9to5Google⠀⇛


                      # ⚓ ASUS_is_looking_for_beta_testers_for_ZenFone_8_Flip’s
                        Android_12_update⠀⇛


                      # ⚓ When_is_Android_12_coming_to_Xiaomi_phones?⠀⇛


                      # ⚓ How_To_Find_The_Privacy_Dashboard_In_Android_12⠀⇛


                      # ⚓ Motorola_Android_11_update:_List_of_eligible_devices
                        &_release_date⠀⇛


                      # ⚓ Redmi_Note_11_appears_on_GeekBench_with_Dimensity_810
                        &_Android_11_–_Gizchina.com⠀⇛


                      # ⚓ Chrome_For_Android_Adds_Three_New_Widgets⠀⇛


                      # ⚓ Google_Pixel_6_&_Pixel_6_Pro_review:_The_best_Android
                        phones_you_can_buy_|_CNN_|_CNN_Underscored⠀⇛


                      # ⚓ The_40_best_free_Android_games_for_your_phone_or
                        tablet_|_Stuff⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_DEAD_EYES,_and
                        more_–_9to5Toys⠀⇛


                      # ⚓ Google_Adds_Sweet_New_Android_12_Weather_Widget
                        Option⠀⇛


                      # ⚓ Xiaomi_optimizes_MIUI_Android_12_development_version
                        –_Gizchina.com⠀⇛


                      # ⚓ Lilbits:_Raspberry_Pi-powered_storage_server,_Android
                        12′s_new_Internet_tile,_and_Palm’s_new_earbuds_–
                        Liliputing⠀⇛


                      # ⚓ Samsung_prepares_Android_12_beta_for_Galaxy_Z_Fold_3,
                        Flip_–_9to5Google⠀⇛


                      # ⚓ Best_Android_apps_of_2021_–_CNET⠀⇛


                      # ⚓ Best_Android_phone_for_2021:_Which_one_should_you
                        buy?_–_TechRepublic⠀⇛


                      # ⚓ Qualcomm_Just_Upgraded_A_Bunch_Of_Its_Chips_For_2022
                        Android_Phones⠀⇛


                      # ⚓ Murena_smartphones_and_cloud_will_protect_our
                        privacy⠀⇛


                             More than ever the market is demanding a new
                             approach for digital products: more and more
                             people around the world want something
                             different, more ethical, more sustainable,
                             with real guarantees about personal data
                             protection.


                             Four years ago, I wanted to break free from
                             Google and Apple, and therefore we created
                             the “eelo” project, with the simple idea that
                             a different mobile operating system and
                             associated cloud services like email or cloud
                             storage could be possible in this world.


                             Followed by an amazing community of
                             supporters, contributors and now users, the
                             project progressed quickly, and became a
                             reality by the end of 2018. The same year, we
                             had to suddenly abandon our initial project
                             name for a temporary name: /e/.


                             Sometimes, temporary things last longer than
                             expected. And despite being hard to
                             pronounce, difficult to search, and largely
                             criticized by many people, /e/ as a brand
                             name had the benefit to be very singular and
                             helped us appear different. In the end it
                             conveyed the idea that we’re doing something
                             special. […]


                             Nevertheless, as we are reaching more and
                             more people and progressively catching
                             interested from a mainstream audience, we
                             have to introduce a new, strong brand, easier
                             to use, easier to refer to and easier to
                             share with people. The goal of this brand is
                             to have a strong name to call our products,
                             intended to be used by a large number of
                             users in many different countries and
                             cultures.


                             It took some time, since we had many
                             different candidates, both from internal
                             suggestions and from our community. We wanted
                             something that would both convey our
                             project’s values, and that could be within
                             the same lineage of our initial project name.
                             We also had to secure this new brand making
                             sure it was not already in use in the same
                             field of activity, and by entering a long
                             trademark registration processes.


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


                # ⚓ Global_communication_in_open_source_projects⠀⇛


                       I’m really glad that we have some very active
                       people in FreeDOS who are working on translating
                       messages in all these programs. There are a few
                       folks who contribute to FreeDOS by translating
                       messages from one language to another and sharing
                       those message files so we can use them in the
                       FreeDOS distribution.


                       FreeDOS is a small operating system with low memory
                       constraints, so actually our biggest challenge has
                       been technical.


                       In a more modern system like Linux, you can provide
                       message translation through a service like catgets
                       or gettext. Both are programming libraries where
                       the program says, “I need this string [text] in the
                       user’s preferred language,” and the library gives
                       the program that string. This is an example of
                       internationalization, by providing translations in
                       different languages.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ More_Stories_Behind_the_Podcasts:_Slate’s
                              Latest_Curated_Collections_on_Pocket⠀⇛


                                   Slate and Mozilla’s Pocket have
                                   extended their ‘Behind The Podcasts’
                                   collaboration, partnering on a series
                                   of new Pocket Collections to provide
                                   podcast and Pocket fans with even more
                                   opportunities to explore the behind-
                                   the-scenes stories that inspired some
                                   of Slate’s most successful podcasts.


                                   This November, Pocket readers can look
                                   forward to all-new collections curated
                                   by Slate’s podcast hosts, coinciding
                                   with new seasons of One Year, Decoder
                                   Ring and the highly anticipated sixth
                                   season of Slow Burn, one of the most-
                                   popular podcast series in Slate’s
                                   portfolio, garnering more than 65M+
                                   downloads since its launch in 2017. The
                                   curated Pocket Collections, which offer
                                   deep-dive reads, down-the-rabbit-hole
                                   research, and commentary straight from
                                   the hosts’ notes, are the perfect
                                   ‘companion pass’ to round out new
                                   episodes of Slate’s fan favorites.


                # § FSF⠀➾


                      # ⚓ Beatriz_Busaniche_Speaks_Up_in_Defense_of_Richard
                        Stallman⠀⇛


                             I am Beatriz Busaniche from Argentina, and I
                             have been a free software and human rights
                             activist for 20 years. I’m writing because I
                             am very proud to consider myself a longtime
                             friend of Richard Stallman. He has stayed in
                             my home many times. I have organized many of
                             his conferences here in Argentina, and we
                             have shared events, social gatherings, and
                             political and public activities. In all these
                             years Richard has always behaved in a totally
                             respectful, warm, and generous way to me, my
                             family, and my friends.


                             Richard has made huge contributions to the
                             world of technology. He laid the foundation
                             for the culture of free software, which has
                             grown into a movement that is crucial to our
                             world today. He has helped us to think
                             critically about what we do and how we do it.
                             Our movement is forever in his debt, and we
                             must acknowledge that we have not met our
                             responsibility to appreciate Richard as a
                             human being.


                             Those of us who are lucky enough to be well
                             acquainted with him know that he is a
                             sensitive, loving person, with weaknesses and
                             imperfections like anyone. He can make
                             mistakes, just like any of us. Yet, he has an
                             extraordinary capacity for logical thinking,
                             and is able to change his position when
                             presented with clear and reasonable
                             arguments. Sometimes, however, he expresses
                             his ideas in an unusually direct way that may
                             seem strange to some.


                             As a feminist, I have always worked to
                             challenge stereotypes and over-
                             generalizations about people. I believe that
                             we should be inclusive of those with
                             differences and, above all, fight for justice
                             and the rights of all people.


                             I feel that Richard has been treated unfairly
                             in recent months, and I am deeply ashamed for
                             not having raised my voice in his defense
                             more firmly before this.


                # § Programming/Development⠀➾


                      # ⚓ Qt_6.2.1_Released⠀⇛


                             I am happy to announce we have released the
                             Qt 6.2.1 today.


                      # ⚓ Qt_6.2.1_Released_With_200+_Bug_Fixes_–_Phoronix⠀⇛


                             It’s been just shy of one month since Qt 6.2
                             debuted as the first Qt6 Long-Term Support
                             (LTS) release and ported many of the
                             remaining modules over from Qt5.


                      # ⚓ Qt_6.2_and_Windows_11⠀⇛


                      # ⚓ webOS_OSE_for_Qt_6.2_Verified [Ed: What became of
                        Palm or Palm OS remarries Qt now that it is proprietary
                        software (both of them; this isn't "Linux" or even
                        "free software" but privatisation)]⠀⇛


                      # § Python⠀➾


                            # ⚓ Alternative_Python_Implementation_“Pyston”
                              Plans_For_Greater_Performance,_64-bit_ARM⠀⇛


                                   Pyston as the alternative Python
                                   implementation open-sourced originally
                                   by Dropbox is forming ambitious plans
                                   for a bright future.


                                   While Dropbox continued developing
                                   Pyston publicly from 2014 to 2017, they
                                   stopped supporting it with having moved
                                   their performance-sensitive code to
                                   other languages. But the original
                                   developers then restarted work on it
                                   and released Pyston 2.0 in 2020.


                                   Pyston 2.0 was made closed-source along
                                   with the follow-on 2.1 release but then
                                   Pyston 2.2 this year returned it to
                                   being open-source. Then in August it
                                   was announced the Pyston developers
                                   joined Anaconda to continue their work
                                   on this high performance Python
                                   implementation.


                            # ⚓ Pyston_roadmap⠀⇛


                                   We’ve spent some time recently thinking
                                   about the future of Pyston, our faster
                                   implementation of Python, and wanted to
                                   share what’s on our mind. For updates
                                   please check out our wiki.


    * § Leftovers⠀➾


          o ⚓ Most_Americans_Distrust_Partisan_Redistricting,_Prefer
            Independent_Commissions⠀⇛


          o ⚓ Before_Shooting,_IATSE_Film_Crew_on_“Rust”_Walked_Off_Set_to
            Protest_Conditions⠀⇛


          o ⚓ The_E_Terminal_Return⠀⇛


                 Phillip appeared: I see you’re a modern married man. How
                 can you tell? Your clothes are wrinkled. That could be
                 true for a bachelor. No, they pay for wash-and-fold by
                 the bag. They could be poor. No, vanity is totality,
                 appearance obligation, they laundromat it themselves, you
                 machine wash at home and get brainwiped from drying. I
                 hang it on a line outside. Yes, except when you forget
                 because listening is required, you wear the wrinkled
                 badge of courage of the modern feminist man. Sometimes I
                 rebel. Harmlessly, when your socks mismatch. What should
                 I do? As you are, why add more suffering? I see: say
                 nothing and drink alone unseen. Its best, love disguised
                 as peace. The indeterminate illusion of eternity is
                 finite even when you see through it. Enjoy, why not?


                 I want a dinner of sautéed mushrooms and Veuve Clicquot,
                 cioppino and Pouilly-Fuissé, Renoir and Chateau Margaux,
                 Mozart at midnight. Breakfast eggs fried over bacon at
                 dawn’s riverbank sandbar campfire by the hauled out
                 canoes, fresh coolness beckoning another paddle down the
                 shimmering burbling ribbon to light’s wide horizon,
                 somewhere beyond nightfall, behind the thrumming of
                 crickets, prophesying.


          o ⚓ Scammers_Are_Using_Fake_Job_Ads_to_Steal_People’s_Identities⠀⇛


                 It has become a ubiquitous internet ad, with versions
                 popping up everywhere from Facebook and LinkedIn to
                 smaller sites like Jobvertise: Airport shuttle driver
                 wanted, it says, offering a job that involves picking up
                 passengers for 35 hours a week at an appealing weekly pay
                 rate that works out to more than $100,000 a year.


                 But airports aren’t really dangling six-figure salaries
                 for shuttle drivers amid some sudden resurgence in air
                 travel. Instead, the ads are cybercriminals’ latest
                 attempt to steal people’s identities and use them to
                 commit fraud, according to recent warnings from the FBI,
                 the Federal Trade Commission and cybersecurity firms that
                 monitor such threats. The U.S. Secret Service, which
                 investigates financial crimes, also confirmed that it has
                 seen a “marked increase” in sham job ads seeking to steal
                 people’s personal data, often with the aim of filing
                 bogus unemployment insurance claims.


          o ⚓ Houston⠀⇛


          o ⚓ Jean-Luc_Mélenchon_Welcomes_the_Animosity⠀⇛


                 Paris—As an early evening drizzle enveloped the
                 Stalingrad neighborhood of northeastern Paris, 22-year-
                 old Léo Bewa and a dozen other activists gathered outside
                 a public housing complex to knock on doors. They planned
                 to register residents to vote, but the main reason for
                 their organizing was to talk about the presidential
                 campaign of Jean-Luc Mélenchon, the left-populist from
                 the party La France Insoumise, or France Unbowed, making
                 his third consecutive bid for the Élysée Palace.


          o § Science⠀➾


                # ⚓ Another_victim_of_serial_killer_John_Wayne_Gacy’s_has_been
                  identified_using_DNA⠀⇛


                       The identification of Alexander came together when
                       the sheriff’s department teamed up with the DNA Doe
                       Project, a nonprofit that uses genetic information
                       to locate relatives of dead people who have not
                       been identified. The organization compared the DNA
                       profile from the unidentified victim’s remains to
                       profiles on a genealogy website to find potential
                       relatives. That led it to Alexander’s family, and
                       Alexander’s mother and half-brother provided their
                       DNA for comparison.


          o § Education⠀➾


                # ⚓ “The_University_of_Puerto_Rico_Is_Not_for_Sale!”⠀⇛


                       “They are stealing our present. The UPR is not for
                       sale,” read a large banner at the gates of the
                       oldest and largest of the 11 campuses that make up
                       the University of Puerto Rico system. Early in the
                       morning on Monday, October 18, students gathered to
                       join the protests in front of Puerto Rico’s Capitol
                       in San Juan, holding colorful signs: “They violated
                       our past”; “They are stealing our present”; “They
                       are mortgaging our future.” This story was produced
                       for Student Nation, a program of The Nation Fund
                       for Independent Journalism dedicated to
                       highlighting the best of student journalism. For
                       more Student Nation, check out our archive or learn
                       more about the program here. StudentNation is made
                       possible through generous funding from The Puffin
                       Foundation. If you’re a student and you have an
                       article idea, please send pitches and questions to
                       [email protected]


          o § Hardware⠀➾


                # ⚓ There’s_Not_A_Cassingle_Thing_Missing_From_This_Cassette
                  Deck_Masterclass_|_Hackaday⠀⇛


                       For [ke4mcl], this whole cassette craze of late is
                       not a new discovery so much as it is a personal
                       nostalgia machine. Since [ke4mcl] sees a lot of
                       basic questions go unanswered, they made an
                       incredible beginner’s guide to all things cassette
                       deck. This concise wealth of information covers
                       everything from terminology to operation, basic
                       maintenance like repairing the belt and lubricating
                       the motor, and appropriate cleaning methods for the
                       various parts. Yep, we’re pretty sure this covers
                       everything but the pencil winding technique, which
                       you probably already knew about.


          o § Health/Nutrition⠀➾


                # ⚓ ‘Cloak_and_dagger’_military-intelligence_outfit_at_center
                  of_US_digital_vaccine_passport_push⠀⇛


                # ⚓ Deadly_US_Sanctions_Are_Exacerbating_the_Pandemic
                  Globally⠀⇛


                # ⚓ House_Introduces_a_Sweeping_Booster_Seat_Safety_Law_to
                  Protect_Children_in_Car_Crashes⠀⇛


                       Members of Congress today are introducing a law
                       that would establish the most sweeping safety rules
                       for booster seats in more than two decades after
                       determining that the makers of the car seats misled
                       parents about their risks and endangered children’s
                       lives.


                       The new legislation, called the Booster Seat Safety
                       Act, was prompted by a ProPublica investigation
                       last year. The act’s chief sponsors — Reps. Raja
                       Krishnamoorthi, D-Ill., and Katie Porter, D-Calif.
                       — say it will address gaping holes in federal
                       regulations that have allowed booster seat
                       manufacturers to make up their own side-impact
                       crash tests and decide what passes.


                # ⚓ Breaking:_FDA_Panel_Recommends_Pfizer_Covid-19_Vaccine_for
                  Kids_5_to_11⠀⇛


                       The Food and Drug Administration’s independent
                       advisory panel on vaccine safety unanimously
                       approved the Pfizer-BioNTech Covid-19 vaccine for
                       children ages 5 to 11 on Tuesday, paving the way
                       for nearly all school-aged students in the U.S. to
                       have protections from the deadly virus available to
                       them in the coming weeks and months.


                       With just one abstention, the advisory panel voted
                       17-0 to approve the vaccine for younger children
                       following a thorough review of data provided by the
                       drug makers and outside review.


                # ⚓ Opinion_|_Expand_Medicare_or_Say_Hello_Again_to_Senate
                  Majority_Leader_Mitch_McConnell⠀⇛


                       Ask any nurse and they will tell you: dental,
                       vision and hearing care are fundamental aspects of
                       health care. And yet right now, West Virginia Sen.
                       Joe Manchin is a major impediment to finalizing the
                       Build Back Better reconciliation bill in Congress,
                       including a Medicare expansion plan that is wildly
                       popular.


                # ⚓ Melbourne:_The_Longest_in_Lockdown⠀⇛


                       Then came the global COVID-19 pandemic.  Like the
                       nuclear fallout anticipated in Nevil Shute’s On the
                       Beach, the menace had to eventually head down under
                       and do its bit of gathering.  But there was fierce
                       resistance in the country.  The lockdown formula
                       became the policy de jour and there was no greater
                       example of this than Melbourne.


                       In 2021, the Herald Sun would look with envy across
                       the pond to note that Auckland in New Zealand has
                       taken the honours of the EIU’s essentially
                       irrelevant assessment.  Melbourne had suffered a
                       slump, slumming in eighth spot.  The EIU sternly
                       noted that, “The pandemic has caused huge
                       volatility in our biannual liveability index, which
                       ranks 140 cities across five areas: stability,
                       health care, education, culture, and environment,
                       and infrastructure.”  But Melbourne’s Lord Mayor
                       Sally Capp, despite noting the “devastating impact”
                       of lockdowns on the city, could still brightly note
                       that “we remain one of the 10 most liveable cities
                       in the world”.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Openwashing⠀➾


                                  # ⚓ Microsoft_War_Stories_|_Coder_Radio_437⠀⇛


                                         Chatting about the week’s .NET
                                         news leads us into a blue-tinted
                                         tale of woe. When Microsoft
                                         taketh, they also giveth. But is
                                         it enough?


                      # § Security⠀➾


                            # ⚓ Hacked!_How_finding_my_dream_home_almost_led_me
                              to_a_financial_nightmare [Ed: Mozilla is spying
                              on Firefox users and it wants their passwords
                              too... with server-side sync... in the name of
                              security of course (ignore the NSA leaks; that's
                              just "old news")]⠀⇛


                                   My husband and I had relocated to a new
                                   city and had been renting for two and a
                                   half years. We were finally ready to
                                   buy our own place and stop throwing
                                   money away on rent, and we had a
                                   deadline — the end of our lease. But,
                                   unfortunately, right at the time we
                                   started to look last year, the housing
                                   market started going absolutely
                                   bonkers.


                                   Very few houses on that market were
                                   what we were looking for, and
                                   everything was moving so quickly that
                                   houses were selling before they even
                                   hit the market. It was an exciting
                                   time, but also really frantic. We
                                   really felt the pressure. We knew we
                                   had a deadline so once we found
                                   something, we just needed to move. It
                                   felt like there was no room for error
                                   or even time to process.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ If_Courts_Won’t_Protect_People’s_Phones
                                    At_The_Border,_Congress_Needs_To_Act_Now⠀⇛


                                         Invasive searches of people’s
                                         phones at border crossings and
                                         international airports have
                                         become standard operating
                                         procedure for US border control
                                         agencies. The usual
                                         justifications have been made:
                                         national security and preventing
                                         contraband from crossing the
                                         border.


                                  # ⚓ License_Plate_Reader_Company_Continues
                                    Expansion_Into_Private_Neighborhoods_With
                                    The_Help_Of_Some_Useful_Cops⠀⇛


                                         The use of automatic license
                                         plate readers by law enforcement
                                         has steadily increased over the
                                         past decade. The theory is a
                                         never ending documentation of
                                         vehicle movements results in more
                                         solved crimes and recovered
                                         stolen vehicles. Assertions about
                                         law enforcement efficiency have
                                         driven other tech acquisitions,
                                         ranging from repurposed war gear
                                         like Stingray devices to facial
                                         recognition software.


                                  # ⚓ The_Surveillance_State:_It_Knows_Almost
                                    Everything_About_Us,_We_Know_Almost_Nothing
                                    About_It⠀⇛


                                         When considering this concept,
                                         Edward Snowden’s name comes to
                                         mind. Readers will recall that
                                         Snowden was an NSA contractor
                                         when he discovered that that
                                         agency had collected personal
                                         information on masses of people
                                         around the world and in
                                         particular on those in the US.
                                         The Constitution (remember that
                                         quaint founding document from the
                                         revolutionary history of the US?)
                                         protects those in the US from
                                         unreasonable searches and
                                         seizures of our personal
                                         information in the Fourth
                                         Amendment and establishes our
                                         right of free expression that is
                                         enshrined in the First Amendment.
                                         At least that is what some
                                         learned in eight-grade civics
                                         class.


                                         Following the Vietnam War era,
                                         the US Congress limited the
                                         government’s ability to pry into
                                         the lives of those in the US.
                                         That period, in the late 1970s,
                                         was the high point of reining in
                                         the government’s ability to spy
                                         on those in the US without a
                                         warrant and further limited the
                                         government’s ability to conduct
                                         “dirty tricks’ and sabotage of
                                         individuals and groups, as it had
                                         done through the FBI’s
                                         counterintelligence (COINTELPRO)
                                         spying program.


                                  # ⚓ Resisting_the_Menace_of_Face
                                    Recognition⠀⇛


                                         Fortunately, people around the
                                         world are fighting back. A
                                         growing number of communities
                                         have banned government use of
                                         face recognition. As to business
                                         use, many communities are looking
                                         to a watershed Illinois statute,
                                         which requires businesses to get
                                         opt-in consent before extracting
                                         a person’s faceprint. EFF is
                                         proud to support laws like these.


                                         Let’s begin with the ways that
                                         face recognition harms us. Then
                                         we’ll turn to solutions.


                                         Face recognition violates
                                         our human right to privacy.
                                         Surveillance camera networks have
                                         flooded our public spaces. Face
                                         recognition technologies are more
                                         powerful by the day. Taken
                                         together, these systems can
                                         quickly, cheaply, and easily
                                         ascertain where we’ve been, who
                                         we’ve been with, and what we’ve
                                         been doing. All based on a unique
                                         marker that we cannot change or
                                         hide: our own faces.


                                  # ⚓ Facebook_Faces_a_Public_Relations_Crisis.
                                    What_About_a_Legal_One?⠀⇛


                                         But to win a lawsuit accusing the
                                         company of misleading investors,
                                         regulators would have to prove
                                         that executives had intended to
                                         hide or lie about problems.
                                         Regulators would also have to
                                         prove that the information
                                         revealed by Ms. Haugen, or turned
                                         up in an investigation, could
                                         have changed trading or voting
                                         decisions by shareholders if it
                                         had been shared.


                                         It would be even more difficult
                                         to hold top executives personally
                                         responsible. Regulators would
                                         have to demonstrate that Mr.
                                         Zuckerberg or other executives
                                         had explicit knowledge that
                                         Facebook was hiding or lying
                                         about information that could sway
                                         investors.


                                  # ⚓ Data_Protection_in_Kenya:_how_is_this
                                    right_protected?⠀⇛


                                         Our new paper turns to Kenya’s
                                         Data Protection Act to lay the
                                         groundwork for a truly rights-
                                         centric approach to data
                                         protection in Kenya.


                                  # ⚓ Supreme_Court_of_India_says:_Investigate
                                    Pegasus!⠀⇛


                                         The Supreme Court has pronounced
                                         a judgment regarding the use of
                                         Pegasus, constituting a committee
                                         of technical experts to examine
                                         the allegations of unauthorised
                                         surveillance using the Pegasus
                                         spyware. The committee of
                                         technical experts is monitored by
                                         Supreme Court Justice R. V.
                                         Raveendran (retd.) who will be
                                         assisted by Mr Alok Joshi, a
                                         former IPS officer, and Dr.
                                         Sandeep Oberoi. The committee has
                                         been directed to submit its
                                         report expeditiously and the
                                         matter will be taken up 8 weeks
                                         from 27th October, 2021. IFF has
                                         provided legal assistance to two
                                         petitioners – Mr Rupesh Kumar
                                         Singh and Ms Ipsa Shatakshi. Mr
                                         Arvind Datar, Senior Advocate,
                                         represented them before the
                                         Supreme Court.


                                         [...]


                                         The Supreme Court pronounced its
                                         decision on 27th October 2021.
                                         Considering the importance of
                                         protection of journalistic
                                         sources for press freedom, and
                                         the potential chilling effect
                                         snooping techniques may have, the
                                         Court constituted a committee of
                                         technical experts to examine the
                                         allegations of unauthorised
                                         surveillance using the Pegasus
                                         Spyware. The committee’s
                                         functioning will be overseen by
                                         Justice R. V. Raveendran (retd.),
                                         former Judge, Supreme Court of
                                         India. Mr. Alok Joshi, former IPS
                                         officer, and Dr. Sandeep Oberoi,
                                         Chairman, International
                                         Organisation of Standardisation
                                         and the International Electro­-
                                         Technical Commission, have been
                                         tasked with assisting the
                                         overseeing judge. The Technical
                                         Committee, whose bios the Court
                                         provided, shall comprise of:
                                         (Paragraph 60):


                                         “1. Dr. Naveen Kumar Chaudhary,
                                         Professor (Cyber Security and
                                         Digital Forensics) and Dean,
                                         National Forensic Sciences
                                         University, Gandhinagar, Gujarat.
                                         Dr. Chaudhary has over two
                                         decades of experience as an
                                         academician, cyber security
                                         enabler and cyber security
                                         expert. He specializes in cyber
                                         security policy, network
                                         vulnerability assessment and
                                         penetration testing.


                                         2. Dr. Prabaharan P., Professor
                                         (School of Engineering), Amrita
                                         Vishwa Vidyapeetham, Amritapuri,
                                         Kerala. He has two decades of
                                         experience in computer science
                                         and security areas. His areas of
                                         interest are malware detection,
                                         critical infrastructural
                                         security, complex binary
                                         analysis, AI and machine
                                         learning. He has many
                                         publications in reputed journals.


                                         3. Dr. Ashwin Anil Gumaste,
                                         Institute Chair Associate
                                         Professor (Computer Science and
                                         Engineering), Indian Institute of
                                         Technology, Bombay, Maharashtra.
                                         He has been granted 20 US patents
                                         and has published over 150 papers
                                         and authored 3 books in his
                                         field. He has received several
                                         National awards including the
                                         Vikram Sarabhai Research Award
                                         (2012) and Shanti Swarup
                                         Bhatnagar Prize for Science and
                                         Technology (2018). He has also
                                         held the position of Visiting
                                         Scientist at the Massachusetts
                                         Institute of Technology, USA.”


                                         Amongst other things, the Court
                                         has directed the Committee to
                                         enquire, investigate, and
                                         determine whether the Pegasus
                                         Spyware was acquired by the Union
                                         Government or any State
                                         Government, and whether the
                                         spyware was used on phones or
                                         other devices of the citizens of
                                         India to access stored data,
                                         eavesdrop on conversation,
                                         intercept information and/or any
                                         other purpose [Paragraph 61(A)].
                                         The Committee has also been asked
                                         to make recommendations regarding
                                         enactment or amendment to
                                         existing law around surveillance
                                         to secure the right to privacy as
                                         well as regarding establishment
                                         of a mechanism for citizens to
                                         raise grievances on suspicion of
                                         illegal surveillance of orders
                                         [Paragraph 61(B)]. In order to
                                         achieve these ends, the Committee
                                         has been authorised to devise its
                                         own procedure, conduct
                                         investigation as it deems fit,
                                         take statements of any person in
                                         connection with the enquiry, and
                                         crucially ‘call for records of
                                         any authority or individual’
                                         (Paragraph 62).


          o § Defence/Aggression⠀➾


                # ⚓ Mo_Brooks_Says_He’d_Be_“Proud”_of_His_Staff_If_They_Helped
                  Plan_January_6_Attack⠀⇛


                # ⚓ Judge_Dumps_Felony_Manslaughter_Charges_Brought_Against_An
                  Arrestee_After_A_Deputy_Ran_Over_Another_Deputy⠀⇛


                       Felony murder is a truly bizarre artifact of the
                       American justice system. It’s simply not enough
                       that there are thousands of laws that can be used
                       to charge people who have allegedly broken them.
                       But felony murder (and its offshoots, which include
                       other crimes like manslaughter) allows prosecutors
                       to charge people for crimes they didn’t commit.


                # ⚓ “Devastation_and_Anger”_in_Sudan_as_Military_Coup_Halts
                  Country’s_Democratic_Transition⠀⇛


                       We look at the attempted coup in Sudan, where the
                       military, led by General Abdel Fattah al-Burhan
                       overthrew the transitional government Monday,
                       detaining Prime Minister Abdalla Hamdok and other
                       political leaders. As protesters flooded the
                       streets of Khartoum demanding the government be
                       handed back to the civilians, Sudanese soldiers
                       opened fire on them, killing at least 10 and
                       wounding scores more. The United Nations has
                       condemned the coup, and the United States has
                       suspended a $700 million emergency aid package for
                       Sudan. “No one is in support of this coup,” says
                       Walaa Salah, human rights lawyer and activist who
                       attended the ongoing protests and spoke with
                       Democracy Now! by phone from Khartoum on Tuesday.
                       “Military rule is a regression.” We also speak with
                       Isma’il Kushkush, a Sudanese American journalist
                       who lived in and reported from Khartoum for years,
                       who says, for most Sudanese citizens, “the
                       important thing is to see the transfer into a full
                       civilian government, to see elections.”


                # ⚓ The_Short,_Quixotic_History_of_North_Korean
                  Internationalism⠀⇛


                       All tourists in North Korea, which includes me at
                       the end of 2016, are accompanied by state-
                       sanctioned guides. Their job, ostensibly, is not to
                       monitor you but, much like every other tour guide,
                       to show you all the best sights and make sure you
                       stick to the itinerary. Inevitably, you are also
                       shepherded around a very select portion of the
                       country: Most Western tourists only see Pyongyang,
                       the nation’s capital, where the elite live; Chinese
                       day-trippers usually see only Sinuiju, a border
                       city accessible via a bridge to the neighboring
                       Chinese city of Dandong.


                # ⚓ Why_Biden_Should_Continue_Withdrawing_After_Afghanistan⠀⇛


                       One month after the Afghanistan pullout, it is
                       still unclear whether we witnessed the beginning of
                       a series of military withdrawals—as part of Biden’s
                       proclaimed end to the era of regime change wars—or
                       if Afghanistan will remain a mere one-off.


                # ⚓ Opinion_|_A_Few_Early_Thoughts_On_the_American_Coup_of
                  2024⠀⇛


                       As an eyewitness, I can recall the events of
                       January 6th in Washington as if they were
                       yesterday. The crowds of angry loyalists storming
                       the building while overwhelmed security guards gave
                       way. The slavishly loyal vice-president who would,
                       the president hoped, restore him to power. The
                       crush of media that seemed confused, almost
                       overwhelmed, by the crowd’s fury. The waiter who
                       announced that the bar had run out of drinks and
                       would soon be closing…


                # ⚓ The_Department_of_Justice_Is_Letting_the_Coup_Plotters_Get
                  Away⠀⇛


                       Early yesterday, Rolling Stone published an
                       explosive report alleging that two of the people
                       who helped plan the January 6 “Stop the Steal”
                       protests had extensive planning meetings with
                       members of Congress or their staff. These two
                       organizers appear to be cooperating with the
                       January 6 Select Committee, the congressional task
                       force investigating the Capitol attack, which is
                       more than I can say for most of the Trump cronies
                       who actually served in government.


                # ⚓ Invasions_of_Empire_and_the_Masquerade_Ball_of_Language⠀⇛


                       The reader will probably remember Abbottabad 2011,
                       the bin Laden raid, the showdown. Obama’s
                       Counterterrorism chief, John Brennan, told the
                       press Navy SEALs were in a firefight with UBL, and
                       that “while bin Laden had vowed to go down
                       fighting, in his last moments alive the master
                       terrorist hid behind a woman.” As if anticipating
                       criticism for killing the one guy who might have
                       known about future 9/11s, Brennan added that UBL
                       would have been taken had they been able to. He
                       soon walked these details back. A video feed of the
                       raid was said to have gone awry, leaving the
                       narrative to hearsay accounts, and soon several
                       different versions of what happened at the
                       ‘showdown’ were reported. SEALs reached out to the
                       public, 60 Minutes interviewed raiders, the
                       “journalistic” Zero Dark Thirty was made, with the
                       “cooperation” of the White House. There is even the
                       local Pakistani media coverage that told a
                       different tale. But it’s still uncertain what
                       actually took place that early morning in
                       Abbottabad.


                       But there’s another version of those events,
                       KBL–Kill Bin Laden: A Novel Based on True Events by
                       novelist JohnWeisman, which maintains close access
                       to SEAL team members and Weisman, a writer praised
                       by Seymour Hersh, has written about them before.
                       Some facts can only be related as fiction rather
                       than fact, and are truer as a result. In KBL,
                       Weisman gives an account of ‘what actually
                       happened’ at Abbottabad that is disturbing and
                       riveting. SEALs coming up the staircase, facing
                       UBL’s slightly ajar door, we get:


                # ⚓ FBI_Raids_Chinese_Point-of-Sale_Giant_PAX_Technology⠀⇛


                       U.S. federal investigators today raided the Florida
                       offices of PAX Technology, a Chinese provider of
                       point-of-sale devices used by millions of
                       businesses and retailers globally. KrebsOnSecurity
                       has learned the raid is tied to reports that PAX’s
                       systems may have been involved in cyberattacks on
                       U.S. and E.U. organizations.


                # ⚓ Shifts_Since_Fahrenheit_11/9⠀⇛


                       The first shift in society that must be noted is
                       that we got five years closer to the end of it. We
                       went backward, not forward, on climate change and
                       it seems that all leaders across the world lack the
                       urgency to save us from this crisis. It is possible
                       that technology will develop to mitigate the crisis
                       for some, but this quest for a technological future
                       largely remains a satire, with billionaires flying
                       to space thinking they are the solution rather than
                       the problem. The only thing that is delaying the
                       end of humanity is indigenous resistance. In the
                       past 10 years, these communities have stopped an
                       astounding 25% of U.S./Canadian emissions through
                       protest. Their reward is further genocide upon
                       their communities. Go figure. The solution to the
                       end of the world is not technocratic capitalism,
                       which will still use every resource for private
                       profits until we run out of them.


                       The second change in society is a rather surprising
                       one for the globalist neoliberal era. This is a
                       return of nationalist sentiment. Joe Biden
                       continues Donald Trump’s strategy of mobilizing an
                       idea of America. Joe Biden decided to end a forever
                       war and this appeared to largely be because Trump
                       promised to. Biden was honest enough that he blamed
                       the Afghan people for the war on his way out the
                       door. The Pentagon budget went up again, with eyes
                       to China, with Biden echoing Trump’s America First
                       rhetoric. Similarly, Biden has successfully
                       implemented a brutal nationalist immigration policy
                       where Trump never could do cleanly. When it comes
                       to China, where Trump’s nationalist tariffs failed,
                       Biden has upped the ante, appearing to threaten war
                       with China over Taiwan. Biden has been unwilling to
                       deliver on his own campaign promises, butchering
                       negotiations on his signature Build Back Better
                       plan.. This plan was its own version of nationalism
                       embodied in rebuilding America. As it was stripped
                       it was revealed that it would also increase
                       emissions, and therefore would only be fleeting
                       relief for the working class. Remember that Trump
                       ran a campaign on infrastructure but only became
                       interested in building a wall. Biden is a “better’
                       Trump.


                # ⚓ Colin_Powell:_Willful_Victim_of_the_Central_Intelligence
                  Agency’s_Deceit⠀⇛


                       Powell believed he could deal with the CIA, just as
                       he believed he had dealt with Vice President
                       Cheney’s efforts to prepare his speech.  The Cheney
                       draft of a speech, written by his chief of staff,
                       Lewis “Scooter” Libby, was a total distortion, and
                       Powell ignored it.  But Powell was no match for the
                       manipulation of CIA director George Tenet and
                       deputy director John McLaughlin.  They lied to him,
                       and he never forgave them.


                       Tenet and McLaughlin played key roles from
                       September 2002 to March 2003 in manufacturing
                       intelligence to support a decision to go to war. 
                       They gave deceitful briefings to various
                       congressional committees; they sponsored a specious
                       National Intelligence Estimate in October 2002;
                       they instigated an unclassified “White Paper” on
                       the basis of the estimate to distribute on Capitol
                       Hill before the vote to authorize force; and they
                       assisted Cheney’s desires.  Powell knew that Cheney
                       had made numerous trips to the CIA to make sure
                       that the intelligence would corroborate Bush’s
                       decision to go to war.


                # ⚓ How_the_US_enabled_Ethiopia’s_bloodletting,_training_its
                  military_while_playing_innocent_observer⠀⇛


                # ⚓ 2_Polish_troops_hurt_as_migrants_try_forcing_Belarus_border
                  |_Federal_News_Network⠀⇛


                       Officials in Poland said Monday that two soldiers
                       were lightly hurt when a group of some 60 migrants
                       tried to force their way across the border from
                       Belarus.


                       The Border Guards office said the troops — who have
                       been deployed to help protect the European Union’s
                       eastern border from growing migration pressure —
                       were treated at a hospital for facial injuries
                       following the events Sunday near the village of
                       Usnarz Gorny.


                       They said in a statement that the migrants were
                       throwing stones and wielding branches. That part of
                       the border is in a dense forest that also includes
                       bogs. Most of the border with Belarus runs along
                       the Bug river.


                       A video showing men trying to break the razor wire
                       border fence with a branch and helmeted Polish
                       troops watching from nearby was posted on the
                       Border Guards website.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The_Whistleblower_And_Encryption:_Everyone_Has_An_Angle,
                  And_Not_Everyone_Is_A_Policy_Expert⠀⇛


                       Over the weekend, the Telegraph (not the most
                       trustworthy or reliable in a batch of UK news
                       organizations that have long had issues with
                       accuracy in reporting) claimed that the latest (and
                       most high profile) Facebook whistleblower, Frances
                       Haugen, was prepared to come out against
                       encryption. This (quite rightly) raised the hackles
                       of multiple encryption experts. As people were
                       getting pretty worked up about it, the Telegraph
                       (silently, and without notice) changed the headline
                       of the piece (from “Facebook whistleblower warns
                       ‘dangerous’ encryption will aid espionage by
                       hostile nations” to “Facebook whistleblower warns
                       company’s encryption will aid espionage by hostile
                       nations”) as well as the actual text of the story,
                       to suggest a slightly more nuanced (but still not
                       great) view — effectively saying she supported
                       encryption, but was concerned that Facebook would
                       use encryption as a “see no evil” kind of blindfold
                       to problems on its platform.


          o § Environment⠀➾


                # ⚓ ACTION_ALERT:_The_New_Climate_Denial:_Don’t_Worry,_Do
                  Nothing⠀⇛


                       Upon the release of the latest dire report from the
                       UN Intergovernmental Panel on Climate Change (8/9/
                       21), the Washington Post (8/10/21) published a
                       strongly worded editorial under the headline,
                       “Climate Doubters Lose One of Their Last Remaining
                       Arguments.”


                # ⚓ Report_Examines_‘Net_Zero’_Climate_Strategies,_Finds
                  Corporate_Plans_Lacking_in_Lead_up_to_COP26⠀⇛


                       On Sunday, COP26, the 26th United Nations climate
                       change summit, will kick off in Glasgow, Scotland,
                       in what John Kerry, the U.S. special envoy on
                       climate, has called humanity’s “last best chance”
                       to curb the climate catastrophe. Already,
                       politicians and major corporations, including oil
                       and gas producers, are hard at work promoting the
                       idea that the 2015 Paris Agreement’s goals can be
                       met if the financial world coalesces around “net-
                       zero” climate initiatives.


                       But talk about “net zero” has been met with
                       skepticism by many of those on the frontlines of
                       climate change and those advocating on their
                       behalf. A report issued today by advocacy groups
                       Corporate Accountability, Corporate Europe
                       Observatory, Global Forest Coalition, and Friends
                       of the Earth International takes a look at climate
                       strategies marketed by a half-dozen major polluters
                       and finds that the plans come up lacking because of
                       their heavy reliance on “net zero” strategies that
                       presume that the institutions can continue emitting
                       greenhouse gases as long as they are someday
                       actively removed from the atmosphere. 


                # ⚓ Will_We_Take_the_Path_to_a_Livable_Future_or_Will_Rich
                  Corporations_Trash_the_Planet?⠀⇛


                       For the past several decades, Noam Chomsky has been
                       one of the most forceful and persuasive voices
                       confronting injustice, inequity, and the threat
                       posed by human-caused climate chaos to civilization
                       and the Earth. I was eager to know Professor
                       Chomsky’s views on the roots of our current dire
                       predicament and on humanity’s prospects for
                       emerging from this crisis into a livable future. He
                       very graciously agreed to speak with me by way of a
                       video chat. The text here is an abridged version of
                       a conversation we had on October 1, 2021.


                       Professor Chomsky, now 92, is the author of
                       numerous best-selling political works, translated
                       into scores of languages. His critiques of power
                       and advocacy on behalf of the political agency of
                       the common person have inspired generations of
                       activists and organizers. He has been institute
                       professor emeritus at the Massachusetts Institute
                       of Technology since 1976. His most recent books
                       are Consequences of Capitalism: Manufacturing
                       Discontent and Resistance, with Marv Waterstone,
                       and Climate Crisis and the Global Green New Deal:
                       The Political Economy of Saving the Planet,with
                       Robert Pollin and C.J. Polychroniou.


                # ⚓ Worst_Polluters_Spending_Over_Two_Times_More_on_Border
                  Militarization_Than_on_Climate_Action⠀⇛


                       As the climate emergency wreaks havoc and displaces
                       growing numbers of vulnerable people around the
                       globe, the world’s richest countries and biggest
                       greenhouse gas emitters are responding in a
                       dangerous manner—by prioritizing border
                       militarization over efforts to mitigate fossil fuel
                       pollution and adapt to a hotter planet.


                       “This militarization of borders is partly rooted in
                       national climate security strategies that since the
                       early 2000s have overwhelmingly painted migrants as
                       ‘threats’ rather than victims of injustice.”


                # ⚓ Climate_Change_Has_Exposed_the_Decline_of_the_American
                  Empire⠀⇛


                       Thirteen thousand feet high on the far side of the
                       Himalaya mountains, we have entered the past and
                       the future at the same time. We are a medical
                       expedition and also a pilgrimage, consisting of
                       doctors, nurses, Buddhist clerics, supernumeraries
                       like me, and a large staff of guides, muleteers,
                       and camp tenders. We are bound for the isolated
                       villages of Upper Dolpo, a remote region of
                       northwestern Nepal, land of the snow leopard—both
                       the actual animal and the eponymous nonfiction
                       classic by Peter Matthiessen. We are traveling the
                       same trails Matthiessen walked in 1973.


                # ⚓ Latest_UN_Climate_Report_Delivers_‘Another_Thundering_Wake-
                  Up_Call’⠀⇛


                       Countries’ current climate pledges put the world
                       “on track for a catastrophic global temperature
                       rise” of about 2.7°C, United Nations Secretary-
                       General António Guterres warned Tuesday, calling a
                       new report released ahead of a key summit “another
                       thundering wake-up call.”


                       “The era of half-measures and hollow promises must
                       end.”


                # ⚓ Opinion_|_Critical_Climate_Races_for_Governor_in_Virginia
                  and_New_Jersey⠀⇛


                       With tight races for Governor in two states, Vote
                       Climate U.S. PAC is issuing their first-
                       ever, Gubernatorial Voter’s Guide in Virginia and
                       New Jersey for the elections on Tuesday, November
                       2, 2021, rating candidates on climate change. There
                       is a major divide between candidates on climate
                       change in both critical Gubernatorial races.
                       Climate-action voters could make a difference if
                       they turn out and vote climate.


                # ⚓ Climate_Movement_Hails_‘Mind-Blowing’_$40_Trillion_in
                  Fossil_Fuel_Divestment_Pledges⠀⇛


                       Over the past decade, nearly 1,500 investors and
                       institutions controlling almost $40 trillion in
                       assets have committed to divesting from fossil
                       fuels—a remarkable achievement that climate
                       campaigners applauded Tuesday, while warning that
                       further commitments and action remain crucial.


                       “Divestment has helped rub much of the shine off
                       what was once the planet’s dominant industry. If
                       money talks, $40 trillion makes a lot of noise.”


                # ⚓ ‘Really_Fantastic’:_Europe’s_Largest_Pension_Fund_Announces
                  Fossil_Fuel_Divestment⠀⇛


                       Climate campaigners are cheering Wednesday in
                       response to the news that Dutch pension fund
                       ABP—the fifth-largest in the world—is divesting its
                       assets from fossil fuel producers.


                       “This is really fantastic, after all these years of
                       campaigning, we finally succeeded,” said Liset
                       Meddens, director at Fossielvrij NL, calling the
                       development “a huge victory for the climate, human
                       rights, and all life on Earth.”


                # ⚓ ‘A_Political_Scam,_Not_a_Serious_Plan’:_Groups_Blast
                  Australia_Climate_Pledge⠀⇛


                       Prime Minister Scott Morrison’s government on
                       Tuesday announced Australia’s plan for net-zero
                       emissions by 2050—a plan that includes no further
                       ambition toward 2030 targets, relies on unproven
                       carbon capture technology, and does not phase out
                       fossil fuels.


                       “We need to slash emissions today, tomorrow, this
                       year, and this decade—not in 2050.”


                # ⚓ Opinion_|_Mobilizing_Climate_Finance_to_Avoid_Catastrophe⠀⇛


                       Rich countries have put the world on the brink of
                       climate catastrophe. They have gotten away with
                       decades of inaction on reducing emissions, and on
                       providing finance for the world’s poorer countries
                       to do the same and to support their frontline
                       communities in coping with increasingly severe
                       climate impacts.


                # § Wildlife/Nature⠀➾


                      # ⚓ Opinion_|_Wildfires:_Heartbreaks_and_Healing_Places⠀⇛


                             Wildfire impacted folks mostly from Chico in
                             Butte County, the North Central California
                             region hard hit by climate fires, will
                             carpool together to paint a giant street
                             mural with paint made from wildfire ashes and
                             charcoal from burned trees on their
                             properties. We will protest against the
                             financiers of fossil fuels and PG&E for the
                             last big chance before Cop26 starts on
                             Halloween day. On October 29 in San Francisco
                             in front of BlackRock HQ, the largest
                             financial investor in fossil fuel projects
                             and major shareholder of PG&E is the perfect
                             target to make our stand to
                             #ProtectTheSacred. Their profitable
                             investments set our communities on fire,
                             killed my neighbors, and wrecked lives. 


          o § Finance⠀➾


                # ⚓ Democrats_Eye_Billionaire_Tax_With_Potential_Backing_From
                  “Centrists”⠀⇛


                # ⚓ New_Poll_Finds_Broad_Support_for_Strikes_Across_the
                  Country⠀⇛


                # ⚓ Virginia_Democrats_Sue_USPS_Over_Delays_That_Could_Impact
                  State_Governor_Race⠀⇛


                # ⚓ Social_Infrastructure_Bill_Has_Been_Gutted._Progressives
                  May_Not_Let_It_Pass.⠀⇛


                # ⚓ Can_Billionaires_Save_the_World?⠀⇛


                # ⚓ A_Forensic_Look_at_Jerome_Powell’s_“Pants_on_Fire”
                  Explanation_for_His_$1_Million_to_$5_Million_Stock_Sale⠀⇛


                       The story went viral and forced the Federal Reserve
                       to offer a preposterously lame excuse for what was
                       obviously a desire by Powell to reduce his exposure
                       to the stock market, despite his having access to
                       more insider information than any other human on
                       the planet.


                       The same day that Kuttner’s story ran, Mike Derby,
                       a reporter for the Wall Street Journal, wrote that
                       a Fed representative had characterized the large
                       Vanguard sale as “for family expenses.”


                # ⚓ Reconciliation_Framework_‘Not_Enough’_to_Push_Through
                  Infrastructure_Bill,_Progressives_Warn⠀⇛


                       U.S. House progressives led by Reps. Pramila
                       Jayapal, Alexandria Ocasio-Cortez, and Cori Bush
                       dug in their heels Tuesday as right-wing Democrats
                       attempted to salvage a $1.2 trillion infrastructure
                       bill while sidelining the more ambitious Build Back
                       Better package championed by the party’s left wing
                       and President Joe Biden until after the weaker
                       bipartisan legislation is passed.


                       “It’s not enough for me. And there are more of us.”


                # ⚓ Phil_Knight’s_Big_Tax_Dodge:_A_Q&A_With_Tax_Attorney_Bob
                  Lord⠀⇛


                # ⚓ The_Strategic_Brilliance_of_‘Striketober’⠀⇛


                       Yet, this is precisely what we are seeing, as
                       during the month of October, over 100,000 workers
                       have either threatened to strike or actually have
                       walked off the job to demand wage increases,
                       improvements to their work conditions, and basic
                       human dignity.


                       Dubbed ‘striketober’ by activists and pundits
                       alike, this strike wave is occurring across the
                       country, in various industries.


                # ⚓ McDonald’s_Workers_Join_‘Striketober’_and_Walk_Out_Over
                  Sexual_Harassment⠀⇛


                       Amid of wave of worker walkouts that supporters are
                       collectively calling “Striketober,” McDonald’s
                       employees in at least 12 U.S. cities took to the
                       streets Tuesday to raise concerns about how the
                       fast food giant has handled sexual harassment and
                       to demand a union.


                       “No matter what McDonald’s says, not much has
                       changed for workers like me.”


                # ⚓ Democrats_Urged_to_Seize_‘Historic_Chance’_on_Billionaire
                  Wealth_Tax⠀⇛


                       “The billionaire wealth tax merits an extra push
                       since it is the most powerful tool on the table for
                       tackling the wealth inequality that is undermining
                       our economy and threatening our democracy.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Campaigning_“From_the_Middle_Out”_Won’t_Save_Democrats⠀⇛


                       While we don’t know what sort of Build Back Better
                       bill Democrats will end up passing, we do know that
                       it will be a shadow of President Biden’s original
                       plan. The core of the climate agenda is out. Free
                       community college is out. The extension of Medicare
                       to cover vision, hearing, and dental is under
                       threat. Senator Kyrsten Sinema (D-Ariz.) perversely
                       seems intent on killing the plan to lower
                       prescription drug prices, a reform even Republican
                       voters support. Instead of the “Roosevelt moment”
                       Biden promised, we’ve suffered another tawdry
                       chapter about the power of deep-pocketed interests
                       and the pervasive corruption of our politics.


                # ⚓ Pelosi_and_Hoyer_to_Progressives:_Just_Pretend_Democrats
                  Are_Winning_(Even_If_Corporate_Lobbyists_Are)⠀⇛


                       Democratic leadership advised House progressives
                       behind closed doors Monday night that they better
                       start acting like they are getting a major win even
                       if the reality is that President Joe Biden’s
                       signature domestic infrastructure plan seems on the
                       verge of “being gutted beyond recognition” thanks
                       to an aggressive assault by corporate lobbyists and
                       the obstructionism of a small handful of right-wing
                       lawmakers within the party.


                       “If we don’t act like we are winning, the American
                       people won’t believe it either,” House Majority
                       Leader Steny Hoyer (D-Md.) told Democrats during a
                       private meeting, according to Politico.


                # ⚓ Conor_Lamb_Is_a_Centrist_in_Sheep’s_Clothing⠀⇛


                       Last weekend, Representative Conor Lamb, a
                       frontline Democrat from Pennsylvania who’s running
                       for the Senate in 2022, vowed to support carbon-
                       free energy payments, a key climate provision
                       Senator Joe Manchin is currently trying to strip
                       from Democrats’ social spending package. Lamb
                       officially jumped in the race in August to replace
                       retiring Republican Senator Pat Toomey, in what is
                       expected to be one of the most contentious contests
                       in next year’s midterm elections.


                # ⚓ ‘Bottom_Line,’_Says_Bernie_Sanders,_Deal_Must_Include
                  Medicare_Expansion,_Lower_Drug_Prices⠀⇛


                       As congressional leadership pushes Democrats to
                       “act like we are winning” even as a few corporate-
                       backed party members and business lobbyists water
                       down the Build Back Better bill, Senate Budget
                       Committee Chair Bernie Sanders reiterated Tuesday
                       that the package must expand Medicare and include
                       reforms to lower prescription drug prices.


                       “Congress must finally have the courage to stand up
                       to the greed of Big Pharma.”


                # ⚓ Watch:_Bernie_Sanders_Argues_‘We_Must_End_the_Greed_of_Big
                  Pharma’⠀⇛


                       U.S. Senate Budget Committee Chair Bernie Sanders
                       plans to deliver a live, online address Tuesday
                       night arguing that “we must end the greed of Big
                       Pharma.”


                       The speech—scheduled for 8:00 pm ET at
                       live.berniesanders.com—comes as Sanders (I-Vt.) and
                       other progressives in Congress are fighting for a
                       Build Back Better package that allows Medicare to
                       negotiate with the pharmaceutical industry for
                       lower prescription drug prices and expands the
                       federal healthcare program to cover dental,
                       hearing, and vision services.


                # ⚓ ‘Manchin_Wasn’t_Done’_Killing_Climate_Action:_Coal_Baron
                  Objects_to_Methane_Fee⠀⇛


                       Progressives are fuming amid reports that right-
                       wing Democratic Sen. Joe Manchin is pushing his
                       party to weaken or remove the reconciliation bill’s
                       proposed fee on methane pollution, even as
                       scientists warn that humanity’s fate depends on
                       rapidly slashing emissions of the potent greenhouse
                       gas.


                       “As anyone with a leaky roof will tell you, making
                       sufficient investments early on is key to avoiding
                       catastrophic costs down the line.”


                # ⚓ How_One_Ballsy_Senator_Stole_a_President’s_Gummy_Candy⠀⇛


                       What have we instead? Joe Manchin of Virginia, a
                       once-little-known-senator Democratic senator
                       essentially holding the Democratic Party hostage.
                       He is also rejecting the purported will – not to
                       forget the needs– of 80% of Americans who approve
                       of the most progressive, far-reaching program drawn
                       up by legislators in two generations.


                       Manchin is as pig-headed, as resolute, as
                       overconfident as any Republican. And he’s usurped
                       Harris’s role as the clinching vote. (His party
                       can’t handle him or his Arizona cohort Kyrsten
                       Sinema.)


                # ⚓ Sunrise_Movement_Corrects_Manchin:_US_‘Has_Done_More_Than
                  Any_Other’_to_Cause—Not_Solve—Climate_Crisis⠀⇛


                       As activists with the Sunrise Movement confronted
                       Sen. Joe Manchin in Washington, D.C. Tuesday—their
                       seventh day of a hunger strike for climate
                       justice—the leader of the youth-led green group
                       shot down a claim by the fossil fuel-funded West
                       Virginia Democrat that the United States leads the
                       world in tackling the planetary emergency.


                       “If the U.S. doesn’t pass massive climate action
                       this fall, it is too late. This is one of our last
                       chances.”


          o § Misinformation/Disinformation⠀➾


                # ⚓ Billionaire_political_meddlers,_disinformation_agents
                  launch_‘Good_Information_Inc.’_to_fight_disinformation⠀⇛


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


                # ⚓ A_Guide_To_The_U.S._Government’s_Appeal_In_The_Assange
                  Extradition_Case⠀⇛


                       On October 27, the High Court of Justice in the
                       United Kingdom will hear the Crown Prosecution
                       Service argue on behalf of the United States
                       government that a lower court improperly blocked
                       the U.S. from extraditing WikiLeaks founder Julian
                       Assange.


                # ⚓ The_PATRIOT_Act_And_The_Whistleblowers_Who_Challenged_Mass
                  Surveillance_After_9/11⠀⇛


                       [Editor’s Note: To mark the 20th anniversary of the
                       rise of the American security state after the
                       September 11th attacks, The Dissenter continues a
                       retrospective on this transformation in policing
                       and government.]


                # ⚓ US/UK:_“Drop_the_charges,_stop_the_extradition_and_free
                  Julian_Assange,”_says_Amnesty_head⠀⇛


                       Ahead of the US appeal hearing on the extradition
                       of Julian Assange Amnesty International’s Secretary
                       General has called on US authorities to drop the
                       charges against him and the UK authorities not to
                       extradite him but release him immediately.


          o § Civil Rights/Policing⠀➾


                # ⚓ “Worked_to_Death”:_IATSE_Film_Crew_on_“Rust”_Walked_Off_Set
                  to_Protest_Conditions_Before_Shooting⠀⇛


                       We look at how the tragic shooting death of
                       cinematographer Halyna Hutchins during the filming
                       of “Rust” last Thursday on a set in New Mexico is
                       drawing attention to cost-cutting decisions and
                       overall safety in the film industry. Yahoo News is
                       reporting the gun that killed Hutchins had been
                       used by crew members just hours beforehand for
                       live-ammunition target practice. The film’s lead
                       actor and producer Alec Baldwin later shot the
                       revolver after he was reportedly handed it by the
                       first assistant director, David Halls, who told him
                       it was a “cold gun,” meaning it was not loaded with
                       live ammunition. Halls was fired in 2019 from his
                       position as assistant director on the movie
                       “Freedom’s Path” after a gun “unexpectedly
                       discharged” and injured a crew member. All of this
                       happened after some of the unionized IATSE below-
                       the-line crew members had walked off the set of
                       “Rust” earlier on the day of the shooting to
                       protest their housing, payment and working
                       conditions. New Mexico is a “right to work” state,
                       so producers were able to hire nonunion
                       replacements and continue working on the film. We
                       speak with Dutch Merrick, prop master and armorer
                       for over 25 years and past president of IATSE Local
                       44 Property Craftspersons, Hollywood, who notes,
                       “Hollywood handles firearms every single day,” and
                       calls the process “carefully regulated.” Despite
                       safety protocol and expertise, he says, Hollywood
                       crews are getting “worked to death” with 80- to
                       100-hour workweeks, which he suggests played into
                       the accidental shooting.


                # ⚓ Former_Black_Panther_Russell_“Maroon”_Shoatz_Freed_From
                  Prison_After_49_Years⠀⇛


                # ⚓ Why_I_Opposed_the_Patriot_Act⠀⇛


                       Today marks the 20th anniversary of the US Patriot
                       Act. This legislation, rightfully, has long been
                       critiqued for sweeping in unprecedented government
                       surveillance. The anniversary is an opportunity to
                       also reckon with how the Patriot Act distorted our
                       democracy’s checks and balances—and what needs to
                       be done to realign them.


                # ⚓ Confronting_Ignorance_and_Ignorant_Confrontations⠀⇛


                       People respected him so they’d ask about the pain
                       or discomfort they were experiencing or seeing in
                       their children or babies. My father loved to help
                       people, and oftentimes people were worried because
                       they didn’t know, “how bad is it?” They found his
                       expertise reassuring.


                       Everyone knows that two aspirin will not cure
                       everything, and they aren’t a diagnostic tool, but
                       it is a troubleshooting step; using nonsteroidal
                       anti-inflammatory drugs to respond to minor aches
                       and pains is like unplugging your router or modem
                       when your internet is not working.


                # ⚓ Honoring_Elliot_Harmon—EFF_Activism_Director,_Poet,
                  Friend—1981-2021⠀⇛


                       Elliot understood how intellectual property could
                       be misused to shut down curiosity, silence artists,
                       and inhibit research—and how open access policies,
                       open licensing, and a more nuanced and balanced
                       interpretation of copyright could reverse those
                       trends. A committed copyleft activist, he led
                       campaigns against patent trolls and fought for open
                       access to research. He campaigned globally for
                       freedom of expression and access to knowledge, and
                       his powerful articles helped define many of these
                       issues for a global community of digital rights
                       activists.


                       This photo was taken shortly before Elliot went to
                       speak on top of a truck at a Stop SESTA/FOSTA rally
                       in Oakland.


                       Elliot’s formidable activism touched upon every
                       aspect of EFF’s work. In his early days with us, he
                       continued the work that he began at Creative
                       Commons campaigning for the late Palestinian-Syrian
                       activist, technologist, and internet volunteer
                       Bassel Khartabil. He also ran a successful campaign
                       for Colombian student Diego Gomez, fighting against
                       that country’s steep copyright infringement laws
                       and advocating for open access and academic
                       freedom. Following the same values, Elliot
                       spearheaded EFF’s Reclaim Invention campaign urging
                       universities to protect their inventions from
                       patent trolls. He went on to help steer our
                       campaign to get the FCC to restore net neutrality
                       rules, framing the issue as a matter of free speech
                       and calling on “Team Internet” to join him in the
                       fight. In all of these efforts and more, Elliot
                       brought a natural sense of how to build and nurture
                       community around a shared cause. 


                # ⚓ Hitler_can_now_dine_in_italian_restaurants⠀⇛


                       A few weeks ago, the world noticed that Italy was
                       about to “bring in the strictest COVID-19 measures
                       in Europe”. Starting on October 15th, that is,
                       Italy “would become the first European country to
                       require the so-called green pass – the digital or
                       paper proof of vaccination, immunity or a negative
                       test in the past 48 hours – in all places of work,
                       both private and public.”


                       [...]


                       On one hand, both Italians and foreign visitors are
                       safe. It’s pretty unlikely that they will bump into
                       Hitler in any public place in Italy. On the other,
                       there are two classes of concrete problems here.


                       One is public health, and paradoxically it may be
                       the smaller one: most places here do ask to show
                       Green Passes, but almost none actually verifies
                       that name and age on a Green Pass match the person
                       who shows it. So yes, anybody infected could sneak
                       without getting caught into many public spaces,
                       with those cards.


                       That may not be a lot of people. The No-vax, no-
                       green-pass crowd is a noisy but dwindling minority
                       in Italy, not to mention that some of them are dumb
                       enough to make Green Passes the last of their
                       problems.


                       The main problems are that first, those fake passes
                       are valid everywhere in Europe, not just Italy, and
                       it seems similar passes are available in Poland and
                       Russia. Second, there is almost the same thing I
                       mentioned months ago.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Team_Biden_Finally_Gets_Around_To_Staffing_U.S._Telecom
                  Regulators⠀⇛


                       It was the longest delay in staffing U.S. telecom
                       agencies in Presidential history, but a White House
                       announcement states the administration will promote
                       interim boss Jessica Rosenworcel to be permanent
                       FCC boss, while appointing former Tom Wheeler
                       advisor and consumer advocate Gigi Sohn to fill the
                       third empty Democratic Commissioner seat. Sohn
                       played a major role in both the crafting of net
                       neutrality rules (since demolished by telecom
                       sector lobbyists during the Trump era) and the
                       FCC’s broadband privacy rules (also since
                       demolished by telecom sector lobbyists during the
                       Trump era).


                # ⚓ Senate_Urged_to_Quickly_Confirm_Net_Neutrality_Advocates_to
                  FCC_Posts⠀⇛


                       “There’s no time to waste and so much to get done.”


                       “Finally! Now let’s get this agency back to work.”


          o § Monopolies⠀➾


                # ⚓ The_Facebook_Papers:_Docs_Reveal_Tech_Giant’s_Complicity_in
                  Hate,_Lies_&_Violence_Around_the_World⠀⇛


                       Thousands of internal Facebook documents leaked to
                       media outlets continue to produce damning
                       revelations about how the social media giant has
                       prioritized its profits over user safety. The
                       Facebook Papers have provided fresh evidence of how
                       the company has let serious problems fester on its
                       platform, including hate, misinformation, and human
                       trafficking, and failed to invest in moderation
                       outside English-speaking countries. The former
                       Facebook product manager who shared the documents,
                       Frances Haugen, is pressing lawmakers to more
                       tightly regulate the company’s activities and
                       testified Monday before the British Parliament
                       ahead of scheduled meetings with officials in
                       France, Germany and the European Union. Facebook
                       CEO Mark Zuckerberg says the leaked documents paint
                       a “false picture” based on cherry-picked evidence,
                       but we speak with UCLA information studies
                       professor Ramesh Srinivasan, who says they confirm
                       what many critics have warned about for years.
                       “This new form of digital capitalism that I believe
                       Facebook is trailblazing is one that is playing
                       with our intimate emotions on every single level.”


                # ⚓ FTC_Study_Highlights_How_‘Big_Telecom’_Privacy_Practices
                  Are_Even_Worse_Than_‘Big_Tech’⠀⇛


                       I’ve noted for a few times that the very obvious
                       dysfunction in “big tech” has proven to be the gift
                       that keeps on giving for “big telecom.” While tech
                       giants like Google, Amazon, and Facebook get the
                       entirety of (often very justified) attention for
                       dodgy business practices and terrible judgement,
                       telecom has basically been forgotten in the DC
                       Policy conversation. While lawsuits and
                       Congressional posturing all focus on expanding
                       oversight of “big tech,” “big telecom” and “big
                       media” have been able to lobotomize most of the
                       oversight of its own businesses, despite engaging
                       in all the same (and sometimes worse) dubious
                       business practices.


                # ⚓ What_About_International_Digital_Competition?⠀⇛


                       Antitrust has not had its moment since the 1911
                       breakup of Standard Oil. But this past year,
                       policymakers and government leaders around the
                       globe have been taking a hard look at the
                       technology markets. ‘Break up Big Tech’ is the
                       newest antitrust catchphrase. On both sides of the
                       Atlantic, policies have been introduced to foster
                       digital competition.


                       Congress has introduced several competition and
                       anti-trust bills, including a bipartisan package
                       that passed out of committee. The Biden
                       administration has nominated antitrust advocates to
                       key positions: Lina Khan as chair of the Federal
                       Trade Commission, Jonathan Kanter as the Assistant
                       Attorney General for Antitrust at the Department of
                       Justice, and Tim Wu at the National Economic
                       Council. And across the Atlantic, the European
                       Commission is marking up two key pieces of
                       legislation, the Digital Markets Act and the
                       Digital Services Act, that would create new rules
                       for digital services and enhanced competition in
                       the technology sector.   


                       Early this summer and on his first international
                       travel trip, President Biden headed to Brussels to
                       talk about creating a new U.S.- EU Tech and Trade
                       Council (TTC) and a Joint Technology Competition
                       Policy Dialogue (JTCPD). There have been few
                       details aside from the initial press releases on
                       what policy approaches would be considered.
                       However, it is a clear sign that there is a
                       transatlantic appetite for tackling competition in
                       the technology space. But what would an
                       international competition policy look like?


                # ⚓ European_design_protection_–_worth_your_money? [Ed:
                  Monopolies fees collected by EU agency, EUIPO, which then
                  uses_the_money_for_corruption]⠀⇛


                       Every company that spends money and resources on
                       research, development and marketing for its
                       products needs assurance that competitors (or other
                       third parties) cannot take advantage of its
                       innovation. Profiting from innovation requires a
                       good business model and an IP strategy is an
                       important part of that business model.


                       Unlike trademarks, patents and copyright – which
                       are well known and commonly used – design
                       protection is sometimes forgotten or
                       underestimated. However, the design of products,
                       packaging, logos, drawings and artwork plays a key
                       role in distinguishing new products from those of
                       competitors.


                # ⚓ Tesla_Amps_Up_Fight_With_Rivian,_Cites_Battery_Secrets
                  Theft [Ed: Copying is not theft and it's not a crime to just
                  know something you learned somewhere; Musk pretended to be
                  sharing with his “all out patents are belong to you” post;
                  look at him getting all litigious now.]⠀⇛


                       Tesla Inc. escalated its trade secrets fight with
                       Rivian Automotive Inc., accusing the maker of
                       electric pickups of continuing to poach its
                       employees and stealing “highly proprietary” battery
                       technology.


                # ⚓ Your_mom_was_right:_Facebook_is_bad_for_you!⠀⇛


                       Two whistleblowers have revealed that Facebook is
                       well aware of the real world harms it causes to its
                       users and to democratic ideals worldwide, but it
                       chooses to prioritise profit over doing the right
                       thing. We wrote to the Parliamentary Standing
                       Committee on Information Technology asking them to
                       initiate an inquiry into the revelations made,
                       specifically about India and to call the relevant
                       stakeholders to testify before it.


                # § Patents⠀➾


                      # ⚓ UK:_DABUS:_AI’ll_Be_Back [Ed: Every serious court and
                        patent office has repeatedly rejected this provocateur,
                        likely a publicity stunt by Surrey University; but
                        patent litigation firms love to distort the outcome for
                        their radical for-profit agenda]⠀⇛


                             In a hotly awaited decision, the English
                             Court of Appeal has ruled that AI-based
                             machines cannot be named as inventors,
                             upholding the original decision of the High
                             Court and Comptroller general.


                             Dr Stephen Thaler has become well known in
                             the intellectual property field ever since
                             filing patent applications for two
                             inventions: one entitled “Food Container”
                             (GB18116909.4) and the other entitled
                             “Devices and Methods of Attracting Enhanced
                             Attention” (GB181816.0). However, despite its
                             title, it is not the subject matter of the
                             invention that has been attracting attention,
                             but the named inventor: ‘DABUS’, an AI
                             machine owned by Dr Thaler.


                      # ⚓ Counsel_expect_STRONGER_Patents_Act_to_drop_again
                        soon [Ed: Corrupt_and_bribed_politician_Coons_as_merely
                        a_mole_of_the_litigation_profiteers_who_try_to_buy_laws
                        through_him]⠀⇛


                             Sources say Senator Chris Coons could
                             reintroduce an amended STRONGER as soon as
                             this week, possibly as a counter to the
                             Restoring the America Invents Act


                      # ⚓ Samsung_Patent_Board_Challenges_OK_Despite
                        Confidentiality_Pact⠀⇛


                             Samsung Electronics Co. convinced two Federal
                             Circuit judges that a confidentiality
                             agreement concerning licensing negotiations
                             doesn’t bar it from filing patent office
                             challenges.


                      # ⚓ Apple’s_Tribunal_Wins_Against_Camera_Patents_Upheld
                        on_Appeal⠀⇛


                             The board found all the challenged patent
                             claims were invalid because they were
                             anticipated or obvious.


                      # ⚓ The_U.S._Court_of_Appeals_for_the_Federal_Circuit
                        assesses_the_equitable_powers_of_a_legislative_court:
                        the_Court_of_Appeals_for_Veterans_Claims.⠀⇛


                             The case involves the plight of Bruce R.
                             Taylor, a Vietnam era Army veteran seeking
                             compensation for disabilities resulting from
                             his service. Before serving two tours
                             overseas, Mr. Taylor volunteered to serve his
                             country in a unique fashion—as a test
                             subject. In 1969, the Army sought soldiers on
                             which it would test toxic chemicals such as
                             nerve gas. The Army’s purpose was to learn
                             how its soldiers would function when exposed
                             to agents that combatants might experience in
                             service. Soldiers were given doses of an
                             array of toxic substances and subjected to
                             training exercises to measure performance. As
                             a result of Mr. Taylor’s participation, he
                             suffers from disabilities that the VA found
                             eliminate his ability to work. In accordance
                             with statute, the VA awarded Mr. Taylor
                             monthly compensation.


                      # ⚓ A_Unified_Patent_Court_for_Europe_–_Coming_Soon? [Ed:
                        No, stop_printing_lies_as_headlines]⠀⇛


                             Europe may soon have its Unified Patent Court
                             and Williams Powell is ready to assist you.
                             With attorneys qualified for the European
                             Patent Litigation Certificate (which gives
                             UPC rights of representation) and as a Patent
                             Attorney Advocate & Litigator (which gives
                             rights of representation in the UK Courts) we
                             are well-placed not only to obtain IP
                             protection but to conduct IP litigation, both
                             in Europe and in the UK.


                      # ⚓ Kathi_Vidal_nominated_as_USPTO_director [Ed: Another
                        'bought' Director for the litigation lobby?]⠀⇛


                             The White House officially announced its
                             intention to nominate the Winston & Strawn
                             partner to the position today, confirming
                             rumours


                      # ⚓ Next_UPSTO_Director:_Kathi_Vidal [Ed: More aggressive
                        lawyers instead of scientists in USPTO? The patent
                        extremists are happy, so that’s a bad sign already;
                        lobbying_buys_nominations]⠀⇛


                             President Biden has nominated leading patent
                             litigator Kathi Vidal as the next USPTO
                             director. Vidal is currently at Winston &
                             Strawn, leading the company’s Silicon Valley
                             office. She was previously with Fish &
                             Richardson. [Announcement]


                             Vidal has all the qualifications. Bachelor’s
                             and Master’s degrees in electrical
                             engineering (starting college at age 16); JD
                             from Penn (EIC of the law review); Federal
                             Circuit clerkship (Judge Schall); registered
                             patent attorney; and litigated patent cases
                             in courts across the country, including the
                             PTAB. She represented Chamberlain whose
                             garage door opener patents were obliterated
                             by the eligibility revolution of Bilski–Mayo-
                             and-Alice. At the same time, Vidal has
                             represented many accused infringers.


                      # ⚓ The_English_High_Court_applies_German_law_on_EPC_2000
                        claims_in_Royalty_Pharma_v_Boehringer [Ed: By Bristows
                        of_Team_UPC]⠀⇛


                             On 8 October 2021, His Honour Judge Hacon
                             (sitting as a Judge of the High Court) handed
                             down his decision in an action brought by
                             Royalty Pharma Collection Trust (“Royalty
                             Pharma”) for approximately €23 million in
                             royalty payments from Boehringer Ingelheim
                             GmbH (“Boehringer”) (Royalty Pharma
                             Collection Trust v Boehringer Ingelheim GmbH
                             [2021] EWHC 2692 (Pat)). The action relates
                             to products sold by Boehringer containing the
                             active pharmaceutical ingredient (“API”)
                             linagliptin for the treatment of type 2
                             diabetes. Boehringer manufactures the API in
                             Germany. Some API is also formulated,
                             labelled and packed into products in Germany,
                             but some is exported by Boehringer to other
                             countries.


                             Boehringer entered into a non-exclusive
                             licence with Prosidion Limited in 2005. The
                             agreement had a somewhat unusual governing
                             law and jurisdiction clause in that it was
                             governed by German law but provided that the
                             Courts of England and Wales have jurisdiction
                             over any dispute. The agreement was assigned
                             from Prosidion to Royalty Pharma in 2011 and
                             was amended in 2015 (but not with respect to
                             the jurisdiction or governing law clauses).
                             Royalty Pharma claimed outstanding royalties
                             pursuant to the amended agreement. One of the
                             patents licensed by Royalty Pharma to
                             Boehringer was the German designation of EP 1
                             084 705 (“EP 705”), and it is this patent
                             which formed the subject of the dispute.


                      # ⚓ Dutch_court_rejects_Ericsson_motion_for_anti-antisuit
                        injunction,_but_Apple_may_still_be_enjoined_if_need_be:
                        another_jurisdiction_adopts_Munich_approach⠀⇛


                             Ericsson means business, and it’s not going
                             to undervalue its patents in the renewal of
                             its license agreement with Apple. Earlier
                             this month, Ericsson filed a declaratory
                             judgment action–on its own FRAND
                             compliance–in the Eastern District of Texas.
                             I’ve now become aware of a decision the
                             Rechtbank Den Haag (Court of The Hague)
                             published (in Dutch) last week. Judge D.
                             Nobel denied an Ericsson petition for an
                             anti-antisuit injunction against Apple. It
                             may be counterintuitive, but all things
                             considered the decision is clearly better for
                             Ericsson–though it’s “the loser” at first
                             sight–than for Apple. As matter of fact,
                             Apple itself has a history of bringing cases
                             that serve a strategic purpose even if a
                             court rejects a motion or complaint (such as
                             when it demonstrated to the rest of the
                             industry that it would enforce its design
                             rights around the globe, even though it
                             ultimately failed everywhere but in its home
                             court).


                             [...]


                             Claim 1 of EP 705 is in the EPC 2000 form and
                             covers a class of effectors of particular
                             enzymatic activity for use in lowering the
                             blood glucose level of mammals for the
                             alleviation of diabetes.


                             The German courts have ruled that EPC 2000
                             claims correspond to purpose-limited product
                             claims and can be directly infringed via an
                             act in s.9(1) German Patents Act 1980. Case
                             law further indicates that the subject-matter
                             of such claims lies in the suitability of the
                             substance “for” a certain medical use. In
                             order to determine whether an infringer’s
                             product is “for” the treatment of the
                             indication specified in the claim, the German
                             courts have developed the doctrine of
                             sinnfällige Herrichtung. If the product of
                             the claim is sufficiently tied to (or
                             “earmarked for”) the use specified in the
                             claim, the requirement of sinnfällige
                             Herrichtung is satisfied.


                             [...]


                             It is interesting to consider whether the
                             same decision would be reached if Hacon HHJ
                             had had to apply English law rather than
                             German law.


                      # ⚓ Dissent_in_PTAB_edict_could_spur_surge_of_Arthrex-
                        extension_bids [Ed: Fake 'journalists' (lobbyists
                        funded by patent litigation firms) cherry-picking
                        dissenters rather than case outcomes in an effort to
                        tilt media coverage in favour of the side which
                        actually lost]⠀⇛


                             Stakeholders could try to use Judge Pauline
                             Newman’s dissent in Mobility Workx to extend
                             USPTO director review to PTAB institution
                             decisions, say sources


                # § Copyrights⠀➾


                      # ⚓ MPA_Wants_Cryptocurrency_Exchanges_To_Help_Identify
                        Online_Pirates⠀⇛


                             The Motion Picture Association would like the
                             US Government’s executive cybersecurity order
                             to be optimized to identify operators of
                             pirate sites and services. Among other
                             things, the order should require U.S.-based
                             IaaS providers, including hosting services,
                             DNS servers, reverse proxies, and
                             cryptocurrency exchanges, to robustly verify
                             the identities of foreign customers.


                      # ⚓ Former_UFC_Star_Paige_VanZant_is_Hunting_Down_Photo
                        Pirates_on_Discord⠀⇛


                             Former UFC star and Dancing With The Stars
                             runner-up Paige VanZant is reportedly making
                             more money from selling pictures and videos
                             of herself online than she ever did with the
                             MMA organization. Unsurprisingly, some fans
                             refuse to pay for her content so in response,
                             VanZant has now gone to court in the US to
                             force Discord to hand over their personal
                             details.



                    ䷩ 𝚕𝚒𝚗𝚎 5824

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/10/2021:_XOrg_Server_21.1_and_Makulu_Shift_Ubuntu_Variant_Released⠀✐


Posted in News_Roundup at 5:43 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Best_Linux_desktop_for_2021:_Which_one_should_you_buy?⠀⇛


                       Linux on the desktop is a thing to behold. It’s not
                       only incredibly powerful and secure, but it’s also
                       flexible enough to become exactly what the user
                       needs. And although you can successfully run Linux
                       on just about any type of desktop machine (running
                       lightweight Linux distributions on older hardware),
                       to really get the most out of modern-day variants,
                       it’s best to have hardware up to the task.


                       Linux doesn’t require nearly the hardware needed to
                       run Windows 11 or macOS, but why not give the open-
                       source operating system extra power, so you can run
                       more applications and services. So, why not send
                       your money to companies that support open source in
                       return?


                       Which desktops are best suited for the task? Let’s
                       take a look at the five best options you have for
                       2021.


          o § Kernel Space⠀➾


                # ⚓ Maintaining_Yocto_Project_Documentation_–_Bootlin’s_blog⠀⇛


                       For many years, Bootlin has been a strong user and
                       a contributor to the Yocto Project, delivering
                       numerous customized embedded Linux distributions
                       and Board Support Packages based on Yocto Project
                       and OpenEmbedded to its customers, for a wide range
                       of hardware platforms and architectures.


                       In 2021, we have been able to bring this engagement
                       further, as Bootlin engineer Michael Opdenacker has
                       been given the opportunity to work as a maintainer
                       for Yocto Project’s documentation, thanks to
                       funding from the Linux Foundation. Since the
                       mourning of Scott Rifenbark, the former maintainer,
                       in early 2020, the project was in need for someone
                       to fill this role.


                # ⚓ Qualcomm_MSM_DRM_Driver_Improvements_Submitted_Ahead_Of
                  Linux_5.16_–_Phoronix⠀⇛


                       The MSM DRM driver for supporting the open-source
                       display/graphics support with Qualcomm Snapdragon
                       SoCs has submitted their main feature pull request
                       to DRM-Next ahead of the upcoming Linux 5.16 merge
                       window.


                       The MSM DRM driver changes for Linux 5.16 aren’t
                       too exciting but do include a few items worth
                       mentioning. First up, Embedded DisplayPort (eDP)
                       support has been added to MSM’s DisplayPort sub-
                       driver for newer SoCs having native eDP output.


                # ⚓ Apple_Silicon_GPIO_Driver_Queued_Ahead_Of_Linux_5.16_–
                  Phoronix⠀⇛


                       Along with the Apple Silicon PCIe driver, another
                       new driver for supporting Apple Silicon (primarily
                       with a focus on the Apple M1 for now) with the
                       upcoming Linux 5.16 cycle is a new pinctrl/GPIO
                       driver.


                       Queued overnight into the linux-pinctrl.git’s “for-
                       next” branch is the 500+ lines of code driver
                       developed by Arm’s Joey Gouly and Corellium’s Stan
                       Skowronek for bringing up the pinctrl/GPIO support
                       for Apple SoCs.


                # ⚓ Nintendo_Switch_Controller_Driver_Finally_Set_For_Linux
                  5.16_–_Phoronix⠀⇛


                       After stalling last year when it was queued up in
                       HID’s “for-5.10/nintendo” branch only to not make
                       it into HID-next at the time, that threshold has
                       now been crossed with the latest Nintendo Switch
                       controller driver now ready for introduction in
                       Linux 5.16. This open-source driver enables the
                       Nintendo Switch Joy-Con and Pro controllers to work
                       under Linux with a mainline kernel driver.


                # § Graphics Stack⠀➾


                      # ⚓ xorg-server_21.1.0_released⠀⇛


                             This is the final release of X server 21.1.
                             There has been just one fix since
                             the second RC and at this time there are no
                             known regressions since the 1.20
                             release series.

                             I expect that increased usage after the final
                             release may still uncover
                             something interesting, so there is a
                             potential for subsequent 21.1.1 patch
                             being released in the coming weeks rather
                             than after the usual interval of
                             several months.

                             Notable changes since 1.20 include:

                               - The meson support is now fully mature.
                             While autotools support will still be
                               kept for this release series, it will be
                             dropped afterwards.

                               - Glamor support for Xvfb.

                               - Variable refresh rate support in the
                             modesetting driver.

                               - XInput 2.4 support which adds touchpad
                             gestures.

                               - DMX DDX has been removed.

                               - X server now correctly reports display
                             DPI in more cases. This may affect
                               rendering of client applications that have
                             their own workarounds for hi-DPI
                               screens.

                               - A large number of small features and
                             various bug fixes.

                             Note that since 21.1 series XWayland is
                             released separately and thus this
                             release does not include it.
                      # ⚓ X.Org_Server_21.1_is_Here_After_More_Than_Three_Years
                        of_Development⠀⇛


                             More than three years after X.Org Server
                             1.20, released in May 2018, X.Org Server 21.1
                             finally has been released.


                             The X.Org Server has a long history behind
                             it. It’s the reference implementation of the
                             X Window system first released in June 1984
                             by its author Robert W Scheifler at
                             Massachusetts Institute of Technology (MIT).


                             X.Org Server is an open source and freely
                             distributed implementation of the X Window
                             System, provided by the X.Org Foundation.
                             It’s part of the X.Org software, the popular
                             X Window System used in many POSIX operating
                             systems, including almost all Linux
                             distributions.


                      # ⚓ X.Org_Server_21.1_Released_With_Variable_Rate_Refresh
                        In_Modesetting_Driver,_Other_Work_–_Phoronix⠀⇛


                             X.Org Server 21.1 is now officially available
                             as this first xorg-server update in three
                             years and what began development as X.Org
                             Server 1.21 prior to the versioning change.


                             X.Org Server 21.1 brings GLAMOR acceleration
                             for the Xvfb, Variable Rate Refresh (VRR /
                             FreeSync / Adaptive-Sync) support within the
                             generic xf86-video-modesetting driver
                             assuming the underlying DRM/KMS kernel driver
                             supports VRR, much better Meson build system
                             support, X Input 2.4 is integrated that adds
                             support for touchpad gestures, the DMX DDX
                             (Distributed Multihead X) code has been
                             removed, improved display DPI reporting, and
                             a wide variety of other minor improvements
                             and bug fixes.


                      # ⚓ NVIDIA_495.74_Proprietary_Drivers_Released⠀⇛


                             NVIDIA Corporation introduced the first
                             stable release of the new branch of the
                             proprietary NVIDIA 495.74 driver. At the same
                             time, an update was proposed for the NVIDIA
                             stable branch 470.82.00. The driver is
                             available for Linux (ARM64, x86_64), FreeBSD
                             (x86_64) and Solaris (x86_64).


          o § Applications⠀➾


                # ⚓ Top_6_CAD_viewers_for_Linux⠀⇛


                       Computer-Aided Design (CAD) uses computers to
                       assist in the creation, modification, analysis, or
                       optimization of a design. The software is used to
                       increase the designer’s productivity, boost the
                       quality of a design, improve communications through
                       documentation, and create a database for production
                       or manufacturing.


                       CAD is an essential part of many streams of
                       engineering. It is professionally used in
                       architecture, auto parts design, aeronautics,
                       interior design, and space shuttle research.


                       Several professional-grade Computer-Aided Design
                       programs like SolidWorks and Autodesk AutoCAD are
                       not natively supported on the Linux platform. So,
                       in this article, we will be looking at the top-
                       performing CAD programs available for Linux.


                       Besides reviewing the available programs, we have
                       also provided the installation instructions for
                       each software. Furthermore, we will give you links
                       to the respective software website to learn more
                       about other distros’ installation procedures.


          o § Instructionals/Technical⠀➾


                # ⚓ Anticipating_Your_Memory_Needs_–_Further_learnings⠀⇛


                # ⚓ bkr_job_status
                  ⠀⇛


                # ⚓ What_packages_are_Needed_to_build_the_Kernel_|_Adam_Young’s
                  Web_Log⠀⇛


                       In my quest to automate the testing of the Linux
                       Kernel, I need to automate the build of the Linux
                       Kernel. To build the Kernel, you need the requisite
                       packages. What are they? Let’s find out.


                       I am staring with a Baremetal Fedora Image. It has
                       344 packages installed already. I’m going to assume
                       that this set is available when I do my automated
                       build as well, or that the needed packages will get
                       pulled in by dependencies. If not, I will find out
                       when my automation fails to run and I will add them
                       at that point.


                       Most Fedora and CentOS based documents on building
                       the Kernel have you do a group install of the
                       “Development Tools” yum package group. I don’t want
                       to do this for two reasons. First, I want to use
                       the beaker format which just lists the packages in
                       the job description. Second, I want to minimize the
                       non-required packages, and Development Tools is
                       general purpose group for coding; not everyone
                       needs everythingm, and I don’t want to put non-
                       essential packages on the system.


                # ⚓ Yaru-colors:_Give_Ubuntu_folders_a_colourful_Touch_–_Linux
                  Shout⠀⇛


                       We have a default theme Yaru on Ubuntu 20.04 LTS
                       and in other recent versions of Ubuntu Linux, to
                       give a new feel we can change the accent color of
                       this default theme using Yaru-colors.


                       Well, there are lots of customized themes available
                       to install & apply on Ubuntu, however, what if you
                       don’t want to change the default look of your
                       Linux. I mean the one your getting via Yaru. But
                       still need some new touch & feel on your system.
                       Then try out Yaru-Colors, it will be the visual
                       theme (style of widgets, colors, icons, and GNOME
                       Shell) for official them Yaru of Ubuntu. It is
                       increasingly polished and closely follows the line
                       marked by GNOME. However, not everyone likes the
                       combination and, changing the right thing, Yaru
                       Color is an ideal complement to get away from the
                       characteristic orange, but keep the essence of the
                       distribution.


                # ⚓ Android_9_on_Linux_|_Linux.org⠀⇛


                       Many people would sometimes like to have access to
                       Android. In this article, I will cover the steps to
                       install Android 9 on a Virtual Box machine.


                       Having access to Android on your system can make it
                       easier for accessing apps that are only available
                       on Android.


                # ⚓ How_to_install_the_latest_version_of_Minetest_on_a
                  Chromebook⠀⇛


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


                # ⚓ How_Can_You_Install_Google_Browser_on_Debian?⠀⇛


                       Google Chrome is a widely used web browser in the
                       world. Google Chrome is fast and secure as well.
                       However, it is not an open-source web browser.
                       Hence, Debian comes with a pre-loaded Chromium
                       browser, and not a Chrome. Chromium is an open-
                       source browser.


                       If you still want to install the Google Chrome
                       browser on Linux, this article is for you.
                       Installing Chrome on Linux has a little twist as
                       it’s not an open-source browser. So let’s check out
                       how you can easily install Chrome browser from a
                       Linux terminal.


                # ⚓ How_to_Install_and_Set_Up_PM2_on_Linux_Servers⠀⇛


                       Deployment is one of the most crucial and
                       conclusive stages of software development. A proper
                       deployment strategy is vital in delivering the best
                       experience to your users while utilizing your
                       services efficiently. However, this process also
                       brings its own set of challenges with it.


                       Node.js, the open-source JavaScript runtime, is a
                       popular choice for building the backend
                       infrastructure of your application by allowing you
                       to run JavaScript outside web browsers. But what if
                       your Node.js application crashes in production?
                       Find out how you can avoid such scenarios in this
                       article.


                # ⚓ Create_and_assign_Users_to_Oracle_Databases_–_Unixcop⠀⇛


                       Hi There ! In this write up, we will discuss about
                       how to create & assign users to the oracle DB


                       As always, begin by connecting to your server where
                       Oracle is hosted, then connect to Oracle itself as
                       the SYSTEM account.


                       The SYSTEM account is one of a handful of
                       predefined administrative accounts generated
                       automatically when Oracle is installed. SYSTEM is
                       capable of most administrative tasks, but the task
                       we’re particularly interested in is account
                       management.


                # ⚓ How_to_Start_Weblogic_Admin_and_Node_Manager_without
                  password_–_Unixcop⠀⇛


                       After installing Oracle Weblogic, it’s necessary to
                       give username & password every time it’s prompt.
                       It’s sometime a hassle, for some extent, we don’t
                       want to provide username & password every time.


                       Hello guys ! Today we will learn, how to start the
                       weblogic Admin Server & Node Manager without
                       providing username & password every time.


                       While starting the Admin Server (or) Managed
                       Servers for the first time after the domain
                       creation you must have been prompted for the
                       username and password, In order to handle it, there
                       is a task we need to do.


                # ⚓ How_to_install_OpenTTD_on_Elementary_OS_6.0_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       OpenTTD on Elementary OS 6.0.


                # ⚓ How_to_reset_weblogic_Admin_user_Password_–_Unixcop⠀⇛


                       Hi there ! In today’s write up, we will get to
                       know, how to reset the weblogic console/admin
                       password in case you forgot that. This might be a
                       shot article. If you want to learn more about
                       weblogic, please refer to my previous tutorial
                       about instllation & configuration weblogic 14c
                       server on centos 8 from here https://unixcop.com/
                       oracle-weblogic-14c-on-centos-8/


                       To reset the password, we first need to go the
                       weblogic domain home.


                # ⚓ How_to_Create_database_on_Oracle_Database_–_Unixcop⠀⇛


                       SQL statement is a more manual approach to creating
                       a database than using Oracle Database Configuration
                       Assistant (DBCA). One advantage of using this
                       statement over using DBCA is that you can create
                       databases from within scripts.


                       Hi guys ! In this write up, we will learn, how to
                       create database on oracle database using the manual
                       approach (CMD)


                       When you use the CREATE DATABASE statement, you
                       must complete additional actions before you have an
                       operational database. These actions include
                       building views on the data dictionary tables and
                       installing standard PL/SQL packages. You perform
                       these actions by running the supplied scripts.


                       To Create the database, we have to work through
                       step by step, we will discuss about these below.
                       Seat tight and hold your breath !


                # ⚓ Automate_SAP_HANA_System_Replication_in_Cluster_on_IBM
                  Power_Virtual_Servers_in_One_Hour [Ed: SUSE's Web site has
                  become too focused on selling SAP instead or promoting Free
                  software]⠀⇛


                # ⚓ How_to_install_Go_(Golang)_in_Arch_Linux/Manjaro_–
                  Citizix⠀⇛


                       This tutorial will help you install Go(Golang) on a
                       Manjaro/Arch Linux system. This guide can also work
                       for other Linux systems like Debian or Ubuntu or
                       Redhat based systems.


                       Go is a statically typed, compiled programming
                       language designed at Google by Robert Griesemer,
                       Rob Pike, and Ken Thompson. It’s has always been
                       said to be an easy language for developers to learn
                       quickly.


                       Golang is very useful for writing light-weight
                       microservices, infrastructure like networked
                       servers and also tools and systems for developers.
                       It can alsobe used for generating APIs that
                       interact with front-end applications. If you want
                       to build a small functional microservice quickly,
                       then Golang is a great tool to use.


                # ⚓ Give_Ubuntu_Folders_a_Colorful_Makeup_with_Yaru-Colors⠀⇛


                       Yaru-Colors is a theme project to bring different
                       colors to Ubuntu’s Yaru theme. Here’s how to
                       install it.


                       Yaru is the default theme for Ubuntu, backed by the
                       community. It is the user interface theme that has
                       been used in Ubuntu since 18.10. The name “Yaru”
                       follows the Japanese influence on Ubuntu’s theme
                       naming and it means “to do.”


                       But what is theme? In short, a theme is what
                       determines the colors, borders, shadows, size, and
                       shape of individual elements on the screen.


                # ⚓ How_to_Install_SaltStack_Minion_on_CentOS_8/_RHEL_8_–
                  Unixcop⠀⇛


                       Salt (sometimes referred to as SaltStack) is
                       Python-based, open-source software for event-driven
                       IT automation, remote task execution, and
                       configuration management. Supporting the
                       “infrastructure as code” approach to data center
                       system and network deployment and management,
                       configuration automation, SecOps orchestration,
                       vulnerability remediation, and hybrid cloud
                       control.


                       SaltStack minion is the agent software that is
                       installed on the managed node.


                       Used to execute and run the commands on that node
                       and report back to SaltStack master server.


                # ⚓ How_to_Install_SaltStack_Master_on_CentOS_8/_RHEL_8_–
                  Unixcop⠀⇛


                       Salt (sometimes referred to as SaltStack) is
                       Python-based, open-source software for event-driven
                       IT automation, remote task execution, and
                       configuration management. Supporting the
                       “infrastructure as code” approach to data center
                       system and network deployment and management,
                       configuration automation, SecOps orchestration,
                       vulnerability remediation, and hybrid cloud
                       control.


                       SaltStack Master is the server node, it is the
                       central server that controls all the Salstack
                       Minions.


                       Master server holds the Inventory and Public Keys
                       of Minions and perform remote execution on them.


                       The Salt master daemon, used to control the Salt
                       minions.


                # ⚓ Generate_File_of_Specific_Size_on_Linux_(With_Commands)_–
                  Linux_Nightly⠀⇛


                       Generating files of a specific size can be useful
                       for testing purposes. There are several different
                       commands in Linux that can create files of certain
                       sizes. Check out the commands and examples below to
                       learn how.


                # ⚓ How_To_Install_Brave_Browser_on_AlmaLinux_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Brave Browser on AlmaLinux 8. For those of you who
                       didn’t know, Brave is a free and open-source web
                       browser developed by Brave Software, Inc. based on
                       the Chromium web browser. Brave is a privacy-
                       focused Internet web browser, which distinguishes
                       itself from other browsers by automatically
                       blocking online advertisements and website trackers
                       in its default settings. Brave is also called a
                       “crypto browser” because it uses the Ethereum
                       blockchain that is used to secure user data.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you through the step-by-
                       step installation of the Django web framework on an
                       AlmaLinux 8. You can follow the same instructions
                       for CentOS and Rocky Linux.


                # ⚓ How_to_install_Go_in_Fedora_and_Rocky_Linux/Centos/RHEL_–
                  Citizix⠀⇛


                       This tutorial will help you install Go(Golang) on a
                       Fedora or a RHEL based system i.e. Centos/Rocky
                       Linux/Alma Linux/RHEL. This guide can also work for
                       other Linux systems like Debian and Ubuntu besides
                       the Redhat specifics like the running the yum
                       commands.


                       Go is a statically typed, compiled programming
                       language designed at Google by Robert Griesemer,
                       Rob Pike, and Ken Thompson. It’s has always been
                       said to be an easy language for developers to learn
                       quickly.


                       Golang is very useful for writing light-weight
                       microservices, infrastructure like networked
                       servers and also tools and systems for developers.
                       It can alsobe used for generating APIs that
                       interact with front-end applications. If you want
                       to build a small functional microservice quickly,
                       then Golang is a great tool to use.


                # ⚓ How_to_install_MX_Linux_21_–_Invidious⠀⇛


                       In this video, I am going to show how to install MX
                       Linux 21.


                # ⚓ Yarn_Introduction_and_Tutorial⠀⇛


                       Yarn is an abbreviation of “Yet Another Resource
                       Negotiator” and is a package manager of various
                       software programs. The best thing about yarn is
                       that it permits you to share and utilize code
                       securely and rapidly among distinct developers all
                       around the globe.


                       If you want to create your own software and you are
                       facing difficulty in it then Yarn will help you to
                       use the solution of other developers. When you are
                       using Yarn and there is an existing issue in it
                       then we will report it and when the issue is
                       resolved then you can again use the updated yarn.


                       Module or package is the means to share a code. The
                       package consists of a code along with all its
                       description in the “package.json” file.


                # ⚓ How_to_install_the_Tsurugi_Linux_distribution_–
                  TechRepublic⠀⇛


                       Digital forensics and incident response are
                       complementary activities that not only require
                       solid knowledge of operating systems and the
                       internet, but also a lot of tools, depending on the
                       desired goal. One investigator might want to simply
                       recover a file from a forensically acquired hard
                       drive, while another might want to do a full
                       analysis of a system and check multiple items about
                       it. Tsurugi Linux allows doing all of this.


                # ⚓ How_to_Convert_Between_Linux_Packages_Using_Alien⠀⇛


                       Do you want to convert a Linux package to some
                       other format? Perhaps the package you’re looking
                       for isn’t available for your distro but you still
                       want it no matter what. Or maybe you are a
                       developer and want to save your time by quickly
                       repackaging your program to other formats without
                       having to build the package again.


                       Fortunately, Linux has got the tool you need. With
                       Alien, you can easily convert your existing Linux
                       package to other formats through the command line.
                       Let’s start by installing the tool on your system
                       first.


                # ⚓ How_to_Boot_into_Rescue_Mode_or_Emergency_Mode_in_Ubuntu⠀⇛


                       Ubuntu and other Linux distributions often might
                       get broken due to many reasons. Sometimes, you may
                       just lose access to your operating system or forget
                       the root password. In those circumstances, chances
                       are that you would probably think of erasing your
                       current OS and reinstalling the Ubuntu OS again. In
                       addition, to back up the data you might also use
                       the GParted tool. But, all the above solutions are
                       really time-consuming and not so much techy-geeky
                       to recover an unbootable Linux OS. Instead of
                       reinstalling, you can boot into rescue mode or
                       emergency mode in Ubuntu to fix the system. Please
                       follow the methods mentioned below carefully if
                       you’re a newbie to Ubuntu and had already got your
                       system broken.


          o § Games⠀➾


                # ⚓ Godot_Engine_–_Multiplayer_in_Godot_4.0:_ENet_wrappers,
                  WebRTC.⠀⇛


                       Howdy Godotters! Time for yet another status update
                       on networking in Godot.


                       This time, we are going to dig a bit deeper into
                       the low-level territory, showing some of the new
                       ENet features exposed in Godot 4, and the effort of
                       bringing WebRTC on all Godot-supported platforms.


                # ⚓ Release_candidate:_Godot_3.4_RC_2⠀⇛


                       The upcoming Godot 3.4 release will provide a
                       number of new features which have been backported
                       from the 4.0 development branch (see our release
                       policy for details on the various Godot versions).
                       With this second Release Candidate, we have frozen
                       feature development and are nearly ready to release
                       the stable version.


                       If you already reviewed the changelog for RC 1, you
                       can skip right to the differences between RC 1 and
                       RC 2.


                # ⚓ Vintage_Arcade_Used_Negative_Voltage_To_Turn_Volume_Up_To
                  11_|_Hackaday⠀⇛


                       When [Nicole Express] got her hands on the logic
                       board for the 1986 SNK arcade game Athena, she ran
                       into a rather thorny problem: The board expected to
                       be fed negative five volts! [Nicole]’s analysis of
                       the problem and a brilliant solution are outlined
                       in her well written blog post.


                       [Nicole]’s first task was to find out which devices
                       need negative voltage. She found that the negative
                       five volts was being fed through a capacitor to the
                       ground pins on the Mitsubishi M151516L, an obscure
                       12 W audio amplifier. After finding the data sheet,
                       she realized something strange: the amp didn’t call
                       for negative voltage at all! A mystery was afoot.


                       To fully understand the problem, she considered a
                       mid-1980’s arcade and its cacophony of sounds. How
                       would a manufacturer make their arcade game stand
                       out? By making it louder, obviously! And how did
                       they make their game louder than the rest?


                # ⚓ Paradox_needs_a_bit_more_time_to_finish_Crusader_Kings_III
                  –_Royal_Court_|_GamingOnLinux⠀⇛


                       Crusader Kings III, the popular strategy game from
                       Paradox is expanding with the upcoming Royal Court
                       DLC but it’s just not ready yet.


                       Announced on Tuesday, October 26, Paradox said
                       plain and simply that “we are not, at the moment,
                       entirely satisfied with Royal Court’s progress,
                       especially regarding its stability” and so it’s
                       going to release at some point during 2022 but
                       they’re not giving us a date as to when just yet.
                       With this being the first CKIII expansion, Paradox
                       said it will include “a set of features entirely
                       new to the CK series, including cultural evolution
                       and language” and so they are continously
                       experimenting with it.


                # ⚓ Little_Big_Adventure_1_&_2_get_open_sourced_under_the_GPL⠀⇛


                       Little Big Adventure 1 and 2 are two classic titles
                       originally developed by Adeline Software
                       International and now they’ve both had their engine
                       source code officially released.


                # ⚓ Mind-bending_puzzler_Superliminal_is_getting_a_multiplayer
                  mode_|_GamingOnLinux⠀⇛


                       Superliminal is a pretty great puzzle game all
                       about using the ambiguity of depth and perspective
                       and to celebrate a year since the Steam release
                       it’s getting multiplayer.


                       In the main single-player game, you interact with
                       various objects in the world based on your position
                       and how you’re looking at them. It enables you to
                       grab these items, make them big or small and use
                       them to overcome some pretty fun puzzles. The new
                       mode is an “experimental” Battle Royale that will
                       be “available through the holiday season” (whatever
                       that means).


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE_Connect_Your_iPhone_to_Linux⠀⇛


                             One of the biggest benefits of being all-in
                             with Apple’s ecosystem is integration. My
                             text messages automatically appear on my Mac
                             and sharing files from iOS to macOS is a
                             breeze. Even the clipboard integrates my
                             mobile devices with my desktop. Now, a
                             project called KDE Connect brings much of
                             that tight integration to Linux.


                      # ⚓ I’m_livestreaming_Kalendar_development!⠀⇛


                             Today (Wednesday 27th Oct) at 18:00 CEST I
                             will be streaming some Kalendar development
                             live on YouTube and on KDE’s Peertube
                             instance.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ Makulu_Shift_Ubuntu_Variant_Released⠀⇛


                             We have just released the much awaited Beta
                             build of Shift ( the Ubuntu Variant ), It is
                             marked as a stable Build that can be used as
                             a daily Runner.


                      # ⚓ First_Shift_Patch_sent_out⠀⇛


                             We have just sent out the First big Patch for
                             the new Makulu shift ( Ubuntu Variant
                             released earlier today ). This patch now
                             completes the Desktop Manager and makes some
                             significant changes. Please keep in Mind that
                             Shift Ubuntu is a build we are now constantly
                             working on and updating, therefore you will
                             notice a lot of changes over a short period
                             of time, so expect many updates. ISO’s will
                             also regularly get updated on the Website.
                             You can see the Full video of what’s new in
                             the latest patch here :


                # § FSF-Approved⠀➾


                      # ⚓ Release_announcement:_Trisquel_9.0.1_Etiona_security
                        update⠀⇛


                             Images are available at https://
                             trisquel.info/download or directly at https:/
                             /cdimage.trisquel.info/ and its mirrors.


                             This minor update to the 9.x “Etiona” series
                             is intended to provide an up to date set of
                             ISO images, both for use as an installation
                             medium and as a live environment with newer
                             packages.


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


                      # ⚓ Min_Browser_»_PCLinuxOS⠀⇛


                             Min Browser has been updated to 1.22.0. Min
                             is a fast, minimal browser that protects your
                             privacy.


                      # ⚓ Zoom_»_PCLinuxOS⠀⇛


                             Zoom desktop has been updated to 5.8.3.145.
                             Zoom is a meeting client for the Linux
                             desktop.


                      # ⚓ Signal_Desktop_»_PCLinuxOS⠀⇛


                             Signal Desktop has been updated to 5.21.0.
                             Signal is Private Messenger for Linux.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ SUSE_heads_for_the_Edge_Computing_with_SUSE_Linux
                        Enterprise_Micro_5.1⠀⇛


                             Once upon a time, we got Linux distributions
                             because they were the Swiss-Army Knives of
                             operating systems. They came with every
                             program you might ever need. You can still
                             get those, of course. But, lately, businesses
                             have been wanting lightweight, secure Linux
                             distros for cloud and edge computing
                             containers and virtual machines (VM)s. To
                             meet that demand, the latest business-class
                             Linux is SUSE’s new SUSE Linux Enterprise
                             Micro 5.1 (SLE Micro).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Assess_resource_consumption_with_Ansible_callback
                        plugins⠀⇛


                             When you need metrics about playbook
                             execution, callback plugins can help you
                             drill down into the data and troubleshoot
                             issues.


                      # ⚓ Red_Hat_OpenShift_4_Migration:_Modernizing_your_cloud
                        platform⠀⇛


                             So you’re still using Red Hat OpenShift 3 in
                             your production environment, and everything
                             is running smoothly. “Why should I update to
                             Red Hat OpenShift 4? Version 3 works just
                             fine,” you might say.


                             Maintenance Support for Red Hat OpenShift
                             3.11 ends June 2022, followed by a final two-
                             year end-of-life phase. You might not be sure
                             how to start your migration to Red Hat
                             OpenShift 4 or understand what it offers. In
                             this post, we’ll walk you through some new
                             features and benefits to help you get
                             started.


                      # ⚓ Red_Hat_Developer_roundup:_Best_of_October_2021⠀⇛


                             We’re baaack (just in time for Halloween)
                             with the monthly highlights from our
                             developer experts working at Red Hat. This
                             month features hands-on introductions to VS
                             Code for Java extension 1.0, the new
                             developer console for Red Hat OpenShift 4.9,
                             and Helm Chart for Red Hat JBoss Enterprise
                             Application Platform. We also have a quick
                             guide to using Multipath TCP (included with
                             Red Hat Enterprise Linux 8) to cut through
                             the noise in your network. Keep reading for
                             these highlights and more.


                      # ⚓ Announcing_Service_Binding_Operator_1.0_GA_|_Red_Hat
                        Developer⠀⇛


                             In the context of Kubernetes, the exposure of
                             Secrets for connecting applications to
                             external services such as REST APIs,
                             databases, and event buses is manual and
                             bespoke. This action is usually referred to
                             as binding. The process of configuring and
                             maintaining the binding is error-prone and
                             can lead to challenges and debug failures.
                             Indeed, each service provider suggests a
                             different way to access their Secrets, and
                             each application developer in turn consumes
                             those Secrets in a custom way for their
                             applications.


                             Service Binding Operator 1.0, now in general
                             availability (GA), expands the developer
                             capabilities available on Red Hat OpenShift.
                             As we’ll see in this article, Service Binding
                             Operator makes it easy for developers to
                             connect their applications to backing
                             services like REST APIs, databases, event
                             buses, and others, providing a consistent and
                             predictable experience.


                      # ⚓ Send_S3_data_to_Telegram_with_Red_Hat_OpenShift
                        Serverless_Functions⠀⇛


                             Red Hat OpenShift Serverless Functions is a
                             framework with tooling to support function
                             development. The framework is built on top of
                             the open source Knative project. It has been
                             available in Tech Preview since Red Hat
                             OpenShift 4.7 and is available on 4.6 (EUS)
                             as well. The central tool in OpenShift
                             Serverless Functions is the kn func command,
                             a plug-in extending the Knative kn command-
                             line interface (CLI) to enable function
                             development on the Knative platform.


                             Development of this plug-in is led by Red Hat
                             through the Boson Project. This open source
                             project has generated interest in the Knative
                             community because function development
                             capabilities atop Knative have been long-
                             awaited and highly anticipated. The Boson
                             Project has been officially donated to the
                             Knative project and its community.


                             Let’s take a look at some of the new features
                             added recently to OpenShift Serverless
                             Functions. To demonstrate these capabilities,
                             we will implement a simple Quarkus function
                             that consumes data from an AWS S3 bucket and
                             sends it to a Telegram chat.


                      # ⚓ IT_careers:_10_ways_to_prove_yourself_during_remote
                        work_|_The_Enterprisers_Project⠀⇛


                             If an IT professional achieves a big win in
                             her home office in the country, does it make
                             a sound?


                             Perhaps you’re aware of the term “proximity
                             bias:” the unconscious human tendency to
                             favor what is closest to us. Veteran remote
                             workers have long been aware of the
                             predisposition for – and, in many cases, a
                             clear cultural practice of – valuing more
                             highly those employees who physically come
                             into the office every day. People now
                             navigating a hybrid work environment for the
                             first time may also see this dynamic.


                             “It can be difficult to prove your value in a
                             remote work situation because no one can see
                             you and get a visual sense of how you’re
                             performing,” says Cliff Milles, lead
                             technical recruiter at Sungard Availability
                             Services.


                             This can be a particular challenge for IT
                             leaders. “In more senior positions there is
                             more emphasis on relationship-building,
                             stakeholder management, and leading by
                             example, which then sets the tone and culture
                             for others,” says Lars Hyland, chief learning
                             officer of Totara Learning, a provider of
                             enterprise learning, engagement, and
                             performance management technology.


                      # ⚓ 4_IT_leadership_tips_for_turbulent_times_|_The
                        Enterprisers_Project⠀⇛


                             Even as many IT teams delivered results with
                             little disruption in the last 18 months, the
                             pandemic brought into focus the importance of
                             soft skills in technology leadership. This is
                             where businesses need to invest the most time
                             in the remaining weeks of 2021 and beyond.


                             Technical expertise has always been a given
                             in IT roles, but the ability to motivate
                             staff, help build their skills, and look
                             after their emotional wellbeing requires a
                             different set of capabilities entirely.
                             Successfully blending the two elements is the
                             ultimate challenge of any tech leader.


                             Here are some key areas to focus on to ensure
                             future success for your IT teams.


                      # ⚓ ELevate_project_to_simplify_migration_from_CentOS_7
                        to_RHEL_8_based_distributions⠀⇛


                             AlmaLinux distribution developers based
                             company CloudLinux in response to a premature
                             folding support CentOS 8, presented tools
                             ELEVATE , to simplify migration of operating
                             systems on CentOS 7.x distributions built on
                             packet-based RHEL 8, preserving applications,
                             data and settings. The project currently
                             supports migration to AlmaLinux, Rocky Linux,
                             CentOS Stream and Oracle Linux.


                             The migration process is based on the use of
                             the Leapp utility developed by Red Hat ,
                             which is supplemented with patches that take
                             into account the specifics of CentOS and
                             third-party distributions built on the RHEL
                             package base. The project also uses an
                             extended set of metadata describing the steps
                             for transferring individual packages from one
                             branch of the distribution to another.


                # § Debian Family⠀➾


                      # ⚓ Sparky_6.1_RC1_ARMHF⠀⇛


                             Sparky 6.1 Release Candidate 1 ARMHF for
                             single board machines RaspberryPi is out.


                             It is based on Debian Bullseye packages and
                             build using the pi-gen script.


                             The system works on Linux kernel 5.10.63 and
                             is available, as before, in two versions:
                             – Openbox – with small set of applications
                             – CLI – text mode only to do it yourself


                             user: pi, password: sparky
                             root user password: toor


                      # ⚓ Bluez_5.62_compiled_in_OpenEmbedded⠀⇛


                             EasyOS 3.1 has package bluez5 version 5.54.
                             There have been improvements since then, so I
                             have compiled 5.62 in OE.


          o § Devices/Embedded⠀➾


                # ⚓ Tiny_SBC_runs_Linux_on_new_RAM-equipped_Allwinner_RISC-
                  V_SoC⠀⇛


                       MangoPi is prepping a tiny “MangoPi-MQ1” SBC with
                       the new Allwinner F133-A (D1s), a spin-down of
                       Allwinner’s D1 that adds 64MB RAM. Both SoCs use
                       the XuanTie C906, one of several RISC-V cores that
                       Alibaba T-Head is now open sourcing.


                       A MangoPi project from Beijing Wadora Technology
                       Co. has announced a Linux-driven MangoPi-MQ1 SBC
                       equipped with a new Allwinner F133-A (D1s) SoC.
                       Allwinner’s F133-A is a slightly scaled down
                       version of the Allwinner D1 SoC, which powers
                       Sipeed’s Nezha SBC. Both SoCs are equipped with a
                       RISC-V architecture XuanTie C906 core, which last
                       week Alibaba’s T-Head subsidiary announced is being
                       open sourced along with several other cores (see
                       farther below).


                # ⚓ Raspberry_Pi_4_achieves_Vulkan_1.1_conformance,_gets_up_to
                  60%_GPU_performance_boost⠀⇛


                       Khronos has just granted Vulkan 1.1 conformance to
                       Raspberry Pi 4 SBC, and following the
                       implementation of various optimizations and new
                       features such as geometry shaders, the v3dv Mesa
                       driver delivers up to 60% higher GPU performance in
                       Unreal Engine 4.


                       Iglia started Vulkan driver work for Raspberry Pi 4
                       almost two years ago, with the triangle demo
                       showcased in February 2020, followed by Vulkan 1.0
                       conformance in November 2020, and now the driver is
                       certified conformant to Vulkan 1.1. While many GPUs
                       are conformant, the Raspberry Pi 4 is only joined
                       by a couple of complete platforms including several
                       NVIDIA Jetson modules (Vulkan 1.2), and possibly
                       some Intel and Google platforms shown as
                       “Confidential” at this time.


                # ⚓ CompuLab_IOT-GATE-RPI4_gateway_targets_industrial_control
                  and_monitoring⠀⇛


                       Compulab IOT-GATE-RPI4 is another industrial
                       gateway based on the Raspberry Pi CM4 module that
                       offers a different feature set and form factor
                       compared to solutions like TECHBASE iModGATE-AI
                       gateway or QWave Systems CatsPi Industrial carrier
                       board.


                       Designed with industrial control and monitoring in
                       mind, the IOT-GATE-RPI4 gateway offers multiple
                       RS485, RS232 and CAN FD ports, Ethernet, 4G LTE/4G,
                       WiFi 802.11ac, and Bluetooth 5.0 connectivity, as
                       well as a wide -40°C to 80°C operating temperature
                       range, plus a wide input voltage from 8V to 36V as
                       well as PoE support.


                # § Open Hardware/Modding⠀➾


                      # ⚓ ESP32_Clock_Takes_Time_to_Give_Weather_Info,_Too⠀⇛


                             It’s fall in the northern hemisphere, so
                             [Mike Rankin]’s kids are back in school and
                             have returned to consulting him every morning
                             about the weather and what they should wear.
                             Since he’s no meteorologist, [Mike] built a
                             beautifully dim and diminutive clock that
                             does all the work for him, plus much more. It
                             glows a lovely dark orange that’s perfect for
                             the nightstand and those early morning
                             interrogations.


                             In default mode, this clock displays the
                             time, CO2 level, room temperature, and
                             humidity in that eye-friendly orange. But
                             wave your hand in front of the time of flight
                             sensor, and it goes external, displaying the
                             low and high temperatures for the day, plus
                             the weather conditions forecast. After a few
                             seconds of that, it goes back to default
                             mode. The ESP fetches the time from an NTP
                             server, then gets the weather from the
                             OpenWeather API. The indoor weather comes
                             from a combination sensor on the board.


                      # ⚓ 3D_Printed_IoT_Weather_Station_Dashboard⠀⇛


                             This is my dashboard for my 3D Printed IoT
                             Weather Station project, you can build your
                             own by following my build guide.


                      # ⚓ I_Upgraded_My_3D_Printed_Weather_Station_Using_Your
                        Suggestions⠀⇛


                             Today we’re going to be making some upgrades
                             to my previously built IoT weather station
                             using suggestions that you guys made in the
                             comments section. We’ll see how well the
                             weather station performs after the upgrades
                             and I’ve included a link to the public
                             Thingspeak channel, so you can have a look at
                             the most recently recorded data.


                      # ⚓ Add_Mycelium_To_Your_Mesh_Networks⠀⇛


                             In many parts of the world, days after a good
                             rainfall, it’s fairly common to see various
                             species of mushrooms popping up out of the
                             ground. These mysterious organisms aren’t the
                             whole story, though. The living being is a
                             vast network of hidden fibers, called
                             mycelium, spreading through the ground and
                             into any other organic material it can
                             colonize. Its air of mystery and its vast
                             reach are the inspiration for entire Star
                             Trek shows and, of course, projects like this
                             LoRa-based mesh network called Mycelium.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Future_proof:_Fairphone_has_gone_5G⠀⇛


                             It is not new news that we strive to make the
                             most of the materials used in our products.
                             We’re moving closer to a circular economy by
                             using materials from more responsible
                             sources, emphasizing reuse and recycling, and
                             designing our phones to last as long as
                             possible. We do this for a simple reason: the
                             longer you use your phone, the smaller your
                             environmental footprint. But we want to take
                             this one step further and future proof your
                             phone. The only way to do this is to provide
                             you with a 5G device – a tech spec of the
                             future – for Fairphone 4.


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


                # § Events⠀➾


                      # ⚓ Virtual_Conferences:_a_love-hate_relationship⠀⇛


                             I love conferences. Now, that most
                             conferences are either virtual or hybrid
                             (both virtual and on-premises), people often
                             say that it must be heaven for me. I can
                             visit many more conferences and give many
                             more talks. Well, it is not just this simple.
                             Virtual conferences are a love-hate
                             relationship for me. Of course, there are
                             some advantages, but also disadvantages.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Tired_of_spam?_A_burner_email_account_could_be
                              the_answer.⠀⇛


                                   Have you ever been in that situation
                                   where you need to give your email
                                   address over, but you don’t want to?
                                   There could be a security reason. Can
                                   you trust who you’re sharing with not
                                   to spam your inbox? Are you certain
                                   they won’t expose you to data breaches
                                   due to lax security on their part? Can
                                   you protect your email from being sold
                                   in lists, used for ad tracking and
                                   targeting or even be uploaded to
                                   platforms like Facebook to track and
                                   target you there? Or it could be a case
                                   of inbox fatigue. Or maybe you just
                                   don’t want your email associated with
                                   some entities and in their database?
                                   Enter the burner email account.


                # § FSFE⠀➾


                      # ⚓ Router_Freedom_at_risk:_Latvia_allows_restrictions_to
                        consumers’_rights⠀⇛


                             Latvia’s reform of the telecom law weakens
                             Router Freedom in the country. The national
                             regulator, SPRK, has allowed ISPs to restrict
                             the use of personal routers on the grounds of
                             “technological necessity”. We explain why
                             this is problematic and what impact it can
                             have for end-users’ rights.


                             Router Freedom is the right end-users have to
                             choose and use their own modems and routers
                             to connect to the Internet. Since 2020,
                             European countries have been in a process of
                             implementing this right within a reform of EU
                             telecommunications law. In this context,
                             Latvia has created a risky precedent against
                             end-users’ rights by allowing internet
                             service providers (ISPs) to determine
                             restrictions on the use of personal routers
                             and modems based on “technological
                             necessities”. The FSFE has engaged with the
                             Latvian regulator, SPRK, to stress the
                             necessity to change the law as it represents
                             a big loss for consumer rights.


                # § Programming/Development⠀➾


                      # ⚓ A_Clang_compiler,_a_hidden_visibility,_and_a_weak
                        symbol⠀⇛


                             The LLVM packaging team recently ran into a
                             compiler problem. A build of the LLVM package
                             with Clang, with link-time optimization
                             activated, failed validation. This article
                             steps through how we explored, identified,
                             and ultimately fixed the problem.


    * § Leftovers⠀➾


          o ⚓ The_Animal_Years⠀⇛


                 Discussing why anthropomorphism came to dominate early
                 animation, and why that trend never really faded away,
                 while rubber-hose animation quickly did.


          o § Science⠀➾


                # ⚓ Product_release_cycles_are_killing_the_environment,_techies
                  tell_British_Computer_Society⠀⇛


          o § Health/Nutrition⠀➾


                # ⚓ Four_COVID_vaccine_shots._-FDA_(No_thanks.)⠀⇛


                       Now the FDA is saying we might “need” a fourth. I’m
                       not going to do it.


                       The third, for me, was the weirdest.


                       The side effects lingered for about a month before
                       they went away. They involved burning sensation in
                       my arm, slight chest pain, fatigue, some memory
                       problems, and hot flashes, and while it seems to be
                       over with, I don’t think I’ll be getting a fourth
                       shot. I can’t risk this getting worse each time.


                       How many of these things are you supposed to take?
                       How much are the side effects going to continue
                       escalating? And at what point has it either
                       “worked” or not “worked” well enough that you don’t
                       need any more doses for the foreseeable future?


                       [...]


                       If they wanted to throw gasoline on the anti-vaxxer
                       fire that was already raging, I can’t think of a
                       better way to do it.


                       This sends the message that no matter how many
                       doses you take, your phone will be buzzing off the
                       hook anyway and it’ll be the government stating
                       that you need more.


                       [...]


                       It’s bad enough to have to make choices like this
                       when you’re almost 40 and half your life is
                       probably over anyway, and certainly your prime
                       years, but children? This is going somewhere I had
                       hoped it wouldn’t.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Wednesday⠀⇛


                                   Security updates have been issued by
                                   Debian (mosquitto and php7.0), Fedora
                                   (python-django-filter and qt), Mageia
                                   (fossil, opencryptoki, and qtbase5),
                                   openSUSE (apache2, busybox, dnsmasq,
                                   ffmpeg, pcre, and wireguard-tools), Red
                                   Hat (kpatch-patch), SUSE (apache2,
                                   busybox, dnsmasq, ffmpeg, java-11-
                                   openjdk, libvirt, open-lldp, pcre,
                                   python, qemu, util-linux, and
                                   wireguard-tools), and Ubuntu (apport
                                   and libslirp).


                            # ⚓ Linux_Foundation:_confidential_computing_market
                              to_reach_$54_billion_in_2026 [Ed: ZDNet writing
                              more Linux_Foundation ‘spam’ today. They’re paid
                              to do this. They paint_surveillance_as_“security”
                              and_“confidential”.]⠀⇛


                            # ⚓ Kali_Linux_Wordlist:_What_you_need_to_know⠀⇛


                                   wordlist can be referred to as a
                                   password dictionary since it is a
                                   collection of passwords stored as plain
                                   text. Kali Linux is the most advanced
                                   penetration testing distribution. It is
                                   primarily designed for penetration
                                   testing and digital forensics hence
                                   funded and maintained by Offensive
                                   Security.


                                   Most Kali Linux wordlists can be
                                   downloaded online, including those
                                   provided in this article. In addition,
                                   there are a collection of common and
                                   uncommon passwords that are still or
                                   were once used by real people.
                                   Remember, you can also create your
                                   wordlist if you prefer to or stick to
                                   the ones already compiled. Wordlists
                                   are derived from data breaches such as
                                   circumstances where the company gets
                                   hacked. Data stolen from the hacked
                                   companies are leaked on websites such
                                   as Pastebin or sold on the dark web.


                            # ⚓ FBI_Releases_Indicators_of_Compromise
                              Associated_with_Ranzy_Locker_Ransomware⠀⇛


                                   The Federal Bureau of Investigation
                                   (FBI) has released a Flash report
                                   detailing indicators of compromise
                                   (IOCs) associated with attacks using
                                   Ranzy Locker, a ransomware variant
                                   first identified targeting victims in
                                   the United States in late 2020.


                            # ⚓ Warehouse_belonging_to_Chinese_payment_terminal
                              manufacturer_raided_by_FBI⠀⇛


                                   US feds were spotted raiding a
                                   warehouse belonging to Chinese payment
                                   terminal manufacturer PAX Technology in
                                   Jacksonville, Florida, on Tuesday, with
                                   speculation abounding that the machines
                                   contained preinstalled malware.


                                   PAX Technology is headquartered in
                                   Shenzhen, China, and is one of the
                                   largest electronic payment providers in
                                   the world. It operates around 60
                                   million point-of-sale (PoS) payment
                                   terminals in more than 120 countries.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ License_plate_scanners_were_supposed_to
                                    bring_peace_of_mind._Instead_they_tore_the
                                    neighborhood_apart.⠀⇛


                                         License plate readers are rapidly
                                         reshaping private security in
                                         American neighborhoods, bringing
                                         police surveillance tools to the
                                         masses with an automated watchdog
                                         that records 24 hours a day.


                                         With “safety-as-a-service”
                                         packages starting at $2,500 per
                                         camera a year, the scanners are
                                         part of a growing wave of easy-
                                         to-use surveillance systems
                                         promoted for their crime-fighting
                                         powers in a country where
                                         property crime rates are at all-
                                         time lows.


                                         Once found mostly in gated
                                         communities, the systems have —
                                         with help from aggressive
                                         marketing efforts — spread to
                                         cover practically everywhere
                                         anyone chooses to live in the
                                         United States. Flock Safety, the
                                         industry leader, says its systems
                                         have been installed in 1,400
                                         cities across 40 states and now
                                         capture data from more than a
                                         billion cars and trucks every
                                         month.


                                         “This is not just for million-
                                         dollar homes,” Flock’s founder,
                                         Garrett Langley, said. “This is
                                         America at its core.”


                                  # ⚓ Here’s_the_FBI’s_Internal_Guide_for
                                    Getting_Data_from_AT&T,_T-Mobile,_Verizon⠀⇛


                                         A newly obtained document written
                                         by the FBI lays out in unusually
                                         granular detail how it and other
                                         law enforcement agencies can
                                         obtain location information of
                                         phones from telecommunication
                                         companies.


                                         Much of the information
                                         reiterates what we already knew
                                         about law enforcement access to
                                         telecommunications data—how
                                         officials can request location
                                         data from a telecom with a
                                         warrant or use court orders to
                                         obtain other information on a
                                         phone user, for example. But the
                                         document does provide insights on
                                         what exactly each carrier
                                         collects, a more recent run-down
                                         of how long each telecom retains
                                         certain types of data for, and
                                         images of the tool the FBI makes
                                         available to law enforcement
                                         agencies across the country to
                                         analyze cell phone tower data.


                                         Ryan Shapiro, executive director
                                         of nonprofit organization
                                         Property of the People, shared
                                         the document with Motherboard
                                         after obtaining it through a
                                         public record act request.
                                         Property of the People focuses on
                                         obtaining and publishing
                                         government records.


                                  # ⚓ How_the_FBI_Gets_Location_Information⠀⇛


                                         Vice has a detailed article about
                                         how the FBI gets data from cell
                                         phone providers like AT&T, T-
                                         Mobile, and Verizon, based on a
                                         leaked (I think) 2019 139-page
                                         presentation.


                                  # ⚓ Google_said_it_had_successfully_‘slowed
                                    down’_European_privacy_rules,_according_to
                                    lawsuit.⠀⇛


                                         Google said in an internal
                                         document that it had successfully
                                         “slowed down” European privacy
                                         rules in collaboration with other
                                         tech companies, according to a
                                         legal filing released on Friday.


                                         Ahead of a 2019 meeting with
                                         other major tech companies,
                                         Google said in a memo that it had
                                         “been successful in slowing down
                                         and delaying” the European
                                         Union’s ePrivacy Regulation
                                         process and had been “working
                                         behind the scenes hand in hand
                                         with the other companies,”
                                         according to the filing.


                                  # ⚓ More_than_100,000_people_have_had_their
                                    eyes_scanned_for_free_cryptocurrency⠀⇛


                                         More than 100,000 people have had
                                         their eyes scanned in return for
                                         a cryptocurrency called
                                         Worldcoin, as a project to
                                         distribute digital money more
                                         widely around the world
                                         accelerates.


                                         Worldcoin has distributed about
                                         30 iris-scanning hardware
                                         devices, which they call “orbs,”
                                         to early users on four
                                         continents, who get rewards for
                                         signing up more people. Orbs take
                                         photos of a user’s eyeballs,
                                         creating a unique code that can
                                         be used to claim free digital
                                         tokens.


          o § Environment⠀➾


                # ⚓ Plastic_industry_pollution_to_overtake_coal_in_US_by_2030,
                  report_says⠀⇛


                       Plastic pollution usually conjures images of
                       grocery bags blowing in the wind or nurdles lodged
                       in a seabird’s stomach. But soon, plastic pollution
                       may take on another meaning, as a new report
                       forecasts that the industry’s greenhouse gas
                       emissions in the US will outpace those of coal by
                       the end of the decade.


          o § Civil Rights/Policing⠀➾


                # ⚓ EU_fines_Poland_€1_million_per_day_over_judicial_reforms⠀⇛


                # ⚓ U.S._FTC_needs_rulemaking_to_protect_privacy_and_civil
                  rights_–_Access_Now⠀⇛


                       Today, Access Now joined Free Press and partner
                       organizations in calling on the U.S. Federal Trade
                       Commission (FTC) to initiate a rulemaking to
                       protect privacy, promote civil rights, and set data
                       protection standards. This call aligns with
                       Senators’ request for the same rulemaking process.


                       How data is collected, processed, and shared has a
                       direct impact on economic opportunities and falls
                       squarely within the FTC’s authority. Companies use
                       personal data to enable and even perpetuate
                       discriminatory practices against people of color,
                       women, members of the LGBTQ+ community, religious
                       minorities, people with disabilities, and other
                       marginalized groups.


                # ⚓ Where_the_EU’s_DSA_is_heading_—_and_where_it_needs_to_go_–
                  Access_Now⠀⇛


                       The EU Digital Services Act (DSA) is an ambitious
                       proposal with the potential to empower people in
                       today’s online ecosystem. It is the first
                       legislative proposal worldwide that seeks to
                       establish systemic regulation of “Big Tech”
                       platforms like Facebook or Google to address their
                       impact on public discourse. If done right, the DSA
                       could be an effective tool for preventing the
                       spread of illegal content, protecting fundamental
                       rights, and correcting the power imbalance between
                       users and platforms. Done wrong, however, the DSA
                       could harm the vulnerable communities it is
                       supposed to help, and erode the freedom of
                       expression and opinion — not just in the EU but
                       around the world.


                       So where does this promising regulation stand now?
                       And what needs to happen to ensure its efficacy? We
                       look at the introduction of the DSA, how the
                       negotiations have progressed, and where we need to
                       go from here to safeguard human rights.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Disney+_streams_to_Linux-based_VIDAA_Smart_OS⠀⇛


                       Disney+, a world-renowned streaming application,
                       and VIDAA, a Linux-based smart TV operating system,
                       announced that Disney+ will be coming soon to VIDAA
                       Smart OS-powered Hisense and Toshiba smart
                       televisions, with the latest firmware version.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Marxist_Astronomy:_The_Milky_Way_According_to_Anton
                        Pannekoek_–_The_Public_Domain_Review⠀⇛


                             Can a person’s experiences on earth alter how
                             they perceive the stars? Lauren Collee peers
                             through the telescope of Anton Pannekoek, the
                             Dutch astronomer whose politics informed his
                             human approach to studying the cosmos.


                      # ⚓ William_Baillie-Grohman’s_*Sport_in_Art*_(1913)_–_The
                        Public_Domain_Review⠀⇛


                             William Baillie-Grohman’s text on the art of
                             hunting reproduces 243 illustrations and 400
                             years of arcane knowledge related to the
                             pursuit of animals.


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