𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, September 10, 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/2021/09/10/


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

⦿ EPO Exposé: The Besieged Baltic States – Part IXX – The EUIPO Connection | Techrights

⦿ [Meme] The Coloniser Campinos, Preying on the Poor | Techrights

⦿ [Meme] [Teaser] Thanking and Rewarding My Rigga’ in Riga | Techrights

⦿ Challenging David Kappos, Seeking Accountability Over His Corporate Legacy as IBM/Microsoft ’Mole’ Inside the U.S. Patent and Trademark Office | Techrights

⦿ [Meme] 12 Years of Corporate Deplorables Running the USPTO | Techrights

⦿ What Patent Colonialism Looks Like | Techrights

⦿ IRC Proceedings: Thursday, September 09, 2021 | Techrights

⦿ [Meme] EPO and EUIPO Aren’t Democratic Institutions | Techrights

⦿ [Meme] ’Open Source’ Study/Report From the European Commission Promotes Software Patents in Europe | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/09/10/baltic-euipo-connection/#comments
		http://techrights.org/2021/09/10/campinos-colonies/#comments
		http://techrights.org/2021/09/10/campinos-rigging/#comments
		http://techrights.org/2021/09/10/challenging-david-kappos/#comments
		http://techrights.org/2021/09/10/corporate-uspto/#comments
		http://techrights.org/2021/09/10/epo-patent-colonialism/#comments
		http://techrights.org/2021/09/10/irc-log-090921/#comments
		http://techrights.org/2021/09/10/rigging-epo-and-euipo/#comments
		http://techrights.org/2021/09/10/study-european-commission/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/09/10/liveslak-1-3-10/#comments
		http://techrights.org/2021/09/10/sci-hub-turns-10/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 72

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/baltic-euipo-connection/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/baltic-euipo-connection/

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Gemini_version_available_♊︎


✐ EPO_Exposé:_The_Besieged_Baltic_States_–_Part_IXX_–_The_EUIPO_Connection⠀✐


Posted in Europe, Patents at 12:07 am by Dr. Roy Schestowitz


Series index:


   1. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_I_–_More_Captured
      Delegates?
   2. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_II_–_Old_Wine_in_New
      Bottles…
   3. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_III_–_Introducing_the
      Finnish_“Facilitator”
   4. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_IV_–_Martti_Enäjärvi_and
      His_“Good_Brother”_Networks
   5. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_V_–_A_Man_With_a
      Conviction…
   6. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_VI_–_“A_Good_Friend_of
      Estonia_and_a_Steady_Cooperation_Partner”
   7. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_VII_–_A_Self-Appointed
      “Select_Committee”
   8. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_VIII_–_Pulling_for_the
      Portuguese_Pretender?
   9. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_IX_–_António’s_Faithful
      Acolyte_in_Alicante
  10. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_X_–_A_Pan-European_“Good
      Brother”_Network_Celebration?
  11. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XI_–_With_a_Little_Help
      From_My_Friends…
  12. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XII_–_Battistelli_and_His
      Baltic_Fiefdoms
  13. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XIII_–_Out_With_the_Old,_in
      With_the_New?
  14. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XIV_–_Business_as_Usual_in
      Tallinn
  15. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XV_–_Worse_Than_“a_Backward
      Kolkhoz”…
  16. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XVI_–_A_Promising_Start
      Followed_by_an_Unfortunate_Cock-Up
  17. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XVII_–_Secret_Bank_Accounts
      in_Switzerland_and_Germany
  18. EPO_Exposé:_The_Besieged_Baltic_States_–_Part_XVIII_–_A_Baltic_Circus_in
      Riga
  19. You are here ☞ The EUIPO Connection
                       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Ieva-Viļuma⦈_

António_Campinos on an OHIM mission to Riga (Latvia) in September 2013 where he
was received by the acting director of the Latvian Patent Office, Ieva Viļuma.


Summary: The Baltic ‘crusade’ of Tony, son_of_the_“Carnation_Revolution”, goes
more than a decade back


The main theme of the present series so far has been the relationship between
the national patent offices of the Baltic States and the European Patent
Organisation.


“The main theme of the present series so far has been the relationship between
the national patent offices of the Baltic States and the European Patent
Organisation.”In this part the focus will shift to the connections between
these national offices and the EU trademark agency EUIPO (formerly known as
OHIM).


In this regard, it is important not to lose sight of the fact that the “patent
offices” of the Baltic States are not limited to dealing with patents. They are
also responsible for other aspects of “IP” administration such as the
registration of trademarks and industrial designs.


“In this regard, it is important not to lose sight of the fact that the “patent
offices” of the Baltic States are not limited to dealing with patents.”This
means that these “patent offices” play an equally significant role in the
political horse-trading that goes on in the context of the EU’s trademark
agency EUIPO.


Indeed, it is probably fair to say that EUIPO – rather than the EPO – is the
more important institution for the Baltic States, at least from the perspective
of their local economies.


This is because these states have a relatively_low_level_of_patenting_activity,
especially when compared to the more developed member states of the EPO, such
as their Nordic neighbours Denmark, Sweden and Finland. The small size of the
domestic markets also means that these countries are of secondary interest to
foreign multinationals seeking patent protection in Europe.


“…these “patent offices” play an equally significant role in the political
horse-trading that goes on in the context of the EU’s trademark agency
EUIPO.”However, despite the fact that their industrial manufacturing economies
are not so well developed, the Baltic States have a long tradition as
mercantile trading nations going back to the days of the Hanseatic_League.


For this reason, other forms of “IP” – in particular trademarks and industrial
designs – are of more significance for the primary economic activities of these
countries.


Just like his mentor Benoît_Battistelli, António Campinos is fully aware of the
importance of “capturing” the Baltic votes. This is demonstrated by his
presence at the secretive_conclave which took place in Tallinn in January 2010
when he was preparing_his_bid to become Chief Executive of the EU trademark
agency OHIM/EUIPO.


“The small size of the domestic markets also means that these countries are of
secondary interest to foreign multinationals seeking patent protection in
Europe.”Following the success of his efforts to secure the top job in Alicante
in 2010, Campinos was a regular visitor on the Baltic “IP” circuit.


For example, he turned_up_in_Riga_in_September_2013 [PDF] where he was received
by the “acting director” of the Latvian Patent Office, Ieva Viļuma.


The following month he attended an EU-sponsored conference on “Intellectual
property_protection_in_the_EU:_risks,_challenges_and_prospects” which took
place in the Lithuanian capital Vilnius on 8 and 9 October 2013.


“…Campinos turned up in the Estonian capital Tallinn where he met with the
newly appointed Director-General of the Estonian Patent Office, Margus Viher.”A
year and a half later, Campinos was back in Riga at an international conference
“Intellectual_Property_and_Beyond” which took place on 3 and 4 March 2015. This
conference was organized by the World Intellectual Property Organization (WIPO)
in cooperation with the Latvian Patent Office, the Latvian Presidency of the
Council of the European Union, and OHIM/EUIPO.


Campinos was billed as a guest_speaker_to_deliver_a_talk [PDF] on the topic of
“European Trade Mark and Design Network (ETMDN) – New Challenges Ahead”.


Some months later, in October_2015, Campinos turned up in the Estonian capital
Tallinn where he met with the newly appointed Director-General of the Estonian
Patent Office, Margus Viher.


                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Campinos-Tallinn⦈_
       Campinos on an OHIM mission to Tallinn (Estonia) in October 2015.


During his tenure as head of the EU trademark agency EUIPO, Campinos carefully
cultivated the goodwill of the Latvian, Lithuanian and Estonian “patent
offices”. By doing so he made sure that he could count on the three Baltic
votes in 2017 when he was lining himself up for election as Battistelli’s
successor at the EPO in Munich.


“During his tenure as head of the EU trademark agency EUIPO, Campinos carefully
cultivated the goodwill of the Latvian, Lithuanian and Estonian “patent
offices”.”In the final part of the series we will continue our examination of
the interaction between the Baltic States and EUIPO and conclude by attempting
to shed some light on the sudden and unexpected departure of Sandris
Laganovskis from the Latvian Patent Office towards the end of 2020. █


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⠜⠉⠉⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⢀⢠⣴⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⠑⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠙⢿⣿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣦⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡍⠁⠄⠈⣽⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣽⣓⣀⣀⣀⡀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 264

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/campinos-colonies/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/campinos-colonies/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Coloniser_Campinos,_Preying_on_the_Poor⠀✐


Posted in Deception, Europe, Patents at 1:09 am by Dr. Roy Schestowitz


Related: Ethiopian_Media_Gamed_by_EPO_Management,_Just_Like_European_Media


2 days ago: (EPO.org_URL)


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


A decade of EUIPO rigga’ in Riga:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Latvia_is_very_important_for_us;_Some_voters_are_cheaper
than_others⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Latvia_is_very_important_for_us;_Some_voters_are_cheaper
than_others⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Portugal_flag:_Then_you_shoot_the_campinos_(farmers)_who
resist_the_occupation⦈_


Summary: EPO President António_Campinos is still doing in former Portuguese
colonies what Benoît_Battistelli used to do in former French colonies (and
beyond)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠠⠤⡅⠠⠌⡏⣡⣬⢹⣿⠛⠛⡟⣛⢻⢛⡃⣿⣿⢃⠹⡇⠤⠌⡋⢸⠠⠌⠙⢡⣤⠙⣿⡇⡟⠛⠟⢻⠛⠛⡛⠟⣛⠋⢘⠛⣿⡟⡛⢛⢻⢛⠛⡇⠟⣛⢻⢛⣿⡋⡛⢛⠛⠛⡇⡟⢛⢻⢸⢛⡛⠟⡛⢻⣿⣿
⣿⣇⣘⣛⣃⣰⣾⣧⣙⣋⣼⣿⣐⣂⣃⣿⣸⣘⣁⣿⣇⣶⣆⣁⣶⣌⣃⣸⣰⣶⣷⣈⣋⣰⣿⣇⣄⣂⣠⣘⣀⣀⣇⣀⣛⣁⣸⣀⣿⣇⣇⣸⣸⣐⣀⠃⣆⣛⣸⣸⣿⣇⣃⣸⣐⣂⣃⣇⣿⣸⣸⣸⣇⡄⠃⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿
⣿⡏⢡⠉⢉⡌⣤⢹⢡⡍⡏⡼⠁⠈⠉⡌⢡⢹⢨⠈⡌⡏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣤⣴⣴⣷⣤⣼⡂⢀⣧⣷⣬⣦⣤⣧⣼⣼⣼⣤⣧⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⠙⠿⠿⢿⠿⠿⠟⠻⠿⡿⢿⡿⠿⠿⠿⠿⢿⠿⠿⡿⠿⢿⠿⠿⣿⣿⠿⠿⡿⠿⢿⠉⣿⠿⢿⠿⠿⢿⠿⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⣶⡅⠒⢈⠀⢾⡇⠘⡄⠃⠸⡀⠇⢸⡀⠇⠸⠀⠅⡀⠌⢸⠀⠄⣽⣯⠐⠗⡄⠒⢨⠀⢇⠸⢀⠇⠸⠘⣆⢀⣿⣿
⣿⡿⢿⠿⠿⠿⠿⢿⠿⠿⠟⢿⠿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣾⣿⣿
⣿⣧⣼⣥⣤⣄⣤⣤⣤⣤⣤⣥⣤⣼⣥⣤⣤⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⣿⢿⠿⡿⢿⠿⠿⠿⠿⣿⢿⢿⠿⠿⠿⡿⠿⠿⣿⡿⡿⢿⠿⡿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠋⠰⠻⡿⠿⠿⢿⠿⡿⠻⠿⠿⢿⠿⠿⠿⠿⠿⠻⢿⡿⠿⢿⠿⠿⠿⠿⡿⠿⢿⠿⢿⠿⠿⠟⢿⢿⢿⣿
⣿⣧⣤⣯⣤⣤⣧⣤⣦⣤⣤⣤⣧⣥⣤⣧⣤⣼⣤⣤⣄⣼⣬⣤⣼⣤⣯⣤⣤⣨⣤⣤⣤⣤⣤⣤⣌⣧⠀⣴⣦⣥⣧⣶⣤⣤⣤⣬⣤⣤⣤⣭⣦⣼⣤⣤⣤⣤⣵⣮⣥⣤⣤⣄⣥⣼⣤⣤⣼⣤⣥⣁⣤⣤⣤⣤⣼⣿
⣿⡏⠉⠉⠉⡏⠍⠋⢹⠉⠋⠋⠉⠙⢹⡋⠋⡏⠉⠋⢻⢉⠉⠉⠉⠉⢩⢻⠉⠉⠋⠉⠉⢩⠋⠃⠉⠁⠈⠙⠉⠙⠉⠉⠙⠹⢹⢉⢉⠉⠉⠋⠋⠉⢹⠩⠉⡉⠉⠉⡍⠍⠋⠋⠉⠉⢹⠫⢉⠏⠉⠉⡉⠭⡉⣿⣿⣿
⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡷⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⡿⠿⠿⡿⣿⣿⢿⣿⡾⣿⣿⣷⣿⡿⣿⣷⢾⣿⢿⣿⣿⡿⣿⢿⣿⡷⡿⠿⣿⣿⡿⣿⣾⣿⠿⣿
⣿⣧⣤⣦⣤⣧⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣇⣤⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣬⣤⣤⣇⣀⣀⣀⣀⣀⣀⣧⣤⣦⣤⣧⣤⣤⣤⣤⣠⣤⣤⣧⣤⣤⣴⣤⣤⣤⣤⣼⣤⣤⣤⣷⣤⣴⣤⣤⣤⣧⣦⣤⣀⣠⣤⣤⣤⣤⣿
⣿⡟⠹⠉⡋⢉⡋⠝⡏⡙⠛⠙⠛⠛⢻⠉⠙⠛⠛⠛⠙⠛⠛⠉⠛⠛⣯⢩⠛⠋⢛⠙⡛⠛⡟⠛⡛⠛⠛⠛⠛⠛⢛⠛⠛⡟⠍⠋⡉⢉⡉⢩⢩⡟⡛⠛⠛⠛⡛⠛⠛⢛⠛⠛⡙⣿⢩⠙⠙⠻⡏⠛⡋⠙⠛⣿⣿⣿
⣿⡷⣷⣾⣾⣾⣷⢾⣷⣿⣶⣶⣶⣿⣾⢶⡾⣷⣶⣶⣶⣿⣶⣶⣾⣾⣿⣾⣷⣶⣾⣿⣷⣶⢷⣾⣷⣶⢾⣷⣶⣾⢿⣷⡶⢷⣾⣷⠷⠾⢷⠶⣿⣷⢾⡷⣶⣾⠷⢶⣿⣿⣷⣶⣾⣿⣿⡾⡿⣾⣿⣾⣷⣷⣷⣿⣿⣿
⣿⣇⣀⣠⣂⣀⣀⣸⣄⣄⣄⣀⣧⣠⣀⣀⣄⣰⣀⣸⣀⣰⣀⣀⣠⣀⣀⣀⣰⣀⣸⣀⣰⣐⣀⣀⣔⣀⣀⣀⣠⣿⣀⣠⣇⣰⣄⣼⣀⣃⣤⣃⣴⣀⣤⣂⣸⣀⣀⣠⣢⣠⣀⣇⣀⣠⣂⣤⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠭⠛⠛⡛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣵⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠉⠛⣿⡍⠙⠛⠛⠛⠿⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⢃⠃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠦⠀⡀⠀⡀⠈⠀⠀⠆⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⣀⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠉⠉⠉⢿⣿⣿⡿⠟⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣴⣄⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣯⣭⣭⣭⣩⣅⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⢠⣿⣿⣧⣿⣿⣿⣿⣿⣿⠃⠀⣐⠒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣭⣭⣍⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⠛⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠡⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⢿⡅⢈⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣶⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣤⣌⠉⠉⠉⠉⠙⠀⠀⠀⠙⠿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢹
⠁⠀⠀⠈⠉⢻⣿⣿⡿⢿⡿⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⣿⡟⢰⣷⠶⢶⡆⠀⠀⠀⠀⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠙⠿⢿⣟⣾
⠀⠀⠀⡀⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⣿⣿⣿⠁⢰⣿⠉⠁⡈⠏⠀⠸⠃⠀⠈⠒⣤⣈⣉⠀⠈⢻⣿⣿⣿⣿⣿⣿⡆⣠⣴⡿⠻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⠃⣿⣿⠇⠀⢸⡟⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠙⠟⠁⠀⠋⠀⣠⣿⡟⠀⠀
⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠈⠉⠙⠛⠛⠛⠘⠛⠛⠋⠙⠸⢿⢿⡇⠀⢸⣿⠂⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠀⠀⣿⡆⠈⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⠁⣤⠘⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢘⣷⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢫⣤⣀⣰⣇⡌⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣯⣐⣿⡀⠫⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀
⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⢿⣿⠟⠉⠀⠈⣿⣿⣿⣿⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣶⣶⣶⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠠⠻⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⡿⢿⣿⢿⣿⣷⡀⣿⠿⣿⡿⢿⣿⡿⠿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠂⣾⣷⡔⣶⣶⡔⢰⣶⣶⢴⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡂⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⢸⣿⣿⢸⣟⢸⡿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣍⣴⣭⡄⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⡈⠁⣉⣩⣭⣭⡌⣩⣾⡎⢉⣤⡝⠋⣀⣉⠉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣶⣌⠙⢿⣿⣾⣿⠟⠁⠸⢿⡇⢸⣿⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⢨
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣵⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠉⠛⣿⡍⠙⠛⠛⠛⠻⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⢋⠁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠉⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣀⣒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠉⠉⠉⢿⣿⣿⡿⠟⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣴⣄⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣯⣭⣭⣭⣩⣅⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⣷⣧⣿⣿⣿⣿⣿⣿⡃⠀⢰⢒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠬⣶⣼⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣭⣭⣍⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⠛⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡟⠡⠾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⢿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣴⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣤⣌⠉⠉⠉⠉⠙⠀⠀⠀⠙⠿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹
⠁⠀⠀⠀⠉⠻⣿⣿⡿⢻⡿⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢉⣿⡟⢰⣷⠶⢶⡆⠀⠀⠀⠀⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠙⠿⢿⣟⣾
⠀⠀⠀⡀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⣿⠋⠁⡈⠏⠀⠸⠃⠀⠈⠒⣤⣈⣉⠀⠈⢻⣿⣿⣿⣿⣿⣿⡦⣠⣴⡿⠻
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡇⣿⣿⡏⠀⢀⣟⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠙⠟⠁⠀⠏⠀⣠⣿⡟⠀⠀
⠀⠀⠀⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠈⠉⠙⠛⠛⠛⠘⠛⠛⠋⠙⠰⢿⢿⡇⠀⠘⣿⠂⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠀⠀⣿⡇⠀⢿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⠇⣠⠀⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢫⣤⣀⣰⣇⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣀⣿⡄⠉⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀
⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⢿⣿⠟⠉⠀⠈⣿⣿⣿⣿⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣦⣶⣶⣄⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠻⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⡿⢿⣿⢿⣿⣷⠀⣿⠿⣿⡿⠿⣿⡿⢿⡇⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠐⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡔⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡂⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⢸⣿⣿⢸⣟⢸⡟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣩⣭⣍⣍⣴⣭⡄⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⣈⠁⣉⣩⣭⣭⡌⣩⣾⣮⢉⣤⣝⠋⣀⣉⠉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣷⣄⠙⢿⣿⣿⣿⠟⠁⠸⢿⡇⢰⣿⣿⣷⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣵⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠉⠛⣿⡍⠙⠛⠛⠛⠻⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⢍⠁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠦⠀⡀⠀⡀⠈⠀⠀⠂⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣒⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠙⠉⠉⠉⢿⣿⣿⡿⠟⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣴⣄⣀⡀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣯⣭⣭⣭⣩⣅⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠐⠀⠀⢠⣿⣷⣧⣿⣿⣿⣿⣿⣿⠃⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡬⣶⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣭⣭⣍⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⠛⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣉⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠡⠾⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⢿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣶⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣤⣌⠉⠉⠉⠉⠙⠀⠀⠀⠙⠿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠉⠀⠉⠛⣿⣿⡿⢿⡿⢻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠉⣿⡟⢰⣷⠶⢶⡆⠀⠀⠀⠀⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⡙⠿⠿⣟⣾
⠀⠀⠀⡀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡃⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⣿⣿⣿⠋⠀⣾⠋⠁⡈⡏⠀⠸⠃⠀⠈⠒⣤⣈⣉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⣠⣴⡿⠻
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡇⣿⣿⡟⠀⠀⣿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠙⠟⠁⠀⠏⠀⣤⣿⡟⠀⠀
⠀⠀⠀⢠⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠉⠉⠛⠛⠛⠛⠚⠛⠛⠋⠙⠰⢿⢿⣷⠀⠀⣿⠀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠀⠀⣾⡇⠀⢿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⡏⢀⠀⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢯⣤⣀⣰⣆⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣀⣾⡄⢹⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀
⡄⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⠿⠋⠀⠈⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣶⣿⣿⣷⢽⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣦⣶⣶⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠠⠻⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡆⠀⠀⠀⡿⢿⣿⢿⣿⣷⠀⣿⠿⣿⡿⢿⣿⡿⠿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⠱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠐⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢳⣆⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠂⣾⣷⡔⣶⣶⡄⢰⣶⣶⢲⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡂⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣍⣴⣭⡄⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⡈⠁⣉⣩⣭⣭⡌⣩⣾⣮⢉⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣷⣌⠙⢿⣿⣾⣿⠟⠁⠸⢿⡇⢰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣵⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠉⠛⣿⡍⠙⠛⠛⠛⠻⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⢍⠁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠶⣀⡀⠀⡀⠈⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠉⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠙⠉⠉⠉⢽⣿⣿⡿⠿⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣴⣄⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣯⣭⣭⣭⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⢠⣿⣿⣧⣿⣿⣿⣿⣿⣿⡃⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡬⢶⣼⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣭⣭⣍⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⠛⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⡟⠡⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⣿⣏⠉⣻⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣤⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣤⣬⠉⠉⠉⠉⠙⠀⠀⠀⠹⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⡀⠉⠀⠉⠛⣿⣿⡿⢿⡿⢻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠉⣻⡟⢰⣷⠶⢶⡆⠀⠀⠀⠀⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⡙⠿⠿⣟⣾
⠀⠀⠀⠀⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⡓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⣿⣿⣿⠏⠀⣾⠉⠁⡈⡟⠀⠸⠃⠀⠈⠒⣤⣌⣉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⣠⣴⡿⠻
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡇⣿⣿⡟⠀⠀⣿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠙⠟⠁⠀⠏⠀⣤⣿⡟⠀⠀
⠀⠀⠀⢠⡀⠈⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠉⠉⠛⠛⠛⠛⠚⠛⠛⠋⠙⠐⢿⢿⣷⠀⠀⣿⠀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀
⠀⠀⠀⣼⣇⠀⢿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⡿⠀⠀⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠹⣹⣿⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢘⣿⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢯⣤⣀⣰⣇⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣁⣾⡆⢉⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀
⡄⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⢿⣿⠿⠋⠀⠈⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⢿⣤⣶⣦⣄⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠾⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡆⠀⠀⠀⡾⢿⣿⢿⣿⣷⠀⡿⠿⣿⡿⢿⣿⡿⠿⡇⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠐⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡖⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠂⣾⣷⡔⣶⣶⡄⢰⣶⣶⢰⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡀⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⢸⣿⣿⢸⣟⢸⡟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣍⣴⣭⡄⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⡈⠁⣉⣩⣭⣭⡌⣩⣾⣮⢉⣤⣝⠋⣀⣉⠉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣷⣄⠙⢿⣿⣾⣿⡿⠋⠸⢿⡇⢰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣵⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠛⣿⡍⠙⠛⠛⠛⠻⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⢍⠃⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢶⣀⡀⣀⠀⠈⠀⠀⠊⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣒⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠙⠋⠉⠉⢿⣿⣿⡿⠿⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣰⣄⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣯⣭⣭⣭⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠐⠀⠀⢠⣿⣷⣧⣿⣿⣿⣿⣿⣿⡃⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠤⣴⣼⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣽⣭⣭⣍⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⠛⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠡⠾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢛⣤⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣤⣌⠉⠉⠉⠉⠙⠀⠀⠀⠹⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⡀⠉⠀⠈⠙⢿⣿⡿⢿⡿⢻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠋⣹⡟⢰⣷⠶⢶⡆⠀⠀⠀⠈⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⡙⠿⠿⣟⣾
⠀⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⣿⣿⣿⡏⠀⣶⠉⠁⡈⡟⠀⠸⠃⠀⠈⠲⣤⣈⣉⠁⠈⢻⣿⣿⣿⣿⣿⣿⣦⣠⣴⡿⠻
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡿⠀⠀⣿⠀⠘⠇⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠙⠟⠁⠀⠏⠀⣠⣿⡟⠀⠀
⠀⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠉⠉⠛⠛⠛⠛⠚⠛⠛⠋⠙⠱⢿⢿⣿⡀⠀⣿⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠀⠀⣸⡇⠀⢻⣿⣿⡿⠟⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⡿⠁⠀⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣹⣿⠀⠀⠀⠀⣀⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⡀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢯⣤⣀⣰⣦⡈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣁⣸⡆⠹⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀
⡄⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⢿⣿⠿⠋⠀⠈⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣶⣾⣿⣷⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣤⣴⣦⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠿⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⡾⢿⣿⢿⣿⣷⠀⡿⠿⣿⡿⢿⣿⡿⠿⡇⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⠱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡖⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢰⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡀⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⣟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣩⣴⣭⡄⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣵⣭⣭⣥⣬⣥⣈⠁⣉⣩⣭⣭⡌⢉⣼⣮⢉⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣷⣄⠙⢿⣿⣴⣿⣿⠋⠸⢿⡇⢰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣷⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠛⣿⡍⠛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⢀⢏⠂⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢶⣀⡀⣀⡀⠘⠀⠀⠂⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣂⡒⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⡟⠈⠉⠉⠙⢽⣿⣿⣿⠿⠟⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣰⣄⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣯⣭⣭⣭⣩⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠐⠀⠀⢠⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠬⢶⣼⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣭⣭⣍⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⠛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡟⠩⠾⠛⠿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
⣿⣿⣿⡉⢙⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣤⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣤⣬⠉⠉⠉⠉⠉⠀⠀⠀⠻⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⣘⠛⠁⠈⠙⢻⣿⡿⢿⡿⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢙⡟⢰⣷⠶⢶⡆⠀⠀⠀⠈⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣧⡙⠿⠿⣟⣾
⠀⠈⠀⠀⠘⠀⠈⣿⣿⣿⣿⣿⣿⣿⡓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⣿⣿⣿⡟⠀⢰⠈⠁⡈⡟⠀⠸⠃⠀⠈⠲⣤⣌⣉⠁⠀⠻⣿⣿⣿⣿⣿⣿⣦⣠⣴⡿⠻
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⢈⠀⠘⠇⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠙⠟⠁⠀⠏⠀⣠⣿⡟⠀⠀
⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠈⠉⠙⠛⠛⠛⠚⠛⠛⠋⠙⠡⢿⢿⣿⣄⠀⣿⠀⣀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠀⠀⢰⣷⠀⢸⣿⣿⡿⠟⠋⠁⠀⠀⠀⢻⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⠏⠀⣻⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⠀⠀⠀⠀⣀⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢫⣤⣀⣰⣇⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣇⣰⡆⠸⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀
⡀⠐⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⢿⣿⡿⠋⠀⠈⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣶⣿⣿⣷⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠸⢿⣤⣤⣤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠿⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⢿⣿⡿⣿⣿⡄⠀⠀⠀⡾⢿⣿⣿⣿⣷⠰⡿⠿⣿⡿⢿⣿⡿⠿⡯⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢲⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡀⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⡿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣭⣴⣭⡀⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⣈⠁⣉⣩⣭⣭⡌⢉⣴⣮⣉⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣷⣄⠙⢿⣿⣶⣿⣿⠛⠸⢿⡏⢰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢈
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣾⣯⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠛⣿⡍⠛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠆⢀⡀⠀⠀⠘⡇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢶⣀⣀⣀⠀⠘⠀⠀⠈⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠉⠉⠉⢻⣿⣿⣿⠿⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣰⣄⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣯⣭⣭⣭⣉⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠂⠀⠀⣼⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣮⣒⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣭⣭⣍⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣷⡆⠛⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠉⠶⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣶⣤⣤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⣡⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⠉⠉⠉⠉⠉⠀⠀⠀⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹
⢀⣙⡟⠉⠀⠉⠛⣿⡿⢿⡿⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⡟⢰⣷⠶⢶⡆⠀⠀⠀⠈⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣧⡛⠿⢻⣟⣾
⠀⠈⠃⠀⠘⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⣿⣿⣿⡿⠁⠰⠈⠁⠈⡟⠀⠸⠃⠀⠉⠲⣤⣈⣉⡁⠈⠻⣿⣿⣿⣿⣿⣿⣦⣀⣴⡿⠻
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠘⠆⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠙⠟⠁⠀⠟⠀⣠⣿⡟⠀⠀
⠀⠀⠀⠀⢠⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠉⠉⠛⠛⠛⠚⠛⠛⠋⠙⠡⢿⢿⣿⣤⠀⢹⠀⣀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠀⠃⢀⣿⡄⠘⣿⣿⡿⠟⠋⠁⠀⠀⠀⢻⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⢴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⡿⠀⣸⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠻⣻⣿⠀⠀⠀⠀⣀⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⡇⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢯⣄⣀⢠⣆⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣯⣀⡄⠸⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀
⡀⠐⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⢿⣿⡿⠋⠀⠈⣿⣿⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣶⣶⣷⣶⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣠⣤⣤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠿⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⣿⡿⠿⠿⠿⣿⡿⣿⣿⡄⠀⠀⠀⡿⢿⣿⣿⣿⣷⠸⡿⠿⣿⡿⢿⣿⡿⠿⡷⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠂⣾⣷⡔⣶⣶⡄⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡀⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⡟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣭⣴⣭⡄⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⣈⠁⣉⣩⣭⣭⠌⢉⣼⣮⣍⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣷⣄⡙⣿⣿⣾⣿⡿⠋⠸⢿⡏⢰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣾⣽⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠛⣿⡍⠛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠆⢀⡀⠀⠀⠐⠷⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣶⣀⣀⢀⡀⠘⠁⠀⠰⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠏⠉⠉⠉⠻⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣰⣄⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣸⣯⣭⣭⣭⣉⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠒⠀⠀⢤⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣵⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣭⣭⣍⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣭⣭⣥⡄⠛⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡏⠱⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣸⡿⠿⢿⣿⣿⣷⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣏⠉⢻⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣤⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⠉⠉⠉⠉⠉⠀⠀⠀⢻⣻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⢹
⢀⣻⣿⠋⠀⠈⠙⢿⡿⢿⡿⢻⣿⣷⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⢰⣷⠶⢶⡆⠀⠀⠈⠈⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⡛⠿⢿⣟⣾
⠀⠘⠟⠀⠘⠂⠀⢸⣿⣿⣿⣾⣿⣿⡏⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡏⣿⣿⣿⣿⠁⠀⠀⠁⠈⡟⠀⠸⠃⠀⠉⢲⣤⣉⣉⡁⠀⠻⣿⣿⣿⣿⣿⣿⣦⣀⣴⡿⠻
⠀⠀⠅⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠈⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⢿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡇⣿⣿⣿⡏⠀⠀⠀⠘⠆⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠘⠿⠁⠀⠟⠀⣠⣿⡟⠀⠀
⠀⠀⣤⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠚⠛⠛⠋⠙⠁⢿⢿⣿⣥⠀⢸⠀⣀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠈⠀⢰⣿⠏⠀⠀⠀
⠀⠀⡟⠀⣼⡇⠀⣿⣿⠿⠛⠉⠀⠀⠀⠀⢹⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⣿⠀⢸⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠻⣻⣿⠀⠀⠀⠀⣀⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡷⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢟⣀⠀⢀⣎⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⣇⡀⠸⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀
⡀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⢿⣿⡿⠛⠁⠈⣿⣿⣿⣿⣷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣶⣶⣷⣶⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⢟⣠⣤⣤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠺⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣿⡿⠿⠿⠿⣿⡿⣿⣿⡄⠀⠀⠀⣿⢿⣿⣿⣿⣶⠸⡿⠿⣿⡿⢿⣿⡿⠿⡿⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢳⣆⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠂⣾⣷⡔⣶⣶⡄⢰⣶⣶⢴⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⠀⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⡿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⢫⣾⣧⣭⣥⣭⣭⣭⣍⣭⣴⣭⡀⠀⠉⣬⣥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⣈⠁⣉⣩⣭⣭⠈⠉⠀⣨⣍⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⢿⣿⣿⣷⣄⠙⠿⣿⣀⣤⣾⣿⣿⢿⡏⢰⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣶⣶⣯⣿⣿⣿⣷⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠉⠉⠛⣿⡍⠛⠛⠛⠻⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠆⢀⡀⠀⠀⠀⣪⠇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢶⣀⣀⣀⡀⠘⠁⠀⠀⠆⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⢟⠻⠛⠋⠻⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⣀⣀⣠⣄⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣸⣯⣭⣭⣭⣉⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠆⠀⠀⢠⣿⣿⣯⣿⣿⣿⣿⣿⡇⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⣴⣾⣾⣽⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣭⣭⣍⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣻⣭⣭⣭⡄⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠩⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣸⠿⠿⢿⣿⣿⣷⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⡉⢙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⣤⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⠉⠉⠉⠉⠁⠀⠀⢈⣻⣻⣿⡇⢈⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⢻
⠈⢻⣿⡏⠁⠈⠙⢻⡿⢿⣿⢻⣿⣿⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢰⣷⡶⢶⡆⠀⠀⠘⠛⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⡛⠿⣿⣟⣿
⠀⠘⠿⠃⠈⠃⠀⠀⣿⣿⣿⣾⣿⣿⡏⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⠃⠀⠀⠁⠀⡿⠁⠸⠏⠀⠈⢳⣤⣉⣉⡁⠀⠻⣿⣿⣿⣿⣿⣿⣆⢀⣼⡿⠻
⠀⠀⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠈⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡇⣿⣿⣿⡏⠀⠀⠀⠸⠇⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠘⠿⠉⠀⡟⠀⣠⣿⡟⠀⠀
⠀⠀⣿⠆⠀⡀⠀⣾⣿⣿⣿⣿⣿⠟⠁⠀⢾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠉⠙⠛⠛⠚⠛⠛⠋⠙⠃⢿⢿⣿⣱⠀⢰⠀⣀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡄⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠐⣿⠀⣰⣧⠀⢻⡿⠟⠋⠉⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⣿⠀⢸⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⣻⣿⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢟⣀⠀⢀⣎⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⣿⡀⠸⣠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀
⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⡿⠛⠁⠈⣿⣿⣾⣿⣷⣴⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢁⣿⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⣷⣶⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠟⣠⣤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠰⠿⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⣾⢿⣿⣿⣿⣷⠘⢿⠿⣿⡿⢿⣿⡿⠿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣇⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣾⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡆⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠫⣾⣧⣭⣥⣭⣭⣭⣍⣭⣴⣭⡀⠀⠉⢬⣥⣭⣭⣬⣵⣿⣬⣿⣵⣭⣭⣥⣬⣥⣈⠁⣉⣭⣭⣭⠈⠉⠀⠈⢉⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢠
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⢿⣿⣿⣷⣄⡙⠿⣿⠀⠀⠀⠀⠾⢿⡟⢠⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢘
⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣴⣶⣾⣿⣿⣿⣷⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠉⠉⠉⠛⣻⡍⠛⠛⠛⠻⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠆⢀⡀⠀⠀⠀⢸⠏⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢶⣀⣀⡀⠀⠘⠁⠀⠀⠌⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠆⠀⠉⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⠻⠛⠛⠻⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣀⣀⣠⣄⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣨⣯⣭⣭⣭⣉⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠿⠛⠣⠄⠀⢀⣿⣿⣞⣿⣿⣿⣿⣿⡇⠀⢰⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣴⣾⣽⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣭⣭⣍⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣛⣭⣭⣭⡄⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⡉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⡿⢫⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣸⡿⠿⢿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿
⣿⣿⣿⣿⡍⠉⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣡⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⠉⠉⠉⠉⠁⠀⠀⢈⣻⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⢿
⠙⣿⣿⡟⠁⠀⠉⠛⡿⢿⣿⢻⣿⣿⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢰⣷⡶⠶⡆⠀⠀⠉⠙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣧⡛⢿⢿⣟⣿
⠀⠘⢿⡇⠀⠃⠀⠀⣿⣿⣿⣾⣿⣿⡏⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡏⣿⣿⣿⣿⠃⠀⠀⠀⡈⡿⠀⠸⠏⠀⠈⠳⣤⣉⣉⡁⠀⠻⣿⣿⣿⣿⣿⣿⣆⢀⣼⡿⠻
⠀⠀⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣾⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡇⣿⣿⣿⡟⠀⠀⠀⠸⠇⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠘⠿⠉⠀⠟⠀⣠⣿⡟⠀⠀
⠀⠀⣿⡆⠀⢀⠀⢸⣿⣿⣿⣿⡿⠟⠁⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠀⠀⠉⠉⠛⠛⠚⠛⠛⠋⠙⠃⢿⠿⣿⣹⠀⢰⠀⣀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡆⠀⠀⠈⠀⣰⣿⠏⠀⠀⠀
⠀⠰⣿⠇⢀⣿⠀⢸⡿⠟⠋⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⣿⠀⢸⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⣻⣿⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢟⣀⠀⠀⡆⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣽⣿⣿⡆⠈⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⠀
⡄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠛⠁⠀⢿⣿⣶⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣶⣿⣶⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠿⣠⣤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠐⠻⢿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⢿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⢼⠿⣿⣿⣿⣷⡀⠿⠿⣿⡿⢿⣿⡿⠿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡖⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢴⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⣼⣸⣿⣿⢸⣟⢸⡿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣾⣧⣭⣥⣭⣭⣭⣍⣭⣴⣭⡀⠀⠉⢬⣥⣭⣭⣬⣥⣿⣬⣿⣵⣭⣭⣥⣬⣥⣈⠁⣉⣩⣭⣭⠈⠉⠀⠈⢩⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢠
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣄⡙⢿⣿⡀⠀⠀⠀⠼⢿⡟⢀⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⢘
⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣤⣶⣶⣾⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠉⠉⠉⠛⣻⡟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠀⠀⠀⢼⡟⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢶⣀⣀⣀⣀⠘⠁⠀⠀⡐⠁⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠦⠀⠉⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡆⠒⠒⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⠻⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣀⣀⣠⣄⣀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣨⣯⣭⣭⣭⣉⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣿⠟⢋⡅⠀⠈⣹⣟⣟⣿⣿⣿⣿⣿⡇⠀⢰⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⣁⣴⣟⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣭⣭⣍⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣭⣭⣥⡄⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⡉⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣿⣷⣾⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⣶⣾⣷⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣨⠿⠻⢿⣿⣿⣿⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿
⣿⣿⣿⣿⡏⠉⣻⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⢃⠀⠁⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣭⠉⠉⠉⠉⠁⠀⠀⢀⣻⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠙⣿⣿⣿⠉⠀⠉⠙⢿⠿⣿⢻⣿⣿⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⣷⡶⠶⣦⠀⠀⠈⠛⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣯⠻⠿⠿⣿⣿
⠀⠘⢻⣿⠀⠃⠀⠀⢸⣿⣿⣾⣿⣿⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠏⠀⠀⠀⡀⣿⠁⠘⠏⠀⠈⠻⣦⣍⣉⡁⠀⠻⣿⣿⣿⣿⣿⣿⣆⢠⣼⡿⠻
⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⠀⠀⠀⠘⠇⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠈⠿⠋⠀⠟⠀⣠⣿⡟⠀⠀
⠀⠀⣿⣷⠀⢀⠀⢰⣿⣿⣿⣿⡿⠟⠁⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠉⠉⠈⠛⠘⠛⠛⠛⠙⠃⢿⠿⣿⣽⠀⠀⠀⣀⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡆⠀⠀⠈⠀⢰⣿⠏⠀⠀⠀
⠀⢰⣿⡇⠀⣼⠀⢸⡿⠛⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢠⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⡎⡉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣼⣿⣿⡆⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⠀
⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠁⠀⢿⣷⣶⣿⣿⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣾⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣶⣷⣶⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠿⣠⣤⣤⣄⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⢼⠿⣿⣿⣿⣷⡀⠻⠿⣿⡿⢿⣿⠿⠿⣿⠀⢰⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣾⣧⣭⣡⣭⣭⣭⣍⣍⣴⣭⠀⠀⠉⢨⣥⣭⣭⣬⣥⣿⣬⣿⣵⣭⣭⣥⣬⣥⣈⠁⣉⣭⣭⣭⠈⠉⠀⠈⢩⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠉⠀⠀⢠
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣷⣤⣽⣿⣿⡇⠀⠀⠀⠾⢿⡿⢀⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘
⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣴⣶⣲⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠉⠉⠉⠛⣻⡟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠀⠀⠀⢰⡽⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢶⣀⣀⣀⡀⣘⠁⠀⠀⠰⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠦⠀⠉⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠘⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡆⠒⠒⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣀⣀⣠⣄⣀⠀⡀⠀⠛⠀⠀⠈⠀⠀⠀⠀⠀⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣨⣯⣭⣭⣭⣉⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢻⣿⣿⠿⠛⠋⠛⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⢐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠣⠀⢰⢾⣷⣏⣿⣿⣿⣿⣿⣧⣤⣼⣭⣭⣍⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣭⣭⣥⡄⠘⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⡉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣆⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡿⠿⢿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿
⣿⣿⣿⣿⣏⠉⢹⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⠋⠰⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣭⡉⠉⠉⠉⠁⠀⠀⢀⣻⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⣿
⠙⣿⣿⣿⠋⠀⠈⠙⠿⠿⣿⢻⣿⣿⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡆⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠃⣷⡶⠶⣦⠀⠀⠈⠙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣏⠻⠿⠿⣿⣿
⠀⠈⢿⣿⠀⠃⠀⠀⢸⣿⣿⣾⣿⣿⡏⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⣿⣿⣿⣿⡏⠀⠀⠀⡀⣿⠁⠐⠏⠀⠈⠻⣦⣍⣉⡁⠀⠻⣿⣿⣿⣿⣿⣿⣆⢠⣼⡿⠻
⠀⠀⣽⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠈⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠘⠇⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡄⠈⠿⠋⠠⠏⠀⣰⣿⡟⠀⠀
⠀⠀⣿⣿⠀⢀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠇⠀⠀⠈⠉⠀⠛⠚⠛⠛⠛⠙⠃⢿⢿⣿⣽⠀⠀⠀⣀⣀⣦⣄⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⢰⣿⣿⠀⢼⡆⢰⠿⠛⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⠁⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀
⠀⠀⠀⣨⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⡍⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢼⣿⣿⡆⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⠀
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⡿⠛⠁⠐⣶⣦⣼⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣷⣾⡛⠿⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⠟⣀⣤⣤⣄⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠐⠿⣿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⡿⠿⠿⠿⣿⡿⣿⣿⠀⠀⠀⠀⢰⠿⣿⣿⣿⣷⡄⠸⠿⣿⡿⠿⣿⡿⠿⣿⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡆⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣼⣧⣍⣡⣭⣭⣭⣍⣭⣴⣭⠀⠀⠉⢨⣥⣭⣭⣬⣥⣷⣬⣿⣵⣭⡍⢥⣬⣥⣌⠁⢉⣭⣭⣭⠈⠉⠀⠈⢩⣤⣝⠋⣀⣉⡉⣡⡄⠙⠋⠈⠙⠋⠀⠀⢠
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠎⠉⢻⣿⣷⣿⣿⡿⣿⠀⠀⠀⠀⠾⢿⡿⢀⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘
⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣤⣤⣶⣾⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠉⠉⠛⣻⡟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠀⠀⠀⣰⢿⠥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢶⣄⣀⣀⡀⡘⠃⠀⠀⠐⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⡀⠶⠀⠉⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠘⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣆⠒⠒⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⣀⣀⣠⣄⣀⡀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣈⣯⣭⣭⣭⣉⣇⣀⣀⣀⡀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⢈⣿⣯⡾⣿⣿⣿⣿⣿⣧⣤⣼⣭⣭⣍⣉⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣭⣭⣥⡄⠘⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⡉⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⣀⣜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡿⠛⢿⣿⣿⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿
⣿⣿⣿⣿⣯⠉⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⣶⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣧⣭⡉⠉⠉⠉⠁⠀⠀⢀⣻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠉⣿⣿⣿⡏⠀⠈⠙⠿⠿⣿⢻⣿⣿⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠉⠈⢙⣿⣿⣿⣿⣿⡏⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠃⣷⡶⠶⣦⠀⣀⠈⠙⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣏⠻⠿⠿⣿⣿
⠀⠈⠻⣿⠃⠃⠀⠀⢸⣿⣿⣾⣿⣿⡏⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⡀⣿⠁⠀⠟⠀⠈⠹⣦⣉⣉⡁⠀⠹⣿⣿⣿⣿⣿⣿⡆⣠⣼⡿⠻
⠀⠀⣽⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠁⠀⠀⠘⠇⠏⠀⠂⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄⠈⠿⠋⠠⠏⠀⣤⣿⡟⠀⠀
⠀⠀⣿⣿⠀⢀⠀⠀⣿⣿⣿⣿⠿⠋⠀⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⠀⠀⠀⠈⠉⠀⠚⠛⠛⠛⠛⠙⠃⢿⡿⣿⣿⡄⠀⠀⣀⣠⣦⣤⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡆⠀⠀⠈⠀⢰⣿⠏⠀⠀⠀
⠀⢰⣿⣿⠀⢸⡆⠀⠿⠛⠉⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢾⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠃⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀
⠀⠀⠀⣠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡷⠂⠀⠀⢈⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⣿⣿⣇⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⠿⠋⠀⢀⣀⡀⣼⣿⣷⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⡛⠻⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢁⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣵⣶⣶⣤⣄⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠻⠇⢀⣤⣤⣄⡀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠠⠻⣿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⠷⠿⠿⢿⣿⡿⣿⣷⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⡆⠘⠿⣿⡿⠿⣿⡿⢿⣿⠀⢠⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢳⣆⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣲⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡆⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣟⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣼⣧⣍⣡⣭⣭⣭⣉⣭⣤⣍⠀⠀⠉⠨⣥⣭⣭⣬⣥⣿⣬⣿⣵⣭⣍⠁⢨⣥⣌⠁⢉⣭⣉⣉⠌⠉⠀⠈⢩⣦⣝⠋⣀⣉⡉⣡⣄⠙⠋⠈⠙⠉⠀⠀⢀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⠿⣿⣾⣿⣿⣟⡀⠀⠀⠀⠾⢿⡿⢀⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣤⣤⣤⣤⣴⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠙⣻⡏⠙⠛⠛⠛⠻⠿⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠀⠀⠀⠠⣽⠣⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⣄⣀⣀⣀⣈⠃⠀⠀⠀⠁⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠸⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠘⠋⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣄⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⣁⣀⣠⣄⣀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣿⣭⣭⣭⣍⣁⣀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠈⠈⠉⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠛⠉⠉⠙⣿⠟⣫⣿⣿⣿⣿⣿⣧⣤⣼⣯⣭⣭⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣭⣭⣭⡤⠘⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⢹⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠲⢿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡿⠛⢿⣿⣿⣷⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿
⣿⣿⣿⣿⣯⠉⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣦⣤⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣬⡉⠉⠉⠉⠉⠀⠀⢀⣹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⡀⣿
⠈⣿⣿⣿⡏⠁⠈⠙⠻⠿⣿⢿⣿⣿⣦⠐⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠏⠀⠚⠛⢿⣿⣿⣿⣿⣿⡏⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠃⣷⡶⠶⣶⠀⢀⠈⠙⣻⣿⡿⠀⣿⣿⣿⣿⣿⣿⣏⠛⠿⢿⣿⣿
⠀⠀⠻⣿⡇⠃⠀⠀⢸⣿⣿⣾⣿⣿⡏⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⡀⢻⠁⠀⠟⠀⠀⢙⣦⣍⣉⡁⠀⠹⣿⣿⣿⣿⣿⣿⡆⣠⣼⡿⠻
⠀⠀⣼⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠿⢿⣿⣿⣿⡏⢿⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⠃⠀⠀⠐⠇⠘⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠈⠻⠋⠠⠏⠀⣤⣿⡟⠀⠀
⠀⠀⣽⣿⡆⠀⡀⠀⣾⣿⣿⣿⠿⠋⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠀⠀⠀⠈⠉⠁⠀⠓⠛⠛⠛⠙⠃⢿⡿⣿⣿⡆⠀⠀⣀⣀⣦⣤⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡆⠀⠀⠈⠀⣰⣿⠏⠀⠀⠀
⠀⢰⣿⣿⡇⢰⡇⠀⠿⠛⠉⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠃⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀
⠀⠀⠀⣀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡶⠂⠀⠀⢩⠙⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣷⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⣷⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢁⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣥⣶⣶⣄⡨⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠻⠇⢀⣤⣤⣤⡀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣀⠀⠠⠿⣿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣿⠷⠿⠿⢿⣿⡿⣿⣷⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣆⠈⠻⣿⡿⠿⣿⡿⠿⣿⠀⢠⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢳⣆⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢨⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣼⣧⣍⣡⣭⣭⣭⣉⣭⣤⡍⠀⠀⠉⠈⣥⣭⣭⣬⣥⣿⣬⣿⣵⣭⣍⠁⠨⣥⣌⠁⣉⣉⣭⣭⣌⠉⠀⠈⢩⣤⣝⠋⣀⣉⡉⢡⣄⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⠷⣦⣿⣿⣿⣿⣦⣀⣀⣾⣿⣿⢀⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠙⢻⣯⠉⠛⠛⠛⠻⠿⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠶⠀⣀⠀⠀⠀⢀⠿⠪⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⢆⣀⣀⡀⠀⡋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠸⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣒⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢁⣀⣀⣦⣀⡀⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣿⣭⣭⣭⣍⣹⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⡖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠛⠋⠛⢿⡿⠛⣻⣿⣿⣿⣿⣷⣤⣬⣯⣭⣭⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣥⣤⠘⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣉⡉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣼⣷⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡿⠛⠿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿
⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣴⣅⣀⣤⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣬⡍⠉⠉⠉⠉⠀⠀⢀⣙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⡀⣿
⠈⢿⣿⣿⡟⠁⠈⠉⠻⠟⣿⠟⣿⣿⣧⡀⠂⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡟⠁⠄⠻⢿⣿⣿⣿⣿⣿⣿⠉⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠃⣾⡶⠶⣶⠀⢀⡈⠙⢻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣏⡻⠿⢿⣿⣿
⠀⠀⠛⣿⡏⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠉⠀⠀⠀⢻⠃⠀⠟⠀⠀⠙⢷⣬⣉⣉⠀⠙⢿⣿⣿⣿⣿⣿⣆⢀⣼⡿⠻
⠀⠀⢸⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡼⠿⣿⣿⣿⣏⠙⣧⣿⣿⣿⣿⣿⣸⣿⣿⣿⡇⠀⠀⠐⠇⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠈⠻⠋⠀⡟⠀⣠⣿⡿⠀⠀
⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣿⡿⠋⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⡇⠀⠀⠀⠉⠉⠈⠘⠛⠛⠛⠋⠋⢿⡿⣿⣿⡇⠀⠀⢀⣀⣦⣤⡀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀
⠀⠰⣿⣿⡇⠀⣇⠀⠿⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣿⣿⡇⠁⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢟⣿⡇⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀
⠀⠀⠀⢀⠇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠈⡙⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣷⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⡿⠟⠁⠀⠀⠀⢰⣾⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣭⣴⣶⣄⡀⣻⣷⣿⣿⣿⣿⣦⠀⠀⠀⠘⠿⢀⣤⣤⣤⣀⠀⢈⣯⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠿⢿⡷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⠿⠾⠿⠿⣿⡿⣿⣿⠄⠀⠀⠀⠀⠿⢿⣿⣿⣿⣷⠈⠻⣿⡿⠿⣿⡿⠿⣿⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠐⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡦⢶⡶⢢⣶⡆⢸⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢲⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣿⡜⢸⣿⣿⢸⣟⢸⡿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣼⣧⣍⣡⣭⣭⣭⣍⣉⣴⣭⠀⠀⠉⠈⢥⣭⣭⣬⣥⣿⣬⣿⣥⣭⣭⡁⡨⣥⣌⡁⢉⣩⣭⣭⣬⣭⣾⡌⢩⣤⣝⠋⢀⣉⡉⢡⣄⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠙⠿⣦⡙⣻⣿⣿⣿⣯⣀⣾⢿⣿⣀⣿⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣴⣶⣶⣤⣤⣴⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠙⢻⣯⠉⠙⠛⠛⠛⠿⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⢀⠌⡞⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠴⢦⣀⡀⠀⢀⡋⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠸⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣐⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢁⣀⣀⣦⣀⣀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣽⣭⣭⣭⣭⣹⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡖⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛⠛⠙⠻⣿⠟⣫⣿⣿⣿⣿⣿⣤⣤⣯⣭⣭⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣭⣭⣭⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡰⣿⣞⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡿⠛⠻⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⠉⢙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⡍⠉⠉⠉⠉⠀⠀⢀⣘⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⡀⣿
⠀⢻⣿⣿⡟⠁⠈⠉⠻⠟⣿⡟⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠋⠀⠈⠿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣾⣶⠶⣶⠀⢀⡈⠉⢻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣏⡛⠿⢿⣟⣿
⠀⠀⠙⣿⡏⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠱⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⠉⠀⠀⠀⢹⠇⠀⠟⠁⠀⢉⢷⣌⣉⣉⠀⠘⢿⣿⣿⣿⣿⣿⣦⢀⣼⡿⠛
⠀⠀⢸⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠿⢿⣿⣿⣿⡍⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠻⠏⠀⡟⠀⣠⣾⡿⠁⠀
⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣿⡿⠛⠁⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠉⠉⠁⠀⠛⠛⠛⠋⠛⢻⡿⣿⣯⡇⡄⠀⢀⣀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⡷⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀
⠀⠐⡿⢿⡇⠀⣇⠀⡿⠛⠉⠁⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣿⣿⡇⠁⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀
⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠈⡉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⣿⣿⣿⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠃⠀⠀⠀⢠⣷⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣴⣶⣦⡀⣹⣿⣾⣿⣿⣻⣿⡄⠀⠀⠀⠻⠇⣠⣤⣤⣄⠀⢈⣯⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠿⢿⡷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⡿⠾⠿⠿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠾⢿⣿⣿⣿⣷⡘⢿⣿⡿⠿⣿⡿⢿⣿⠆⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢳⣇⣶⢶⡶⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢲⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣼⣧⣭⣡⣭⣭⣭⣭⣩⣴⣭⡄⠀⠉⠈⢡⣭⣭⣬⣥⣿⣬⣿⣵⣭⣭⡁⣬⣥⣌⡁⢉⣩⣭⣭⠈⢉⣼⣮⣭⣤⣝⡋⢀⣉⣉⢡⣄⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⢿⣿⣦⣉⠻⣿⣾⣿⣿⠋⢿⠿⣿⠁⣾⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠉⠙⢛⣯⠉⠙⠛⠛⠛⠿⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠀⠀⡼⠻⠡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠦⠄⠀⠀⠀⡉⡀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡄⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣐⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠁⣀⣀⣶⣀⣀⡀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣽⣭⣭⣭⣭⣽⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣖⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠛⠛⠛⢿⡟⢋⣿⣿⣿⣿⣿⣤⣤⣯⣭⣭⣍⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣭⣭⣤⠀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⢿⣷⣧⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡿⠛⠻⢿⣿⣿⣷⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣤⣠⣤⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡌⠉⠉⠉⠉⠀⠀⠀⣘⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣟⣿⣇⡀⢻
⠀⢹⣿⣿⡟⠁⠈⠉⠻⠟⣿⡟⣿⣿⣿⡤⡌⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠟⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢺⣶⠖⣶⡆⢀⣀⠉⢻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣏⡛⠿⠿⣟⣿
⠀⠀⠙⣿⡟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠑⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⠋⠀⠀⠀⢸⠏⠀⠿⠁⠀⢈⢳⣬⣉⣉⠀⠘⢿⣿⣿⣿⣿⣿⣦⢀⣼⡿⠛
⠀⠀⢸⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠂⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠿⠿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠻⠸⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣆⠀⠻⠏⠀⡟⠀⣠⣾⡿⠁⠀
⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣿⡿⠟⠁⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⠉⠉⠁⠈⠛⠛⠋⠛⠸⡿⣿⣿⡇⡄⠀⢀⣀⣶⣤⡄⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣷⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀
⠀⠀⠿⢿⣇⠀⣆⠀⠿⠛⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣿⣿⡇⠁⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀
⠀⠀⠀⣀⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡶⠀⠀⠈⢉⠛⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⣿⣿⣿⡀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⣿⠿⠋⠀⠀⠀⠀⣶⣿⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣶⣶⣦⣀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⠇⣠⣤⣤⣄⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠿⢿⡷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⠿⠿⠿⣿⣿⢿⣿⣷⠀⠀⠀⠀⠼⠿⣿⣿⣿⣷⡘⠿⣿⡿⠿⣿⡿⢿⣿⠇⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣇⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢼⣟⢸⣟⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⣼⣧⣭⣡⣭⣭⣭⣭⣉⣴⣭⣤⠀⠉⠈⢡⣭⣭⣬⣥⣿⣮⣿⣥⣭⣭⣥⣬⣥⣌⡁⢉⣩⣭⣭⠈⠉⢀⡈⢩⣦⣝⡋⢀⣉⣉⢡⣄⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠉⢿⣿⣿⣦⣍⠻⢿⣀⣠⣾⣿⢾⠿⣿⠃⣾⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣶⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠉⠉⠉⢛⣯⠉⠉⠛⠛⠛⠿⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⣠⢻⠯⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠴⠦⠤⠀⠀⠀⠉⢀⡀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⡄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠛⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣀⣒⣒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠁⣀⣀⣶⣀⣀⣀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠰⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣼⣯⣭⣭⣭⣭⣅⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣖⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⠿⠛⠛⠛⢿⣿⠟⣻⣿⣿⣿⣿⣤⣤⣯⣭⣭⣍⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣭⣭⣤⠀⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣷⣯⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣀⡼⠟⠛⢿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣬⣀⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣌⠉⠉⠉⠉⠁⠀⠀⣌⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣟⣿⣇⣀⢹
⠀⠹⣿⣿⣟⠁⠈⠉⠻⣟⣿⡟⣿⣿⣿⡦⣜⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠉⠠⠙⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢸⣶⠖⣶⡆⠀⣀⠉⢛⣿⣿⠀⣿⣿⣿⣿⣿⣿⣏⡛⠿⠿⣟⣿
⠀⠀⠘⣿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠑⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠛⠁⠀⢀⢸⡏⠀⠻⠁⠀⠈⢳⣬⣉⣉⠀⠈⢿⣿⣿⣿⣿⣿⣦⢀⣼⡿⠛
⠀⠀⢰⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡼⠿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠻⠸⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⠀⠹⠟⠁⡟⠀⢠⣾⡿⠃⠀
⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣿⡿⠟⠁⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠉⠉⠉⠀⠙⠛⠛⠛⠹⡿⣿⣯⡇⣶⠀⢀⣀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀
⠀⠀⠿⠿⡇⠀⣇⠀⡿⠛⠉⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣿⣿⡇⠚⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀
⠀⠀⠀⣀⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⢉⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⣿⣿⣿⡀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣾⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠈⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣥⣶⣶⣄⠸⣿⣶⣿⣿⣏⣿⡇⠀⠀⠀⠸⠗⣠⣤⣦⣤⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠻⢿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠷⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡜⠿⣿⡿⠿⣿⡿⣿⣿⠇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣇⣶⢶⡶⢸⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣷⣶⡔⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⢼⣧⣭⣡⣍⣭⣭⣭⣉⣴⣭⣤⠀⠉⠈⠡⣭⣭⣬⣥⣿⣮⣿⣥⣭⣭⣥⣬⣥⣌⡁⢉⣩⣭⣭⠈⠉⠀⠈⢩⣤⣝⡋⢀⣉⣉⢡⣄⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⣿⣿⣿⣦⣍⠻⢿⣀⣀⠀⠀⢾⠿⣿⠃⣼⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣤⣶⣦⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⢛⣯⠍⠉⠙⠛⠛⠻⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⢀⠚⠎⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠴⠦⠤⠀⠀⠀⠉⣀⣀⣀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠰⠇⠀⠀⠀⠀⠀⠀⡀⠀⢠⡄⠀⠀⠙⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣰⣀⣓⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠅⣀⣀⣶⣀⣀⣀⣀⡈⠋⠀⠀⠈⠀⠀⠀⠀⠰⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣼⣯⣭⣭⣭⣭⣅⣀⣀⣀⣀⣀⠀⠀⠀⠀⠙⠀⠉⠉⠋⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣖⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠟⠛⢿⣿⠿⢻⣿⣿⣿⣿⣤⣤⣯⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣽⣽⡤⠀⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⣿⣴⣹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⡸⠟⠛⢿⣿⣿⣷⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⣿⣿⣿⣯⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣦⣀⣀⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠉⠉⠉⠉⠁⠀⠀⣈⣻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣀⢹
⠀⠹⣿⣿⣟⠁⠀⠉⢻⣟⣻⡟⣿⣿⣿⣤⣔⠀⠀⠀⠀⠀⠀⠀⠛⢿⢿⣿⣿⠋⠩⠹⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣶⠖⢶⡆⠀⣀⠉⠙⣿⣿⠇⢸⣿⣿⣿⣿⣿⣯⡙⠿⠿⣿⣿
⠀⠀⠘⣻⡏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠻⠋⠀⢀⢸⡏⠀⠻⠁⠀⠨⠻⣮⣍⣉⠀⠈⢻⣿⣿⣿⣿⣿⣧⢀⣴⣿⠟
⠀⠀⢰⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠽⠿⢿⣿⣿⣿⣿⡙⢿⣿⣿⣿⢸⣿⣿⣿⡯⠀⠀⠀⠻⠘⠁⠐⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠙⠟⠁⠟⠀⢠⣾⡿⠃⠀
⠀⠀⠈⣿⡇⠀⠀⠀⣾⣿⣿⣿⡿⠟⠁⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠈⠉⠉⠁⠈⠛⠋⠛⠸⣿⢿⣿⡧⣶⡄⢀⣀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⠀⠀⠀⠁⠀⣿⡟⠁⠀⠀
⠀⠀⠿⠿⡇⠀⡇⠀⡿⠟⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣲⣿⣿⡏⢸⠃⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡟⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀
⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⡇⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠟⠁⠀⠀⠀⣰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣤⣦⡀⠀⣶⣶⣿⣿⡏⣿⡆⠀⠀⠀⠸⠇⣠⣤⣶⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡀⠀⠿⢿⡷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠷⠿⠿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠰⠿⣿⡿⣿⣿⣆⠿⣿⡿⠿⣿⡿⣿⣿⠇⠀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣇⣶⢶⡶⢸⡶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡜⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⢸⣧⣭⣥⣍⣩⣭⣭⣍⣤⣭⡄⠀⠉⠈⠁⣭⣭⣬⣥⣷⣬⣿⣥⣭⣭⣥⣬⣥⣌⡁⢉⣩⣭⣭⣌⠉⠀⠈⢩⣦⣝⡋⢀⣉⣉⢡⣤⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⣿⣿⣿⣶⣌⣻⣿⣿⠀⠀⠀⢾⠿⣿⠇⣸⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣤⣶⣦⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠛⣿⠍⠉⠉⠛⠛⠻⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⠀⢠⠾⡞⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠤⠷⠤⠄⠀⠀⠉⠀⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠠⠇⠀⠀⠀⠀⠀⠀⡀⠀⢠⡆⠀⠀⠉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣰⣄⣛⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠥⢤⣀⣶⣄⣀⣀⣀⣀⡋⠀⠀⠈⠁⠀⠀⠀⠐⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⢼⣯⣭⣭⣭⣭⣅⣀⣀⣀⣀⣀⠀⠀⠀⠀⠙⠉⠉⠙⠻⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣐⣐⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠿⣿⣿⡿⢟⣿⣿⣿⣿⣦⣶⣿⠭⢭⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣽⣵⣶⠆⢙⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡈⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣿⣰⣪⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣀⣸⠟⠛⢻⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿
⣿⣿⣿⣿⣯⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠂⢈⣡⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣄⠀⠁⠉⠉⠁⠀⠀⣄⣽⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣀⢸
⠀⠸⣿⣿⣟⠁⠀⠉⢿⣟⣻⡟⣿⣿⣿⣦⣀⠂⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⣷⠖⢲⡆⠀⣀⠉⠙⣿⣿⠇⢸⣿⣿⣿⣿⣿⣯⡙⠿⠿⣿⣿
⠀⠀⠘⣻⡏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡁⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢻⠏⠁⠀⠘⡏⠀⠹⠃⠀⠈⠹⣦⣭⣉⡀⠈⢻⣿⣿⣿⣿⣿⣷⢀⣴⣿⠟
⠀⠀⢠⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠿⠿⢿⣿⣿⣿⡏⢿⣿⣿⣿⢸⣿⣿⣿⣿⠘⠀⠀⠘⠀⠁⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠙⠟⠁⡞⠁⢠⣾⡿⠃⠀
⠀⠀⠀⣿⡆⠀⠀⢠⣿⣿⣿⣿⠿⠟⠁⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠈⠉⠉⠀⠛⠋⠛⢸⣿⢿⣿⣿⢰⡆⢀⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀
⠀⠀⠿⠿⡇⠀⡄⠸⡿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡳⣿⣿⣟⢸⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀
⠀⠀⠀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣿⣿⣿⣏⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⣭⣤⣶⡂⠀⣤⣤⣿⣿⡟⣿⡆⠀⠀⠀⠸⠗⢀⣤⣶⣦⣄⠀⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣅⡀⠀⠾⢿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⠶⠿⠿⢿⣿⡿⡿⣿⠀⠀⠀⠀⠀⠿⢿⣿⢿⣿⣧⠻⣿⡿⠿⣿⣿⣿⣿⡇⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢸⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡜⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠘⣧⣭⣥⣍⣉⣭⣭⣍⣤⣭⡄⠀⠉⠈⠁⢭⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⣬⣥⣌⣁⠉⣉⣭⣭⣬⡍⠀⠈⢉⣤⣝⡋⢀⣉⣉⠁⣦⡙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠃⠙⣿⣿⣷⣿⣿⣿⣿⠁⠀⠀⢾⠿⢿⢇⣸⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⣴⣶⣦⣶⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠉⣿⠍⠉⠉⠙⠛⠻⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⠀⠀⠀⠀⢀⠞⠞⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠤⠷⠤⠤⠀⠀⠈⠀⡀⣀⡀⠈⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠇⠀⠀⠀⠀⠀⠀⣀⠀⢠⡆⠀⠀⠉⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣍⣙⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠥⢤⣤⣶⣄⣀⣀⣀⣀⡋⠀⠀⠀⠁⠀⠀⠀⠐⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⢼⣿⣿⣭⣭⣭⣥⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⠉⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣐⣐⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⢿⣿⡿⢛⣿⣿⣿⣿⣶⣶⣿⠭⠭⠭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣽⣷⣶⠆⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣈⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣿⣴⣬⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣀⣸⠟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿
⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠂⢀⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣆⠀⠀⠈⠉⠁⠀⠀⣀⣽⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸
⠀⠸⣿⣿⣟⠁⠀⠙⣿⣟⣻⡟⣻⣿⣿⣦⣄⠂⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⢈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⢷⠖⢲⡆⠀⣀⡉⠙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣯⡘⠻⠿⣿⣿
⠀⠀⠈⣻⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡉⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠟⠁⠀⠀⡏⠀⠸⠃⠀⠀⠹⢦⣭⣍⡀⠈⠻⣿⣿⣿⣿⣿⢷⢀⣴⣿⠟
⠀⠀⢠⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⠿⠿⣿⣿⣿⣧⠻⣿⣿⣿⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠙⠟⠁⡼⠁⢠⣾⡿⠃⠀
⠀⠀⠀⣿⡆⠀⠀⢰⣿⣿⣿⣿⠿⠛⠁⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠈⠉⠀⠛⠋⠛⢹⣿⢿⣿⣿⢸⡆⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀
⠀⠀⠿⠿⡇⠀⠀⢸⡿⠛⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⣿⣿⣿⢸⡇⢸⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀
⠀⠀⠀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⡁⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠉⠀⠀⠀⢠⣿⣷⣤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⣭⣤⣤⡀⠀⣠⣄⣾⣿⣿⣿⣧⠀⠀⠀⠘⠛⢀⣤⣶⣦⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣅⡀⠀⠿⠿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣿⠦⠿⠿⢿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠿⢿⣿⢿⣿⣧⠈⢻⡿⠿⣿⣿⣿⣿⡇⠀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡶⢰⡶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢲⣆⣶⢲⣶⢆⢰⣶⠆⣾⣷⡔⣶⣶⡜⢰⣶⣶⢲⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⢃⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⢧⣭⣥⣍⣉⣭⣭⣍⣠⣭⣼⠀⠉⠈⠁⢩⣭⣬⣥⣷⣬⣿⣥⣭⣭⣥⡈⠁⢨⣁⠉⣉⣭⣭⣬⣉⡀⠈⢉⣦⣝⡋⢀⣉⣉⠁⣦⡙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠀⠈⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⠍⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⠀⠀⠀⠀⢀⠮⠞⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠷⠤⠤⠤⠀⠈⠀⠀⣀⡀⠌⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⠀⠇⠀⠀⠀⠀⠀⠀⣀⠀⢀⡆⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣰⣏⣙⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠭⠤⣤⣶⣄⣀⣀⣀⣀⣋⠀⠀⠀⠁⠀⠀⠀⠀⠆⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⢼⣷⣿⣯⣭⣭⣥⣄⣀⣀⣀⣀⡀⠀⠀⠀⠈⠊⠉⠉⠛⠡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣰⣐⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠟⠛⠻⣿⡿⠛⣿⣿⣿⣿⣶⣶⣿⠭⠭⠭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣽⣷⡶⠆⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣄⣸⠟⠛⠻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿
⣿⣿⣿⣿⣇⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣀⣀⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠉⠁⠀⠀⣄⣹⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸
⠀⠸⢿⣿⣿⠀⠀⠙⣿⣟⣻⡟⢻⣿⣿⣶⣄⠄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡟⠉⠩⢿⣿⣿⣿⣿⣿⣿⣿⢸⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠘⢷⠖⢲⡆⠀⣀⡉⢙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣘⠻⠿⣿⣿
⠀⠀⠈⣻⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡉⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠉⠀⠀⡎⠀⠹⠃⠀⠀⠹⢦⣬⣍⡀⠈⠻⣿⣿⣿⣿⣿⡷⢀⣴⣿⠟
⠀⠀⠠⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠻⠿⠿⣿⣿⣿⡹⣿⣿⣿⢸⣿⣿⣿⣿⢸⠃⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠙⠟⠁⡼⠁⢠⣾⣿⠃⠀
⠀⠀⠀⣿⡆⠀⠀⣴⣿⣿⣿⣿⠿⠟⠁⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠁⢺⠋⠛⢸⣿⢿⣿⣿⢸⣦⢀⣤⣼⣦⣄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀
⠀⠀⠿⠿⠇⠀⠀⢿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⣿⣿⣿⢸⣷⢠⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀
⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⡤⠀⠀⠈⡙⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠋⠀⠀⠀⢠⣶⣿⣾⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣥⣤⡄⠀⢀⣄⣸⣿⣿⢸⣷⠀⠀⠀⠈⠛⢀⣤⣶⣶⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⡀⠀⠿⠿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⠦⠼⠿⠿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠿⢿⡿⢿⣿⣿⡈⢹⣿⠿⣿⣿⣿⣿⡇⠀⡾⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⢻⡿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡗⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣶⡆⢸⣆⣶⢲⣶⢎⢱⣶⠆⣾⣷⡔⣶⣶⡜⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⢳⠀⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⢧⣭⣥⣍⣉⣉⣭⣭⣠⣭⣼⡆⠉⠈⠁⢩⣭⣬⣥⣿⣬⣿⣥⣭⣭⣥⡈⠁⠈⠁⠉⣩⣭⣭⣮⣭⣤⣌⣉⣤⣽⣯⣤⣉⣉⠁⣦⡙⠋⠈⠙⠋⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⠍⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⡀⠀⠀⠀⢀⠞⠞⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠤⠤⠤⠀⠈⠀⠀⢀⡀⠈⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣏⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠭⠤⢤⣶⣆⣀⣀⣀⣀⣋⠀⠀⠀⠁⠀⠀⠀⠀⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⢼⣷⣾⣿⣯⣬⣥⣤⣄⣀⣀⣀⡀⠀⠀⠀⠈⠁⠉⠉⠙⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣠⣐⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⠿⠿⠛⠛⠛⣿⡿⠋⣿⣿⣿⣿⣶⣶⣿⠬⠭⠭⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣽⣷⣶⠆⠙⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣼⣧⣧⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣸⠟⠛⠻⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿
⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣄⣀⣤⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣦⠀⠀⠀⠈⠁⠀⠀⣀⣩⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸
⠀⠸⢿⣿⣿⠀⠀⠙⣿⣟⣻⡿⢹⣿⣿⣶⢤⠐⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠉⠄⠻⣿⣿⣿⣿⣿⣿⣿⢸⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠘⠳⠖⢲⡆⠀⣀⡈⠙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣘⠻⠿⣿⣿
⠀⠀⠈⣻⡍⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡁⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠉⠀⠀⡄⠀⠸⠃⠀⠀⠹⢦⣬⣍⡀⠀⠻⣿⣿⣿⣿⣿⠷⢄⣶⣿⠟
⠀⠀⠀⣿⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⠿⢿⣿⣿⣾⣏⣿⣿⣿⢹⣿⣿⣿⣿⢸⡇⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠘⠟⠁⠸⠁⢀⣶⣿⠃⠀
⠀⠀⢀⣿⡆⠀⠀⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠈⠁⠺⠟⠙⠙⣿⢿⣿⣿⢸⣷⠀⣤⣼⣦⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀
⠀⠀⠿⠿⠇⠀⠐⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⣿⣿⣿⢸⡿⢠⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈⢹⣹⣿⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀
⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣦⠄⠀⠀⢙⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀
⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠁⠀⠀⠀⣶⣿⣦⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠙⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣽⣥⣤⡄⠀⢀⣤⣸⣿⣿⢹⣿⡆⠀⠀⠀⠛⢃⣤⣶⣶⣤⡀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⡀⠀⠿⠿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠷⠼⠿⠿⢿⣿⢿⢿⡧⠀⠀⠀⠀⠸⢿⡿⠿⣿⣿⣄⢹⣿⡿⣿⣿⣿⣿⡇⠀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢈⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⢆⢸⣶⠆⣾⣷⡄⣶⣶⡜⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⢣⡆⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⢧⣭⣥⣍⣉⣉⣩⣭⣄⣭⣼⡇⠉⠈⠁⠩⣭⣬⣥⣿⣮⣿⣥⣭⣭⣥⡌⠁⠈⠁⠉⣩⣭⣭⣮⣭⣼⣈⢉⣤⣝⣋⣀⣉⣉⠁⣤⡙⠋⠈⠙⠋⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⠍⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⡀⠀⠀⠀⢀⠆⡏⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠤⠤⠤⠤⠌⠀⠀⠀⠀⡈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣏⣉⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠭⠤⠤⣶⣆⣀⣀⣀⣀⣋⠀⠀⠀⠁⠀⠀⠀⠀⠆⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⢼⣷⣾⣿⣧⣤⣧⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠁⠈⠈⠉⠃⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣰⣀⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠛⠋⠙⢿⡿⢉⣽⣿⣿⣿⣶⣶⣾⠼⠭⠭⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣽⣷⣶⠆⠙⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣸⠟⠛⠻⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⣿
⠿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣥⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣦⠀⠀⠀⠈⠁⠀⠀⣀⣹⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸
⠀⠸⢿⣿⣿⠀⠀⢹⣿⣟⣻⣟⢹⣿⣿⣶⢦⡐⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⠁⠐⠙⠿⣿⣿⣿⣿⣿⣿⢸⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⠷⠖⢲⡆⠀⣀⡈⠙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣙⠻⠿⣿⣻
⠀⠀⠈⣹⡍⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡁⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡟⠁⠀⠀⡀⠀⠸⠃⠀⠀⠹⢦⣬⣭⡀⠀⠻⣿⣿⣿⣿⣿⠷⢄⣴⣿⠟
⠀⠀⠠⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠿⠿⢿⣿⣿⣾⣿⢿⣿⣿⢿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠘⠟⠁⠸⠁⢀⣶⣿⠇⠀
⠀⠀⢀⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠨⢿⠛⢹⣿⢿⣿⣿⢸⣷⠀⣤⣼⣦⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀
⠀⠀⠿⠿⠇⠀⢸⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⣿⣿⣿⢸⣿⢠⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈⢹⣹⣿⠀⠀⠀⢀⣸⡿⠁⠀⠀⠀
⠀⠀⠀⣀⣶⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⢩⠛⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀
⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣿⡿⠟⠁⠀⠀⠀⣾⣿⣷⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠙⠛⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣭⣥⣤⣄⠀⠀⣤⣴⣿⣿⣧⣿⡇⠀⠀⠀⠙⢃⣤⣶⣶⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⡀⠀⠿⠿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠶⠿⠿⢿⣿⡿⣿⣿⠀⠀⠀⠀⠸⢿⡿⠿⣿⣿⣌⣿⣿⡿⣿⣿⣿⣿⡇⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⡼⠈⠏⠱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢉⢲⣆⣶⢶⡶⢰⡶⣶⢰⣶⡟⡀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣶⡆⢸⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡜⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⢢⣭⣥⣍⣉⣉⣭⣭⣄⣭⣼⣧⠉⠈⠁⠉⣭⣬⣥⣿⣮⣿⣥⣭⣭⣥⣌⠁⣬⣁⡉⣩⣭⣭⣬⣭⣼⠌⢉⣦⣝⡋⢀⣉⣉⠁⣤⡙⠋⠈⠙⠋⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⠈⠙⠿⣎⣽⣿⣿⣿⣧⣤⣸⣿⣿⣇⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⠍⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠃⢤⠀⠀⠀⠀⢠⠎⠋⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠻⠦⠠⠄⠤⠌⠄⠀⠀⠀⡌⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⢀⡆⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣏⣭⣍⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⠤⠤⠶⡦⠀⢀⣀⣀⡋⠀⠀⠀⠁⠀⠀⠀⠀⠆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⢼⣷⣶⣶⣶⣴⣥⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⣸⣈⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠉⠁⠉⢻⡏⡥⢻⣿⣿⣿⣶⣶⣾⠾⠷⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⣶⡶⠂⠙⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⢂⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠟⠛⠻⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿
⠿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣶⣾⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣀⣹⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⣀⣸
⠀⠘⢿⣿⡿⠀⠈⢻⣿⣟⣻⣟⣹⣿⣿⣶⢶⡔⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠏⠀⠁⠉⠛⣿⣿⣿⣿⣿⣿⢸⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠘⠗⠒⣲⡆⠀⢄⡈⢉⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣙⠻⠿⣿⣻
⠀⠀⠈⣩⡅⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠁⠀⠀⠀⠀⠹⠃⠀⠀⠹⢶⣤⣤⡀⠀⠻⣿⣿⣿⢿⣿⠷⢄⣤⣿⠟
⠀⠀⠰⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠻⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⡀⠘⠛⠁⠸⠁⢀⣶⣿⠃⠀
⠀⠀⢀⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠐⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢿⠇⠀⠀⠀⠀⠀⠉⠙⠃⠿⡟⢘⣿⢿⣿⣿⢸⣷⠀⣤⣼⣦⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀
⠀⠀⠿⠿⠇⠀⢺⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⣿⣿⣿⣸⡿⢠⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈⢹⣽⡿⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀
⠀⠀⠀⣀⡄⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⢨⢉⠛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⢾⣿⠁⠀⠀⠀⠀
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡻⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⣷⣷⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⠙⠛⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣥⣶⣶⣄⠀⣶⣶⣿⣿⡇⣿⣧⠀⠀⠀⠘⢃⣤⣶⣶⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⡀⠀⠻⠿⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠷⠿⠿⢿⣿⡷⣿⣿⠀⠀⠀⠀⠸⠿⡿⠿⣿⣿⣏⣿⣿⡿⣿⣿⣿⣿⡇⠀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⢈⢲⣆⣶⢶⡶⢰⡶⣶⢰⣶⡞⡄⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡜⢰⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡜⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢠⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⢠⣭⣥⣍⣉⣩⣭⣭⡄⣩⣼⣷⠉⠈⠁⠉⢭⣬⣥⣿⣮⣻⣥⣭⣭⣥⣬⣥⣌⣁⡉⢉⣭⣭⣌⣭⣾⡎⢉⣤⣝⡋⢀⣉⣉⠁⣦⡙⠋⠈⠙⠋⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠻⣿⣷⣦⣩⣿⣿⣿⠟⠁⠸⠟⢿⣇⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠩⠿⠌⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣤⠀⠀⠀⠀⡜⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠓⠤⠤⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡤⠘⠃⠀⠀⠀⠀⠀⠀⣀⠀⢰⡆⠀⠀⠉⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣬⣭⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠋⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠥⠤⠤⠶⠤⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠐⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⣾⣶⣶⣶⣶⣼⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠉⠉⠙⣿⣟⡽⣿⣿⣿⣿⠀⢀⣌⣉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⡸⢿⣿⣿⣿⣿⣿⣿⣶⣶⣷⠶⠶⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣷⣶⠶⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣤⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣦⣤⣴⣤⣤⣤⣤⣤⡼⠛⠉⠻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿
⠿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠿⠋⠀⠉⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⣀⣭⣽⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣀⣸
⠀⠸⣿⣿⡇⠀⠙⣿⣿⣛⣻⡏⣿⣿⣿⡶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣿⣿⣿⣿⣿⣿⣿⣿⠉⢸⡿⠛⣿⡇⠀⢄⡀⢉⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣉⠿⠿⣿⣿
⠀⠀⠈⣩⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠈⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢻⡏⠀⠀⠈⠀⠀⠛⠁⠀⠀⠹⢦⣤⣤⡀⠈⠻⣿⣿⣿⢿⡿⠷⢄⣴⡿⠋
⠀⠀⢰⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣃⠙⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠘⠋⠀⡜⠁⢠⣾⡿⠃⠀
⠀⠀⢸⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠻⠟⠻⢻⠿⣻⣿⡇⣽⡷⢠⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀
⠀⠀⠿⠿⠀⠀⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣇⣹⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢰⣧⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢠⢿⡟⠀⠀⠀⠀⠀
⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⣿⡿⠟⠉⠀⠀⢶⣶⣿⣿⣿⣾⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣯⠙⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣶⣿⣷⣶⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⢛⣴⣾⣿⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡀⠀⠿⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⢉⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡜⢰⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡌⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⣭⣥⣭⣉⣭⣭⣭⡄⣭⣾⣷⡍⠈⠁⠉⢩⣬⣥⣿⣮⣿⣥⣭⣭⣭⣮⣥⣬⣁⠉⢉⣭⣭⠌⠉⠀⠈⢩⣦⣝⡋⢀⣉⣉⢁⣤⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⠻⠛⣿⣿⣿⣿⣦⡙⢻⡄⠀⠀⠀⠸⠛⢿⣃⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⢁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠩⠷⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠀⣤⠀⠀⠀⢠⠊⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠚⠓⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⡄⠘⠂⠀⠀⠀⠀⠀⢀⡀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣭⣭⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠹⣿⣿⣿⡿⠿⠻⠿⣿⡿⣿⣿⣿⣿⣿⠂⠠⠤⠤⠶⠤⠤⠀⠀⠈⣁⠀⣀⠀⠀⠀⠀⠀⠐⢂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠠⣾⣶⣶⣶⣶⣾⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⢠⣿⣾⣿⣿⣿⣿⣿⠀⢀⣏⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣀⣤⣶⣷⣾⣿⣿⣿⣿⣿⣿⣶⣶⡷⠶⠶⠤⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣽⣶⣶⠖⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠉⠶⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣴⣤⣤⣤⣤⣤⡼⠛⠛⠻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿
⠿⣿⣯⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⣀⣽⣽⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸
⠀⠸⣿⣿⡇⠀⢹⣿⣿⣛⣿⣏⣿⣿⣷⡾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⠁⢸⡟⠋⣿⡇⠠⢄⡀⢙⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⡈⠻⢿⣿⣿
⠀⠀⠈⡉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⠈⠀⠀⠛⠀⠀⠠⠹⢦⣤⣤⡀⠈⠻⣿⣿⡿⢿⡿⠷⢄⣴⡿⠋
⠀⠀⢸⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣀⠙⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⠻⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⡀⠙⠋⠀⡞⠀⢠⣾⡿⠁⠀
⠀⠀⢸⣷⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⢹⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠟⠙⢿⠿⣿⣿⡇⣿⡇⢠⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀
⠀⠀⠿⠟⠀⠀⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠘⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣇⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢫⣿⡇⠀⠀⠀⣠⣼⠏⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠋⣤⣄⣠⣷⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠰⢿⡟⠀⠀⠀⠀⠀
⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣻⡿⠛⣁⣀⠀⢹⣿⣿⣿⣿⣼⡆⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⡏⠙⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⣴⣿⣿⣷⣦⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡄⠀⠿⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠈⢳⣇⣶⢶⡶⢰⣶⣶⢸⣶⡟⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡆⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡜⢹⣶⣶⢶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣟⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⢩⣥⣭⣭⣭⣭⣭⣤⣉⣾⣷⡍⠈⠁⠉⠩⣬⣥⣷⣬⣿⣥⣭⣭⣭⣮⣥⣬⣁⠉⢉⣭⣭⠈⠉⠀⠈⢩⣦⣝⡋⢈⣉⣉⢡⣆⡙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣷⣦⣉⢻⡤⠀⠀⠀⠘⠛⢿⣡⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⠷⠀⠈⠉⠉⠉⠛⠉⠙⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣤⠀⠀⠀⢠⠃⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⢀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠚⠓⠂⠀⠀⠀⠤⠤⠄⠀⠄⠀⠀⠀⠈⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠄⠀⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣬⣭⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⡿⠿⢛⠉⠉⠙⣿⣿⢿⣿⣿⣿⣿⠂⠀⠤⠤⠷⠤⠤⠤⠄⠈⠁⠀⣀⣀⡀⠀⠀⠀⠘⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠰⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⢅⠀⣄⣽⣻⣿⣿⣿⣿⣿⣿⠀⢀⣯⣭⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣶⡷⠶⠶⠦⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣷⣶⣶⡖⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⡏⠀⠉⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⢶⣦⣤⣤⣤⣤⡞⠋⠉⠻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿
⠿⣿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡶⠆⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⠀⠀⠀⠀⠀⠀⣤⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸
⠀⠹⣿⣿⠃⠈⢻⣿⣿⣏⣿⣏⣿⣿⣷⡾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⠁⢻⡟⠋⣿⡇⠠⢄⡀⢹⣿⣿⠀⢿⣿⣿⣿⣿⣿⣧⡈⠛⢿⣿⣿
⠀⠀⢀⡉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠈⠁⢀⠉⠀⠀⠀⠻⢶⣦⣤⡀⠈⠻⣿⣿⡿⢻⡿⠷⢠⣶⡿⠋
⠀⠀⢸⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣀⠽⠁⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠛⠛⠿⠿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠙⠋⠀⠚⠀⢰⣾⡿⠁⠀
⠀⠀⣸⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⢸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⡟⣿⣿⡇⣿⡇⢠⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀
⠀⠀⠟⠃⠀⠘⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣦⠤⠀⠈⣟⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⣿⣇⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢫⣿⡇⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀
⠀⠀⣀⡄⠀⠀⠹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠉⣶⣶⣶⣿⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠰⢿⡏⠀⠀⠀⠀⠀
⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣻⣋⣁⣤⣄⣸⣿⣿⣿⣿⣼⣇⠀⠀⠀⢀⣄⠀⠀⣀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⡏⠉⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⣴⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡄⠀⠿⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣼⠈⠏⢱⠣⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠈⢳⣇⣶⢶⡶⢰⣶⣶⢸⣶⡟⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡆⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡜⢱⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣟⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠛⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠩⣥⣭⣭⣭⣭⣭⣤⣩⣼⣷⣍⠈⠁⠉⠉⣬⣥⣿⣬⣿⣥⣭⣭⣭⣮⣥⣬⣁⠉⢉⣭⣭⠈⠉⠀⠈⢩⣤⣝⡋⢈⣉⣉⢡⣆⠙⠋⠈⠙⠉⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠟⠋⣿⣿⣿⣿⣿⣦⣉⢻⡴⠀⠀⠀⠘⠛⢿⣡⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠹⠷⠀⠀⠈⠉⠉⠛⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠠⡦⠀⠀⠀⠀⠆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⢀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠚⠓⠂⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⢻⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡆⠘⠀⠀⠀⠀⠀⠀⢀⡄⠀⠸⢂⠀⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⣶⣬⣭⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠟⢋⠁⠀⠉⣿⣯⡞⣿⣿⣿⣿⠒⠂⠤⠴⠿⠤⠤⠤⠤⠈⠁⠀⠀⢀⣀⠀⠀⠀⠘⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠒⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣠⣼⣹⣿⣿⣿⣿⣿⣿⠀⢠⣯⣭⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣶⣾⡷⠶⠶⠶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣾⣶⣟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⠿⠟⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⡶⠶⠶⣦⣦⣤⣤⡞⠋⠉⠻⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿
⠿⣿⣅⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠗⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⣀⠀⠀⠀⠀⠀⠀⣤⣯⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣸
⠀⠹⣿⣿⠀⠈⢻⣿⣿⣯⣿⣏⣿⣿⣷⡾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣿⣿⣿⣿⣿⣿⣿⠁⣻⡟⠩⣿⡇⠠⢤⡀⢰⣿⣿⠀⢿⣿⣿⣿⣿⣿⣧⡈⠛⠿⣿⣿
⠀⠀⢀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⠀⡀⠈⠀⢀⠉⠀⠀⠀⠻⢶⣶⣤⡀⠈⠻⣿⣿⠿⢻⡿⠿⢠⣾⡿⠋
⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⡿⠃⢠⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠙⠛⠿⠿⣿⡟⣿⣿⣿⣿⣿⡞⣿⣿⣿⡇⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠘⠃⠀⠚⠀⢰⣿⡿⠁⠀
⠀⠀⣸⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠘⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠛⠓⢾⣿⣿⡇⣿⡇⢠⣦⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀
⠀⠀⠛⠃⠀⠘⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⠦⠀⠈⣹⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀
⠀⠀⣀⡄⠀⠀⠹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠁⢹⣿⣶⣿⣿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠰⢻⡏⠀⠀⠀⠀⠀
⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣿⣛⣥⣤⣤⣌⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣤⡀⠀⣀⣀⠀⠀⣈⣿⣿⣿⣿⣿⣿⡏⠉⢛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⣱⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡄⠀⠿⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣆⣶⢶⡶⢰⣶⣶⢸⣶⡟⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡆⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡜⢱⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢸⣟⢸⣟⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⣥⣭⣭⣭⣭⣭⣤⣩⣼⣷⣭⠈⠁⠉⠉⢨⣥⣿⣬⣿⣥⣭⣭⣭⣮⣥⣬⣅⡉⢉⣭⣭⠈⠉⠀⠈⢩⣤⣝⡋⢈⣉⣉⣡⣄⡙⠋⠈⠙⠋⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠉⣿⣿⣿⣿⣿⣦⣍⢻⡖⠀⠀⠀⠙⠛⠻⣥⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠉⠉⠛⠉⠉⠉⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠉⢠⡆⠀⠀⠀⠀⡜⠘⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⢛⡓⠒⠂⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠘⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆⠘⠀⠀⠀⠀⠀⠀⢠⡄⠀⠸⢀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣧⣬⣭⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⣿⡿⠟⢛⡥⠀⢈⣻⣟⡟⣿⣿⣿⣿⠒⠒⠶⠶⠿⠤⠤⠤⠤⠬⠁⠀⠀⠀⠀⢀⠀⠀⠘⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣐⣲⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⠀⣀⠀⠀⠀⠈⠀⠀⠐⠀⠀⢀⣐⣀⣰⣴⣯⣿⣿⣿⣿⣿⣿⠀⢠⣧⣭⣭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣾⡷⠒⠶⠶⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣒⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⢿⣅⡀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣶⣶⡶⠶⠶⠶⠶⢶⣤⡟⠉⠉⠻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠛⣿
⠿⣿⡀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⠿⠛⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣤⣼
⠀⠻⣿⣿⠀⠈⢿⣿⣿⣯⣿⣏⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⣀⣛⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣀⣹⣿⣿⣿⣿⣿⡏⠃⣻⠟⢹⣿⠁⠠⢤⡀⠸⣿⡿⠀⢿⣿⣿⣿⣿⣿⣧⡈⠛⢻⣿⣿
⠀⠀⢀⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠸⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠃⠀⡀⠈⠀⢀⠉⠀⠀⠠⠛⢶⣶⣤⣀⠈⠻⣿⣿⠿⢿⠿⠓⢠⣾⡟⠁
⠀⠀⢸⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣀⡿⠃⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠘⠛⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣷⡀⠉⠁⠀⠏⠀⣰⣿⡟⠁⠀
⠀⠀⣸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠛⢳⣿⣿⡇⣿⡇⢰⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡏⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀
⠀⠘⠛⠃⠀⠘⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⡖⠀⠈⢩⡙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣿⠇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡇⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀
⠀⠀⣀⡄⠀⠀⠹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⢹⣿⣿⣿⣿⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠸⢻⡏⠀⠀⠀⠀⠀
⠀⠈⡻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣽⣫⣥⣴⣦⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣤⡀⢀⣀⣀⡀⠀⣬⣿⣿⣿⣿⣿⣿⡇⠉⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢰⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡄⠀⠿⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣼⠈⠏⢱⠣⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣇⣶⢶⡶⢰⡶⣶⢸⣶⡟⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡆⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡌⢱⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣟⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⢡⣭⣭⣭⣭⣭⣤⣩⣼⣷⣭⠈⠁⠉⠉⠨⣥⣿⣬⣿⣥⣭⣭⣭⣮⣥⣬⣅⡉⢉⣭⣭⠈⠉⠀⠈⢩⣦⣝⡋⣈⣉⣍⣡⣦⠙⠋⠈⠙⠋⠀⠀⠀
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢺⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠛⠉⢿⣿⣿⣿⣿⣦⣍⢻⠄⠀⠀⠀⠙⠙⢻⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⠈⠁⢰⡆⠀⠀⠀⠀⠘⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠼⠗⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡒⣛⣒⠒⠒⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠘⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠆⠉⠀⠀⠀⠀⠀⠀⢠⡄⠀⠾⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣧⣬⣭⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢈⣿⠟⢛⡭⠀⠀⣹⣿⣝⣻⣿⣿⣿⠒⠒⠒⠾⠷⠤⠤⠤⠤⠬⠄⠀⠀⠀⠀⠀⠀⠀⠙⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣐⣲⣿⣿⣿⣶⣶⣷⣶⣤⣤⣤⣤⣤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⣔⣠⣤⣶⣏⣿⣿⣿⣿⣿⡯⠀⢴⣥⣭⣭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⠒⠲⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣟⣋⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠿⢿⣧⣄⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⡶⠶⠶⠶⠶⠦⢤⠟⠉⠉⢻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠛⣿
⠿⣧⡀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠛⠃⠀⣉⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡄⣀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣤⣽
⠀⠻⣿⡇⠀⠈⣿⣿⣿⣭⣿⣻⣿⣿⣿⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣀⣉⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⡏⠃⣿⠋⢹⣿⠀⠢⢄⡀⠸⠿⠿⠀⢿⣿⣿⣿⣿⣿⣧⡉⠛⢿⣿⣿
⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠁⢈⡆⠈⠀⢀⠉⠀⠀⠠⠛⢶⣶⣦⡀⠈⠻⣿⣿⠟⣿⠟⠓⢠⣾⡟⠁
⠀⠀⣗⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣧⡀⠉⠁⠀⠏⠀⣰⣿⠟⠀⠀
⠀⢀⣸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠛⠛⢻⣿⣿⡇⣿⠇⣴⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀
⠀⠘⠛⠀⠀⠘⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡖⠀⠀⢩⡙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣿⠃⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠇⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀
⠀⢀⣠⡀⠀⠀⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⠟⠁⢸⣿⣿⣿⣿⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠼⣿⡇⠀⠀⠀⠀⠀
⠀⢈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣯⣫⣥⣶⣶⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣤⡀⢀⣠⣤⣀⠀⣬⣿⣿⣿⣿⣿⣿⡇⠉⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀
⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡄⠐⠿⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣇⣿⢶⡶⢰⡶⣶⢸⣶⡞⡍⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣶⡆⢸⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡌⢱⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠡⣭⣭⣭⣭⣭⣤⣉⣼⣷⣭⠈⠁⠉⠉⠈⣥⣷⣬⣿⣥⣭⣭⣭⣮⣥⣬⣁⡉⢉⣭⣭⠈⠉⠀⠈⣩⣤⣝⠋⣬⣉⣍⣡⣆⠙⠋⠈⠙⠋⠀⠀⠰
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠛⠉⢺⣿⣿⣿⣿⣦⣍⢻⠆⠀⠀⠀⠙⠙⢻⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⢕⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠈⠁⢶⠀⠀⠀⠀⠀⠰⠁⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠠⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣚⣛⡒⠒⠒⠀⠀⠀⠀⠠⠄⠠⡄⠀⠀⠀⠘⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢶⠀⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⢼⣦⣭⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡃⠀⠈⢻⣿⠿⢿⣯⠁⠀⣹⣿⣻⢻⣟⣿⡗⠒⢒⠒⠾⠧⠤⠤⠤⠤⠬⠀⠀⠀⠀⠀⠀⠀⢀⢃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣺⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⡀⢀⡀⠀⠀⠀⠀⠀⠘⠋⠁⠀⣄⣂⣀⣦⣟⣿⣿⣿⣿⣿⡇⠠⢼⢤⣥⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣛⣓⠒⢺⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣟⣁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡿⢿⣃⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠶⠶⠶⠶⢶⠏⠉⠉⢻⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣯⣭⠉⠻⣿
⢿⣄⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⡦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠛⠂⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⠀⢀⠀⠀⠀⢠⣴⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣽⣿⣦⣤⣿
⠘⢻⣿⠀⠀⠹⣿⣿⣯⣽⣿⣹⣿⣿⡿⠻⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣸⣿⣿⣿⣿⡿⠏⢸⣿⠋⣿⣿⠀⠢⣄⡀⠼⠿⠇⠸⣿⣿⣿⣿⣿⣿⣦⠉⠛⢿⣿⣿
⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢻⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⣿⣿⢹⣿⠀⢠⡀⠇⠀⡈⠁⠀⠀⠌⠛⣶⣶⣦⡀⠈⢿⣿⡿⠛⣿⠛⠓⣴⣿⠋⠈
⠀⠀⡇⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣇⣼⠟⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠛⠻⠿⢿⢻⣿⣿⣿⣿⣿⣿⣧⣽⣿⢸⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠉⠀⠠⠁⠀⣾⣿⠋⠀⠀
⠀⢀⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠛⢻⣿⣽⢸⣿⠀⣶⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠇⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀
⠀⠛⠛⠀⠀⢸⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣖⣀⠀⢹⡙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀
⠀⢀⣤⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠟⠁⢸⣿⣿⣿⣿⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠞⣿⠁⠀⠀⠀⠀⠀
⠀⢙⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣯⣯⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⣦⠀⢀⣤⣤⣄⡠⣭⣿⣿⣿⣿⣿⣿⠆⠉⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀
⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⡄⠰⠟⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣇⣷⢶⡶⢰⣶⣶⢸⣶⡞⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡇⢸⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡌⢱⣶⣶⣶⣞⠶⠀⠀⠀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⢰
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠩⣭⣭⣭⣭⣭⣤⣩⣼⣷⣭⠈⠁⠉⠉⠈⢥⣿⣬⣿⣥⣭⣭⣭⣮⣥⣬⣁⡉⢉⣭⡍⠈⠉⠀⠈⣩⣦⣝⠋⣬⣉⣉⣡⣄⠙⠋⠈⠙⠋⠀⠀⢸
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠋⠁⠻⣿⣿⣿⣿⣦⣉⡻⠆⠀⠀⠀⠉⠙⢧⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠟⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠉⠀⡶⠀⠀⠀⠀⠀⢠⠋⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⠤⠿⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣚⣓⡒⠒⠂⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⢿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡶⠈⠁⠀⠀⠀⠀⠀⠀⣤⠀⠸⠇⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣿⢤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠀⠀⢩⣿⣿⠿⣟⡉⠉⠙⣿⣿⢿⣿⣿⡗⠒⡒⠒⠻⠒⠠⠠⠤⠤⠥⠤⠀⠀⠀⠀⠀⠀⠈⢡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣿⣿⣿⣷⣶⣾⣶⣶⣦⣤⣤⣤⣤⣄⡀⢀⡀⠀⠀⠀⠈⠀⠀⠃⠉⠀⢠⣅⣀⣀⣽⣻⣿⣿⣿⣿⠅⠠⣦⢤⣤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣛⣓⠒⣲⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣟⣋⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⢿⣟⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠶⠶⠶⠶⠾⠉⠀⠙⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⢻⣿
⣯⡀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⡦⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠒⠀⠚⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⢀⣀⣀⣀⡀⠀⠀⢤⡶⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣯⣽⣿⣤⣼⣿
⠘⢿⡇⠀⠀⢻⣿⣿⣯⣿⣏⣿⣿⣿⠟⠻⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠿⠁⢸⡟⠁⣿⡇⠐⠢⣄⠀⠿⠿⠃⠸⣿⣿⣿⣿⣿⣿⣦⠙⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡈⣿⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣶⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⡇⠀⣰⠠⠀⠀⠉⠀⠀⠀⠞⠻⣶⣶⣄⡀⠙⢿⣿⠟⠻⡿⠛⢃⣾⡿⠁⠈
⠀⢸⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣥⣼⠗⠀⢠⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⢸⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠁⠀⠸⠀⢠⣿⡟⠁⠀⠀
⠀⣸⡆⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢛⠛⢻⣿⣬⢸⡿⢰⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀
⠀⠛⠃⠀⠀⢻⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣖⣀⠈⢩⡙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⡟⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡏⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀
⠀⣠⣄⠀⠀⠘⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠟⠁⠸⣿⣿⣿⣿⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠐⢻⣿⠀⠀⠀⠀⠀⠀
⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣯⣯⣴⣶⣶⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⣶⠀⢀⣤⣤⣤⣠⣽⣿⣿⣿⣿⣿⣿⠀⠉⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀
⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⠀⠰⠟⠿⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣇⣷⢶⡶⢰⡶⣶⢸⣶⡞⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡌⢰⣶⣶⣶⣞⠶⠀⠀⢀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣾⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠛⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⠀⣸
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠡⣭⣭⣭⣭⣭⣤⣩⣼⣷⣭⠈⠁⠉⠉⠈⢡⣿⣬⣿⣥⣭⣭⣭⢮⣥⣬⣁⠉⢉⣭⡉⢈⠉⠀⢈⣩⣦⡝⢋⣬⣉⣉⣡⡄⠙⠋⠈⠙⠋⠀⠀⢿
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠉⠀⠹⣿⣿⣿⣿⣦⣉⡿⠀⠀⠀⠀⠉⠙⢷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣣⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⠀⠀⠀⠁⠰⠆⠀⠀⠀⠀⠀⠀⠞⠃⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠠⠼⠿⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣛⣒⠒⠒⠒⠐⠂⠀⠀⠀⠠⠤⠠⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⠆⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⡧⢤⣤⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠃⠁⢙⢾⣿⣿⡿⣟⠛⠛⢿⣿⣿⣿⣿⠒⠒⡒⣚⡛⠒⠂⠀⠤⠠⠤⠤⠄⠄⠀⠀⠀⠀⢈⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣷⣶⣷⣶⣶⣶⣤⣤⣤⣤⣤⣄⠀⡀⠀⠀⠀⠈⠁⠀⠲⡊⠁⠀⡈⠅⠀⣀⡾⣿⣷⣿⣾⠄⠠⡧⢤⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⢲⣴⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣟⣛⣓⡒⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⣿⣿⣟⣋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠋⠘⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠿⠶⠶⠶⠶⠶⡟⠁⠈⠹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⡍⠙⣿⣿
⣅⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⢇⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠴⠦⠄⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⣀⡀⠀⠀⢤⡶⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣴⣿⣿
⠻⣿⠁⠀⠈⣿⣿⣿⣭⣿⣿⣿⣿⣿⡟⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⡿⠏⠁⣿⠋⢹⣿⠇⠐⠦⣄⠸⠿⠿⠀⢿⣿⣿⣿⣿⣿⣷⡄⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠸⣷⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠃⠀⡆⠸⠀⢨⠉⠀⠀⠀⠛⢳⣶⣶⣄⠀⠻⣿⡿⠛⢻⡟⠛⢰⣾⠟⠁⠙
⠀⠇⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣤⣿⠃⠀⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠟⠛⠻⠿⠏⣿⣿⣿⣿⣿⣿⣿⣷⡜⡇⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⡄⠈⠀⠀⠍⠀⣸⣿⠏⠀⠀⠀
⢀⣰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠈⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢛⠛⢛⣿⡄⣿⡇⢰⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀
⠘⠛⠀⠀⠀⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠖⠀⠈⢩⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣧⣿⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡇⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀
⢀⣠⡄⠀⠀⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠟⠁⢹⣿⣶⣾⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀
⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣯⣯⣤⣴⣤⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠰⣶⠀⣀⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⡗⠈⢉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣆⠀⠰⠛⠻⠷⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⢿⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣇⣿⢶⡶⢰⣶⣶⢸⣶⡞⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡇⢺⣆⣶⢶⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡌⢰⣶⣶⣶⣞⠶⠀⠀⣀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⠀⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⣭⣭⣭⣭⣭⣤⣩⣼⣷⣭⠈⠁⠉⠉⠈⢡⣿⣬⣿⣥⣭⣭⣭⢮⣥⣌⣁⠉⣩⣭⠉⠈⠉⠀⢨⣩⣦⠙⣋⣬⣉⣉⣥⡀⠙⠋⠈⠙⠋⠀⠰⣿
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠛⠉⠀⠻⣿⣿⣿⣷⣦⣹⠟⠀⠀⠀⠈⠉⠛⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠺⠃⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡀⠀⠀⠈⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠟⠑⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠿⠧⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣈⣓⣒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠠⠄⠼⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠉⠀⠀⠀⠀⠀⠀⣤⠀⠀⠿⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⠦⢤⣤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡛⠜⠈⢿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣟⠒⢒⣒⣚⠓⠒⠂⠀⠀⠤⠄⠤⠄⠄⠀⠀⠀⠀⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⠀⠄⠀⠀⠀⠉⠁⠠⠿⠟⠉⠀⣘⠁⠀⢠⣿⣷⣿⣯⡷⢼⠤⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣷⣷⣾⣿⣾⣿⣿⣿⣿⣿⣛⣛⣓⣺⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠋⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠷⠶⠶⠶⠶⠶⠏⠁⠈⢻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣽⣯⠉⠻⣿⣿
⡀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⡿⢢⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢁⣤⡀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣄⣀⣀⣀⠀⠀⠠⢤⣶⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣦⣿⣿
⢿⡏⠀⠀⠹⣿⣿⣯⣽⣿⣸⣿⣿⣿⠻⠇⠉⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⡿⠇⠨⡿⠉⢿⣿⠀⠒⢤⡀⠸⠿⠇⠘⣿⣿⣿⣿⣿⣿⣷⡄⠉⢻⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢹⣇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⣧⣿⣿⣿⣿⣷⣿⣿⡿⣿⣏⣿⠀⢠⡆⡇⠀⠈⠁⠀⠀⠒⠛⢷⣶⣦⣀⠈⠻⣿⡿⠛⣿⠛⠓⣰⣿⠋⠈⠙
⠐⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣧⣬⡿⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠻⠿⠿⣿⣿⣿⣿⣇⣿⣿⣷⡘⡹⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠉⠀⠀⠃⢀⣾⡿⠃⠀⠀⠀
⢀⣆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠉⠛⣷⣼⣿⠁⣶⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀
⠛⠛⠀⠀⢸⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠦⠀⠈⢙⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⣼⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀
⢀⣤⠀⠀⠀⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⢻⣷⣶⣼⣷⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠛⣿⠃⠀⠀⠀⠀⠀⠀
⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣽⣫⣥⣦⣄⣬⣿⣿⣿⣿⢿⣷⡀⠀⠀⠰⣶⠀⢀⣤⣤⣴⣮⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡄⠀⠐⠛⠻⠿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⢧⣿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣇⣷⢶⡶⢰⡶⣶⢸⣶⡟⡍⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⠀⣀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⠀⢸⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠉⢭⣭⣭⣭⣭⣤⣩⣼⣷⣭⡈⠁⠉⠉⠈⢥⣿⣬⣿⣥⣭⣭⣭⢮⣥⣌⣁⣩⣭⣭⠉⡈⠉⠀⣬⣭⣦⠙⣋⣬⣉⣉⣅⠀⠙⠋⠈⠙⠋⠀⢸⣿
⠀⠄⠰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠉⠀⠻⣿⣿⣿⣿⣿⣻⠏⠀⠀⠀⠈⠉⠻⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠟⠃⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡀⠀⠀⠉⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⠤⠿⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣙⣓⡒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠠⠤⠤⡌⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠶⠀⠁⠀⠀⠀⠀⠀⠀⣤⠀⠘⠇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠤⢤⣤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⠟⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⢒⣒⣛⠓⠒⠂⠀⠤⠠⠄⠤⠤⠀⠀⠀⠀⠈⢡⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣾⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⡀⣀⡀⠀⠀⠉⠛⠀⣾⣿⡿⠛⠉⠛⠂⡀⣸⣿⣹⡿⣠⣶⠤⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣶⣽⣴⣶⣯⣿⣿⣿⣿⣿⣛⣛⣒⣺⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⡁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠶⠶⠶⠶⢾⠋⠁⠉⢿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣽⣯⠉⢻⣿⣿
⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣾⡿⣰⡦⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⢀⡀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣀⣀⣀⣀⠀⠀⢠⣶⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢿⣽⣿⣴⣾⣿⣿
⣿⠁⠀⠀⢻⣿⣿⣯⣽⣏⣿⣿⣿⢿⠻⠀⠙⠛⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⢻⣿⣿⣿⣿⡿⣿⣧⣼⣿⣿⣿⠿⠉⢸⡟⠁⣿⡯⠀⠲⢤⡀⠹⠿⠃⠸⣿⣿⣿⣿⣿⣿⣦⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡆⠀⠀⠁⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⣿⣿⣿⣸⣿⣿⣿⣿⡇⣿⣿⡿⣿⢸⡏⠀⣰⠀⠃⠀⡍⠁⠀⠀⠊⠛⣷⣶⣦⡀⠘⢿⣿⠟⠋⡿⠛⢃⣾⡿⠁⠈⠛
⠸⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣼⡿⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⠿⠿⢻⣿⣿⣿⣿⡇⣿⣿⣷⡘⢸⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣦⠀⠁⠀⠸⠁⢠⣿⡟⠁⠀⠀⠀
⣰⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣍⠉⠉⣳⢸⣿⠀⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀
⠛⠃⠀⠀⢸⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠛⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⣿⣼⣿⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀
⣀⣄⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠋⢰⣶⣤⣠⣶⡄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠐⢻⣿⠀⠀⠀⠀⠀⠀⠀
⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣛⣭⣤⣄⣀⣿⣿⣿⣿⢿⣿⣄⠀⠀⠀⢶⡆⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⠂⠉⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⠀⠀⠈⠛⠻⠷⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⠿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⢧⡿⡼⠈⠏⢱⠳⠀⠀⠀⠀
⠀⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣿⢶⡶⢰⡶⣶⢸⣶⡟⡏⣷⢰⣶⣰⣶⢸⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⢀⣀
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⠀⣸⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣭⣭⣭⣤⣍⣼⣷⣭⣬⡁⠉⠉⠈⢡⣿⣬⣿⣥⣭⣭⣭⢮⣥⣌⡁⢉⣭⣍⣩⣬⡉⠀⣬⣭⡤⢙⣋⣬⣍⣭⣁⠀⠙⠋⠈⠙⠋⠀⢿⣿
⠀⠀⠲⢦⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⣿⣿⣿⣿⠀⣠⡄⠀⠀⢻⣿⣿⣿⠟⠉⠀⠙⣿⣿⣿⣶⣼⣿⣿⣿⡃⠀⠁⠉⢳⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⣰⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠸⠛⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⠀⠀⠀⠁⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠸⠿⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣛⣒⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠤⠤⠄⢸⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠸⠄⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⣤⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠿⣿⡿⠛⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡒⣒⣒⡛⠒⠒⠀⠀⠠⠤⠠⠤⠤⠀⠀⠀⠀⠈⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠈⠓⠆⢐⣿⡿⠟⠋⠻⠂⠀⢀⣿⣯⣿⣒⣷⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡊⠁⠀⠀⠀⠀⠀⠀⠉⢁⣀⣰⣮⣦⣴⣾⣽⣿⣿⣿⣟⣛⣛⣒⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣿⣿⣿⣯⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⣩⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠶⠶⠶⠶⡿⠉⠀⠙⣿⣿⣿⠃⣺⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⣿⣿⣿
⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⠇⣴⠼⠄⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⢟⣦⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣀⣀⡀⠀⠀⠤⣾⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⢯⣿⣷⣴⣼⣿⣿
⡟⠀⠀⠈⣿⣿⣿⣭⣿⣯⣿⣿⣿⡟⠟⠈⠙⠑⡶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⠿⠀⢿⠏⠹⣿⡇⠐⠢⣄⠀⠿⠿⠀⢻⣿⣿⣿⣿⣿⣷⣆⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⠀⠀⠈⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⡿⣻⡇⠀⣤⢸⠀⢠⠉⠀⠀⠐⠘⠻⣿⣶⣄⡀⠙⣿⡿⠛⢹⡟⠛⣰⣿⡏⠁⠉⠛
⠂⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣠⣿⣧⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⡿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣷⡀⣼⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠈⠀⠀⠘⠀⣸⣿⠏⠀⠀⠀⠀
⣠⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠈⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠉⠉⠁⢿⡇⢰⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀
⠛⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣦⡄⠀⠐⠛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⣠⣾⡇⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀
⣠⡄⠀⠀⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠉⢲⣦⣄⣴⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣶⣾⣿⣿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀
⠻⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣫⣥⣤⣀⣸⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣆⠀⣀⣠⣸⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢹⣇⡀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⠀⠀⠈⠛⠻⠷⠆⠀⠀⠀⢠
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡷⠀⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⢷⡿⡼⠈⠏⢱⠳⠀⠀⠀⠘
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡍⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⣠⣈
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣾⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⠀⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⣭⣭⣭⣤⣭⣸⣷⣭⣬⣅⠉⠉⠈⠱⣿⣬⣿⣥⣭⣭⣭⣮⣥⣌⡁⢉⣩⡍⢉⠈⠉⢀⣬⣭⡄⢙⣋⣬⣭⣭⡁⠀⠙⠋⠈⠙⠋⠀⣿⣿
⠀⠀⠰⢲⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢻⣿⣿⣿⡧⠀⠀⠀⠀⠹⣿⣿⣿⠿⠋⠁⠸⣿⣿⣿⣦⣌⣿⣷⣶⡆⠀⠁⠙⢳⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⣰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠺⠛⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⠈⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠻⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣘⣓⡒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⢰⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠉⠀⠀⠀⠀⠀⠀⢠⡄⠀⠻⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣤⣤⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⡿⣿⠍⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡖⣒⣚⡛⠒⠂⠀⠀⠤⠄⠀⠤⠤⠄⠠⠀⠀⠉⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣷⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠈⠛⠓⣐⣽⡿⠛⠉⢙⠁⠠⢠⣿⣷⣭⣯⣷⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⡛⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡆⠉⠀⠀⠀⠀⠀⠀⠨⢥⣤⣴⣿⣿⣾⣿⣾⣿⣿⣿⣟⣛⣛⣒⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⡀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡏⠱⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠶⠷⠶⡿⠉⠀⠙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠙⣿⣿⣿
⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢰⣿⢆⣴⠿⡇⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣀⣀⣀⡀⠀⠀⢴⣾⣾⣿⠀⣿⣿⣿⣿⣿⣿⡿⢯⣿⣷⣶⣿⣿⣿
⡇⠀⠀⠘⣿⣿⣿⣽⣿⣹⣿⣿⣿⠟⠏⠘⠋⠳⡶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣼⡟⣿⣿⣿⣿⣿⢿⣿⣧⣼⣿⣿⡿⠇⠁⣿⠉⢸⣿⠇⠐⠢⣄⠀⠿⠟⠀⢿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⠀⠀⠈⡱⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣇⣿⣿⣿⣿⣿⢸⣿⣿⡿⣯⣿⠁⠀⡆⠘⠀⢨⠉⠀⠀⠐⠘⠻⣿⣶⣄⡀⠹⣿⡿⠛⣹⠛⢙⣸⣿⠏⠀⠉⠛
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⡇⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠿⠿⡟⣿⣿⣿⣿⣿⢸⣿⣿⣿⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡄⠀⠀⠀⠃⢀⣾⡿⠋⠀⠀⠀⠀
⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⢹⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠉⡉⠀⣿⡇⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀
⠿⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣦⠄⠀⠛⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠀⡇⢠⣿⡇⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠋⠹⣿⣶⣼⣶⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣶⣷⣿⣿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣛⣭⣤⣄⣠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣦⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠀⢉⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠀
⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠈⠛⠿⠿⠆⠀⠀⠀⣰
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣷⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⢘
⠀⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢾⡶⢸⣶⣶⢸⣶⡟⡈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⣤⣸
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣿⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠛⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⠀⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⣭⣭⣭⣤⣭⣤⣧⣭⣬⣥⠉⠉⠈⠱⣿⣬⣿⣥⣭⣭⣭⣮⣥⣌⡁⢉⣭⡉⢉⠈⠉⢠⣮⣭⡄⢙⣫⣬⣭⣭⡁⠀⠙⠋⠈⠙⠋⠘⣿⣿
⠀⠀⠲⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⣿⣿⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⠿⠋⠁⠸⣿⣿⣿⣶⣬⡿⢃⢀⠀⠀⠀⠉⢲⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⢀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⣰⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠚⠃⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⠉⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣚⣓⠒⠒⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⢸⠁⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠉⠀⠀⠀⠀⠀⠀⣤⠀⠀⠻⠄⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣭⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⢿⣿⡿⢉⣿⣿⣿⣿⣿⠿⠻⢿⣿⡿⣿⣒⣒⣚⠓⠒⠒⠒⠀⠠⠀⠠⠤⠤⠄⠄⠀⠀⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣾⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠛⠃⢸⣿⠟⠋⠑⣋⠁⠀⣲⣿⣾⣟⣿⡷⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠟⡛⢻⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡆⠉⠀⠀⠀⠀⠀⠀⠀⣥⣤⣼⣿⣿⣾⣿⣿⣿⣿⣿⣛⣛⣛⣲⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣥⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⡀⠀⠀⠀⠀⣉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡃⠚⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠾⠷⠶⡟⠁⠀⠙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⠈⠙⣿⣿⣿
⢹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣷⢆⣤⠿⡄⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣀⣀⣀⡀⠀⠀⢶⣾⣿⣿⢀⣿⣿⣿⣿⣿⣿⡿⢾⣿⣶⣦⣿⣿⣿
⠃⠀⠀⠹⣿⣿⣿⣽⣿⣹⣿⣿⣿⡿⡇⠘⠛⢲⡆⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣾⡇⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡿⢇⠠⣿⠉⢸⣿⠁⠐⠢⣄⠘⠿⠏⠀⢿⣿⣿⣿⣿⣿⣷⡄⠙⣻⣿⢿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣷⠀⠀⠈⣡⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⠀⢠⡆⡆⠀⢨⠉⠀⠀⠐⠘⢻⣿⣶⣄⡀⠹⣿⠟⠋⣽⠋⢉⣾⣿⠃⠀⠉⠛
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣏⣨⣿⡇⡄⠈⠁⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠿⢟⣿⣿⣿⣿⣿⣼⣿⣿⣿⡜⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠃⢀⣾⡿⠁⠀⠀⠀⠀
⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠉⡉⠀⣿⡇⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠿⠀⠀⠸⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣶⠄⠀⢙⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⣗⢀⣿⡃⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠈⣿⣷⣼⣷⡄⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣶⣿⣾⣿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠿⠇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⣭⣶⣤⣠⣹⣿⣿⣿⣿⣿⡄⠀⠀⠠⣦⠀⢀⣀⣘⣿⣿⣿⣿⣿⣿⡿⠀⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⣿⡅⡀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠈⠛⠻⠿⠆⠀⠀⠀⣴
⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠠⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣷⢿⡿⡼⠈⠏⢱⠳⠀⠀⠀⢙
⠖⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⡀⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣿⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⠀⣤⣼
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⣴⣧⣭⣬⣥⠉⠉⠈⠁⣿⣬⣿⣥⣭⣭⣭⣮⣥⣌⡁⢉⣩⡍⡉⠈⠉⢠⣬⣭⡄⢙⣫⣬⣭⣭⡁⠀⠙⠋⠈⠙⠋⢘⣿⣿
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⠿⠋⠁⠘⣿⣿⣿⣶⣬⡟⢃⣀⠀⠀⠀⠉⢳⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⢀⣴⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠉⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⠻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠠⠿⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⡓⠒⠂⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⡸⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠁⢀⠀⠀⠀⠀⠀⣤⠀⠀⠃⠄⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⣭⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠙⣿⣿⣿⣿⣿⠟⠛⢿⣿⢿⣷⣒⣒⣚⡓⠒⠒⠒⠀⠠⠀⠀⠠⠤⠤⠄⠀⠀⠡⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣾⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⠛⠇⢴⣿⡟⠋⠙⡊⠀⠀⣾⣿⣾⣾⣿⡧⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⢿⣛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣷⡔⠉⠀⠀⠀⠀⠀⠀⠠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣺⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⡄⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡁⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⠿⠿⠷⠶⡏⠁⠈⠹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠹⣿⣿⣿
⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣶⢀⣤⣿⡆⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⡇⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣤⣀⣀⣀⡀⠀⠀⢶⣿⣿⣏⢠⣿⣿⣿⣿⣿⣿⠷⢾⣿⣶⣦⣿⣿⣿
⠂⠀⠀⢻⣿⣿⣟⣻⣿⣹⣿⣿⣿⠿⠇⠛⠛⢶⡆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡏⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡿⠇⠩⡿⠁⢸⣿⠀⠐⠢⣄⠘⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⡀⠙⣿⣿⢿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡅⢻⣆⠀⠀⠈⣡⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣇⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⢠⡆⡇⠀⠬⠉⠀⠀⠀⠙⢻⣿⣶⣄⠀⠹⣿⠟⠉⡿⠉⢉⣾⡿⠁⠀⠉⠛
⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⡀⠀⠜⠁⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠿⠿⢟⣿⣿⣿⣿⣧⣿⣿⣿⣿⡏⣿⡀⠀⠁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠁⢀⣿⡟⠁⠀⠀⠀⠀
⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⠉⡉⠀⣾⡃⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠿⡿⣿⡇⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀
⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣶⠄⠀⠙⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⣷⠀⣿⠃⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠏⠈⣿⣷⣾⣷⡄⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣾⣿⣶⣿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⠆⠀⠐⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⣭⣤⣦⣤⣼⣿⣿⣿⣿⣿⡄⠀⠀⠠⣦⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⡇⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠈⠛⠻⠿⠆⠀⠀⠀⣾
⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⢠⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⢿⡟⡼⠈⠏⢱⠳⠀⠀⠀⢛
⠿⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⡀⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢀⣤⣼
⠃⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⣼⣧⣭⣬⣅⠉⠉⠈⠁⢿⣬⣿⣥⣭⣭⣭⡮⣡⣌⡁⢉⣩⡉⠉⠈⠉⠠⣬⣩⡄⣙⣫⣬⣭⣭⡁⠀⠙⠋⠈⠙⠋⢸⣿⣿
⠰⠆⠲⣶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⠿⠋⠁⠈⢿⣿⣿⣶⣬⡟⠁⡀⠀⠀⠀⠉⢺⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⢀⣴⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠁⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠠⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⡒⠒⠂⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⡌⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠈⠁⢀⠀⠀⠀⠀⠀⣤⠀⠈⠣⠀⠀⠀⠀⢀⡀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⣭⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⣯⠹⣿⣿⣿⣿⣿⠟⠛⢿⣿⢿⣗⣒⣒⣛⡓⠒⠒⠒⠂⠀⠀⠀⠀⠤⠤⠤⠀⠀⠡⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⠚⠆⣾⣿⡟⠋⠙⡊⠀⣀⡾⣿⣿⣿⣾⠶⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢿⣿⣛⡛⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠐⠁⠀⠀⠀⠀⠀⠠⠬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣺⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣯⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠻⢿⣿⣿⠟⠁⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠻⠿⠿⠷⢾⠏⠀⠀⠹⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠹⣿⣿⣿
⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣶⡶⢠⣤⣿⡀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣴⠇⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄⣀⣀⣀⡀⠀⠐⢶⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠷⣿⣿⣶⢲⣿⣿⣿
⠂⠀⠈⢻⣿⣿⣛⣿⣏⣿⣿⣿⣿⢿⠇⠛⠓⢶⡆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⠿⠏⠸⡟⠁⢿⣿⠀⠐⠲⣄⠘⠛⠃⠘⢿⣿⣿⣿⣿⣿⣿⡈⢹⣿⣿⢿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣆⠀⠀⠊⣤⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣶⣾⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⠀⢰⡀⡇⠀⡌⠁⠀⠀⠒⠙⢻⣿⣶⣄⠈⠻⣿⠟⠉⡿⠉⣡⣿⡿⠁⠀⠉⠛
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⡀⠀⡜⠋⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠿⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⡄⠀⠀⠘⠁⣰⣿⠟⠀⠀⠀⠀⠀
⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣋⠉⡉⠉⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⡿⣿⠁⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀
⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⠀⠀⢉⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⢀⣗⢀⣿⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠈⣿⣷⣾⣷⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣾⣿⣾⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠄⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣝⣭⣴⣶⣤⣼⣿⣿⣿⣿⣿⡀⠀⠀⢰⣦⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠀⢀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⠛⠻⠿⠆⠀⠀⠀⣾
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⢰⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⢿⡿⡼⠈⡏⢱⠳⠀⠀⠀⣛
⡿⠇⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⡀⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢶⡶⢢⣶⡇⢲⣆⣶⢶⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢠⣦⣽
⠒⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⣼⣧⣭⣬⡅⠉⠉⠈⠁⢻⣬⣿⣥⣭⣭⣭⠎⣡⣌⡁⢉⣩⡉⠉⠈⠉⢰⣮⣩⠀⣙⣫⣬⣭⣭⠁⠀⠙⠋⠈⠙⠋⢸⣿⣿
⢰⠆⠲⣶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⠟⠋⠀⠀⢻⣿⣿⣶⣬⠟⣀⡀⠀⠀⠀⠙⢾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⠿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⢀⣴⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⡀⠀⠐⠛⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡿⠿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⠠⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⡒⠒⠒⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⡌⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠈⠁⢀⠀⠀⠀⠀⠠⡤⠀⠘⠣⠀⠀⠀⠀⢀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⢿⢿⠟⠉⣿⣿⣿⣿⡿⠛⠛⢿⣿⢿⣗⣒⣒⣛⠒⠒⠒⠒⠀⠀⠀⠀⠀⠠⠤⠄⠀⠈⠡⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⠒⠂⢰⣿⠟⠋⢉⡋⠀⣀⡾⣷⣷⣵⣿⠶⠦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢿⣿⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠠⣥⣤⣾⣿⣿⣿⣿⢿⣿⣿⣿⣛⣛⣓⣺⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⡄⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠻⢿⣿⣿⠟⠘⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠻⠿⠶⢾⠏⠀⠀⠻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡆⠈⢻⣿⣿⣿
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⡷⢠⣼⢿⡀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡴⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄⣀⣀⣀⡀⠀⠘⢿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠷⣿⣷⣶⢸⣿⣿⣿
⠀⠀⠈⢿⣿⣿⣯⣿⣏⣿⣿⣿⣿⢿⠁⠛⠓⣶⠆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠤⢶⣿⢿⣿⣿⣿⣿⡿⣿⣿⣯⣤⣿⣿⠿⠈⢸⡏⠁⣿⡏⠀⠐⢦⣄⠘⠛⠃⠘⣿⣿⣿⣿⣿⣿⣯⡈⢛⣿⡿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣆⠀⠀⢉⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣿⣿⣸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢸⠀⠃⠀⡌⠁⠀⠀⠑⠙⢿⣿⣶⣄⠈⢻⣿⠋⢉⡟⠉⣱⣿⡟⠀⠈⠙⠻
⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣁⣼⣯⡄⢀⠝⠋⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠿⠻⣿⣿⣿⢿⡇⣿⣿⣿⣿⣟⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠘⠀⣰⣿⠏⠀⠀⠀⠀⠀
⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⠉⡉⢹⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀
⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⡂⠀⢉⡝⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⢀⣇⢨⣿⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠈⣿⣿⣾⣿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣾⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣵⣶⣶⣤⣼⣿⣿⣿⣿⣿⡀⠀⠀⢰⡆⠀⣀⣤⣬⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⡀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⠛⠻⠿⠆⠀⠀⢠⣿
⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⡿⠆⢸⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣶⠇⡟⡼⠈⠏⢱⠳⠀⠀⠈⣛
⡿⡇⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡟⡀⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢠⣤⣿
⠒⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣟⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⠩⣭⣭⣤⣭⣴⣧⣭⣬⡅⠉⠉⠈⠁⠻⣬⣿⣥⣭⣭⣭⢎⣡⣌⡁⢉⣭⡉⠉⠈⠉⢸⣬⣩⠀⣙⣫⣬⣭⣍⠁⠀⠙⠋⠈⠙⠋⢸⣿⣿
⠠⠆⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⡿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⠟⠉⠀⠀⢻⣿⣷⣦⣽⠟⡀⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⢀⣶⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠘⠛⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡽⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⠸⠿⠄⠀⠀⠀⠀⠀⢀⠀⠀⠠⡤⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⡍⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠈⠁⣀⠀⠀⠀⠀⢠⡄⠀⠘⠣⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢤⣤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⢿⠿⠟⠙⣿⣿⣿⣿⡿⠛⠛⢿⡿⣿⣗⣒⣒⣛⠒⠒⠒⠒⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠙⠚⠂⢲⣿⠟⠉⢙⡉⢀⣐⡾⣷⣷⣵⣿⠶⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⣛⠛⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣯⣿⣿⡿⢿⣿⣿⣟⣛⣛⣓⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣧⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣀⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠛⢿⣿⣿⠏⠈⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠿⠿⠿⠶⢾⠋⠀⠈⢿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠉⢿⣿⣿⣿
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⣠⡼⢿⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠴⠇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡷⢠⣄⣀⣀⣀⠀⠀⠘⢿⣿⣿⡇⣼⣿⣿⣿⣿⣿⡿⠶⣿⣷⡶⣸⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣭⣿⣏⣿⣿⣿⡟⢿⠐⠛⠓⣿⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⣴⣿⢸⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⠿⠀⢼⠏⠀⣿⡇⠀⠒⢦⡄⠘⠛⠁⠹⣿⣿⣿⣿⣿⣿⣇⠘⢻⣿⡿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⡆⠀⠀⢡⣴⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣿⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⣼⢸⠀⠀⡍⠁⠀⠀⠀⠛⢿⣿⣦⡀⠘⢿⡿⠋⢉⡟⠉⣱⣿⡏⠀⠈⠙⠿
⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣀⣿⣯⡆⢠⡿⠋⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⠻⣿⣿⡿⣿⣵⣿⣿⣿⣿⣏⣇⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠘⠀⣸⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠈⠀⠀⠀⠸⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹⠉⡉⢹⣿⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡶⣂⠀⢉⡝⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⡇⢸⡟⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⢸⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠈⣿⣿⣾⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣾⣿⣾⣿⣾⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠗⠀⠀⠺⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣵⣾⣶⣶⣼⣿⣿⣿⣿⣿⡀⠀⠀⢰⡆⠀⣀⣤⣬⣿⣿⣿⣿⣿⣿⠇⠀⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢸⣇⠀⡀⠀⠀⠀⠀⠀⢠
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠈⠛⠻⠷⠆⠀⠀⢰⣿
⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⢼⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣶⠇⡿⡼⠈⠏⢱⠳⠀⠀⢘⣻
⠛⠇⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡟⡈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡇⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢠⣬⣿
⠋⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣟⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⣴⣧⣭⣬⡅⠉⠉⠈⠁⠹⣬⣿⣥⣭⣭⡭⢎⣡⣈⠁⣉⣍⡉⠉⠈⠉⢸⣮⡍⢀⣙⣫⣬⣭⣍⠁⠀⠙⠋⠈⠙⠋⣼⣿⣿
⠰⠆⠰⢶⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⡟⠉⠀⠀⢻⣿⣷⣦⣽⠋⣀⡀⠀⠀⠀⠑⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⢀⣶⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠘⠛⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠘⠿⠄⠀⠀⠀⠀⠀⢀⠀⠀⢠⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠤⠤⡍⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠈⠀⡀⠀⠀⠀⠀⢠⡄⠀⠙⠤⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠿⢟⠋⢹⣿⣿⣿⣿⡿⠛⠛⣿⡿⣿⣗⣒⣚⣛⠒⠒⠒⠒⠀⠀⠀⠀⠄⠤⠄⠀⠀⠈⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠙⠚⠄⣴⣿⠟⠁⢙⡉⠀⣐⡿⣷⣿⣵⣿⠶⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠄⣤⣤⣾⣿⣿⣿⡿⣿⣿⣿⣟⣛⣛⣛⣗⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣭⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⡄⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡀⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⠿⠷⠶⢿⠋⠀⠈⢿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠇⣠⠾⢿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣀⣀⡀⠀⠀⠸⢿⢿⣿⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣶⡆⣼⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣭⣿⣹⣿⣿⣿⡟⠿⠈⠛⠛⡿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⡀⣉⣿⢹⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡿⠿⠀⢿⠏⠘⣿⡇⠁⠒⢦⡀⠻⠿⠀⢻⣿⣿⣿⣿⣿⣿⣆⠉⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣇⠸⣷⡀⠀⠀⣱⣦⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠿⣿⣿⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⣴⢸⠀⢠⠉⠀⠀⠈⠊⠛⣿⣷⣦⡀⠙⢿⡿⠛⢹⠏⠉⣰⣿⠏⠀⠉⠛⢿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣥⡆⢸⡟⠁⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⡿⣿⢸⣿⣿⣿⣿⣏⡅⡀⠀⣈⡀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠋⠀⣼⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠈⠀⠀⠀⠸⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣵⠀⠈⢸⡇⢰⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣂⡀⢉⡙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢀⡇⢸⡇⢸⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠈⣿⣿⣿⣿⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣾⣷⣾⣿⣿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠘⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣵⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⢰⡆⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⣰
⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠁⠛⠿⠷⠆⠀⠀⣴⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⣶⠏⡿⡼⠈⠏⢱⠳⠀⠀⢙⣻
⣿⠇⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⠈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢺⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢠⣼⣿
⠉⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣿⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢠⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⡴⣧⣭⣬⡁⠉⠉⠈⠁⠹⣬⣿⣥⣭⣭⡭⢊⣥⡈⠁⣉⣍⡉⠉⠈⠉⣼⣮⡍⢠⣙⣫⣬⣭⡉⠁⠀⠙⠋⠈⠙⢋⣼⣿⣿
⠰⠆⠰⢶⠀⠠⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⡛⠁⠀⠀⢻⣿⣷⣬⡽⠋⢀⡀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⢀⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠽⠿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⠉⠉⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠤⡍⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠉⠀⡀⠀⠀⠀⠀⢠⠄⠀⠛⠤⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠿⢿⠟⢉⣿⣿⣿⣿⡿⠛⠛⣿⡿⣿⣓⣒⣚⣛⠒⠒⠒⠒⠀⠀⠀⠠⠄⠤⠄⠀⠀⠁⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠙⠚⠀⣾⣿⠟⠉⢈⡉⢀⣰⡿⣷⣿⣷⡷⠶⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⡿⢿⣿⣿⣟⣛⣛⣛⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣥⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡄⠀⠀⠀⠀⣎⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠛⢿⣿⣿⣏⡈⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⠶⠷⠶⣿⠉⠀⠸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠹⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⢂⣴⠿⢿⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠇⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡆⣤⣀⣀⣀⣀⠀⠀⠻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⡆⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣯⣽⣿⣼⣿⣿⡿⡛⡇⠈⠙⠙⡇⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⢺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡿⠇⠁⣿⠉⢸⣿⠋⠁⠲⣦⡁⠻⠟⠀⢿⣿⣿⣿⣿⣿⣷⡈⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣗⠀⠀⢈⣴⡆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣷⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠁⢀⡇⠈⠀⢀⠉⠀⠀⠈⠊⠻⣿⣶⣄⠀⠻⣿⡿⠋⣹⠋⢙⣾⣿⠋⠀⠙⠻⢿
⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣵⠆⣸⠟⠁⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢿⣿⣿⡿⣿⣸⣿⠿⣿⣿⣏⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠈⠀⠀⠃⢀⣾⡿⠁⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠁⠀⠀⠀⠸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣦⠀⠀⣹⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣂⡀⢩⡙⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⢐⡇⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠈⣿⣿⣿⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣷⣿⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣷⣿⣷⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⢶⡄⠀⣠⣤⣼⣿⣿⣿⣿⣿⡿⠀⢈⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡀⠀⡀⠀⠀⠀⠀⠀⣼
⣠⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠈⠑⠛⠻⠷⠆⠀⠀⣾⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠷⠠⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣧⣶⠏⡿⡼⠈⠏⢱⠳⠀⠀⢛⣿
⠿⠇⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡶⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⡉⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡇⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢠⣽⣿
⠉⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⡴⣧⣭⣬⠁⠉⠉⠈⠁⠹⣬⣿⣥⣭⣭⡭⢊⣅⡈⠁⣭⣉⠉⠉⠈⠉⣼⣮⡉⢠⣝⣫⣬⣭⡉⠁⠀⠙⠋⠈⠙⢋⣾⣿⣿
⠐⠆⠰⢲⠀⠠⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⡛⠁⠀⠀⢻⣿⣶⣬⡟⢁⣀⠀⠀⠀⠉⢺⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢀⣾⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⠀⠀⠚⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣤⠽⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠭⠍⠉⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠤⠍⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢀⡀⠀⠀⠀⠀⣤⠀⠀⠓⠄⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⠶⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠿⢟⠏⠙⣿⣿⣿⣿⡿⠛⠛⣿⡿⣿⣒⣒⣚⡓⠒⠒⠒⠂⠀⠀⠀⠀⠀⠤⠄⠀⠀⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠙⠠⠀⣰⣽⠟⠉⢙⡉⢀⣰⠿⣿⣿⣷⡷⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⣆⠈⠁⠀⠀⠀⠀⠀⠀⠌⣤⣤⣿⣿⣿⣿⡿⣿⣿⣿⣟⣛⣛⣺⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣯⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⠀⠀⠀⠀⠀⣟⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡏⠘⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠷⠾⠶⠶⡿⠉⠀⠹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠻⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡿⢀⣶⢿⡿⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⡾⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄⣀⣀⣀⢀⠀⠀⠻⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣶⢠⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣯⣿⣧⣿⣿⣿⢿⣻⠃⠉⠉⠙⠂⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡿⠇⠸⡿⠉⢸⣿⠉⠑⠲⣄⠈⠿⠏⠘⢿⣿⣿⣿⣿⣿⣷⡈⠹⣿⣾⣿⣿⣿⣿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣇⠀⠀⢨⣶⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣾⣿⣧⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⠀⢠⡆⡇⠀⢈⠉⠀⠀⠀⠚⠻⣿⣶⣄⠈⠻⣿⠟⠋⣿⠋⢃⣾⡿⠁⠈⠛⠿⣿
⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡶⠆⣾⠟⠁⠀⢾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⢿⣿⣿⢿⣇⣿⣿⢹⣿⣿⡇⣀⠀⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠘⠁⢀⣿⡟⠁⠀⠀⠀⠀⠈
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠁⠀⠀⠀⠸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣫⣆⢀⠀⣿⠃⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠃⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢗⣀⡀⢹⡉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢘⠀⣿⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠘⣿⣿⣿⣷⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣶⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣶⣿⣷⣶⣿⣿⣿⣿⣸⣧⠀⠀⠀⢶⠄⠀⣠⣤⣼⣿⣿⣿⣿⣿⡇⠀⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⢀⣾
⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠈⠐⠛⠿⠷⠆⠀⢠⣾⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠇⠰⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣧⡶⠏⡟⡼⠈⠏⢱⠣⠀⠈⢛⣿
⠿⠇⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⡉⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡇⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢀⣿⣿
⠈⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣿⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢩⣭⣭⣤⣭⣴⣷⣭⣬⠁⠉⠉⠈⠁⠹⣬⣿⣥⣭⣭⡥⢊⣅⠈⢡⣭⡉⠉⠉⠈⢉⣼⣮⠉⣤⣝⣫⣬⣍⠉⠁⠀⠙⠋⠈⠙⣫⣼⣿⣿
⠠⠇⠰⢲⠀⠠⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠁⠀⠀⢻⣿⣶⣭⠟⠁⡀⠀⠀⠀⠙⢺⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣠⠿⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠋⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠁⢀⠀⠀⠀⠀⠀⣤⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⠿⠙⠋⠛⣿⣿⣿⣿⡿⠿⠿⣿⡿⣿⣐⣒⣛⡓⠒⠒⠒⠂⠀⠀⠀⠠⠄⠀⠀⠀⠈⢡⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡉⠟⠋⠙⡂⢀⢰⣿⣾⣯⣿⡷⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⠿⠟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣶⣶⣿⣾⣿⣿⣿⣛⣛⣛⣺⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣷⣿⣏⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠀⣀⡀⠀⢸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠋⠘⠛⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⢾⡟⠉⠀⠻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣿
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⠗⣰⡾⣿⠗⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄⣀⣀⣀⡀⠀⠀⢿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢿⣿⣷⣤⣸⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣶⣿⣧⣿⣿⣿⢟⡛⠀⠉⠉⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣼⣿⠿⡀⢸⡟⠁⣿⡯⠉⠐⢶⣄⠨⠿⠃⠸⣿⣿⣿⣿⣿⣿⣶⠈⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣠⠀⠀⣴⣶⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⠀⣸⠀⠃⠀⡈⠁⠀⠀⠐⠛⢻⣶⣦⡀⠙⢿⣿⠟⢛⡿⠛⢳⣿⡟⠁⠙⠻⢿⣿
⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠾⢰⣿⠋⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠿⠿⡿⢿⣧⣿⡿⣿⣿⣿⣆⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠁⠀⠸⠀⢰⣿⠟⠀⠀⠀⠀⠀⢹
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⠈⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣱⡆⠀⢈⣿⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢗⡀⠀⣩⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⣘⢸⣿⢀⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛⠁⠸⣿⣷⣿⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣶⣾⣶⣦⣿⣿⣿⣿⣿⡆⠀⠀⠐⠷⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⠇⠀⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⢠⣿
⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠀⠀⠀⠁⠀⠻⠿⠷⠆⠀⢰⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⢿⣿⣿⠿⣿⡆⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠀⠼⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣤⡆⠇⡟⡼⠈⠏⢱⠣⠀⠸⢿⣿
⡊⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡁⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢘⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⢭⣩⣭⣤⣭⢸⣷⣭⡌⠁⠉⠉⠈⠁⠹⣬⣿⣥⣭⣭⠭⢈⣁⠈⣡⣍⡉⠉⠉⠈⣩⣼⡎⢉⣤⣝⣫⣬⣍⠉⠁⠀⠙⠋⠈⠙⣫⣼⣿⣿
⠀⠆⠰⢠⠀⠠⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠁⠀⠀⢻⣷⣤⡹⠋⢀⡀⠀⠀⠈⠃⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣸⢿⡧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠐⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠂⠐⠒⠀⠀⠸⠁⠈⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈⠁⣀⠀⠀⠀⠀⠠⡄⠀⠘⠣⠀⠀⠀⠀⢀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣒⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣒⣒⣛⠒⠒⠒⠒⠂⠀⠀⠤⠤⠄⠀⠀⠀⠈⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠹⡿⠛⡯⠅⡀⢨⣿⣼⣿⣿⡶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⣶⣭⣴⣿⣼⣿⣿⣿⣛⣛⣓⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣏⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡄⠀⣀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⠏⠹⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⢾⡟⠉⠈⢿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣯⡍⠛⣿⣿⣿⣿⣿
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⠃⣴⣾⡷⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣤⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣀⣀⣀⡀⠀⠐⢿⣿⣿⡇⣼⣿⣿⣿⣿⣿⡿⢯⣿⣧⣤⣸⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣾⣿⣼⣿⣿⡿⢟⡃⠀⠉⠉⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⢾⢽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠿⠀⢿⡏⠉⣿⡇⠋⠐⢶⣄⠹⠿⠁⢻⣿⣿⣿⣿⣿⣿⡆⠙⢻⣷⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠸⣷⡄⠀⠀⣴⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣴⢸⠀⠀⡉⠁⠀⠀⠐⠛⢷⣶⣤⡀⠙⣿⣿⠟⠻⡟⠛⣶⣿⡟⠁⠙⠿⣿⣿
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣧⠈⢰⡿⠋⠀⠀⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠻⠿⠿⢿⣺⣿⠟⣿⣿⣿⣀⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠈⠁⠀⠜⠀⣸⣿⠏⠀⠀⠀⠀⠀⢻
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠁⠀⠀⠀⠀⢻⣿⣿⣷⣦⣀⠀⠀⠀⠀⢠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣵⡀⠀⢸⡟⠐⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡷⠂⠀⠉⡍⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⢸⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⢳⣶⣴⣿⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣭⣶⣶⣤⣼⣿⣿⣿⡇⣿⡀⠀⠀⠸⠇⠀⠀⣠⣤⣮⣿⣿⣿⣿⣿⠀⠈⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⢹⡇⠀⠀⡀⠀⠀⠀⠀⣰⣿
⣢⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠈⠁⠐⠻⠿⠷⠆⠀⣴⣿⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⠿⠿⢿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠀⠾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣤⠄⠇⡟⡼⠈⠏⢱⠣⠀⠻⣿⣿
⣒⠃⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡞⡉⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢸⣿⣿
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⠉⣭⣩⣭⣤⣭⣸⣷⣍⠈⠁⠉⠉⠈⠁⠙⣬⣿⣥⣭⣭⠍⠈⡁⠈⣡⣍⣉⠉⠉⠈⣩⣾⡎⢉⣤⣝⣯⣬⡉⠉⠁⠀⠙⠋⠈⢙⣫⣼⣿⣿
⠰⠇⠰⢠⠀⠰⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⣻⣷⣌⡿⠃⢀⡀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢀⡀⠀⠘⠛⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⣻⣟⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠘⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⠒⠀⠀⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠈⠀⣀⠀⠀⠀⠀⢠⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠻⡟⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⣒⣚⣛⠒⠒⠒⠒⠀⠀⠀⠤⠤⠄⠀⠀⠀⠉⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⡯⠀⢀⣻⣧⣾⣿⣿⠶⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⠛⠛⠛⠿⠿⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⣶⣙⣶⣯⣿⣿⣿⣟⣛⣛⣛⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣾⣿⣋⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⢀⣀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⠋⠭⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠷⠶⣾⠏⠉⠈⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠻⣿⣿⣿⣿⣿
⠻⢿⣿⣿⣿⣿⣿⢿⣿⣿⣀⣸⡿⢃⣶⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠻⣿⡆⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣀⣀⡈⡀⠀⠸⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⣤⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣷⣾⣿⣼⣿⣿⡿⣏⠃⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⡿⠿⠀⣿⠏⠉⣿⡇⠋⠒⢦⡄⠹⠿⠀⢿⣿⣿⣿⣿⣿⣷⡆⠙⢿⣷⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣇⡄⠀⢠⣶⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠃⠀⣅⢸⠀⢀⡉⠁⠀⠀⠂⠛⢷⣶⣄⠀⠻⣿⡿⠛⢛⡟⠛⣸⣿⠏⠈⠛⠿⣿⣿
⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣇⠀⣾⡟⠁⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠛⠻⠿⠿⢸⣿⠿⣿⣿⣷⡄⡀⠈⣈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⡄⠈⠀⠀⠏⠀⣼⡿⠋⠀⠀⠀⠀⠈⣿
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠁⠀⠀⠀⠈⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣶⠀⡀⢹⡇⢰⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡶⠀⠀⢩⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡃⣻⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣾⠇⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠀⣶⣤⣼⣷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣷⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠘⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣡⣤⣤⣤⣹⣿⣿⣿⣸⣆⠀⠀⠀⠿⠂⠀⠀⣠⣤⣶⣽⣿⣿⣿⣿⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠁⠀⠀⡀⠀⠀⠀⠀⣼⣿
⣰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠈⠀⠐⠿⠿⠷⠆⠀⣼⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠿⢿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠀⠿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⣿⣴⠀⠇⡿⡼⠈⠏⢱⠳⠀⠻⣿⣿
⡛⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢸⣿⣿
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣍⣩⣭⣤⡍⣴⣷⡍⠈⠁⠉⠉⠈⠁⠘⣬⣿⣥⣭⣭⠍⠈⠁⠈⣥⣉⡉⠉⠉⠈⣩⣾⡌⢩⣤⣽⣯⣬⡉⠉⠁⠀⠙⠋⠈⢙⣯⣼⣿⣿
⠰⠆⠰⢲⠀⠠⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠋⠀⠀⠀⣰⣶⣬⡿⢃⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⢀⣀⣠⣤⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠘⠛⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠿⢋⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠶⠊⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠈⠀⡀⠀⠀⠀⠀⢠⡄⠀⠛⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⢿⠛⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣒⣚⣛⠒⠒⠒⠒⠀⠀⠠⠤⠤⠄⠀⠀⠀⠉⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⡍⠀⣈⣿⣵⣿⣿⡷⠶⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⣤⣹⣾⣽⣿⣿⣿⣟⣛⣛⣛⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣟⣁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⠄⢀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣷⣿⣿⡿⠩⠍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠶⠶⠶⠶⣿⠛⠁⠙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠻⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⡟⢀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣷⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⣀⣀⣀⡠⡀⠀⠸⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣦⣄⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣷⣾⣧⣿⣿⣿⠿⣋⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⣨⣿⡿⠇⠁⣿⠋⢹⣿⠛⠃⠒⢦⡀⠽⠿⠀⢿⣿⣿⣿⣿⣿⣷⡆⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⢹⣧⡄⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠁⠀⡇⠘⠀⢈⠙⠀⠀⠀⠐⠛⢷⣶⣄⠈⠻⣿⡿⠛⢻⠟⠛⣸⣿⠋⠈⠛⠿⣿⣿
⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡇⠀⣾⠟⠁⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠉⠛⠛⠿⠿⢸⣿⢿⣿⣿⣷⡀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⡄⠈⠀⠀⠋⠀⣾⡿⠃⠀⠀⠀⠀⠈⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠁⠀⠀⠀⠘⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣮⠀⠀⣿⡇⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⡦⠀⠈⢩⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢘⠃⣿⡇⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⣾⠁⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠋⠰⣶⣤⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣶⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⣥⣤⣄⣠⣿⣿⣿⣿⢼⡀⠀⠀⠐⠿⠀⠀⠀⣠⣤⣶⣼⣿⣿⣿⡿⠀⢈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿
⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠈⠀⠰⠟⠿⠷⠆⢀⣾⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣷⠀⠿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⣷⣴⠀⠇⡟⡼⠈⠏⢱⠳⠀⢻⣿⣿
⡩⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣿⢶⡶⢰⡶⣶⢸⣶⡞⡄⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⡋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣍⣭⣭⣤⣍⣼⣧⠉⠈⠁⠉⠉⠈⠁⠘⢮⣿⣥⣭⣭⠍⠈⠁⠈⣥⣍⡉⠉⠉⠈⣭⣼⡌⣩⣤⣽⣯⣬⡉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠋⠀⠀⠀⢀⣶⣌⠟⠁⠀⠀⠀⠀⠉⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡀⠀⠀⠀⢀⣀⣠⣤⣤⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡿⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠖⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⢀⡀⠀⠀⠀⠀⢤⠀⠀⠛⠄⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⡒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢁⣒⣚⡓⠒⠒⠒⠒⠀⠀⠠⠤⠤⠄⠀⠀⠀⠁⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣿⣿⡿⠛⠉⢻⣿⣽⣷⣿⠶⠶⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠥⢆⣝⣻⣿⣿⣿⣏⣛⣛⣛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠀⢀⡀⠀⢰⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣯⣿⣿⡿⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠶⠶⠶⠶⣿⠋⠁⠙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⢻⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⡿⣿⣿⣷⣀⣿⠟⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⠟⠀⠈⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣄⣀⣀⣀⣠⡀⠀⠸⢾⣿⣿⢀⣿⣿⣿⣿⣿⣿⠿⣽⣿⣤⣄⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣷⣿⣧⣿⣿⣿⢾⡋⠀⠈⠉⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⡿⢇⠸⣿⠉⢹⣿⠘⠃⠒⢦⡄⠽⠟⠀⢿⣿⣿⣿⣿⣿⣷⡆⠙⣿⣾⣿⣿⣿⣿⣿
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣦⡄⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢿⠀⢠⡇⠇⠀⢈⡙⠀⠀⠀⠀⠛⣷⣶⣄⠈⠻⣿⠿⠛⣹⠟⠛⣾⣿⠋⠈⠛⢿⣿⣿
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⡇⠀⣾⠟⠁⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⠇⠉⠉⠛⠛⠿⢾⣿⢻⣿⣿⣼⡀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠉⠀⠀⠃⢀⣾⡿⠁⠀⠀⠀⠀⠈⣿
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠈⠁⠀⠀⠀⢻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡆⢀⠀⣿⡃⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣦⠄⠀⠘⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢸⢀⣿⠃⣾⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⢸⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠉⢀⣀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣾⣿⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠘⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣛⣁⣄⣀⡈⣿⣿⣿⣇⣇⠀⠀⠀⠸⠷⠀⠀⠀⣠⣤⣶⣬⣿⣿⣿⡿⠀⢈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿
⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠈⠀⠐⠟⠻⠷⠄⢠⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠿⠿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣧⠠⠿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⣧⡶⠀⠇⡟⡼⠈⠏⢱⠳⠘⣻⣿⣿
⡃⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣇⣾⢶⡖⢰⡶⣶⢸⣶⡗⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢳⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⢩⣍⣭⣭⣭⣤⢩⣼⡆⠉⠈⠁⠉⠉⠈⠁⠈⢮⣿⣥⣭⣭⠍⠈⠁⠈⣥⣉⠉⠉⠉⠈⣩⣼⠈⣉⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠲⣦⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠀⠀⠀⠀⣲⣌⡟⠁⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠒⠀⠠⠆⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠁⢀⡀⠀⠀⠀⠀⣤⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⡒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢑⣒⣚⡓⠒⠒⠒⠂⠀⠀⠠⠤⠤⠀⠀⠀⠀⢁⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢻⣿⣿⣿⠿⠛⢿⡿⣻⣧⣾⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⠛⠛⠛⠛⠛⠛⠛⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⣂⡀⡾⢿⣿⣿⣿⣛⣛⣛⣻⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⣾⣟⣁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠀⣀⡀⠀⢰⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣏⣶⣾⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠶⠶⠶⠶⣿⠋⠉⠙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣯⡍⠙⢿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣀⣿⠛⢰⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⡿⠁⠚⠀⢙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄⣀⣀⣀⢰⡀⠀⠸⢾⣿⡏⢠⣿⣿⣿⣿⣿⣿⣯⣿⣷⣤⣼⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣶⣿⣧⣿⣿⣿⢻⡉⠐⠈⠉⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠿⠇⠸⡿⠉⢸⣿⠘⠁⠒⢦⡀⠽⠇⠘⣿⣿⣿⣿⣿⣿⣶⡾⠻⣿⣾⣿⣿⣿⣿⣿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣦⡄⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⠀⢠⡆⠃⠀⣈⡉⠀⠀⠀⠊⠛⣶⣦⣄⠈⢻⣿⠟⠛⣻⠟⠓⣸⣿⠋⠈⠛⢿⣿⣿
⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⡆⢰⣿⠟⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠇⠀⠉⠉⠛⠃⠿⣿⣿⡿⣿⣼⢀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠉⠀⠀⠃⢀⣾⡿⠁⠀⠀⠀⠀⠘⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠈⠀⠀⠀⠀⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⣿⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠁⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⣤⣄⠀⠀⠚⡻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢠⣿⠀⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⢸⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣿⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠘⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⣁⡀⠀⢸⣷⣿⣿⣷⠀⠀⠀⠀⠾⠇⠀⠀⠀⢀⣴⣶⣦⣿⣿⣿⡇⠀⢨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡟⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠰⠟⠻⠷⠆⢰⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⠿⠿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣧⠰⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⣧⡶⠀⠇⡟⡼⠈⠏⢱⠳⠘⣻⣿⣿
⡆⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢺⣇⣷⢶⡶⢰⡶⣶⢸⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢰⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⣭⣉⣭⣭⣭⡄⣍⡄⠀⠉⠈⠁⠉⠉⠈⠁⠀⢪⣿⣥⣭⣭⠍⠈⠁⢈⣡⣉⠉⠉⠉⠈⣭⣼⠈⣉⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠲⣤⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⡟⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⢀⠀⣬⠟⢁⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⣰⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⡄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⠂⠂⢠⠄⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠁⢀⡀⠀⠀⠀⠀⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢐⣒⣛⡓⠒⠒⠒⠂⠀⠀⠀⠤⠠⠀⠀⠀⠈⢁⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠘⠃⠈⠈⠉⠙⣿⣿⣿⣿⡿⠿⣿⣿⢿⣧⣾⠶⠶⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⠉⠛⠛⠛⠛⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠡⠀⡀⣼⣷⣿⣿⣿⣛⣛⣛⣻⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⣿⣟⣁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡤⠀⣀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣩⣵⣧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠷⠶⠶⠶⠶⣿⠋⠉⠙⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⢿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⡿⣿⣿⣇⣀⣿⠛⣰⣎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⠋⠔⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄⣀⣀⣀⢱⡀⠀⠸⢾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣿⣧⣤⣸⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣶⣿⣥⣿⣿⣿⢿⡉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⢾⣇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⠿⠇⢸⡟⠉⢹⣿⠚⠁⠒⢤⡀⠽⠇⠘⣿⣿⣿⣿⣿⣿⣶⣿⠿⣿⣾⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣤⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡿⣿⠀⢨⡄⠁⠀⡈⡉⠀⠀⠀⠈⠛⣶⣦⡀⠈⢿⣿⠟⠛⣻⠟⠃⣼⣿⠋⠈⠻⢿⣿⣿
⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⡄⣴⣿⠏⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⠇⠀⠈⠉⠉⠃⠻⢿⠿⠿⣿⣱⢀⠀⢁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠁⠀⠀⠃⢀⣾⡿⠁⠀⠀⠀⠀⠘⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠈⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⣿⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣤⣄⣀⠀⠀⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⣼⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠛⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⠛⠁⠀⠀⢲⣦⣿⣿⣀⠀⠀⠀⠀⠿⠆⠀⠀⠀⢀⣴⣶⣦⣽⣿⣿⡇⠀⢨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠁⠀⠰⠟⠻⠷⠆⢰⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣿⣿⣿⣿⣿⣷⡰⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣧⡆⠀⠇⡟⡼⠈⠏⢱⠣⠸⢿⣿⣿
⡇⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⠀⢲⣇⣶⢶⡶⢰⡶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⢡⣭⣉⣭⣭⣭⣤⣩⠀⠀⠉⠈⠁⠉⠉⠈⠁⠀⢨⣿⣥⣭⣭⠭⠈⠁⢈⣥⣉⠉⠉⠉⢈⣭⣼⠈⣉⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠲⣤⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢹⢻⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏⠁⠀⠀⢀⠀⢩⠟⠁⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⢲⠀⠀⠐⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠁⢀⠀⠀⠀⠀⠀⣤⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢑⣒⣛⡓⠒⠒⠒⠂⠀⠀⠠⠤⠤⠀⠀⠀⠈⢡⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣣⣾⠶⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⠙⠛⠛⠛⠛⠛⠛⠛⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠡⠀⢀⣸⣷⣿⣿⣿⣛⣛⣛⣻⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⣿⣟⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⠀⣀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣭⣴⣧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠷⠶⠶⠶⢶⣿⠟⠉⠙⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣛⠛⠻⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⠃⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⠋⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄⣀⣀⣀⣹⡄⠀⠠⣴⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣿⣤⣤⣸⣿⣿⣿⣿⣿
⠀⢻⣿⣷⣶⣿⣴⣿⣿⣷⢻⡁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⡆⠀⠀⠾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣾⣿⠿⠁⢸⡟⠉⣽⣯⠚⠃⠲⢤⡀⠽⠇⠸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣤⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⢾⣽⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡟⠀⢸⡀⠀⠀⣈⡏⠀⠀⠀⠚⠛⣶⣦⡀⠘⢿⣿⠟⠛⣻⡿⠃⣼⣿⠋⠘⠻⣿⣿⣿
⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡄⢾⡿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠉⠉⠁⠻⢷⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠉⠀⠀⠋⢀⣾⡟⠁⠀⠀⠀⠀⠹⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠊⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆⡀⢸⣿⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠾⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠃⠀⠀⣸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢛⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠿⠟⢁⠀⠀⣤⣤⣿⣿⡄⠀⠀⠀⠐⠿⠂⠀⠀⠀⢀⣤⣶⣦⣼⣿⣿⡇⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣷⣦⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⡀⠀⠀⠁⠀⠰⠟⠻⠿⠆⣴⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⠿⢿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡸⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣧⡆⠀⠏⡿⡼⠈⠏⢱⠳⠻⢿⣿⣿
⠁⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢳⣇⣶⢶⡶⢰⡶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠇⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣾⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⣥⣭⣉⣉⣩⣭⢠⣩⠀⠀⠉⠈⠁⠉⠉⠈⠁⠀⢨⣿⣥⣭⣭⡭⠊⠁⢈⣥⣉⠉⠉⠉⢨⣭⣼⠈⣉⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢈⣙⣫⣼⣿⣿
⠀⠆⠰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢸⢻⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟⠁⠀⠀⢀⠀⠙⠟⢁⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣀⠀⠀⠛⠃⠀⠀⠀⠉⠈⠉⠉⠉⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠁⣀⠀⠀⠀⠀⠀⡤⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠘⣒⣛⡓⠒⠒⠒⠂⠀⠀⠄⠤⠀⠀⠀⠀⠈⢡⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⢹⣿⣿⣿⡿⠿⢿⣿⠟⣿⣴⣶⠶⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡎⠉⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠂⣀⢠⣿⣿⣿⣿⣿⣙⣛⣛⣻⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠀⣀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣎⣵⣾⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⢾⣿⡟⠉⠉⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣛⠛⠻⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡿⠃⣼⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣿⡏⠀⠂⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣀⣀⣀⣀⣻⡆⠀⠀⣤⣿⡇⢸⣿⣿⣿⣿⣿⣿⣛⣿⣤⣤⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣶⣿⣼⣿⣿⡗⢟⡁⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢿⠄⡀⠠⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣿⣿⠿⡀⢸⡟⠉⣿⡿⠘⠃⠢⢤⡀⠽⠇⠸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣤⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣿⢸⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⡏⠀⢸⠀⠀⢀⣉⡇⠀⠀⠀⠈⠛⣶⣦⡀⠙⢿⣿⠟⠛⣻⡿⠃⣼⡿⠋⠙⠻⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡄⢻⡿⠋⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠈⠉⠙⠃⠻⣷⠿⢿⣷⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠁⠀⠀⠃⢀⣾⡟⠁⠀⠀⠀⠀⢹⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠊⠁⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⣿⠀⣶⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠾⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣟⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢛⡻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⠿⠋⣁⠀⠀⣶⣶⣿⣿⡆⠀⠀⠀⠐⠿⠂⠀⠀⠀⢀⣤⣶⣶⣽⣿⣿⡇⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿
⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣶⠀⠀⠀⠁⠀⠠⠿⠻⠿⠄⣴⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⠿⢿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡼⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣧⡆⠀⠇⡿⡼⠈⠏⢱⠳⠻⢿⣿⣿
⠀⠀⢰⣶⠀⣶⣶⠰⣶⡖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠈⢻⣇⣶⢶⡶⢰⣶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠁⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⣥⣭⣉⣍⣩⣭⢠⣩⠀⠀⠉⠈⠁⠉⠉⠈⠁⠀⠨⣿⣥⣭⣭⡥⠎⠁⢈⣥⡉⠉⠉⠉⢨⣩⣼⠈⣉⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢈⣙⣫⣼⣿⣿
⠀⠄⠰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠉⠀⠀⠀⠀⠙⠟⢁⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠀⠀⣀⣀⣤⣤⣶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠛⠁⠀⠀⠀⠁⠈⠉⠉⠉⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈⠁⣀⠀⠀⠀⠀⠠⡤⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠑⣓⣛⡒⠒⠒⠒⠂⠀⠀⠀⠤⠀⠀⠀⠀⠈⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠟⠉⠉⢹⣿⣽⣿⣿⡷⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡎⠉⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⡔⣂⣟⣻⣿⣿⣿⣿⣛⣛⣛⣻⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣟⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⣀⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣾⣷⣿⣿⡟⢋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⢾⣿⡟⠉⠉⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⡛⠛⢻⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣸⡿⠃⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⢿⣆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣀⣀⣀⣀⣽⡇⠀⠀⣀⣭⡇⢸⣿⣿⣿⣿⣿⣿⣻⣧⣤⡄⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣷⣶⣿⣼⣿⣿⡗⢟⡁⠀⠀⠉⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⣹⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣤⣿⣿⠿⡀⢺⠏⠉⣿⡏⠛⠋⠂⢤⡀⠽⠇⠸⣿⣿⣿⣿⣿⣯⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⣤⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢸⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⡏⠀⣸⠀⠀⢀⢉⡇⠀⠀⠀⠈⠛⣶⣦⡀⠙⢿⣿⠟⠛⣿⡟⠃⣾⡿⠋⠙⠻⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣾⡀⢻⡿⠋⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠉⠉⠛⠃⠿⣷⣿⣿⣷⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠁⠀⠀⠁⢀⣾⠟⠁⠀⠀⠀⠀⢹⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠊⠀⠀⠀⢸⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢸⣿⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣶⣤⡄⠀⠐⢛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣰⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋⠁⣀⣀⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⢛⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⠟⣋⣠⡄⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⣠⣶⣶⣽⣿⣿⡇⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿
⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠀⠀⠀⠁⠀⠠⠟⠻⠿⠄⣴⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⠿⢿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⣼⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⡆⠀⠇⡿⡼⠈⠏⢱⠳⠻⣿⣿⣿
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢳⣇⣶⢶⡶⢰⣶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⣥⣭⣉⣭⣩⣍⢠⣩⠀⠀⠉⠈⠁⠉⠉⠈⠁⠀⠈⣿⣥⣭⣭⣥⠎⠁⢈⣥⡉⠉⠉⠉⢨⣩⣼⠈⣩⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢈⣙⣫⣼⣿⣿
⠀⠂⠰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⡸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠋⠀⠀⠀⡀⠹⠟⢁⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠁⠀⠀⠀⠁⠈⠉⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡄⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⣀⠀⠀⠀⠀⢠⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠛⠛⠛⠻⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣉⡒⣒⣛⠒⠒⠒⠒⠂⠀⠀⠀⠤⠄⠀⠀⠀⠈⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠥⢀⠠⣼⣿⣿⣷⣿⡷⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡎⠉⠙⠛⠛⠛⠛⠛⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣾⣷⣾⣿⣿⣿⣿⣛⣛⣛⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣷⣿⣏⡀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⢀⣀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⠋⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠶⠶⠶⠶⢾⣿⡟⠋⠉⠻⣿⡇⢸⣿⣿⣿⣿⣿⡿⢟⠛⠛⢿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⣆⣸⡿⠃⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⡆⠀⠀⢼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⣠⣀⣀⣀⣀⣿⡇⠀⠀⣀⣭⡅⢸⣿⣿⣿⣿⣿⣟⢿⣧⣠⡌⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣷⣾⣿⣼⣿⣿⡗⢏⡁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣾⣿⢸⣿⣿⣿⣿⡿⣿⣿⣿⣤⣿⣿⠿⡀⢻⠋⠙⣿⡏⠛⠋⠠⢤⡀⠹⠃⠸⣿⣿⣿⣿⣿⣯⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠸⣷⣤⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣸⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⡇⠀⣼⠀⠀⢀⢉⡇⠀⠀⠀⠀⠛⣶⣦⡀⠙⢿⣿⠟⠛⣿⡿⠃⣾⡿⠁⠙⠿⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⡘⢻⡿⠋⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠉⠉⠛⠛⠑⠿⣷⣿⣿⣯⣇⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠈⠁⠀⠀⠃⢠⣾⠟⠁⠀⠀⠀⠀⢹⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠈⠀⠀⠀⢨⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣟⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠀⠀⠀⠀⢰⣾⠋⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⡤⠀⠀⢹⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠋⠰⣦⣤⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⣛⣉⣤⣄⣀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⣠⣴⣶⣽⣿⣿⠇⠀⣹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿
⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣶⠀⠀⠀⠁⠀⠠⠟⠻⠿⠆⣼⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⠿⠿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣿⣿⣿⣿⣿⣾⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⡆⠀⠇⡿⡼⠈⠏⢱⠳⠻⣿⣿⣿
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢳⣇⣶⢶⡶⢰⡶⣶⢰⣶⡖⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣟⣿⠀⣿⠃⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢠⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⣥⣭⣉⣭⣩⣭⢠⣩⡄⠀⠉⠈⠁⠉⠉⠈⠁⠀⠈⣿⣥⣭⣭⣥⠎⠁⢈⣥⡉⠉⠉⠉⢨⣭⡼⢈⣩⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢈⣙⣫⣼⣿⣿
⠀⠂⠰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⢸⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠁⠀⠀⠀⢹⠟⣁⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⣠⣤⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢠⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠐⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⣀⠀⠀⠀⠀⢠⡄⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠉⠉⢿⣿⣿⡿⠛⠛⢻⣿⣻⣿⣭⡗⣒⣛⠒⠒⠒⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣊⠠⢀⡾⢻⣿⣿⣿⡷⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡊⠉⠙⠛⠛⠛⠛⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣮⣿⣿⣿⠷⠿⣿⣿⣏⣛⣛⣛⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⠄⢀⣀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⡿⠁⠈⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠶⠶⠶⠶⢾⣿⡿⠋⠉⠙⣿⡇⢸⣿⣿⣿⣿⣿⡿⢛⠛⠛⢿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⣄⣸⡿⢃⣴⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢊⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣠⣀⣀⣀⡀⣿⣇⠀⠀⠀⢭⡁⢸⣿⣿⣿⣿⣿⣟⢻⣦⣠⣬⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣷⣾⣿⣼⣿⣿⡗⣏⠃⠀⠀⠈⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠿⡀⠿⠋⠹⣿⡇⠛⠋⠐⢤⡀⠸⠃⠺⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⠸⣷⣄⠀⠀⣶⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⢸⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⡇⠀⣼⠀⠀⡀⢉⠇⠀⠀⠀⠀⠛⣶⣦⡀⠙⢿⣿⠟⠛⣿⡟⠃⣾⡟⠁⠙⠻⣿⣿⣿
⠀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⠘⢴⣿⠟⠁⠀⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠿⠸⢿⣷⣿⣿⣯⣇⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠈⠁⠀⠀⠁⢠⣾⠟⠀⠀⠀⠀⠀⢹⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠊⠁⠀⠀⠀⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡟⢐⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠀⠀⠀⠀⢰⣾⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡶⠂⠀⢉⡍⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⢸⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠈⢿⣿⣿⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣽⣥⣤⣶⣤⣸⣿⣿⣿⣷⣇⠀⠀⠀⠐⠷⠄⠀⠀⠀⣠⣴⣾⣿⣿⣿⠇⠀⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⡄⠀⠀⠁⠀⠰⠟⠻⠷⠆⣼⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠿⠿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣾⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⣷⡆⠀⠇⡿⡼⠈⠏⢱⠳⠛⣻⣿⣿
⠀⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⠀⢲⣇⣶⢶⡶⢰⡶⣶⢸⣶⡟⠀⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⢶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣟⣿⠀⣿⢣⠀⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢠⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⢡⣭⣍⣭⣩⣭⡄⣭⣼⡇⠉⠈⠁⠉⠉⠈⠁⠀⠈⢻⣥⣭⣭⣥⠮⠁⢌⣥⡉⠉⠉⠉⢨⣩⡼⢈⣩⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢈⣙⣫⣼⣿⣿
⠀⠀⠰⣤⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢡⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠏⠁⠀⠀⢀⣹⠛⣁⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣴⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⠀⠘⠛⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠘⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠉⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⣀⠀⠀⠀⠀⢠⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢹⣿⣿⠿⡋⠉⠙⣿⣿⣿⢿⣞⣚⣛⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡨⣀⣢⣽⣛⣿⣿⣿⡷⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡈⠙⠛⠛⠛⠛⠛⠛⠛⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⢟⣛⢿⣿⣏⣛⣛⣛⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⠄⢀⣀⠀⠀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⢿⢇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠷⠶⠶⠶⠶⢾⣿⡿⠋⠉⠙⣿⡇⢸⣿⣿⣿⣿⣿⡿⣛⠛⠛⢿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⣄⣸⡿⠃⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠈⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣀⣀⡀⣿⣧⠀⠀⠀⢨⡁⢸⣿⣿⣿⣿⣿⣟⢻⣧⣠⣼⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣷⣾⣿⣼⣿⣿⡟⣏⡃⠀⠀⠈⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣛⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠿⡀⠿⠉⠹⣿⡇⠛⠋⠐⢤⡀⠸⠃⠸⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠸⣷⣀⠀⠀⣶⡆⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⣿⡇⠀⣼⠀⠀⡀⣉⠃⠀⠀⠀⠀⠛⣶⣤⡀⠙⢿⡿⠟⠛⣿⡟⠃⣾⡟⠁⠙⠻⢿⣿⣿
⠀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⠘⢸⣿⠟⠁⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠙⠛⠻⠿⠸⢿⣷⠿⠿⠋⣇⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠈⠁⠀⠈⠁⢠⣿⠏⠀⠀⠀⠀⠀⢹⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠊⠁⠀⠀⠀⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡟⢰⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠺⣿⡿⠀⠀⠀⠀⢰⣾⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣖⣀⠀⣭⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⣾⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠛⠀⢹⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣮⣭⣴⣶⣶⣄⣿⣿⣿⣿⣸⣆⠀⠀⠀⠺⠆⠀⠀⠀⢠⣴⣾⣿⣿⣿⠇⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿
⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠰⠟⠻⠿⠆⣼⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⣿⣿⣿⣿⡿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢷⡆⠀⠇⡿⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠄⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢠⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⢡⣭⣭⣭⣩⣭⡄⣉⣼⣷⠉⠈⠁⠉⠉⠈⠁⠀⠈⠻⣥⣭⣭⣥⡬⠁⢈⣥⣉⡉⠉⠉⠈⣩⡼⢈⣩⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢈⣙⣫⣼⣿⣿
⠀⠀⠲⣤⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⣩⡏⣁⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣠⣾⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠑⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠉⢻⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⣀⠀⠀⠀⠀⢠⡄⠀⠘⠣⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⣻⣿⢿⣟⠉⠉⢻⣿⣝⣿⣿⣛⣛⠒⠒⠒⠒⠒⠀⠀⠀⠀⠄⠀⠀⠀⠈⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⣠⣦⣟⣹⣿⣿⡿⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡊⠉⠙⠛⠛⠛⠛⠛⠛⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣷⣿⣿⡟⢫⠛⢿⣯⣙⣛⣛⣗⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⡀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⠄⢀⣀⠀⠀⢸⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣤⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠷⠶⠶⠶⢾⣿⣿⠋⠉⠙⢿⡇⢸⣿⣿⣿⣿⣿⡿⣛⡛⠛⢿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⢿⣿⣿⡄⣸⣿⠃⣴⣟⠻⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣀⣀⣀⣿⣿⠀⠀⠀⢨⡅⢸⣿⣿⣿⣿⣿⣿⣻⣷⣤⣤⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣷⣾⣿⣼⣿⣿⡗⢏⡃⠀⠁⠈⠃⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠿⡀⠿⠋⠹⣿⡏⠛⠋⠐⢤⡀⠰⠃⠸⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣄⠀⠀⣶⣆⠀⠘⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⣼⠀⠀⣀⠉⡇⠀⠀⠀⠀⠙⢶⣦⡀⠘⢿⣿⠟⠛⣿⡿⠋⣾⡟⠁⠈⠻⢿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡈⢰⣿⡿⠃⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠛⠻⠿⠡⡿⣿⠿⠿⢇⣇⠀⠀⠀⡉⠁⠀⠁⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠁⠀⠀⠁⢀⣾⠟⠀⠀⠀⠀⠀⢹⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠋⠁⠀⠀⠀⠸⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢸⣟⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢷⣀⣀⣠⣏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣼⡟⢰⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠟⠁⠈⢿⣿⣿⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢛⡻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣯⣶⣶⣷⣶⣼⣿⣿⣿⣷⣿⡀⠀⠀⠰⠷⠀⠀⠀⢀⣴⣾⣿⣿⣿⠇⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿
⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠠⠟⠻⠿⠆⢰⣿⣿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢷⡖⠀⠇⡟⡼⠈⠏⢱⠳⠘⣻⣿⣿
⡅⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣇⣶⢶⡶⢰⡶⣶⢸⣶⡞⡉⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣶⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢳⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠓⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⣭⣭⣭⣭⣭⣤⢩⣼⣧⡍⠈⠁⠉⠉⠈⠁⠀⠈⠛⢥⣭⣭⣥⡬⠅⠈⣡⣍⠉⠉⠉⠈⢭⣼⠈⣉⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠲⣦⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣸⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⢨⡟⢁⠀⠄⠀⠀⠁⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣼⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡈⠚⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠁⣀⠀⠀⠀⠀⠠⡄⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠙⣿⠿⢿⡭⠀⢈⣿⣯⣻⡽⣟⣛⠒⠒⠒⠒⠂⠀⠀⠀⠠⠤⠀⠀⠀⠈⢠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣵⣾⣭⣿⣿⡿⠿⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡎⠉⠉⠛⠛⠛⠛⠛⠛⠛⢻⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⠛⡭⠻⢿⣍⣉⣉⣗⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⢀⣀⠀⠀⢸⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⡦⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⠷⠶⠶⢾⣿⣿⠋⠉⠙⢿⡇⢸⣿⣿⣿⣿⣿⡿⣛⣋⠙⢻⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⢿⣿⣿⡆⣸⣿⠃⣰⣟⡻⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⣤⣀⣀⣀⣀⣸⣿⠀⠀⠀⢨⡅⢸⣿⣿⣿⣿⣿⣿⣛⣿⣤⣦⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣾⣿⣼⣿⣿⡗⢟⡃⠀⠀⠀⠋⠐⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠿⡀⠻⠋⠹⣿⡏⠛⠋⠑⠦⡀⠀⠇⠸⣿⣿⣿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣤⠀⠀⣶⣦⠀⠸⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⡇⣿⣿⢻⣿⡟⡇⠀⣼⠀⠀⣀⠉⡇⠀⠀⠀⠀⠙⢷⣦⡀⠘⢿⣿⠟⠛⣻⡿⠋⣾⡿⠁⠈⠻⢿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡄⢰⣿⡿⠗⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠻⠿⠣⣿⣇⠻⠿⢧⣧⠀⠀⠀⡉⠁⠀⠇⠀⠀⠀⠀⠀⠈⠿⣿⣦⠀⠁⠀⠀⠁⢀⣾⠟⠀⠀⠀⠀⠀⠸⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⢿⣿⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣧⣤⣀⣮⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣼⡟⢠⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⣿⣿⠿⠋⠀⢹⣿⣿⣿⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢛⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣵⣾⣿⣶⣦⣿⣿⣿⣿⣿⣇⠀⠀⠀⠾⠆⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣼⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠠⠛⠻⠿⠆⢰⣿⣿⣿
⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢷⡶⠀⠇⡟⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠴⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡞⡍⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢣⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠇⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢰⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⢩⣭⣭⣩⣭⣤⡍⣼⣷⣭⠈⠁⠉⠉⠈⠁⠀⠈⠛⠡⣭⣭⣥⣬⠅⠈⢡⣍⡉⠉⠉⠈⢩⣼⠈⣩⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠰⢦⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢣⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠏⢀⠀⠀⢈⡟⠁⠀⠄⠀⠀⠉⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⣴⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⣀⠈⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⡄⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠉⢿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⠀⠀⠀⠀⠠⡆⠀⠘⠣⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣿⡿⠟⣫⠅⠀⣹⣿⣝⢿⢿⣛⠒⠒⠒⠒⠒⠀⠀⠀⠀⠤⠠⠀⠀⠈⢠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣬⣶⣯⣽⣿⣿⠿⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣌⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⢉⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⣿⣿⡟⢩⠟⠿⣯⣉⣉⣟⣠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⢀⣀⡀⠀⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣷⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠿⠷⠷⠶⢾⣿⣿⠋⠉⠙⢿⡇⢸⣿⣿⣿⣿⣿⣿⣛⣯⠉⠻⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⢿⣿⢿⣿⣿⡆⣸⣿⠃⣰⣟⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡗⣠⣀⣀⣀⣀⢸⣿⠀⠀⠀⠠⡥⢸⣿⣿⣿⣿⣿⣿⣟⣿⣦⣦⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣾⣿⣼⣿⣿⡗⢏⣋⠀⠀⠀⠛⠐⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣿⣿⣿⡿⣿⣿⣿⣦⣾⣿⠿⡈⠛⠉⠙⣿⡏⠙⠋⠑⠢⣄⠀⠃⠸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣦⡀⠀⣶⣦⠀⠸⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⢿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡟⡇⠀⢼⠀⢀⣀⠉⡇⠀⠀⠀⠀⠘⢳⣦⡀⠈⢿⣿⠟⠛⣻⠿⠋⣾⡿⠁⠈⠛⢿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇⢸⣿⣿⠗⠀⠀⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⠛⠻⠿⠣⣿⣟⠙⠿⢷⣧⠀⠀⠀⡈⠁⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠁⠀⠀⠁⢀⣾⠟⠀⠀⠀⠀⠀⠘⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⢹⣿⣿⣿⣷⣦⣄⡀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣯⣤⣀⣴⡉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⢰⣿⣿⣿⣿⣾⠻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⢿⣿⡿⠋⠀⠸⣿⣿⣿⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢛⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣾⣿⣷⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⠇⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⢨⡇⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠠⠟⠻⠷⠆⢰⣿⣿⣿
⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⣿⣿⣿⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢿⡶⠀⠇⡿⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠿⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣷⢶⡶⢰⡶⣶⢸⣶⡞⡍⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢣⣶⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠁⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢼⣟⢸⣿⣿⠀⣿⢃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣭⣩⣭⣤⡍⣸⣷⣭⡌⠁⠉⠉⠈⠁⠀⠈⠛⠁⣭⣭⣭⣬⠅⠈⠡⣍⡉⠉⠉⠈⢩⣼⠈⣩⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⢠⠀⠀⠀⡟⠁⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠲⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⣿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⢠⠜⠜⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⡄⠐⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠀⠀⠹⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⠀⠀⠀⠀⠠⡆⠀⠘⠣⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢙⡿⠿⣻⠍⠀⣙⣿⣽⣿⢿⣟⠒⠒⠒⠒⠒⠂⠀⠀⠀⠤⠤⠀⠀⠈⢠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣬⣶⣾⣽⣿⣿⠿⠷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣌⠉⠉⠉⠛⠛⠛⠛⠛⠛⢻⣉⣥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⡿⢫⠽⠿⣿⣉⣉⣟⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⢀⣀⡀⠀⢸⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣷⡄⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠿⠿⠷⠶⢾⣿⣿⠋⠉⠙⢿⡏⢸⣿⣿⣿⣿⣿⣿⣛⣭⠉⠻⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⢿⣿⢿⣿⣿⡆⣸⣿⠃⣰⣟⣻⠻⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡗⣤⣀⣀⣀⣀⣸⣿⠀⠀⠤⠼⠆⢸⣿⣿⣿⣿⣿⣿⣟⣿⣧⣴⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣾⣿⣼⣿⣿⡟⢏⣟⠀⠀⠀⠋⠐⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⡟⣿⣿⣿⣧⣼⣿⠿⡈⠛⠉⠙⣿⡏⠙⠋⠁⠢⣄⠀⠃⠸⣿⣿⣿⣿⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣦⣀⠀⣶⣦⠀⠸⠟⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡟⡇⠀⠼⠀⢀⣀⠉⡇⠀⠀⠀⠐⠚⢳⣦⡀⠈⢿⣿⠟⠛⣿⡿⠋⣾⡿⠁⠈⠛⠿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡏⢰⣿⣿⠗⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠙⠛⠛⠿⠣⣿⣟⠙⠿⢿⣧⠀⠀⠀⡈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠁⠀⠀⠁⢀⣾⠟⠀⠀⠀⠀⠀⠘⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢿⣤⣄⣰⣌⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⢰⣿⣿⣿⣿⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⡿⠛⠁⠘⣿⣿⣿⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⢿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢛⡻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣶⣿⣿⣶⣼⣿⣿⣿⣿⣿⠀⠀⠀⠸⠷⠀⠀⠀⢠⣾⣿⣿⣿⣇⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡇⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣶⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡆⠀⠀⠀⠀⠠⠟⠻⠷⠆⢰⣿⣿⣿
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢿⡶⠀⠇⡿⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠞⠃⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡖⢰⡶⣶⢸⣶⡟⡉⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢣⣷⡇⢲⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣟⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣭⣭⣭⣤⣭⢸⣷⣭⡌⠁⠉⠉⠈⠁⠀⠈⠛⠁⢭⣭⣥⣬⠅⠈⠁⣍⡉⠉⠉⠈⢩⣼⠈⣩⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠆⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⡾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⡀⠀⠀⡽⠁⠀⠄⠀⠀⠉⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⢠⣾⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⢀⠄⠘⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⡄⠒⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠙⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⠀⠀⠀⠀⠠⡆⠀⠘⠣⠄⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⢙⢿⠿⢛⡭⠀⢈⣿⣿⣻⣿⡟⠒⠒⠒⠒⠒⠒⠀⠀⠀⠠⠤⠄⠀⠈⠠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⣴⣦⣵⣾⣭⣿⣿⡿⠷⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣌⠉⠉⠉⠛⠛⠛⠛⠛⠛⢻⣉⣽⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⠋⡭⠻⢿⣍⣉⣏⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⢀⣀⡀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠻⠷⠶⢾⣿⡿⠉⠉⠙⣿⡇⢸⣿⣿⣿⣿⣿⣿⣻⣭⠉⠻⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⢿⣿⢿⣿⣿⡆⣸⣿⠃⣠⣟⣛⠻⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡷⣤⣀⣀⣀⣀⢸⣷⠀⠀⠴⠾⡓⢸⣿⣿⣿⣿⣿⣿⣯⣿⣧⣴⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣾⣿⣼⣿⣿⡟⢏⣟⠀⠀⠀⠙⠐⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣧⣼⣿⠿⡈⠛⠉⠙⣿⡏⠘⠛⠀⠲⣄⠀⠁⠘⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣦⡀⠀⣶⣦⠀⢸⠟⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⡇⠀⠬⢀⢀⣀⠉⡗⠀⠀⠀⠀⠈⢻⣦⣄⠈⢻⣿⠟⠋⣿⠟⠋⣾⡿⠁⠈⠛⠿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⢰⣿⣿⠗⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠛⠿⠣⣿⣟⠹⠿⢿⣧⠀⠀⠀⣈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠁⠀⠀⠁⢀⣾⠟⠀⠀⠀⠀⠀⠘⣿
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⠿⡿⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣥⣤⣰⣎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⢰⣿⣿⣿⣿⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠿⣿⡿⠟⠁⠀⢿⣿⣿⣿⡇⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢛⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⡀⠀⠀⠘⠷⠀⠀⠀⢀⣶⣿⣿⣿⣇⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠠⠛⠻⠷⠆⢰⣿⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⢄⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢿⡶⠀⠇⡿⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠞⠂⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⠈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣷⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣭⣍⣭⣤⣭⢰⣷⣭⡌⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣭⣬⡥⠈⠁⣍⣉⠉⠉⠈⢩⣼⠈⣉⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠆⠰⢶⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⡄⠀⠀⢸⠉⠀⠄⠀⠀⠉⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠲⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⢠⣾⣟⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⢀⠴⠉⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⡄⠒⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⡤⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠒⠚⠀⠀⠀⠀⠈⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⠀⠀⠀⠀⠠⡆⠀⠘⠣⠄⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠂⠀⠀⠨⣿⠿⢿⡯⠀⢈⣿⣯⣻⠿⣟⠑⠒⠐⠒⠒⠒⠀⠀⠀⠀⠠⠀⠀⠈⠠⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠀⠀⣠⣢⣵⣶⣯⣿⣿⡿⠷⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⠉⠉⠉⠉⠛⠛⠛⠛⠛⢻⣉⣹⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⠟⡭⠻⢿⣍⣉⣏⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⢀⣀⡀⠀⢸⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⡆⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠻⠶⢾⣿⡿⠉⠉⠙⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣭⡉⠹⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⢿⣿⢿⣿⣿⡆⣸⣿⠃⣠⣟⡛⠛⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣤⣄⣀⣀⣀⢸⣷⠀⠀⠴⢾⡗⢸⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣾⣿⣾⣿⣿⡗⢯⣿⠀⠀⠀⠉⠐⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⡟⣿⣿⣿⣧⣼⣿⠿⡈⠛⠉⠙⣿⡏⠙⠛⠀⠲⣤⠀⠃⠘⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣦⠀⠀⣾⣧⠀⢸⠟⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⡇⠀⠬⢀⣠⢀⠈⡟⠀⠀⠀⠀⠈⢻⣦⣄⠈⢻⣿⠟⠛⣿⠟⢋⣾⡿⠁⠈⠛⠿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡟⢰⣿⣿⠷⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠛⠿⠃⣿⣟⡻⠿⢿⣧⠀⠀⠀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠁⠀⠀⠁⢀⣾⠟⠀⠀⠀⠀⠀⠘⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⣿⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢿⣥⣤⣤⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢰⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣿⡿⠟⠁⠀⢿⣿⣿⣿⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⣛⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣾⣿⣿⣷⣾⣿⣿⣿⣧⣿⡄⠀⠀⠘⠷⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⡇⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿
⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡆⠀⠀⠀⠀⠠⠿⠻⠷⠆⢰⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⢄⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠷⡶⠀⠇⡿⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠿⠆⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣾⢶⡶⢸⣶⣶⢸⣶⡟⠈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢢⣷⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠡⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣭⣭⣭⣤⣭⣴⣷⣭⣌⠁⠉⠉⠈⠁⠀⠈⠛⠁⠩⣭⣭⣮⡥⠈⠁⢉⡉⠉⠉⠈⢉⣼⠈⣉⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠆⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⡄⠀⠀⢨⠉⠠⠀⠀⠀⠉⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⢠⣾⣟⡡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⢀⡄⠁⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⡀⠒⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠒⠺⠀⠀⠀⠀⠈⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⠀⠀⠀⠀⠠⡆⠀⠘⠣⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣹⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠉⣿⡿⢿⡯⠄⢈⣻⣏⣿⡯⣟⠁⠒⠒⠒⠒⠒⠀⠀⠀⠠⠤⠠⠀⠈⠠⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢂⠀⠀⢠⣢⣴⣶⣏⣿⣿⡿⠿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣎⠉⠉⠉⠙⠛⠛⠛⠛⠛⢻⣉⣹⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⠟⡭⠿⢿⣍⣉⣏⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣯⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⢀⣀⡀⠀⢸⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⡄⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠻⠶⢾⣿⣿⠋⠀⠙⢿⡇⢸⣿⣿⣿⣿⣿⣿⣻⣭⡍⠙⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⢿⣿⢻⣿⣿⡆⣸⣿⠃⣠⣟⡛⠻⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣤⣄⣀⣀⣀⣼⣿⠀⠀⠰⢾⡆⢸⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣾⣿⣿⣿⣿⣿
⠀⢿⣿⣷⣾⣿⣾⣿⣿⡗⢏⣟⠀⠀⠀⠈⠐⠐⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣩⣿⣿⣿⣿⡟⣿⣿⣿⣧⣼⣿⠟⡈⠛⠉⠙⣿⡏⠙⠋⠀⠲⣤⠀⠁⠘⣿⣿⣿⣿⣿⣿⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣤⠀⠀⣾⣧⠀⢸⡟⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡏⡇⠀⠬⢀⣠⢀⠈⡗⠀⠀⠀⠐⠊⢻⣦⣄⠈⢻⣿⠟⢋⣿⠟⢋⣾⡿⠁⠈⠛⠿⣿⣿
⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡛⢰⣿⣿⠷⠀⠀⢸⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠙⠛⠛⠿⠣⣿⣿⡻⠿⢷⣧⠀⠀⠀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠐⠁⢠⣾⠟⠀⠀⠀⠀⠀⠘⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⣿⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠿⡿⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢿⣥⣤⣠⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⢰⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⣿⡿⠟⠁⠀⢻⣿⣿⣿⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⣙⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣾⣿⣿⣷⣾⣿⣿⣿⣧⣿⡄⠀⠀⠐⠷⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⡀⠀⠀⠀⣠⣿⣿
⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡆⠀⠀⠀⠀⠠⠛⠻⠷⠆⢰⣿⣿⣿
⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠨⢿⡿⢷⡖⠀⠇⡿⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠿⠇⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⣶⣶⢸⣶⡟⠉⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢢⣷⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠈⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢸⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣭⣭⣭⣤⣭⣴⣷⣭⣌⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣭⣮⡥⠌⠁⢉⣉⠉⠉⠈⢩⣼⠈⣩⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠆⠰⢶⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⡄⠀⠀⢸⠉⠠⠄⠀⠀⠉⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠛⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⢾⡿⡡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⢀⠔⠁⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⡀⠘⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢺⠀⠀⠀⠀⠈⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⠀⠀⠀⠀⠰⡆⠀⠘⠣⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣍⣹⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠈⣻⣿⠿⣛⠉⠉⣻⣟⣿⡿⣿⠁⠀⠐⠒⠒⠒⠀⠀⠀⠀⠄⠤⠀⠈⠤⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠺⠁⠀⢠⣄⣬⣦⣟⣿⣿⣿⠿⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⠉⠉⠉⠉⠉⠛⠛⠛⠛⢛⣉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣾⣿⣿⠟⣻⠿⣿⣍⣉⣏⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣯⡅⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⢀⣀⡀⠀⣼⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠏⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠻⠶⢾⣿⣿⠋⠁⠉⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣭⡍⠙⣿⣿⣿⣿⣿⣿
⠻⣿⣿⡿⢿⣿⢻⣿⣿⡄⣼⣿⠃⣠⣟⡛⠻⠇⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣤⣀⣀⣀⣀⣼⣿⠀⠀⢠⢼⡦⢸⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣾⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣾⣿⣿⡟⢯⣏⠀⠀⠀⠀⠀⠐⢰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⣀⣻⣿⣿⣿⣿⡿⣿⣿⣿⣧⣼⣿⠟⡈⠛⠉⠙⣿⡏⠙⠋⠀⠲⣄⠀⠃⠸⣿⣿⣿⣿⣿⣿⣤⣾⠟⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣦⢀⠀⣾⣇⠀⢸⡟⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡏⡇⠀⠬⢀⣠⢀⠉⡇⠀⠀⠀⠐⠘⢳⣦⡀⠈⢿⡿⠟⢛⣿⠟⢃⣾⡟⠁⠈⠛⠿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡉⢸⣿⣿⠗⠀⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠙⠛⠛⠿⠸⣿⣿⡻⠛⢷⣧⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠘⠁⢠⣾⠟⠀⠀⠀⠀⠀⢸⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⣟⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⡟⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢿⣥⣄⣀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡏⢸⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣿⡿⠟⠁⠀⢻⣿⣿⣿⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⣉⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣶⣿⣿⣷⣾⣿⣿⣿⣧⣿⡄⠀⠀⠐⠷⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠸⡇⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿
⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠠⠿⠻⠷⠆⢰⣿⣿⣿
⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠨⢿⡿⢷⡆⠀⠇⡟⡼⠈⠏⢱⠳⠘⣻⣿⣿
⠻⠃⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡟⠈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣷⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢸⣟⢸⣟⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⢸⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣭⣭⣭⣤⣭⣴⣷⣭⣌⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣭⣮⣥⠌⠁⢉⡉⠉⠉⠈⢩⣼⠈⣉⣤⣽⣯⣤⠉⠉⠁⠀⠙⠋⠈⣙⣫⣼⣿⣿
⠀⠆⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⡄⠀⠀⢨⡁⠀⠄⠀⠀⠉⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠛⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⢀⢾⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⡴⠃⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠚⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢐⠀⠀⠀⠀⠀⢿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⠀⠀⠀⠀⠰⡆⠀⠘⠠⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣽⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠙⣿⣿⣿⣟⡉⠉⢻⣟⣿⣿⣿⠁⠒⠒⠒⠒⠂⠀⠀⠀⠀⠤⠤⠀⠈⢤⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⠉⠀⢈⣅⣢⣤⣟⣿⣿⣿⠿⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣈⡉⠉⠉⠉⠉⠉⠛⠛⠛⢫⣉⣹⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⡿⣛⡿⣿⣍⣉⣏⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⠂⢀⣄⡀⠀⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⡤⠈⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⡛⠛⠛⠳⠶⢾⣿⣿⠟⠉⠙⢻⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⣿⣿⣿⣿⣿⣿
⢻⣿⣿⡿⢿⣿⢻⣿⣿⢄⣼⣿⠃⡼⢟⡛⠻⠃⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣤⣀⣀⣀⣀⣿⣿⠀⠀⠀⣨⡋⢸⣿⣿⣿⣿⣿⣿⢯⣿⣷⣴⣸⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣾⣿⣿⡟⢯⣏⠀⠀⠀⠀⠀⠘⢾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⠟⡈⠛⠉⠙⣿⡏⠛⠋⠑⠢⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣴⣿⢟⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣶⠀⢀⣾⣇⠀⢻⡟⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡏⠁⠀⡬⢀⢠⠀⠉⡇⠀⠀⠀⠀⠙⢷⣦⡀⠘⢿⡿⠟⢻⡿⠋⢁⣿⡟⠁⠙⠻⢿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡋⣸⣿⣿⡿⠃⠀⢸⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠛⠻⠿⠸⣿⣿⡟⠛⠃⣆⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠿⣿⣦⠀⠁⠀⠘⠀⢠⣿⠟⠀⠀⠀⠀⠀⢹⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢠⡏⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⢿⠟⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢿⣥⣄⣀⣎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⢸⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢀⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣿⣿⠟⠁⠀⢿⣿⣿⣿⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣹⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣶⣿⣿⣶⣾⣿⣿⣿⣧⣿⡀⠀⠀⠰⣶⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡆⠀⠀⠀⠀⠠⠿⠻⠷⠆⣼⣿⣿⣿
⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡿⢷⡆⠀⠇⡿⡼⠈⠏⢱⠳⢙⣻⣿⣿
⠶⠃⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢸⡶⣶⢸⣶⡟⠈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢶⡶⢢⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣟⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣭⣭⣭⣤⣭⣴⣷⣭⡌⠁⠉⠉⠈⠁⠀⠈⠛⠁⠩⣭⣭⣬⣥⡬⠁⢉⠉⠉⠉⠈⢉⡼⠈⣩⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⢨⣙⣫⣼⣿⣿
⠀⠆⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⣅⠀⠀⢀⡁⠠⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠛⠛⠛⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⢴⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⡴⠃⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠚⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⢻⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⠀⠀⠀⠀⠰⡆⠀⠘⠠⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⣻⣿⣿⠟⠛⠉⢻⡿⣿⣿⣿⠁⠐⠀⠒⠒⠂⠀⠀⠀⠀⠀⠄⠀⠈⢤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠈⠐⠀⠀⠤⠉⠁⢀⡈⠄⣀⡿⣿⣿⣷⡾⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣈⡉⠉⠉⠉⠉⠙⠛⠛⠛⢋⣉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣽⣿⣿⡿⠟⣿⣯⣉⣉⣏⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣯⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣶⠀⢀⣀⠀⠀⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡏⠀⠉⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣛⡛⠛⠛⠳⠶⢾⣿⣿⡟⠋⠙⢻⣧⢸⣿⣿⣿⣿⣿⣿⣿⣯⠍⠙⢿⣿⣿⣿⣿⣿
⢻⣿⣿⡿⢿⣿⢻⣿⣿⢤⣾⡿⠀⣼⣟⡛⠻⠁⣄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣤⣀⣀⣀⣀⣿⣿⠇⠀⠀⠀⠛⢸⣿⣿⣿⣿⣿⣿⢯⣿⣷⣦⢸⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣾⣿⣿⡛⣯⣇⠀⠀⠀⠀⠀⠘⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠟⡀⠛⠉⠻⣿⡇⠛⠉⠑⠄⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⡿⢟⣷⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣶⠀⢠⣾⣇⠀⢻⠟⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡏⠁⠀⡤⠀⢠⠀⠩⠇⠀⠀⠀⠀⠙⣷⣦⡀⠙⢿⡿⠛⣻⠟⠛⢓⣿⡟⠁⠙⠻⢿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡀⣼⣿⣿⡷⠋⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⠛⠻⠿⢸⣿⣿⡟⠛⠃⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠃⠀⢠⣿⠏⠀⠀⠀⠀⠀⢹⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢀⡏⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⢿⠟⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣁⣀⣀⣏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⡇⢸⣿⣿⣿⣿⣯⠃⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿
⢠⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⡿⠟⠁⠀⢿⣿⣿⣿⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⣉⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣶⣾⣿⣶⣾⣿⣿⣿⣷⣿⠀⠀⠀⠰⡶⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿
⡾⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⠀⠠⠛⠻⠷⠄⣼⣿⣿⣿
⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢷⡆⠀⠇⡿⡼⠈⠏⢱⠳⢛⣻⣿⣿
⡋⠃⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⠈⣿⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢶⡶⢢⣷⡇⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢰⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢩⣭⣭⣭⣤⣭⢸⣷⣭⡌⠁⠉⠉⠈⠁⠀⠈⠛⠁⠩⣭⣭⣮⣥⣬⠅⢉⡉⠉⠉⠈⢉⡼⢈⣩⣤⣽⣯⣬⠉⠉⠁⠀⠙⠋⢨⣝⣫⣼⣿⣿
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⢍⠀⠀⠀⡁⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠛⠛⠛⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠠⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢰⠊⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠚⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⢰⠆⠀⠚⠠⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣍⣍⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢻⣿⣿⣿⠿⠿⣿⣿⣿⣿⣉⠁⠒⠐⠒⠒⠂⠀⠀⠀⠀⠄⠄⠀⠉⢤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠰⣀⠀⣼⣧⣿⣿⣸⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣈⠉⠉⠉⠉⠉⠙⠛⠛⠛⣋⣉⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⣀⣤⣶⣧⣿⣿⣿⣏⣉⣇⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⢀⣀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠟⠩⠾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠛⠳⠶⢾⣿⣿⡿⠛⠛⢻⣇⢸⣿⣿⣿⣿⣿⣿⣿⣯⠍⠙⢿⣿⣿⣿⣿⣿
⢿⣿⣿⡿⢿⣿⣿⣿⣿⢤⣿⡿⠀⣼⣟⡛⠻⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣤⣀⣀⣀⡀⣿⣿⠇⠀⠀⠀⠻⣻⣿⣿⣿⣿⣿⡿⢿⣿⣧⡦⢸⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣷⣿⣿⣿⠻⣯⡇⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣤⡿⠟⡀⠋⠉⠻⣿⡇⠛⠉⠒⠄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣖⠉⢛⣷⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣶⠀⢠⣾⡇⠀⢻⠟⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⠁⠀⡄⠀⢠⠀⢹⠃⠀⠀⠀⠀⠓⣶⣦⡀⠙⢿⡿⠛⣿⠟⠛⣲⣿⡟⠁⠙⠻⣿⣿⣿
⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡀⣼⣿⣿⠗⠁⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⢸⣿⣿⡟⠛⠋⡄⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠹⢿⣿⣄⠈⠀⠀⠃⠀⣰⣿⠋⠀⠀⠀⠀⠀⢻⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⡀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢟⣀⡀⢠⡍⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⡇⢸⣿⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿
⢸⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⡿⠟⠁⠈⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⢈⣝⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣯⣶⣶⣶⣶⣽⣿⣿⣿⣿⣷⠀⠀⠀⠰⡦⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢺⠁⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿
⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠛⠻⠿⠄⣾⣿⣿⣿
⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢶⠆⠀⠇⡟⡼⠈⠏⢱⠳⢛⣿⣿⣿
⠶⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡉⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡆⢷⡶⢣⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠶⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢸⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⢠⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⢭⣭⣭⣭⣤⣭⢸⣷⣭⡌⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣭⣮⣥⣬⡥⢉⠉⠉⠉⠈⣩⡌⢈⣩⣤⣽⣯⣌⠉⠉⠁⠀⠙⠋⢨⣝⣫⣼⣿⣿
⠐⠀⠰⢶⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⠁⠀⠈⠁⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠛⠛⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⣘⢿⣫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⡘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠐⠚⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⢰⠆⠀⠛⠤⠀⠀⠀⠀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠒⠒⠒⠂⠀⠀⠠⠀⠤⠀⠀⠉⢤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⢋⠉⠉⢹⡟⣫⣿⡒⡖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣉⠉⠉⠉⠉⠉⠉⠛⠛⠛⣏⣉⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⢀⡟⣿⣿⣿⣿⣉⣇⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣠⣀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⣶⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠿⠷⠶⢾⣿⣿⡿⠛⠛⢻⣇⢸⣿⣿⣿⣿⣿⣿⣿⣯⠍⠙⢿⣿⣿⣿⣿⣿
⢿⣿⣿⠿⣿⡿⣿⣿⣿⢤⣿⡟⠀⣼⣟⡛⠻⠙⣷⣄⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠈⠁⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⣀⣀⣀⡀⣿⣿⠁⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣦⡤⢸⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣷⣿⣿⣿⠻⣽⡇⠁⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⢿⣿⣿⣿⣿⣤⡿⠇⠉⠋⠉⢻⣿⡇⠛⠉⠢⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣖⠙⣻⣷⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⢹⣷⣶⠀⢠⣿⡆⠀⣿⠟⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⠁⠀⡄⠀⢠⡀⠹⠁⠀⠀⠀⠀⠳⣶⣤⡀⠙⣿⡿⠛⣿⠟⠛⣲⣿⠟⠁⠙⠿⣿⣿⣿
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣀⣾⣿⣿⠗⠁⠀⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠛⠿⠿⢸⣿⣿⡿⠛⠏⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠈⠀⠀⠃⠀⣰⣿⠋⠀⠀⠀⠀⠈⢿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⡀⡆⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢗⡀⠀⢨⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣷⠀⣸⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⡿⠛⠁⠘⣿⣿⣾⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠈⣛⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣽⣶⣶⣶⣶⣿⣿⣿⣿⣼⣇⠀⠀⠀⢶⡆⠀⠀⠀⠀⢀⣿⣿⣿⣄⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⢀⣼⣿⣿
⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⠀⠀⠀⠀⠀⠠⠟⠻⠿⢤⣾⣿⣿⣿
⣝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⢶⠂⠀⠇⡿⡼⠈⠏⢱⠻⢛⣿⣿⣿
⠻⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣶⢶⡶⢰⡶⣶⢸⣶⡟⡍⣷⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣷⣶⡦⢷⡶⢣⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⢸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢪⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣭⣭⣭⣤⣭⣸⣷⣭⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣥⣬⣥⣬⡥⢍⡉⠉⠉⠈⣩⡄⢈⣩⣤⣽⣯⡄⠉⠉⠁⠀⠙⠋⣨⣝⣫⣼⣿⣿
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⠉⠀⠈⠁⠀⠀⠀⠈⠁⢺⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠛⠻⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠐⠃⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⢀⡬⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⢀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⠊⠀⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠚⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡤⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢰⠄⠀⠛⠄⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣇⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠋⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠂⠒⠒⠒⠂⠀⠀⠀⠀⠄⠀⠀⠁⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⢿⣿⡿⢿⡷⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣁⠉⠉⠉⠉⠉⠉⠙⠛⠛⣏⣉⡉⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⣀⣿⣰⣿⣿⣽⣇⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣃⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⣠⣀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⣀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠿⠷⠶⢾⣿⣿⠟⠛⠛⢿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠛⣿⣿⣿⣿⣿⣿
⢿⣿⣿⠿⣿⡟⣿⣿⣷⢠⣿⡟⠀⣼⣛⠛⠛⠹⣿⣷⡈⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡿⠛⠩⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⣀⣀⣀⣀⣿⣿⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⡄⣸⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣷⣿⣿⣿⠻⣽⡍⠁⠀⠀⠁⠀⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⣿⣿⣿⣿⢻⣿⣿⣿⣿⣥⡼⢇⠙⠋⠉⢻⣿⠃⠛⠉⠢⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣌⠹⣻⣧⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⢻⣷⣶⠀⣠⣿⡄⠀⣿⠏⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⡅⠀⢠⡀⠹⠁⠀⠀⠐⠈⢳⣶⣄⠀⠹⣿⡿⠛⣿⠟⠛⣲⣿⠏⠁⠛⠿⣿⣿⣿
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣖⣿⣿⣿⠟⠁⠀⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⠻⠿⢸⡿⣿⡿⠿⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠈⠀⠐⠃⠀⣸⡿⠋⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⢀⣠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⣇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠖⠀⠀⢩⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣿⠀⣼⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠛⠁⠸⣷⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣈⣭⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣥⣶⣶⣦⣦⣿⣿⣿⣿⣿⡆⠀⠀⠀⢶⠄⠀⠀⠀⠀⠀⣻⣿⣿⣄⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⢀⣾⣿⣿
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠀⠀⠀⠀⠀⠠⠛⠻⠷⢦⣿⣿⣿⣿
⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⢶⠀⠀⠇⡿⡼⠈⠏⢱⠻⢛⣿⣿⣿
⠂⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣦⣾⠷⠀⢲⣆⣶⢶⡖⢰⡶⣶⢸⣶⡞⡍⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢶⡶⢢⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣸⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢮⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣭⣭⣭⣤⣍⣸⣷⣍⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣥⣮⣥⣬⣥⡭⣩⠉⠉⠈⣩⡄⢈⣩⣤⣽⣯⡄⠉⠉⠁⠀⠙⠋⣬⣝⣫⣼⣿⣿
⠐⠀⠰⣶⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶
⠐⠂⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⣠⡽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⠰⠃⠈⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⠚⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢴⠀⠀⠛⠄⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣇⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠒⠒⠒⠒⠀⠀⠀⠀⠤⠄⠀⠀⠁⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⠉⠉⠉⠉⠉⠉⠛⠛⠛⣍⣉⣉⣉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣻⢋⣵⣯⣽⣁⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⣠⣀⠀⢀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢒⣀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣛⠛⠛⠿⠶⠶⣿⣿⣿⠋⠉⠛⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⡟⣿⣿⣧⣤⣿⡟⢀⣾⣛⠛⠛⢹⣿⣷⡌⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⣀⣀⣀⣠⣿⡇⠀⠀⠀⠘⠃⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⡄⣼⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣷⣿⣿⣿⠻⣽⡍⠀⠀⠀⠁⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢙⣿⣿⣿⣿⢻⣿⣿⣿⣿⣯⡼⢇⠙⠋⠉⢻⣿⠙⠋⠑⠦⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣜⢙⣻⣷⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⠄⢻⣷⣦⠀⣰⣿⡀⠀⣿⠏⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⢠⡄⠀⢀⡈⠹⠀⠀⠀⠂⠘⢷⣶⣄⠀⠻⣿⡿⠛⡿⠟⠛⣾⣿⠏⠈⠛⢿⣿⣿⣿
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣼⣿⣿⡿⠞⠁⠀⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠻⠿⠟⣾⣿⣿⣿⠿⠿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠈⠀⠐⠃⠀⣼⡿⠋⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣷⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠺⣿⣿⡇⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⠆⠀⠀⢉⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣼⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠛⠁⢰⣶⣤⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣉⣫⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣥⣶⣶⣦⡾⣿⣿⣿⣿⣧⡀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⡀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⢀⣾⣿⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠀⠀⠀⠀⠀⠰⠛⠻⠷⢦⣿⣿⣿⣿
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠯⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡿⢶⠀⠀⠇⡿⡼⠈⠏⢱⠻⢛⣿⣿⣿
⠫⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣷⢶⡶⢰⡶⣶⢸⣶⡞⡉⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢷⡶⢢⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣭⣭⣭⣤⡍⣴⣷⡍⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⠩⣭⣥⣮⣥⣬⣥⣭⢭⠭⠉⠈⣩⡄⢈⣩⣤⣽⣯⡄⠉⠉⠁⠀⠙⠋⣬⣝⣫⣼⣿⣿
⠀⠀⠰⢲⠀⠠⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠛⠉⠀⠁⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠘⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⢀⡼⢿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠊⠀⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠚⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢴⠀⠀⠛⠄⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣅⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠒⠒⠒⠒⠀⠀⠀⠀⠤⠄⠀⠀⠡⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿⠿⠟⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣉⠉⠉⠉⠉⠉⠛⠛⠛⠛⣉⣉⣉⣉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⢻⠟⣉⣿⣽⣡⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⡖⠀⣀⣀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠄⠐⠂⠰⢾⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣛⠛⠛⠿⠶⠶⣿⣿⡟⠉⠉⠻⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⡟⣿⣿⣧⣠⣿⡏⢀⣿⣛⠛⠏⢹⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠾⣿⣶⣿⡿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⣀⣀⣀⣸⣿⡇⠀⠀⠀⡙⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⡄⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣷⣿⣿⣿⠻⣽⡉⠀⠀⠈⠀⠀⢸⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢇⠙⠃⠉⢻⣿⠙⠋⠑⢤⡀⠀⠞⠀⢿⣿⣿⣿⣿⣿⣷⡜⠹⣿⣷⣿⣿⣿⣿⣿⣿
⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣷⡆⠀⣠⣿⡀⠘⣿⠏⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠀⢠⡄⠀⢠⡈⠙⠀⠀⠀⠀⠙⢾⣶⣄⠀⠻⣿⡿⢛⡿⠟⠛⣾⣿⠋⠈⠛⢿⣿⣿⣿
⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣚⣿⣿⡷⠊⠀⠀⢾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠛⠛⠿⠟⣿⣿⣿⢿⡟⠿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⡄⠈⠀⠘⠁⠀⣼⡿⠃⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠀⠀⠀⠀⠐⢾⠃⣼⠀⣸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢿⣿⢿⠇⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⠿⠋⠀⢰⣦⣄⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠉⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣷⣶⣾⣤⣌⣿⣿⣿⣿⣇⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⡀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⡀⠀⠀⢀⣿⣿⣿
⣨⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠐⠛⠻⠷⢴⣿⣿⣿⣿
⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡿⠶⠀⠀⠇⡟⡼⠈⠏⢱⠻⢛⣿⣿⣿
⠙⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣷⢶⡶⢰⣶⣶⢸⣶⡟⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢶⡶⢢⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣾⣟⢸⡟⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣍⣭⣭⣤⡍⣼⣷⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⠩⣭⣥⣮⣥⣬⣥⣭⣭⡭⠉⠈⣩⠄⣈⣩⣤⣽⣯⡄⠉⠉⠁⠀⠙⠋⣬⣙⣫⣼⣿⣿
⠀⠆⠰⢠⠀⠐⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠋⠁⠉⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠐⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⢀⡬⢿⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠊⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠛⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⠀⠀⠃⠄⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣩⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠒⠒⠒⠒⠀⠀⠀⠀⠤⠀⠀⠀⠡⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⡉⠉⠉⠉⠉⠛⠛⠛⠛⢛⣉⣉⣉⢉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⢻⡟⢋⣟⣹⣡⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠰⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⣛⠛⠻⠿⠶⠶⣿⣿⠏⠉⠙⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⡿⣿⣿⡧⣰⣿⠇⢠⣿⣛⠛⠏⢹⣿⣿⣮⠁⠀⠀⠀⠀⠀⠀⠾⣿⣶⣾⣿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢠⣄⣀⣀⣀⢸⣿⠀⠀⠀⢈⣉⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⡄⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣷⣿⣿⣿⢻⣽⡈⠀⠀⠈⠀⠀⢸⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠁⠙⢿⣿⠘⠋⠒⢄⠀⠀⠏⠀⢿⣿⣿⣿⣿⣿⣧⡌⠻⣿⣶⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷⡆⠀⢰⣷⠀⠸⡿⠋⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⣿⣿⣿⣿⡏⣿⠀⢠⠄⠀⣀⡈⠙⠀⠀⠀⠀⠻⣿⣶⣄⠈⠻⣿⠟⢛⡿⠟⢑⣾⣿⠋⠈⠛⢿⣿⣿⣿
⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⢈⣿⣿⠷⠊⠀⠀⢺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠛⠿⠇⣿⣿⣿⢿⡛⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠘⠀⠀⣾⡿⠁⠀⠀⠀⠀⠘⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠈⠉⢾⠃⣠⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠃⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠿⠋⠀⢠⣤⡀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣷⣶⣦⣤⣼⣿⣿⣿⣇⣇⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⢹⣿⣿⣀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⡀⠀⠀⢠⣿⣿⣿
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠐⠛⠻⠷⢶⣿⣿⣿⣿
⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡿⠾⠀⠀⠇⡟⡼⠈⠏⢱⠻⢻⣿⣿⣿
⠈⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣿⢶⡶⢰⡶⣶⢸⣶⡞⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢷⡶⢢⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⢸⣟⢸⡿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠉⣭⣍⣭⣭⣤⣉⣼⡇⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⠩⣭⣥⣬⣥⣬⣥⣭⣭⣭⠉⠈⣩⠀⣌⣭⣤⣽⣯⡀⠉⠉⠁⠀⠙⠋⣬⣙⣫⣼⣿⣿
⠀⠀⠰⢠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠋⠁⠈⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⢀⡬⣿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠊⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠛⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡶⠀⠐⠃⠄⠀⠀⠀⢀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠐⠒⠒⠒⠒⠀⠀⠀⠠⠤⠤⠀⠈⠡⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠟⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣌⡉⠉⠉⠉⠙⠛⠛⠛⠛⢻⣉⣉⡉⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⢻⠟⢋⣿⣹⣡⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠐⠄⠀⡀⡀⠀⠀⠀⠰⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠻⠶⠶⣿⡿⠋⠉⠙⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⢿⣿⣿⡧⣰⣿⠇⢠⣿⣛⠛⠏⢻⣿⣿⣆⠁⠀⠀⠀⠀⠀⠐⢾⣿⣶⣾⡿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣄⣀⣀⣀⢸⣇⠀⠀⠀⢨⡋⠠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣴⢄⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣾⣿⣿⡿⢿⣹⠈⠀⠀⠈⠀⠀⢸⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠈⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢀⠘⠁⠙⢿⣿⠘⠉⠢⣄⠀⠸⠋⠘⢿⣿⣿⣿⣿⣿⣧⡌⠹⣿⣾⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷⡄⢀⣰⣷⠀⠸⡿⠋⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡏⣿⣿⣿⣿⢹⣿⠀⢰⠀⠀⣀⡈⠋⠀⠀⠂⠈⠿⣿⣶⣄⠈⠻⣿⠟⢻⡿⠛⢑⣾⡿⠉⠈⠛⠿⣿⣿⣿
⠠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣈⣿⣿⠷⠊⠀⠀⢺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠙⠛⠻⠇⣿⣿⡿⢻⢸⡟⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠘⠀⢀⣾⡟⠁⠀⠀⠀⠀⠘⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠁⢺⠘⣃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⠁⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡷⠆⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠋⠀⢠⣤⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣷⣶⣶⣤⣼⣿⣿⣿⣇⣇⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠠⡟⠀⠀⠀⠀⡀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣆⠀⠀⠀⠀⠀⠐⠛⠻⠷⢶⣿⣿⣿⣿
⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠿⢿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⡿⠾⠀⠀⠇⡿⡼⠈⠏⢱⠻⣻⣿⣿⣿
⠊⠀⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣿⢶⡶⢰⡶⣶⢸⣶⡞⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢷⡶⢣⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠩⣭⣍⣩⣭⣤⣉⣼⡇⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⢩⣭⣥⣬⣥⣬⣥⣭⣭⣭⠉⠈⢩⠀⣌⣭⣤⣽⣯⡈⠉⠉⠁⠀⠙⠋⣬⣝⣯⣼⣿⣿
⡐⠀⠰⢠⠀⠐⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢸⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠋⠁⠊⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠛⠛⠛⠿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢀⡮⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⢀⠊⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠛⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⢤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠐⠂⠀⠀⠈⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡶⠀⠘⠃⠄⠀⠀⠀⢀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠐⠐⠒⠒⠒⠂⠀⠀⠠⠤⠤⠀⠈⠡⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⠿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠉⠉⠉⠉⠉⠛⠛⠛⠛⢻⣉⣉⠉⡉⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠈⢻⠟⣉⣯⣽⣡⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⡆⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⠀⢀⣀⡀⠄⠐⣂⠰⢾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⠛⠶⠶⣿⡟⠉⠉⠻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⢻⣿⣿⣿⣿⣿⣿
⢹⣿⣿⢿⣿⢿⣿⣿⣧⣸⣿⠇⢠⣿⣛⠛⠏⢻⣿⣿⣎⠁⠀⠀⠀⠀⠀⠐⠾⣷⣶⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣄⣀⣀⣀⢸⡇⠀⠀⠀⢭⡏⢰⣿⣿⣿⣿⣿⣿⠿⣿⣿⣶⢤⣿⣿⣿⣿⣿⣿
⢻⣿⣷⣾⣿⣾⣿⣿⡟⢯⣻⠀⠀⠀⠈⠀⠀⢸⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠈⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠘⠁⠘⢿⣿⠈⠑⠢⣄⠀⠘⠃⠘⢿⣿⣿⣿⣿⣿⣧⡎⠹⣿⣾⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣶⡄⢀⣰⣷⠀⠸⡿⠋⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⣿⣿⣿⣿⢸⡏⠀⢰⠀⠀⣀⠈⠋⠀⠀⠂⠘⢿⣿⣶⣄⠈⢻⣿⠟⢻⡿⠛⢑⣾⡿⠁⠈⠛⠿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣈⣿⣿⠷⠊⠀⠀⢺⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠛⠿⠇⣿⣿⡿⢻⢸⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠘⠀⢀⣾⡟⠁⠀⠀⠀⠀⠘⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁⠀⠀⠀⠀⠀⠀⠁⠺⢸⡟⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⠁⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠐⣶⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⠄⠀⠀⠐⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠈⣵⡟⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⢤⣤⡀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣷⣶⣶⣤⣼⣿⣿⣿⣧⣇⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠘⣿⣏⡀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠰⡏⠀⠀⠀⠀⡀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠻⠷⢶⣿⣿⣿⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⠹⠿⢿⡿⠾⠀⠀⠇⡿⡼⠈⠏⢱⠻⣻⣿⣿⣿
⠒⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣿⢶⡶⢰⡶⣶⢸⣶⡞⡇⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢷⡶⢣⣷⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣾⣟⢸⣟⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠋⣿⣿⡇⣿⣿⡆⢸⣿⣿⢫⡝⣷⢸⣿⣿
⠁⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⢩⣭⣍⣩⣭⣤⣩⣼⣇⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⠁⢭⣭⣭⣬⣥⣬⣥⣭⣭⣭⠉⠈⠉⠀⣬⣭⣤⣽⣯⡈⠉⠉⠁⠀⠙⠋⣬⣝⣯⣼⣿⣿
⠰⠆⠰⢢⠀⠀⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢸⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠛⠉⠊⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢀⡾⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⢀⠋⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡒⠛⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠄⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠒⠐⠀⠀⠈⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡶⠀⠘⠃⠄⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠒⠒⠒⠀⠀⠀⠀⠠⠀⠀⠈⠡⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⣿⣿⣿⣿⣿⣷⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣌⠉⠉⠉⠉⠉⠛⠛⠛⠛⢻⣉⣉⣉⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠋⠉⠉⠉⢻⠟⣉⣯⣽⣡⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⠆⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⠀⣀⠰⢾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠶⠶⣿⠟⠉⠉⢻⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⢻⣿⣿⣿⣿⣿⣿
⠀⣹⣿⢿⣿⢿⣿⣿⡧⣸⣿⠇⣠⣿⣛⠻⠏⢻⣿⣷⣔⠁⠀⠀⠀⠀⠀⠐⢿⣷⣶⣿⡿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣄⣀⣀⣀⢸⡀⠀⠀⢀⢭⡇⢸⣿⣿⣿⣿⣿⣿⣯⣽⣷⣴⢼⣿⣿⣿⣿⣿⣿
⠈⢻⣷⣾⣿⣾⣿⣿⡟⢯⣻⠀⠀⠀⠘⠀⠀⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠈⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠈⠘⠁⠘⣿⣿⠈⠑⢦⡀⠀⠛⠃⠘⣿⣿⣿⣿⣿⣿⣦⡌⠹⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣷⠈⣿⣶⡄⠀⣰⣧⠀⢸⡿⠏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇⣿⣿⣿⣿⢸⡏⠀⢰⠀⠀⣠⠈⠁⠀⠐⠂⠹⢿⣿⣶⣄⠈⢻⣿⠟⢹⡿⠟⢑⣾⡿⠁⠈⠛⠿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣉⣿⣿⠷⠊⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠛⠻⠇⣿⣿⡿⠻⢸⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠀⠀⠀⠘⠀⢀⣾⠟⠁⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠸⢸⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⠄⠀⠀⠒⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢉⣼⡏⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢀⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠁⢠⣤⣀⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠘⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣥⣶⣶⣤⣼⣿⣿⣿⣿⣇⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠸⡏⠀⠀⠀⠀⡀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠛⠻⠷⢶⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠠⢹⠿⢿⡷⠗⠀⠀⠇⡿⡼⠈⠏⢱⠻⣻⣿⣿⣿
⠒⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣿⢶⡶⢰⡶⣶⢸⣶⡟⡇⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡆⢷⡶⢣⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠇⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠈⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣟⣿⠀⣿⢣⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠛⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠒⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠩⣭⣉⣩⣭⣤⣉⣼⡇⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⠡⣭⣭⣭⣬⣥⣬⣥⣭⣭⣍⠉⠈⠉⠀⣬⣭⣤⣽⣯⠀⠉⠉⠁⠀⠙⠋⣬⣝⣯⣼⣿⣿
⠰⠆⠰⢠⠀⠐⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢸⢻⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠟⠋⠋⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢀⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⢠⠋⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡒⠛⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⠀⠀⠈⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡶⠀⠘⠃⠄⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠒⠒⠒⠒⠀⠀⠀⠀⠠⠀⠄⠈⠠⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣅⡉⠉⠉⠉⠉⠉⠛⠛⠛⢻⣉⣉⣉⠙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⠈⢻⢋⣡⣯⣽⣥⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⣿⣿⣷⣶⠆⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠐⣀⡐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠳⠾⡿⠋⠉⠙⢿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣯⡉⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡸⢿⣿⢻⣿⣿⣦⣼⣿⠇⢠⣿⣛⠻⠟⣻⣿⣷⣔⠃⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣄⣀⣀⣀⢠⠀⠀⢀⡬⣽⡇⢸⣿⣿⣿⣿⣿⣿⣯⣿⣧⣴⣼⣿⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣾⣿⣿⡟⢯⣿⠀⠀⠀⠘⠀⠈⢻⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠈⠀⠙⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⣈⠘⠁⠘⣿⡯⠈⠒⢤⡀⠐⠻⠃⠘⣿⣿⣿⣿⣿⣿⣦⡌⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣷⠘⣿⣷⡄⠀⣸⣧⠀⢸⡿⠏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⣿⣿⣿⣿⢸⡏⠀⢰⠀⠀⣤⠈⠁⠀⠐⠂⠻⢿⣿⣶⣄⠈⢻⣿⠟⢹⣿⠟⠛⣾⡿⠉⠈⠛⠿⣿⣿⣿
⠀⠀⠀⢺⣿⣿⣿⣿⣷⣶⣿⣿⣷⣀⣿⣿⠷⠂⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠻⠇⣿⣿⣿⢻⢸⣧⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠚⠀⢀⣾⠟⠁⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠉⠻⢸⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⢿⣿⢿⣿⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⠄⠀⠀⠚⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢩⣾⡏⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢀⣼⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⠁⢠⣤⣀⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣥⣴⣶⣤⣼⣿⣿⣿⣿⡇⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠸⡏⠀⠀⠀⠀⡀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠛⠻⠷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⢿⡷⠇⠀⠀⠇⡿⡼⠈⠏⢱⠻⣻⣿⣿⣿
⠀⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣷⢶⡶⢰⡶⣶⢸⣶⡟⡇⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢷⡶⢣⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠇⣾⣷⡔⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠈⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣷⡄⢸⣿⣿⣼⣟⢸⣿⣿⠀⣿⢃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠃⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠪⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠩⣭⣍⣭⣭⣤⣉⣼⡇⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⢡⣭⣭⣭⣮⣥⣬⣥⣭⣭⡉⠉⠈⠉⠀⣬⣭⣤⣽⣯⠈⠉⠉⠁⠀⠙⠋⣬⣝⣯⣼⣿⣿
⠰⠆⠰⢢⠀⠐⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠟⠫⠛⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠛⠿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢠⣾⡟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⣀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⢀⠋⠘⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠛⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡖⠀⠘⠣⠄⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠻⠿⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⠒⠒⠒⠀⠀⠀⠠⠤⠀⠀⠈⠠⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⠿⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣍⡉⠉⠉⠉⠉⠙⠙⠛⠛⢻⣉⣉⣉⡙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣹⣣⣖⣿⣽⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⣿⣿⣿⣿⣶⠆⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⢤⣶⣀⣩⣤⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠲⠾⡟⠉⠉⠙⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣋⠉⠛⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⢹⣿⢻⣿⣿⣦⣼⣿⠇⢠⣿⣙⠻⠏⣿⣿⣷⣄⠃⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⢠⣄⣀⣀⣀⢀⠀⠀⢤⣼⣽⡇⢸⣿⣿⣿⣿⣿⣿⣟⣻⣦⣴⣼⣿⣿⣿⣿⣿⣿
⠁⠀⠈⣿⣿⣾⣿⣿⡟⢯⣿⠀⠀⠀⠙⠀⠀⢻⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣽⣿⣿⡟⣿⣿⣿⣿⢿⣿⠟⡈⠘⠁⠘⣿⡏⠈⠒⢤⡀⠘⠿⠃⠘⣿⣿⣿⣿⣿⣿⣅⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣷⠘⣿⣷⡆⠀⣸⣇⠀⢸⡿⠟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⣿⣿⣿⢸⡏⠀⢰⠀⠀⣤⠈⠁⠀⠐⠈⠻⢿⣿⣶⣄⠘⢿⣿⠟⢻⣿⠿⠛⣾⡿⠉⠈⠛⢿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣿⣿⣷⣠⣿⣿⠷⠊⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠛⠛⠇⣿⣿⣿⣿⢸⣧⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠚⠀⢀⣾⡟⠁⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠉⠻⢸⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⢿⣿⢿⣿⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢰⡄⠀⢸⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⡤⠀⠀⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢩⣾⡏⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣾⠃⠀⡼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⠁⢠⣄⡀⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣭⣴⣶⣄⣼⣿⣿⣿⣿⡇⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠸⡟⠀⠀⠀⠀⡀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠐⠛⠻⠷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⢿⡷⠇⠀⠀⠏⡿⡼⠈⠏⢱⠻⣻⣿⣿⣿
⠈⠁⢰⣶⠀⣶⣶⠰⣶⠖⣶⣰⡖⣶⢰⣶⡆⠀⣶⣶⣾⠷⠀⢲⣆⣷⢶⡶⢰⡶⣶⢸⣶⡞⡅⣶⢰⣶⣰⣶⢰⡖⣶⣴⣿⡆⣶⣶⡦⢷⡶⢣⣶⡆⢰⣆⣶⢲⣶⠆⢰⣶⠆⣾⣷⡄⣶⣶⡄⢰⣶⣶⣶⣞⠷⢹⣿⣿
⠀⠀⢸⣿⣠⣿⣿⡀⣿⡇⢿⣿⡇⣿⢸⣿⣷⠀⣿⣧⣽⣿⡄⢸⣿⣿⣾⣟⢸⣿⣿⠀⣿⠃⡇⣿⢸⣿⣿⣿⢸⡟⠋⣿⣿⡇⣿⣿⡇⢸⡇⢸⣯⣿⣸⣿⣿⢸⣿⠀⢸⣿⠛⣿⣿⡇⣿⣿⡆⢸⣿⣿⢯⡝⣷⢸⣿⣿
⠺⠀⠈⠉⠉⠉⠉⠁⠉⠁⠈⠉⠁⠉⠉⠁⠉⠀⠉⠁⠙⠋⠀⠀⠉⠁⠩⣭⣍⣩⣭⣤⣉⣼⣧⠉⠈⠁⠉⠉⠈⠁⠀⠈⠛⢡⣭⣭⣭⣮⣥⣬⣥⣭⣭⡉⠉⠈⠉⢀⣬⣭⣦⣽⣯⠈⠉⠉⠁⠀⠙⢫⣬⣝⣯⣼⣿⣿
⠠⠆⠰⢲⠀⠐⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠻⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⡂⠤⢘⡻⠟⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠿⠆⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠿⠛⢛⣛⣉⣩⣽⢸
⣠⣤⣀⠀⠀⠀⠶⠷⠖⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣸
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡁⣈⣲⣤⣀⠀⠀⠠⠴⠦⠀⠀⢸⣿⣿⣿⣿⡇⠛⢉⣉⣉⣁⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠿⠿⠛⢛⣛⣛⣉⣿
⣤⣀⣀⣤⣶⣶⣶⣿⣭⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢴⣤⣄⣀⣤⣤⣴⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡮⢿⡇⠀⠀⠀⠀⠈⠙⣯⢽⠛⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠈⢃⠀⠒⠂⠀⠀⠀⢰⠟⠃⢸⡇⠓⠋⢉⣉⣉⣉⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣛⠋⠍⢉⠿⠛⠛⢿⢿⠁⠀⠀⠀⠘⢿⣿⣿⡏⠀⠀⠠⠽⠂⠠⠄⠈⠉⢠⣤⣶⣶⣿⡿⠿⠿⠿⠛⠛⢛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣤⣤⣴⡄⠀⠀⠀⣿⣆⡄⠀⠀⠀⢀⣠⣴⣿⡇⠀⠐⠆⣰⣶⣶⣶⣶⣿⣿⣿⣿⡿⡇⣿⣿⣟⡿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⣾⣷⣶⣶⣦⣴⣿⣿⣿⣿⣿⣷⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠛⠛⠋⠉⢉⣉⣁⣿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⠻⣿⣿⣿⣿⠍⠛⠿⡿⠟⠿⠋⠉⠛⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⡯⢆⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠐⣾⣯⣭⡍⠉⠿⠿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠉⠉⠀⠈⠛⠂⠀⠘⠉⠘⢿⢿⣛⡧⢻⣿⣿⣿⣿⡇⠉⠈⠿⡿⠀⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠂⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠛⠻⣻⣉⣣⣤⡤⠄⠀⠀⠀⠀⠉⠻⣿⠙⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡜⠿⡇⠀⠐⠀⠀⠀⠀⣘⠓⣿⣿⣿⣿⣿⣿⣿⣿⣸
⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⣄⡀⠘⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⣫⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⢻⣿⣿⣿⣿⣿⣿⣿⣲
⣿⢀⣿⣿⣷⠂⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣉⣃⡀⢀⣀⣀⡀⣙⣛⢛⣛⣁⣀⣀⡀⣀⣀⡀⢀⣙⡛⠉⢁⣀⡀⣀⣀⣀⢀⣀⡀⢀⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠿⣿⣿⣿⣿⣿⣿⠯
⣿⣭⣿⣿⣿⠀⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣽⠿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⠭
⣭⣽⣷⡆⠋⠀⠀⠀⠀⠀⡳⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣠⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣒
⣿⣿⣿⣷⠀⡀⠀⠄⠀⠄⠹⠾⠷⠾⠶⠷⢀⠤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠠⠿⠿⡿⠿⠿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⣿⡿⢿⣟⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⣬⠥⠍⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣍⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⣿⣿⢶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠹⣿⣿⣿⣯⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡂⠤⢘⡻⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠿⠆⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠿⠛⣛⣛⣉⣭⣽⢸
⣠⣤⣀⠀⠀⠀⠲⠿⠖⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣥⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣸
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⠅⣈⢲⣤⡀⠀⠀⠠⠴⠦⠀⠀⢸⣿⣿⣿⣿⡇⠛⢉⣉⣉⣁⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠿⠿⠛⣛⣛⣛⣉⣿
⣤⣄⣠⣤⣶⣶⣶⣾⣭⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣤⣄⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⡮⢿⡇⠀⠀⠀⠀⠈⠙⣯⢽⠛⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢃⠀⠒⠂⠀⢀⠀⢰⠟⠃⢸⡇⠓⠋⢉⣉⣉⣉⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣛⠋⠍⢩⠿⠛⠛⢿⣟⠁⠀⠀⠀⠘⢿⣿⣿⠄⠀⠀⠠⠿⠃⠠⠄⠈⠉⢠⣤⣶⣶⣿⡿⠿⠿⠿⠛⠛⢛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣤⣦⣴⡀⠀⢀⢀⣷⣄⡀⠀⠀⠀⢀⣀⣶⣿⡆⠀⠐⠆⣴⣶⣶⣶⣶⣾⣿⣿⣿⡿⡇⣿⣿⣟⡟⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣾⣷⣾⣶⣤⣤⣿⣿⣿⣿⣿⣷⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠛⠛⠋⠉⣉⣉⣁⣿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⢻⣿⣿⣿⣯⠙⠻⢿⠿⠟⠟⠋⡛⢛⠿⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⢯⢆⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠈⠙⣿⣭⣭⡍⠉⠿⠿⣿⣿⠟⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠛⠂⠀⡘⠉⠘⢿⢿⣛⡇⢻⣿⣿⣿⣿⡇⠁⠈⠿⠿⠀⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⢽
⢛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠛⠻⣻⣉⣣⣤⡤⠄⠀⠀⠀⠀⠉⠻⣿⠙⠙⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡜⠿⡇⠀⠐⠀⠀⠀⠀⣘⠓⣿⣿⣿⣿⣿⣿⣿⣿⣸
⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡁⠘⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⣻⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⢻⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣉⣁⡀⢀⣀⣀⡀⣙⣛⢛⣛⣂⣀⣀⡀⣀⣀⡀⢀⣙⡛⠉⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠿⣿⣿⣿⣿⣿⣿⠾
⣿⣹⣿⣿⣿⠀⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣭⠿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⠭
⣭⣼⣷⡆⠃⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣠⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣒
⣿⣿⣿⣷⠀⠀⠀⠄⠀⠄⠹⠶⠷⠾⠶⠷⢀⠤⠴⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠾⠁⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⣿⠿⢿⣟⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⣬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣍⣁⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⢿⢿⣾⡶⠶⠾⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠵⣿⣿⣿⡯⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⡂⠤⢘⡻⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠿⠆⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡿⠿⠛⣛⣛⣉⣭⣵⢸
⣠⣤⣄⠀⠀⠀⠺⠿⠖⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣥⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡇⣸
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣈⢲⣤⡀⠀⠀⠠⠴⠦⠀⠀⢸⣿⣿⣿⣿⡇⠋⢉⣉⣉⣁⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠿⠿⠛⣛⣛⣋⡉⣿
⣤⣤⣤⣴⣶⣶⣶⣾⣯⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣤⣄⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣮⢿⡇⠀⠀⠀⠀⠈⠙⣭⣿⠛⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠈⡇⠀⠒⠂⠀⣀⠀⠰⠛⠃⢸⡇⠃⠉⣉⣉⣉⣉⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠋⣛⠋⠭⢩⠿⠛⠛⠛⡿⠁⠀⠀⠀⠘⢿⣿⣿⡁⠀⠀⠠⠟⠀⠠⠄⠈⠁⢠⣴⣶⣾⣷⡿⠿⠿⠿⠛⠛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣤⣤⣴⠀⠀⠀⢀⣿⣆⡀⠀⠀⠀⣀⣠⣦⣶⠄⠀⠐⠄⣴⣶⣾⣷⣶⣿⣿⣿⣿⡿⡇⣿⣿⣟⡟⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⢀⣾⣶⣾⣶⣤⣴⣿⣿⣿⣿⣿⣷⣷⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠛⠛⠉⢉⣉⣉⣁⣿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⠛⢿⣿⣿⣿⠛⠻⢿⠿⠟⠛⠋⢟⢿⡿⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣯⢆⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⣿⣭⣭⡍⠉⠿⠿⢿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⡀⠀⠟⠢⠀⡘⠉⠘⣿⢿⣛⡧⢺⣿⣿⣿⣿⡇⠁⠘⠿⠧⠀⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⢀⠀⠀⠀⠈⠀⠀⠁⠁⠛⠻⣛⣉⣣⣤⡤⠄⠀⠀⠀⠀⠉⠻⣿⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⠿⡇⠀⠐⠀⠀⠀⠀⣘⠓⣿⣿⣿⣿⣿⣿⣿⣿⣸
⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡀⠘⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢻⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢀⣿⣿⣷⠂⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣉⣁⡀⢀⣀⣀⡀⣙⣛⢛⣛⣀⣀⣀⡀⣀⣀⡀⢀⣙⡛⠉⢀⣀⡀⣀⣀⣀⢀⣀⡀⣀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠿⢿⣿⣿⣿⣿⣿⠾
⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣭⠟⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⠭
⣭⣾⣶⡄⠉⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣴⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣚
⣿⣿⣿⣷⠀⠀⠠⠄⠀⠆⠻⠾⠷⠾⠶⠷⢀⠤⠴⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠾⠄⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⣿⠿⢿⣛⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣉⣁⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⢿⣿⣿⣶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢵⣿⣿⣿⡯⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⡂⠤⢜⠻⠛⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣾⠿⠆⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡿⠿⠛⣛⣋⣉⣭⣵⢸
⣠⣤⣄⠀⠀⠐⠺⠿⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡇⣸
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⣈⣶⣤⡀⠀⠀⠠⠶⠦⠀⠀⢸⣿⣿⣿⣿⡇⠋⣉⣉⣉⣀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⡿⠿⠟⢛⣛⣛⣋⡉⣿
⣤⣤⣠⣤⣶⣶⣶⣾⣯⣽⣋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣤⣄⣠⣤⣤⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣬⢿⡇⠀⠀⠀⠀⠈⠙⣭⣿⠛⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⡇⠀⠒⠃⠀⣀⠀⠰⠟⠃⢸⡇⠃⢉⣉⣉⣉⣉⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠉⣛⠉⠭⢹⠟⠛⠛⠿⡟⠁⠀⠀⠀⠹⢿⣿⣿⡁⠀⠀⠠⠟⠀⠤⠄⠀⠀⢠⣴⣶⣾⣿⡿⠿⠿⠟⠛⢛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣦⣤⣴⣴⠀⠀⠀⢠⣷⣆⡀⠀⠀⠀⣀⣤⣶⣷⠀⠀⠒⠄⣶⣶⣷⣷⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⡟⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⢠⣾⣦⣿⣶⣤⣴⣿⣿⣿⣿⣿⣷⣷⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠛⠋⠉⣉⣉⣉⣁⣿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠓⣿⣿⣿⣿⠛⠻⣿⠿⠛⠛⠋⠋⢻⡿⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⢷⢂⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠘⣿⣭⣭⡍⠉⠿⠿⢿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠠⡀⠀⠛⠢⠀⡘⠉⠘⣿⢟⣛⡧⢺⣿⣿⣿⣿⡇⠁⠘⠿⠇⠈⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⢀⠀⠀⠀⠈⠀⠀⠁⠁⠛⠻⣛⣉⣣⣤⡤⠄⠀⠀⠀⠀⠈⠻⣿⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⠿⡇⠀⠐⠄⠀⠀⠀⣘⠓⣿⣿⣿⣿⣿⣿⣿⣿⣹
⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡂⠘⡀⠀⠀⢠⣤⡄⠀⠀⠀⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢻⣿⣿⣿⣿⣿⣿⣿⣚
⣿⢀⣿⣿⣷⠂⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣙⣁⡀⢀⣀⣀⡀⣙⣛⢛⣛⣀⣀⣀⡀⣀⣀⡀⢀⣙⡛⠁⢀⣀⡀⣀⣀⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠿⢿⣿⣿⣿⣿⣿⠺
⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣯⠟⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠭
⣭⣾⣶⡄⠃⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢃⣴⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣘
⣿⣿⣿⣷⠀⠀⠠⠄⠀⠆⠻⠾⠷⠾⠶⠗⢀⠤⠴⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢓
⣿⠿⢿⣛⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⣿⣿⣷⣶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠵⢿⣿⣿⡯⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠒⠠⠌⠛⠛⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠂⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡿⠟⢛⣛⣋⣭⣭⡴⢸
⣤⣤⣀⠀⠀⠀⠺⠿⠒⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⣿⣿⣿⣯⣿⣿⡇⣼
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣀⣌⣷⣤⡀⠀⠀⠠⠶⠖⠀⠀⢸⣿⣿⣿⣿⡏⢉⣉⣉⣁⣠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⡿⠿⠛⣛⣛⣛⣉⡉⣿
⣦⣦⣤⣴⣶⣶⣶⣾⣯⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣤⣶⣄⣠⣤⣴⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠿⠌⣿⡇⠀⠀⠀⠀⠈⠘⣭⣿⡋⢸⡏⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⡇⠀⠋⠁⢀⣀⠀⠰⠛⠃⢸⡇⢁⣉⣉⣉⣉⣀⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠋⠉⢉⣉⠉⠩⠹⠟⠛⠛⠻⠏⠀⠀⠀⠀⠿⢿⣿⡿⠁⠀⠀⠠⠛⠀⠤⠄⠀⠀⢠⣶⣶⣾⣗⡿⠿⠟⠛⢛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣦⠀⠀⠀⢸⣷⣀⠀⠀⠀⠀⣀⣴⣾⣷⠀⠀⠒⠄⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣦⠀⢰⣿⣶⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣅⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⣉⣉⣉⣉⣉⣉⣁⢿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣗⠓⣿⣿⣿⡯⠛⠿⣿⡿⠿⠛⠟⠛⢿⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣷⢂⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠺⠢⠀⠀⠀⠀⠀⠀⠀⠈⣿⣭⣭⡍⠉⠿⠿⢿⡿⠛⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠠⠀⠀⠛⠣⠀⡘⠁⠘⢿⢟⢻⡅⢺⣿⣿⣿⣿⡇⠁⠘⠿⠇⠸⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠨⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠁⠁⠙⡻⣛⣉⣧⣤⡤⠀⠀⠀⠀⠀⠈⠻⣿⣛⣛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡈⠿⠇⠀⠐⠄⠀⠀⠀⣈⠓⣿⣿⣿⣿⣿⣿⣿⣿⢹
⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡀⠘⡀⠀⠀⢠⣶⡄⠀⠀⠀⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢻⣿⣿⣿⣿⣿⣿⣿⣚
⣿⢠⣿⣿⣷⠂⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣉⣃⡀⢀⣀⣀⡀⣙⣛⢛⣛⣀⣀⣀⡀⣀⣀⡀⢀⣙⡋⠁⢀⣀⡀⣐⣀⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠿⣿⣿⣿⣿⣿⠺
⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣽⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣿⡟⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠭
⣽⣶⣶⡄⠁⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢊⣴⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣙
⣿⣿⣿⣷⠀⠀⠤⠄⠐⠆⠻⠾⠷⠾⠶⠓⢢⠴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣓
⡿⠿⢿⣛⡆⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⣁⢉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⣿⣿⣷⣶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣝⢿⣿⣿⡯⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠒⠠⠌⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠂⠀⠀⠀⠀⠀⠉⣟⣿⣿⣿⣿⡿⠛⣛⣛⣉⣭⣭⡄⢸
⣤⣤⡀⠀⠀⠐⠺⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣠⣌⣷⣦⡀⠀⠀⠰⠶⠖⠀⠀⣿⣿⣿⣿⣿⡏⣉⣉⣉⣀⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠟⢛⣛⣛⣋⣉⡍⣿
⣤⣦⣤⣴⣶⣶⣶⣾⣿⣭⣗⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣤⣶⣆⣤⣤⣴⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠌⣿⡃⠀⠀⠀⠀⠀⠙⣽⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⡇⠀⠋⠁⢀⣀⠀⠸⠛⠃⢸⡏⣁⣉⣉⣉⣉⣀⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠋⠉⢉⣉⠉⠩⠽⠛⠛⠛⠛⠇⠀⠀⠀⠈⠿⢿⣿⡿⠀⠀⠀⠘⠋⠀⠤⠄⠀⠀⢠⣶⣶⣿⣿⡿⠿⠛⠛⣛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣦⠀⠀⠀⢸⢷⣤⠀⠀⠀⢀⣠⣤⣾⣿⠀⠀⠚⣄⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣆⡀⣰⣿⣶⣿⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣁⢿
⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⠋⣿⣿⣿⠯⠙⠻⣿⠿⠋⠉⠉⠺⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣷⢂⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠛⠢⠈⠀⠀⠀⠀⠀⠀⠨⣯⣭⣭⠉⠉⠿⠿⢿⡿⠛⠻⣯⣿⣿⣿⣿⣿⣿⣿⣷⢺
⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠄⠀⠀⠛⠣⠀⡊⠁⠘⣿⡟⠻⡑⢸⣿⣿⣿⣿⡏⠁⠸⠿⠀⠸⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⠸⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⡯⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠈⠀⠀⠁⠈⠙⣻⣫⣉⣧⣤⡤⠀⠀⠀⠀⠀⠉⠻⣿⣛⣙⢛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠘⠿⠄⠀⠐⠄⠀⠀⠀⣈⠓⣿⣿⣿⣿⣿⣿⣿⣿⢹
⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠀⠘⠀⠀⠀⢠⣶⠀⠀⠀⠀⠈⢿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢻⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢸⣿⣿⣷⠂⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣋⣁⡀⢀⣀⣀⡀⣙⣛⢛⣓⣀⣀⣀⡀⣀⣀⡀⢀⣙⡋⠁⢀⣀⡀⣒⣀⣀⢀⣀⡀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⣿⣿⣿⣿⣿⢺
⣿⢹⣿⣿⣿⠀⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⡯⡟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠭
⣽⣶⣶⡌⠀⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢉⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣹
⣿⣿⣿⣷⠀⠀⠤⠄⠐⠆⠻⠾⠷⠾⠶⠓⢠⠴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠡⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣓
⡿⠿⢿⣛⡆⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠘⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⣉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⣿⣿⣷⡶⡶⠶⠶⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢝⢽⣿⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠒⠠⠜⠛⠛⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠂⠀⠀⠀⠀⠀⠉⣯⣿⣿⣿⣿⡿⠛⣛⣛⣉⣭⣭⡄⣿
⣤⣤⡀⠀⠀⠐⠻⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯⣿⣿⡇⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣠⣌⣷⣦⡀⠀⠀⠰⠶⠆⠀⠀⣿⣿⣿⣿⣿⡈⣉⣉⣉⣁⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠟⠛⣛⣛⣋⣉⡍⣿
⣤⣤⣤⣤⣶⣶⣶⣾⣯⣽⣓⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣤⣶⣄⣠⣤⣴⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠜⣿⠃⠀⠀⠀⠀⠀⠉⣽⣷⠋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⡄⠀⠋⠁⢀⣀⠀⠸⠛⠃⢸⡏⣁⣉⣉⣉⣉⣀⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠋⠉⢉⣉⠉⠩⠽⠟⠛⠛⠛⠋⠀⠀⠀⠈⠻⢿⣿⡿⠁⠀⠀⠔⠋⠀⠤⠄⠀⠀⣠⣶⣶⣿⣿⡿⠿⠛⠛⣛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣦⠀⠀⠀⢸⢷⣦⠀⠀⠀⣀⣠⣴⣾⣿⠀⠀⠒⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣦⠀⣰⣿⣶⣿⣶⣦⣾⣿⣿⣿⣿⣿⣿⣷⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣁⢿
⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⠛⣿⣿⠿⠿⠉⠛⢿⡿⠛⠋⠉⠛⢿⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠨⣿⣿⣿⣿⣿⢷⢂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠈⠑⣯⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺
⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠠⠀⠀⠀⠛⠃⠀⡊⠁⠘⣿⡟⢻⡕⢸⣿⣿⣿⣿⡏⠁⠸⠷⠀⠺⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⡅⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⡯⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠀⢀⠀⠀⠀⠈⠀⠀⠉⠘⠙⣻⣫⢉⣧⣤⡄⠀⠀⠀⠀⠀⠉⠻⣿⣛⣙⡛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠿⠀⠀⠐⠄⠀⠀⠀⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⢹
⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠀⠛⠀⠀⠀⢠⣶⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢻⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢸⣿⣿⣷⠂⠀⠀⠀⠀⠀⣀⣁⠈⣀⣀⡀⣀⡀⣀⣀⣋⣁⡀⢀⣀⣀⡀⣙⣛⢛⣃⣀⣀⣀⡀⣀⣀⡀⢀⣛⡋⠁⢀⣀⡀⣒⣀⣀⢀⣀⡀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⢿⣿⣿⣿⣿⢺
⣿⢹⣿⣿⣿⠀⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⡿⡟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢽
⣭⣾⣶⡈⠈⠀⠀⠀⠀⠈⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢈⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣹
⣿⣿⣿⣧⠀⠀⠠⠄⠐⠆⠿⠾⠷⠾⠶⠗⢠⠤⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣓
⣿⠿⢿⣛⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠘⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠅⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣍⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⢿⣿⣷⣾⡶⠶⠾⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢵⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠤⠜⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠂⠀⠀⠀⠀⠀⠉⣯⣿⣿⣿⣿⡿⠟⢛⣛⣉⣭⣭⡄⣾
⣤⣤⡀⠀⠀⠐⠺⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯⣿⣿⡇⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣠⣌⣷⣦⡀⠀⠀⠠⠶⠆⠀⠀⣿⣿⣿⣿⣿⡈⢉⣉⣉⣁⣠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠿⠛⣛⣛⣛⣉⡉⣿
⣤⣤⣤⣴⣶⣶⣶⣾⣯⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣤⣶⣄⣠⣤⣴⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠎⣿⠇⠀⠀⠀⠀⠀⠙⣭⣟⠋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⡄⠀⠛⠁⢀⣀⠀⠸⠛⠃⢸⡏⢁⣉⣉⣉⣉⣀⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⢉⣋⠉⠩⢹⠟⠛⠛⠛⡅⠀⠀⠀⠈⠻⠿⣿⠿⠅⠀⠀⠔⠋⠀⠤⠄⠀⠀⣠⣶⣶⣾⣿⡿⠿⠟⠛⢛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣦⠀⠀⠀⢸⠿⣦⠀⠀⠀⣀⣠⣤⣿⣿⠀⠀⠒⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⠀⣰⣿⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣉⣉⣉⣉⣉⣁⣿
⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣏⠙⠿⣿⠿⠿⠉⠙⠿⠿⠻⠛⠙⠉⠻⡟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⣷⣿⣿⣿⣿⣿⡏⠀⠨⣿⣿⣿⣿⣿⣷⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠁⠀⠱⣯⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺
⣿⣿⣿⣿⣿⠿⠛⠃⠁⠀⠀⠀⠀⠀⠛⠂⠀⡋⠁⠘⣿⢟⢻⡷⢸⣿⣿⣿⣿⡏⠁⠸⠇⠀⠻⡿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⡅⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⡯⢽
⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠈⠀⠀⠉⠘⠛⣻⣋⢉⣧⣤⡄⠀⠀⠀⠀⠈⠉⠻⣿⢛⢙⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠿⠀⠀⠐⠄⠀⠀⠀⡈⠓⣿⣿⣿⣿⣿⣿⣿⣿⣹
⣿⢽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠀⠛⠀⠀⠀⢠⣴⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢻⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢸⣿⣿⣷⠆⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣋⣃⡀⢀⣀⣀⡀⣙⣛⢛⣃⣀⣀⣀⡀⣀⣀⡀⢀⣛⡛⠁⢀⣀⡀⣓⣀⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⢿⣿⣿⣿⣿⢺
⣿⢹⣿⣿⣿⠀⠀⠀⠀⢀⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣯⠟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠽
⣭⣾⣶⡈⠈⠀⠀⠀⠀⠈⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣹
⣿⣿⣿⣧⢀⠀⠀⠄⠠⠆⠿⠾⠷⠾⠶⠗⢠⠤⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓
⣿⠿⢿⣛⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠘⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣍⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⣷⣶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡱⣿⣿⣿⣯⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠂⠤⢘⡻⠟⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣾⠿⠂⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⡿⠟⢛⣛⣋⣩⣭⡅⣾
⣠⣤⡀⠀⠀⠐⠾⠿⠆⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣟⣻⡇⣿
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣌⣷⣦⣀⠀⠀⠠⠶⠦⠀⠀⣿⣿⣿⣿⣿⡈⠉⣉⣉⣉⣠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠿⠛⢛⣛⣛⣋⡉⣿
⣤⣤⣤⣤⣶⣶⣶⣿⣽⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣄⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠞⢿⡇⠀⠀⠀⠀⠉⠙⣭⣟⠋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⡇⠀⠚⠃⠀⣀⠀⠸⠛⠃⢸⡏⠁⣉⣉⣉⣉⣁⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣛⠋⠭⢹⠿⠛⠛⠿⡟⠀⠀⠀⠈⠹⠿⣿⠿⠇⠀⠀⠠⠛⠀⠤⠄⠀⠀⣠⣴⣶⣾⣿⡿⠿⠿⠛⠛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣤⠀⠀⠀⢰⠿⢦⡄⠀⠀⣀⣠⣴⣿⣿⡃⠀⠒⠄⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣀⣠⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠉⢉⣉⣉⣉⣁⣿
⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⠝⠿⣿⠿⠷⠉⠙⠻⡿⠟⠟⠍⠉⢽⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠛⣿⣭⣭⠍⠉⠿⠿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺
⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠉⠉⠀⠀⠟⠂⠀⡋⠉⠘⣿⢿⣛⡧⢸⣿⣷⣿⣿⡏⠁⠸⠇⠰⢻⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣯⢽
⣛⣛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⢀⠀⠀⠀⠈⠀⠀⠉⠘⠛⡻⣛⢉⣧⣤⠄⠀⠀⠀⠀⠈⠙⠻⣿⠛⠛⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠿⠄⠀⠒⠄⠀⠀⠀⡘⠓⣿⣿⣿⣿⣿⣿⣿⣿⣹
⣿⢽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠛⠀⠀⠀⢠⣤⡀⠀⠀⠀⠈⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⢿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢸⣿⣿⣷⡆⠀⠀⠀⠀⠀⣀⣁⠘⣁⣀⡀⣀⡀⣀⣈⣛⣃⡀⢀⣀⣀⡀⣙⣛⢛⣀⣀⣀⣀⡁⣀⣀⡀⢀⣙⡛⠉⢀⣀⡀⣒⣀⣀⢀⣀⡀⣀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⣿⣿⣿⣿⣿⢺
⣿⢹⣿⣿⣿⠁⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣿⡟⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢭
⣭⣭⣷⡈⠙⠀⠀⠀⠀⠈⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣴⣿⣷⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣘
⣿⣿⣿⣧⢀⡀⠀⠄⠠⠄⠿⠾⠷⠾⠶⠷⢀⠤⠤⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓
⣿⡿⠿⣟⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠘⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣶⣶⣮⣿⣭⣬⠥⠉⢉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣉⣡⣍⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣻⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠂⠤⢘⡻⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠲⣾⠿⠆⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡿⠟⢛⣛⣋⣩⣭⡕⣸
⣠⣤⡀⠀⠀⠐⠾⠿⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡇⣿
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣠⣤⣻⣦⣀⠀⠀⠠⠶⠦⠀⠀⣿⣿⣿⣿⣿⡏⢉⣉⣉⣁⣠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠿⠛⣛⣛⣛⣉⡉⣿
⣤⣤⣤⣴⣶⣶⣶⣿⣭⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⣤⣄⣠⣤⣤⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⢻⡇⠀⠀⠀⠀⠈⠙⣭⣿⠛⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠇⠀⠚⠃⢀⣀⠀⠸⠛⠃⢸⡏⢁⣉⣉⣉⣉⣁⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⣛⠋⠭⢹⠿⠛⠙⠛⠫⠀⠀⠀⠀⠙⠿⠿⢿⡇⠀⠀⠠⠛⠀⠤⠄⠀⠀⢠⣴⣶⣾⣿⡿⠿⠿⠛⢛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣦⡤⠀⠀⠀⢰⡿⢧⠄⠀⠀⣀⣠⣴⣿⣿⡁⠀⠚⠄⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢉⣉⣉⣉⣉⣁⣿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⠙⠻⢿⠿⠿⠉⡉⠻⠿⠛⠟⠙⠛⠻⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠈⠹⣿⣭⣭⡍⠉⠿⠿⢿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠟⠂⠀⡋⠉⠘⣿⢿⣻⡧⢸⣿⣿⣿⣿⡏⠁⠸⠄⠽⠸⡿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠈⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⢽
⣛⣛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠈⠀⠀⠁⠘⠛⡻⣛⢉⣧⣤⠀⠀⠀⠀⠀⠀⠉⠻⣿⠛⠛⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠿⠄⠀⠐⠄⠀⠀⠀⡈⠓⣿⣿⣿⣿⣿⣿⣿⣿⣹
⣿⢽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠛⠀⠀⠀⢠⣤⡀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣺
⣿⢸⣿⣿⣷⡆⠀⠀⠀⠀⠀⣀⣁⠈⣁⣀⡀⣀⡀⣀⣀⣛⣁⡀⢀⣀⣀⡀⣙⣛⢛⣀⣀⣀⣀⡁⣀⣀⡀⢀⣛⡛⠉⢀⣀⡀⣒⣀⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⠿⣿⣿⣿⣿⣿⢺
⣿⢹⣿⣿⣿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣽⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣯⡿⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠭
⣭⣼⣷⡈⠙⠀⠀⠀⠀⠈⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣘
⣿⣿⣿⣧⢀⠀⠀⠄⠠⠄⠻⠾⠷⠾⠶⠷⢀⠤⠴⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓
⣿⡿⢿⣟⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⣬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣍⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⢿⣿⣷⢶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⣻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡒⠠⠌⡻⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠰⠿⠿⠂⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⡿⠛⣛⣛⣉⣭⣭⣴⢸
⣠⣤⣄⠀⠀⠀⠺⠿⠖⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣶⣶⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⡿⢸
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣦⣽⣶⣄⡀⠀⠠⠶⠖⠀⠀⢸⣿⣿⣿⣿⡇⣉⣉⣉⣀⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⡿⠟⢛⣛⣛⣋⣉⣭⣽
⣤⣤⣤⣴⣶⣶⣶⣾⣯⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣶⣄⣤⣤⣤⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠗⢻⡇⠀⠀⠀⠀⠀⠘⣭⣷⡛⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⣃⠀⠉⠁⢀⣀⠀⠸⠛⠃⢸⣇⣉⣉⣉⣉⣉⣠⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠉⠉⣉⠉⠭⢹⠿⠛⠙⢛⢿⠀⠀⠀⠀⠙⠻⠿⠿⣇⠀⠀⠀⠛⠁⠠⠄⠀⠀⢰⣶⣶⣿⣗⡿⠿⠛⠛⣛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⡦⠀⠀⠀⢠⡿⢷⠄⠀⠀⣀⣠⣴⣿⣿⣇⢀⡚⠂⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣟⣟⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣉⣉⣉⣉⣉⣉⣁⢿
⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⠉⠿⠿⠿⠿⠏⣙⠻⣿⠿⠿⠟⠿⠿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣷⣂⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠉⠘⣿⣭⣭⡍⠉⠹⠿⢿⣿⠟⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⣿⣿⠿⠟⠃⠁⠀⠀⠀⠀⠀⠟⠣⠀⡚⠉⠘⣿⠟⢻⡯⢻⣿⣿⣿⣿⡇⠁⠸⠀⠿⠸⠿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽
⣛⣛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠘⠀⠀⠁⠁⠙⠻⣻⣉⣳⣤⠀⠀⠀⠀⠀⠀⠈⠛⣿⣛⣛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡘⠿⠇⠀⠑⠀⠀⠀⢀⣈⠑⣿⣿⣿⣿⣿⣿⣿⣿⢹
⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠀⠀⢠⣴⡆⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠂⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢹⣿⣿⣿⣿⣿⣿⣿⣒
⣿⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠀⣁⣀⡀⣀⡀⣀⣀⣉⣃⡀⢀⣀⣀⡀⣘⣛⢛⣀⣀⣀⣀⡀⣀⣀⡀⢀⣙⡛⠁⢀⣀⡀⣛⣂⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⠿⣿⣿⣿⣿⠒
⣿⣽⣿⣿⣿⠇⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣿⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣯⡿⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠭
⣭⣿⣶⡄⠋⠀⠀⠀⠀⠀⡳⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣰⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣍
⣿⣿⣿⣷⠀⠀⠠⠄⠀⠆⠹⠾⠷⠾⠶⠗⢂⠤⠶⢶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠠⠠⠿⠿⡿⠿⠿⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⣿⠿⢿⣛⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⡿⣿⣿⣶⡶⠷⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡂⠠⠌⡻⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⠛⣛⣛⣉⣭⣭⣴⢸
⣠⣤⣄⠀⠀⠀⠺⠿⠗⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣶⣶⣤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⡿⢸
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣦⣽⣶⣄⡀⠀⠠⠶⠖⠀⠀⢸⣿⣿⣿⣿⡇⣉⣉⣉⣀⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⡿⠟⢛⣛⣛⣋⣉⣭⢹
⣦⣤⣤⣴⣶⣶⣶⣾⣯⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣶⣄⣠⣤⣤⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠗⢹⡇⠀⠀⠀⠀⠀⠘⣭⣗⡛⢸⡇⣿⣿⣿⣿⣿⣿⣿⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠈⣃⠀⠉⠁⢀⣀⠀⠰⠛⠃⢸⣇⣉⣉⣉⣉⣁⣠⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠉⠉⣉⠉⠩⢹⠿⠛⠙⠛⣏⠀⠀⠀⠈⠙⠻⠿⠿⣎⠀⠀⠀⠛⠁⠠⠄⠀⠀⢰⣶⣶⣿⣗⡿⠿⠛⢛⣛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⡶⠀⠀⠀⢠⡿⢷⠄⠀⠀⣀⣠⣴⣿⣿⣇⢀⡒⠂⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣟⡏⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢠⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣉⣉⣉⣉⣉⣁⢿
⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⠻⠿⠿⠟⠋⣍⠛⠿⠿⠿⢗⠤⢻⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣚
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣷⢂⡈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠑⠈⠡⣿⣭⣭⡍⠉⠹⠿⢿⣿⠟⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⢲
⣿⣿⢿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠙⠣⠀⡘⠉⠘⢿⢿⢛⡏⠺⣿⣿⣿⣿⡇⠁⠈⠀⠿⠘⠿⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽
⣛⣛⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠘⠀⠀⠁⠁⠙⠻⣻⣁⣳⣤⠀⠀⠀⠠⠀⠀⠈⠛⢿⣛⣛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡘⠻⠇⠀⠑⠀⠀⠀⠀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⢭
⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠀⠀⢠⣴⡆⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠂⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢹⣿⣿⣿⣿⣿⣿⣿⣒
⣿⢀⣿⣿⣿⣶⠀⠀⠀⠀⠀⣀⣀⠀⣉⣀⡀⣀⡀⣀⣀⣙⣃⡀⢀⣀⣀⡀⣈⣛⢃⣀⣀⣀⣀⡀⣀⣀⡀⢀⣙⡛⠁⢀⣀⡀⣛⣂⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠻⠿⣿⣿⣿⣿⠒
⣿⣽⣿⣿⣿⡏⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣯⠿⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠭
⣭⣿⣶⡆⠃⠀⠀⠀⠀⠀⠳⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣰⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣍
⣿⣿⣿⣷⠀⠀⠠⠄⠀⠆⠸⠾⠷⠾⠶⠗⢂⠤⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠠⠠⠿⠿⡿⠿⠿⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣿⠿⢿⣛⡃⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠍⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⢉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⣿⣶⡶⠷⠷⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⢿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡂⠤⢐⡻⠟⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠆⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⡿⠟⢛⣛⣋⣭⣭⣴⢸
⣀⣤⣄⠀⠀⠀⠲⠿⠖⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⡿⢸
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣬⣷⣦⣄⠀⠀⠠⠶⠶⠀⠀⢸⣿⣿⣿⣿⡇⢉⣉⣉⣁⣠⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⢿⡿⠿⠛⣛⣛⣛⣉⣉⢹
⣤⣤⣤⣴⣶⣶⣶⣾⣭⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣤⣄⣠⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⢻⡇⠀⠀⠀⠀⠈⠘⣭⢟⡚⢸⡇⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⡇⠀⠚⠃⠀⣀⠀⠰⠛⠃⢸⡇⢉⣉⣉⣉⣉⣀⣤⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠙⣋⠉⠩⢽⡿⠿⠻⣿⠟⠛⠛⠛⠛⠻⢿⣿⣿⡇⠀⠀⠠⠛⠁⠠⠤⠀⠀⢰⣴⣶⣾⣷⡿⠿⠟⠛⢛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣮⠀⠀⠀⢠⣶⡄⡀⠀⠀⠀⢀⣈⣴⣿⡆⠀⠒⠄⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣟⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣾⣷⣼⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠉⣉⣉⣉⣉⣉⣁⢿
⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⡿⣿⣿⣿⣿⣯⠟⡻⠿⣿⣿⣿⣯⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣻⣿⣿⣿⣿⣿⣆⡘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠉⠀⠘⠳⠄⠈⠀⠈⠙⠛⠁⠙⣿⣭⣭⡍⠉⠹⠿⢿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠈⠉⠀⠀⠙⠂⠀⡘⠉⠘⣿⢿⣛⡯⠻⣿⣿⣿⣿⡇⠉⠀⠸⡿⠘⠻⡿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭
⣛⣛⣹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢘⠀⠀⠁⠁⠛⠻⣻⣉⣻⡄⠀⠀⠀⡠⠄⠀⠈⠻⢿⡟⠛⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⠻⠇⠀⠑⠀⠀⠀⠀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣩
⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⢠⣤⡆⠀⠀⠀⠈⠫⣿⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⠷⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠨⢻⣿⣿⣿⣿⣿⣿⣿⣒
⣿⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⣀⣀⠀⣉⣀⡀⣀⡀⣀⣀⣙⣃⡀⢀⣀⣀⡀⣈⣛⢀⣀⣀⣀⣀⡀⣀⣀⡀⢀⣙⡛⠉⢀⣀⡀⣙⣂⣀⢀⣀⡀⢀⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠿⠿⣿⣿⣿⣿⠒
⣿⣭⣿⣿⣿⡟⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢻⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣽⡿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠭
⣭⣭⣿⡆⠋⠀⠀⠀⠀⠀⡳⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠛⣡⣾⣷⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⣿⣿⣿⣷⠀⡀⠀⠄⠀⠄⠸⠾⠷⠾⠶⠷⢆⠤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠤⠀⠾⠿⡿⠿⠿⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⣿⡿⠿⣿⡃⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣶⣶⣮⣿⣭⣬⡥⠍⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⣿⢿⣿⣿⣷⡶⠶⠾⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⣟⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠤⢐⠻⠟⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠿⠆⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠟⢛⣛⣋⣭⣭⣴⢸
⣀⣤⡀⠀⠀⠀⠶⠶⠆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⡿⢸
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣓⣠⣌⣷⣦⣀⠀⠀⠠⠶⠶⠀⠀⢸⣿⣿⣿⣿⡏⢉⣉⣉⣁⣠⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⡿⠿⠛⣛⣛⣛⣉⡉⣿
⣦⣤⣤⣤⣶⣶⣶⣯⣽⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⢿⡃⠀⠀⠀⠀⠈⠘⣭⣿⡚⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠘⡄⠀⠚⠃⠀⣀⠀⠰⠛⠃⢸⡇⢁⣉⣉⣉⣉⣁⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣛⠋⠍⣽⣿⠿⢿⣿⡿⠿⠿⠟⠿⢿⣿⣿⣿⡇⠀⠀⠠⠏⠀⠠⠄⠀⠀⢠⣴⣶⣾⣗⡿⠿⠟⠛⢛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⡍⠀⠀⠀⢹⣤⡀⠀⠀⠀⠐⠈⢉⣹⣶⠄⠀⠴⠀⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀⠀⢠⣼⣭⣵⣥⣀⣤⣶⣾⣿⣿⣿⣶⣶⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠋⣉⣉⣉⣉⣉⣁⢿
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⣶⣾⣿⣿⣿⡟⠿⣿⣿⣿⣿⣯⡝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣯⣀⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠛⠉⠉⠰⠦⡌⠉⠉⠙⠛⠣⠙⠹⣿⣭⣭⡍⠉⠹⠿⣿⣿⠟⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⣿⣿⡿⠿⠟⠁⠂⠉⠉⠉⠉⠙⠂⠀⡙⠉⠘⣿⠿⣛⠯⠻⣿⣿⣿⣿⡇⠁⠀⢸⡿⠘⠻⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⠽
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠁⠛⠻⣻⣉⣣⠀⠀⠀⠀⡠⠄⠀⠈⠻⣿⠛⠛⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⠿⡇⠀⠑⠀⠀⠀⠀⡘⠑⣿⣿⣿⣿⣿⣿⣿⣿⢹
⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⢫⣿⡿⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢻⣿⣿⣿⣿⣿⣿⣿⣒
⣿⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⣀⣀⠀⣁⣀⡀⣀⡀⣀⣈⣉⣃⡀⢀⣀⣀⡀⣙⣓⢀⣀⣀⣀⣀⡀⣀⣀⡀⢀⣛⡛⠉⢀⣀⡀⣛⣀⣀⢀⣀⡀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⠿⢿⣿⣿⣿⣿⠒
⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢻⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣽⡿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⠭
⣭⣭⣽⡍⠋⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢛⣠⣾⣶⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣁
⣿⣿⣿⣧⠀⡀⠀⠀⠠⠄⠻⠾⠷⠾⠶⠷⢄⠤⠤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠤⠠⠾⠿⡿⠿⠿⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⣿⣿⠿⢿⡂⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣴⣶⣮⣿⣭⣬⡥⠉⠉⢉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⣿⣿⣿⣿⣷⡶⠶⠾⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⢽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠠⠄⣐⠿⠿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⡶⠿⠆⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡿⠟⢛⣛⣋⣩⣭⡄⣸
⣀⣄⡀⠀⠀⠀⠶⠶⠆⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡇⣿
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⣀⣹⣶⣄⡀⠀⠀⠠⠴⠦⠀⠀⣿⣿⣿⣿⣿⡏⢉⣉⣉⣁⣠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠿⠛⣛⣛⣛⣉⡉⣿
⣤⣠⣠⣤⣴⣶⣶⣭⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣤⣤⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⣿⠂⠀⠀⠀⠀⠈⠙⣭⣿⡋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢙⡀⠀⠚⠃⠀⣀⠀⠸⠛⠃⢸⡏⢁⣉⣉⣉⣉⣁⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⡸⠟⠀⠤⠄⠀⠀⢠⣴⣶⣾⣿⡿⠿⠟⠛⢛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣯⣤⣴⠟⠉⠀⠉⣈⡀⠁⠀⠠⠈⠉⠛⠟⣫⡥⠀⠠⠤⠀⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⡇⣿⣿⣿⡝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣟⠓⣄⠀⠀⣠⣤⣶⣾⣿⣷⣴⣶⡆⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⠋⣉⣉⣉⣉⣉⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠺⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢿⣿⣿⣿⣿⡯⡀⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢾⣿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠿⠿⠟⠛⢠⡈⠙⠟⠛⠛⠀⠀⠘⢸⣿⣭⣭⡍⠉⠿⠿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⣿⣿⣿⠿⠇⠀⠂⠉⠉⠉⠉⠛⠂⠀⡛⠉⠘⣿⠿⣟⡧⢹⣿⣷⣿⣿⡇⠁⠀⢿⡷⠙⠻⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⢽
⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠙⠛⠿⣛⢉⡧⠀⠀⠀⢠⡠⠄⠀⠉⠻⣿⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡙⠿⡇⠀⠑⠂⠀⠀⠀⡘⠑⣿⣿⣿⣿⣿⣿⣿⣿⣹
⣿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠚⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⣯⣿⡇⠀⠀⠀⠘⠂⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⢿⣿⣿⣿⣿⣿⣿⣿⣚
⣿⢸⣿⣿⣿⣦⡄⠀⠀⠀⠀⣀⣀⠘⣁⣀⡀⣀⡀⣀⣈⣙⣃⡀⢀⣀⣀⡀⣙⣃⢀⣀⣀⣀⣀⡁⣀⣀⡀⢀⣙⡛⠉⢀⣀⡀⣒⣀⣀⢀⣀⡀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠻⠿⢿⣿⣿⣿⣿⠺
⣿⢻⣿⣿⣿⠟⠁⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣽⡻⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠭
⣭⣬⣭⡉⠉⠀⠀⠀⠀⠀⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠋⣣⣾⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉
⣿⣿⣿⣧⠀⠀⠀⠀⠠⠄⠻⠶⠷⠾⠶⠷⢄⠤⠤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠤⠠⠾⠿⡿⠿⠿⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓
⣿⣿⠿⢿⡀⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠙⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣴⣶⣮⣿⣭⣬⡥⡉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣉⣁⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⣿⣿⣿⣿⣿⡶⠶⠾⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣺⣿⣿⣿⣟⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠠⠄⣐⠿⠿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠂⠀⠀⠀⠀⠀⠉⣯⣿⣿⣿⣿⡿⠛⣛⣛⣉⣭⣭⡄⣾
⣀⣀⡀⠀⠀⠀⠶⠶⠆⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣟⣻⡇⣿
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠅⣀⢹⣦⣄⠀⠀⠀⠠⠶⠆⠀⠀⣿⣿⣿⣿⣿⡈⣉⣉⣉⣀⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⡿⠟⢛⣛⣛⣋⣉⡍⣿
⣄⣀⣀⣤⣴⣶⣶⣭⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣤⣤⣴⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡻⣿⠁⠀⠀⠀⠀⠈⠙⣭⣷⠋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢻⠀⠀⠚⠁⢀⣀⠀⠸⠛⠃⢸⡏⣁⣉⣉⣉⣉⣠⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡸⠛⠀⠤⠄⠀⠀⢠⣶⣶⣿⣿⡿⠿⠛⢛⣛⣛⣛⡛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣧⣤⣼⠛⠋⠀⠉⡈⠉⠉⠉⠉⠉⠙⠛⠟⣫⡄⠀⠀⠤⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⡿⠂⠀⠀⠀⢀⣠⣴⣶⣿⣧⣴⣶⡆⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣉⣉⣉⣉⣉⣁⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢄⣠⣿⣿⣿⣿⣿⣶⣿⣿⣿⠻⠉⠙⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⡯⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡝⠻⢿⠿⠷⠂⠈⠙⠛⠛⠿⠂⠀⠀⠀⢰⣯⣭⣭⡍⠉⠿⠿⣿⡿⠛⠻⣯⣿⣿⣿⣿⣿⣿⣿⣷⢺
⣿⣿⣿⣿⣿⣿⠿⠇⠂⠒⠈⠉⠉⠉⠟⠂⠀⡟⠉⠘⣿⠿⣛⡧⢹⣿⣷⣿⣿⡇⠁⠠⣿⡷⠙⠻⡿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡇⠀⠀⠀⢸⠅⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⢼
⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠙⠛⠿⣛⢉⡇⠀⠀⠀⢰⡠⠄⠀⠉⠻⣿⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⠿⡇⠀⠁⠂⠀⠀⠀⡈⠓⣿⣿⣿⣿⣿⣿⣿⣿⢹
⣿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠚⠀⠀⠀⢠⣤⡀⠀⠀⠀⠈⣯⣿⠁⠀⠀⠀⠐⠂⡀⠀⠀⠀⠘⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠡⢿⣿⣿⣿⣿⣿⣿⣿⣚
⣿⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⣀⠘⣁⣀⡀⣀⡀⣀⣈⣙⣃⡀⢀⣀⣀⡀⣙⣀⢀⣀⣀⣀⣀⡀⣀⣀⡀⢀⣙⡛⠁⢀⣀⡀⣂⣀⣀⢀⣀⡀⣀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⠿⢿⣿⣿⣿⣿⢺
⣿⢻⣿⣿⣿⠟⠃⠀⠀⠀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣽⡿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠭
⣭⣬⣽⡉⡉⠀⠀⠀⠀⠈⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠋⣠⣾⣶⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉
⣿⣿⣿⣧⠀⡀⠀⠀⠠⠄⠿⠾⠷⠾⠶⠷⢀⠤⠤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠦⠀⠄⠠⠿⠿⡿⠿⠿⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓
⣿⣿⠿⢿⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠙⠻⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣴⣶⣮⣿⣭⣬⡥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⢉⣉⣈⣅⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⣿⠿⢿⠿⠷⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣻⣿⣿⣿⣟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣖⠀⠤⢘⠻⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠂⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡟⣛⣛⣉⣭⣭⣥⡆⣿
⣠⣤⡀⠀⠀⠐⠾⠷⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡿⠇⣿
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⢀⣀⢻⣦⣄⡀⠀⠀⠰⠶⠆⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣀⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⢿⠟⢛⣛⣛⣋⣉⣭⡍⣿
⣤⣀⣤⣴⣶⣶⣶⣿⣽⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⣦⣀⣠⣤⣴⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⡟⠁⠀⠀⠀⠀⠀⡏⠽⣞⠃⢸⢸⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠈⢃⠀⠈⠉⠁⢀⣀⠀⠸⠛⠀⢸⣈⣉⣉⣉⣁⣠⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠋⢉⣉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⠼⠋⠀⠤⠄⠀⠀⣶⣶⣾⣿⣿⠟⠛⣛⣛⣛⣛⣋⡙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡞⠋⠁⠀⢀⠉⠉⠉⠉⠉⠙⠛⠻⠛⣥⡄⠀⠠⠄⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⣟⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣸⠓⠀⠀⠀⢀⣀⣤⣴⣾⣿⣤⣶⣶⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡠⢿
⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠘⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹
⣿⡇⣿⣿⣿⣿⣿⡟⠋⠉⢻⣿⣿⣿⣿⡷⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠙⠿⡿⠿⠟⢀⠉⠻⠿⠛⠈⠀⠀⠀⠀⢾⣯⣭⣭⠉⠉⠿⠿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⡇⣿⣿⣿⣿⠿⠇⠋⠐⠈⠉⠀⠀⠛⠂⠀⡋⠁⠘⡿⢿⣻⡕⢹⣿⣿⣻⣿⡏⠁⠸⣿⡇⠛⠻⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡷⢼
⣟⣃⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠈⠀⠀⠉⠘⠛⡻⣫⢉⠀⠀⠀⠠⣔⠲⠀⠀⠉⠻⣿⣛⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⠿⠀⠀⠉⠂⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠻⠀⠀⠀⣤⣴⠀⠀⠀⠀⠉⢻⡏⠀⠀⠀⠀⢒⣀⠀⠀⠀⠀⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠡⣿⣿⣿⣿⣿⣿⣿⣿⣻
⡇⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⣀⣀⠘⣁⣀⡀⣀⡀⣀⣈⣛⣀⡀⢀⣀⣀⡀⣁⣀⢀⣀⣀⣀⣈⡀⣀⣀⡀⢈⣛⡉⠀⢀⣀⡀⣂⣀⣀⢀⣀⡀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⠿⢿⣿⣿⣿⣟⢺
⣿⣽⣿⣿⣿⠛⠃⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⡿⠟⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢼
⣭⣽⣷⠘⡉⠀⠀⠀⠀⠸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢈⣴⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⢽
⣿⣿⣿⡇⢁⡀⠀⠀⠠⠄⠿⠾⠷⠾⠶⠷⢠⠤⠴⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠰⠿⠿⡿⠿⠟⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣚
⣿⡿⢿⣟⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠚⠛⠛⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡟⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣶⣶⣮⣿⣭⣬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣍⣡⣉⣬⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⣿⢿⣶⡶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡿⣿⣿⡧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣖⠂⠤⠙⠛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣛⣛⣋⣩⣭⣭⣴⡆⣿
⣤⣤⡀⠀⠀⠐⠿⠷⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⣿⠿⠇⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢀⣈⣷⢦⣄⠀⠀⠀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣠⣤⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣛⣉⣭⣭⡍⣿
⣤⣤⣤⣴⣶⣶⣶⣿⣽⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⣀⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⣿⡏⠁⠀⠀⠀⠀⠀⠩⠷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⠇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣇⠀⠈⠉⠁⣀⣀⠀⠚⠋⠀⢹⣈⣉⣉⣁⣠⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠉⠉⢉⣉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠠⠏⠉⠀⠤⠀⠀⠀⣷⣶⣿⣿⣿⠛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡟⠋⠀⠀⢀⠈⠉⠉⠁⠈⠉⠙⠛⢻⣥⠄⠀⠤⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⠓⠀⠀⠀⢀⣀⣤⣶⣿⣿⣶⣶⣖⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣁⣀⡼⢿
⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣼⣿⣿⣿⣿⣷⣾⣿⣿⡻⠋⠈⠙⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⡇⣿⣿⣿⣿⣿⡟⠋⠉⢻⣿⣿⣿⣿⣗⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠿⠿⠒⠀⡉⠙⠛⠋⠀⠀⠀⠀⠀⣿⣿⣭⣿⠉⠉⠟⠻⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⡇⣿⣿⣿⣿⠿⠇⠉⠁⠀⠀⠀⠀⠙⠀⠀⠋⠁⠸⡿⡟⠻⡑⢹⣿⣿⣿⡿⠇⠀⠻⣿⠇⠛⠻⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⢾
⣛⣃⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁⠀⠀⠌⠘⠙⣻⣫⠀⠀⠀⠀⢤⡔⠶⠀⠀⠙⢿⣿⣛⣙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠙⠿⠀⠀⠉⠂⠀⠀⢀⡉⣻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢫⠀⠀⠀⣤⣴⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⣓⣀⠀⠀⠀⠀⢹⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣿⣿⣿⣿⣿⣿⣯⣹
⡇⢸⣿⣿⣿⣇⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣛⣀⡀⢀⣀⣀⡈⣀⣀⢀⣀⣀⣀⣉⡀⣀⣀⡀⢈⣋⡉⠀⢀⣀⡐⣂⣀⣀⢀⣀⡀⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⠿⢿⣿⣿⣿⣟⣺
⣿⣽⣿⣿⣿⠛⠃⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⡯⠛⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡷⢸
⣭⣽⣶⠘⡁⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣠⣾⣿⣷⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⢽
⣿⣿⣿⡇⢁⡀⠀⠀⠠⠀⠿⠾⠷⠾⠶⠗⢠⠤⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠶⠿⠿⡿⠿⠇⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣸
⣿⠿⢿⣛⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⡁⣉⣉⣉⣡⣩⣬⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⢿⡷⣶⠶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢾⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣖⠂⠤⠙⠛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣛⣛⣋⣩⣭⣥⣴⡆⣿
⣤⣤⡀⠀⠀⠐⠿⠷⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣽⠿⠇⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⡘⣷⣦⣀⠀⠀⠀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢩⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⣽⣿
⣤⣤⣤⣴⣶⣶⣶⣿⣭⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⣶⣀⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⣿⠉⠁⠀⠀⠀⠀⠀⠩⢷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣄⠀⠈⠉⠁⣀⣀⠀⠟⠙⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠉⠉⢉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠠⠏⠉⠀⠤⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡟⠋⠀⠈⢋⡈⠉⠉⠁⠈⠉⠙⠻⢛⣥⠄⠀⠴⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⠛⠀⠀⠀⢀⣀⣤⣶⣿⣿⣶⣶⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣁⣀⡼⢿
⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠙⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣷⣿⣿⣿⣿⣿⡟⠋⠉⢻⣿⣿⣿⣿⣗⣀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠿⢿⠿⠗⠀⠈⠙⠟⠛⠀⠀⠀⠀⠐⣿⣿⣽⣿⠉⠉⠟⠻⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻
⣿⡇⣿⣿⣿⣿⡿⠇⠋⠉⠀⠀⠀⠈⠛⠀⠀⠋⠁⠺⡿⣟⠻⡙⢹⣿⣿⣿⡿⠇⠀⠻⣿⠇⠛⢻⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⢾
⣛⣃⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⠘⠙⣛⡋⠀⠀⠀⠀⣤⡶⠆⠀⠈⠙⢿⣿⣋⣙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠙⠿⠀⠀⠉⠂⠀⠀⢀⡉⣻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢣⠀⠀⠀⣤⣴⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⢁⣷⣀⠀⠀⠀⠀⣹⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣿⣿⣿⣿⣿⣿⣯⣹
⡇⣸⣿⣿⣿⣇⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣛⣀⡀⢀⣀⣀⡀⣀⣀⢀⣀⣀⣈⣉⡀⣀⣀⡀⢘⣋⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⠿⢿⣿⣿⣿⣟⣺
⣿⣽⣿⣿⣿⠛⠃⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣽⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠽⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡷⢼
⣭⣽⣶⠸⡁⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣠⣾⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⢽
⣿⣿⣿⡆⢀⡀⠀⠀⠠⠀⠿⠾⠷⠾⠶⠗⢠⠤⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠶⠿⠿⡿⠿⠇⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣸
⣿⠿⢿⣛⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⡁⣉⣉⣉⣁⣩⣬⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⢿⣿⣿⣾⡾⡶⠶⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢿⣿⣿⣿⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣖⠂⠤⠙⠻⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠶⠿⠟⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣴⡆⣿
⣤⣤⡀⠀⠀⠐⠿⠷⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡿⢇⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⡹⣶⣄⡀⠀⠀⠀⠲⠶⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⣽⣿
⣄⣠⣤⣴⣶⣶⣶⣿⣭⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⣀⣤⣤⣴⣶⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠾⣿⠉⠁⠀⠀⠀⠀⠀⢩⢷⣊⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⡀⠀⠈⠉⠁⣀⣀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠋⠉⢉⣉⠉⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠨⠏⠉⠀⠤⠀⠀⠀⣶⣶⣾⣿⣺⠛⢛⣛⣛⣛⣛⣋⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡾⠋⠀⠀⠈⣀⠉⠀⠀⠀⠨⠉⠛⠛⣵⡆⠀⠤⠀⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⡟⠁⡀⡀⠀⣀⣤⣶⣿⡿⣶⣶⣆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡗⣀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣟⠫⠁⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠏⠉⢻⣿⣿⣿⣿⣗⣀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠉⠘⠿⠿⠿⠃⠀⠉⠛⠋⠀⠀⠀⠀⠄⣿⣭⣭⣭⠉⠉⠟⠻⣿⠟⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣗⣻
⣿⣿⣿⣿⣿⣿⡿⠇⠁⠁⠀⠀⠀⠈⠓⠀⠀⠋⠁⠺⡿⣟⡻⡙⢹⣿⣿⣻⠿⠈⠀⠿⣿⠇⠛⢿⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿
⣛⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠈⠘⠛⢻⠃⠀⠀⠀⡤⣤⡲⠄⠀⠈⠹⢿⣿⣋⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠻⢿⠀⠀⠉⠂⠀⠀⢀⡙⣻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣯⡿⠂⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣤⣴⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣧⣶⣀⠀⠀⠀⠀⣽⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣿⣿⣿⣿⣿⣿⣏⣻
⡇⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡀⣀⣀⢀⣈⣀⣉⣉⡀⣀⣀⡀⢙⣛⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣴⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⠿⣿⣿⣿⣿⣟⣺
⣯⣽⣿⣿⣿⠛⠃⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠽⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡷⢼
⣭⣽⣧⠹⠅⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣡⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⢽
⣿⣿⣿⡆⢀⡀⠀⠀⠠⠈⠿⠾⠷⠾⠶⠗⢠⠤⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠶⠿⠿⡿⠿⠃⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣺
⣿⠿⢿⣓⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠛⠛⠛⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⡁⣉⣉⣈⣁⣩⣬⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⢿⢿⣶⠶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢪⢿⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣖⠂⠤⠙⠻⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠶⠿⠟⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠛⣛⣛⣉⣭⣭⣤⣄⣿
⣤⣄⠀⠀⠀⠒⠿⠷⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡿⢸⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣹⣶⣄⡀⠀⠀⠀⠶⠶⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣀⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡀⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⠟⣛⣛⣛⣋⣉⣭⢹⡏
⣤⣠⣤⣴⣶⣶⣶⣿⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⣶⣀⣤⣤⣴⣶⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠜⣿⠉⠁⠀⠀⠀⠀⠀⢩⢷⣊⠁⣿⢹⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡀⠀⠈⠉⠁⣀⡀⠀⠟⠛⠀⣿⣈⣈⣉⣉⣁⣠⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠋⠉⢉⣉⠉⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠨⠍⠉⠀⠤⠀⠀⠀⣶⣶⣾⣿⣺⠛⠛⣛⣛⣛⣛⣋⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡾⠛⠁⠀⠈⣀⡀⠀⠀⠠⠬⠉⠙⠛⣵⡆⠀⠴⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣻⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣟⠑⣀⣀⠀⣠⣤⣿⣿⣿⣷⣷⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿
⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡷⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠏⠉⢻⣿⣿⣿⣿⣇⡀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠿⠿⠟⠃⠠⡈⠉⠙⠀⠀⠀⠈⠑⣿⣯⣭⣭⠉⠉⠟⠿⣿⠟⠛⢿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⣿⡿⠇⠁⠁⠀⠀⠀⠈⠓⠀⢀⠋⠁⢺⡿⡟⡻⠙⢻⣿⣿⠿⠏⠈⠀⢿⣿⠇⠛⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿
⣛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠈⠘⠛⠟⠀⠀⠀⢠⠤⣴⠢⠄⠀⠉⠻⣿⣿⣋⣙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡎⠻⢿⠀⠀⠉⠂⠀⠀⣀⠙⣻⣿⣿⣿⣿⣿⣿⣿⡯⣽
⡿⣿⣿⣿⣯⡿⠂⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣤⣴⠀⠀⠀⠀⠁⠀⠀⠀⠘⣢⣧⣶⡄⠀⠀⠀⠀⣽⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣿⣿⣿⣿⣿⣿⣏⣻
⡇⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣛⣀⡀⢀⣀⣀⡀⣀⣀⢈⣉⣈⣉⣁⡀⣀⣀⡀⢙⣛⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣴⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠿⠿⣿⣿⣿⣿⣗⣺
⣏⣿⣿⣿⡟⠛⠃⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠽⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡧⢼
⣭⣽⣧⠹⠅⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡏⣿⢸⣧⡄⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⢽
⣿⣿⣿⡄⢀⡀⠀⠀⠠⠈⠿⠾⠷⠾⠶⠇⢠⠤⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠶⠿⠿⡿⠿⠃⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣺
⣿⠿⢿⣓⡀⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾
⠀⠛⠛⠛⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣉⣅⣩⣬⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⢿⣿⣶⠶⠶⠾⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⢿⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡖⠂⠤⠝⠛⠛⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠾⠿⠟⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠛⣛⣛⣉⣭⣭⣴⡆⣿
⣤⣤⡀⠀⠀⠐⠿⠗⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡿⢱⣿
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣃⢠⣼⣶⣤⣀⠀⠀⠀⠲⠶⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣀⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣋⣩⣭⢹⡏
⣤⣠⣤⣴⣶⣶⣶⣿⣭⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣶⣶⣠⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢿⠉⠁⠀⠀⠀⠀⠀⢩⣷⣊⠁⣿⢹⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠘⡀⠀⠈⠉⠀⣀⣀⠀⠟⠛⠀⣿⣈⣈⣉⣉⣁⣠⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠋⠉⠉⢉⣉⠉⢿⣿⣿⡿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣏⠀⠀⠠⠋⠉⠀⠤⠀⠀⠀⣶⣶⣾⣿⣺⠛⢛⣛⣛⣛⣛⣋⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⠋⠁⠀⠀⣄⡀⠀⠀⠀⠀⠀⠙⢋⣷⡆⠀⠒⠄⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀⢠⣏⣑⣀⣀⣠⣤⣴⣿⣿⣿⣷⣾⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣤⣿⣿⣿⡿⠿⣿⣿⣿⣟⠛⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣇⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠏⠉⢹⣿⣿⣿⣿⣆⡀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠛⠟⠛⠉⠀⠀⠉⠉⠁⠀⠀⠡⠽⣿⣿⣭⣭⠉⠉⠟⠻⣿⠟⠛⢿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⣿⡿⠇⠁⠉⠀⠀⠀⠈⠓⠄⢐⠋⠁⢺⡿⡛⠿⠙⢻⣿⣿⠿⠁⠈⠀⠿⡿⠃⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿
⣛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡃⠀⠈⠈⠈⠙⠃⠀⠀⠀⣤⡤⣴⠢⠄⠀⠉⠻⣿⣿⣋⣉⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠻⢿⠀⠀⠉⠂⠀⠀⣀⡙⣻⣿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣧⣶⡀⠀⠀⠀⠠⣹⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠽⣿⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣛⣀⡀⢀⣀⣀⡀⣀⣀⢋⣉⣈⣉⣁⡀⣀⣀⡀⢛⣛⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⠿⣿⣿⣿⣿⣗⣺
⣏⣿⣿⣿⡟⠛⠁⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣽⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠽⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡧⢽
⣵⣷⣦⠹⠇⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣡⣾⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡯⢽
⣿⣿⣿⡆⢀⠀⠤⠀⠰⠘⠿⠾⠷⠾⠶⠓⢠⠴⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠶⠿⠿⡿⠿⠇⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣺
⡿⠿⣿⣓⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠥⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⡁⣉⣉⣉⣡⣩⣬⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⢿⣿⣷⣶⠾⠶⠶⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡖⠂⠤⠝⠛⠛⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣴⡆⣿
⣤⣤⡀⠀⠀⠐⠿⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣹⠿⢧⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣠⣌⣷⣦⣀⠀⠀⠀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⢽⣿
⣤⣤⣤⣴⣶⣶⣶⣿⣯⣿⣃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⣶⣠⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠮⢿⠉⠁⠀⠀⠀⠀⠀⠩⢷⣊⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⣄⠀⠈⠉⠁⣀⣀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠋⠉⠉⢉⣉⠉⢽⣾⣿⠿⢿⣿⢿⠿⠿⠿⢿⣿⣿⣿⣏⠀⠀⠠⠋⠉⠀⠤⠀⠀⠀⣶⣶⣾⣿⣺⠛⢛⣛⣛⣛⣛⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⠋⠁⠀⠀⣥⣀⠀⠀⠀⠒⠂⢉⣉⣶⡇⠀⠒⠂⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡆⠀⠀⢠⣯⣉⣠⣄⣄⣴⣶⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡤⣿⣿⣿⣿⠻⢿⣿⣿⣿⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡟⡏⠈⢹⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠛⠉⠁⠐⠀⠈⠉⠁⠀⠀⠠⠘⣿⣿⣭⣭⠉⠉⠟⠻⣿⠟⠛⢿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⣿⡿⠃⠁⠉⠀⠀⠀⠈⠓⠄⢐⠋⠁⠺⡿⡛⢿⠙⢻⣿⡿⠛⠀⠌⠀⠿⡿⠃⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿
⣛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠈⠈⠙⠁⠀⠀⠀⣤⠤⣴⠢⠄⠀⠉⠻⣿⣿⣋⣉⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠙⠿⠀⠀⠈⠂⠀⠀⣀⠉⣻⣿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣧⣶⡀⠀⠀⠀⢰⣽⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡀⣀⣀⢛⣉⣈⣁⣁⡀⣀⣀⡈⢛⣛⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⠿⣿⣿⣿⣿⣗⣺
⣏⣿⣿⣿⡟⠛⠁⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⡿⠛⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡷⢼
⣵⣷⣦⠸⠇⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⢽
⣿⣿⣿⡆⢀⠀⠤⠀⠰⠈⠿⠾⠷⠾⠶⠓⢠⠴⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠴⠿⠿⡿⠿⠏⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣺
⡿⠿⣿⣓⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠡⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⣁⣉⣩⣉⣡⣉⣬⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⢿⣿⣷⣶⠶⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣿⣿⣿⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠂⠤⠙⠛⠛⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠾⠿⠟⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠛⣛⣛⣩⣭⣭⣴⡆⣿
⣤⣤⡀⠀⠀⠐⠿⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣦⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⣽⠿⢹⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣤⣹⣦⣄⡀⠀⠀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣠⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣩⣽⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣛⣉⣭⣭⢽⡟
⣤⣤⣤⣴⣶⣶⣶⣿⣭⣿⣂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⣶⣤⣤⣴⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢽⡏⠁⠀⠀⠀⠀⠀⠩⢷⣋⠁⣿⢹⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣇⠀⠈⠉⠁⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣁⣀⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⠉⠉⢉⣉⠉⠹⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡯⠀⠀⠀⠛⠉⠀⠤⠀⠀⠀⣶⣶⣿⣿⣻⠛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠋⠁⠀⠀⣰⣄⠀⠀⠀⠀⠀⢀⣉⣾⡗⠀⠐⠂⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⠀⠀⢠⣾⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣈⣉⣉⣉⣉⣉⣀⡼⣿
⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠷⠄⣿⣿⣿⣿⠛⠿⣿⣿⣿⠏⠋⠊⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡟⡏⠈⢹⣿⣿⣿⣿⣆⢀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠉⠉⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠪⢸⣿⣽⣿⠉⠉⠟⠛⣿⠟⠛⢿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠀⠀⠀⠈⠛⠄⢀⠋⠁⠺⡿⡛⢿⠙⢻⣿⡿⠛⠠⠌⠀⠿⡿⠃⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣛⣻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠈⠈⠙⠀⠀⠀⢠⣤⠤⣔⠢⠄⠀⠉⢻⣿⣿⣋⣉⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠙⠿⠀⠀⠈⠂⠀⠀⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⡯⢿
⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣧⣷⠀⠀⠀⠀⢰⣽⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡀⣀⣀⢛⣉⣈⣉⣀⡀⣀⣀⡘⢛⣛⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⠿⢿⣿⣿⣿⣗⣺
⣏⣿⣿⣿⡟⠛⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⡯⠛⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡷⢾
⣵⣷⣦⠘⠇⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢉⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⢽
⣿⣿⣿⡆⢀⠀⠤⠀⠰⠈⠿⠾⠷⠾⡶⠓⢠⠴⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸
⡿⠿⣿⣓⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠡⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⣁⣉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⠷⣶⠶⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢽⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡆⠒⠤⠝⠛⠛⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢛⣛⣋⣩⣭⣥⣶⡇⣿
⣤⣤⡀⠀⠀⠘⠿⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣶⣦⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡭⠿⢣⣿
⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣼⣷⣤⡀⠀⠀⠲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣁⣀⣤⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣩⣭⣭⢽⡿
⣤⣤⣤⣶⣶⣶⣶⣿⣯⣽⣂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣶⣶⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⡟⠁⠀⠀⠀⠀⠀⠩⢶⣏⠁⣿⢸⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢫⡀⠈⠉⠁⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣀⣤⣤⣤⣼⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⡉⠉⢉⣉⠉⠈⣿⣿⠿⠿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠜⠁⠀⠴⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣉⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡏⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⢀⣈⣲⣷⠀⠐⠒⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣽⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣧⠀⠀⢠⣾⣦⣴⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣈⣉⣉⣉⣉⣀⣠⡼⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠷⠖⣿⣿⣿⣿⠛⠻⣿⡿⡿⠫⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿
⣿⣿⣿⣿⣿⣿⣿⡟⡋⠈⢹⣿⣿⣿⣿⣖⢀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠉⠉⠀⠐⠃⠀⠀⠀⠀⠀⠀⠊⢸⣿⣿⣿⠉⠉⠛⠛⣿⠛⠛⢿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⣿⡿⠃⠀⠉⠀⠀⠀⠀⠛⠄⢀⠋⠀⠺⡿⡛⠯⠙⢻⣿⠿⠛⠠⠏⠀⠿⡿⠃⠻⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠈⠈⠙⠀⠀⠀⢰⣦⡄⣔⠦⠀⠀⠙⢻⣿⣿⣋⣉⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⠿⠀⠀⠈⠀⠀⠀⣠⡉⣻⣿⣿⣿⣿⣿⣿⣿⡯⢿
⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⢷⣷⠀⠀⠀⠀⢰⣽⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠹⣿⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣛⣀⡀⢀⣀⣀⡀⣘⣈⢛⣉⣈⣉⣀⡀⣀⣀⡘⢛⣛⡉⠀⢀⣀⡀⣀⣀⣀⢀⣀⡀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠿⢿⣿⣿⣿⣟⣺
⣯⣿⣿⣿⡿⠛⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣿⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣿⠟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡷⢾
⣵⣷⣶⠘⡇⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢩⣾⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢽
⣿⣿⣿⡆⢀⠠⠤⠀⠰⠈⠿⠾⠷⠾⡖⠓⢠⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠰⠿⠿⡿⠿⠿⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹
⡿⠿⣟⣛⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠡⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⣉⣉⣍⣁⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⣿⣿⢿⣿⣷⣶⠾⠾⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢽⣿⣿⣿⣿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡦⠐⠠⠝⠛⠛⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣛⣉⣭⣭⣤⣶⡆⣿
⣤⣤⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣶⣶⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠭⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣠⣦⣿⣦⣄⠀⠀⠒⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣀⣠⣤⣤⣤⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⢛⣛⣛⣉⣭⣭⣭⣬⣿
⣤⣤⣤⣴⣾⣷⣶⣾⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣶⣶⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⣿⠁⠀⠀⠀⠀⠀⠩⢖⣏⠁⣿⢸⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠘⡄⠈⠉⠁⣀⡀⠀⠛⠉⢀⢿⣈⣉⣁⣠⣤⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢉⣉⣉⢉⣉⠁⠂⢿⣿⡿⠿⠿⡿⠿⠿⠟⠻⠿⢿⣿⣿⡇⠀⠀⠐⠋⠀⠖⠀⠀⠀⣶⣾⣿⣿⣿⢛⣛⣛⣛⣉⣉⣩⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣎⠁⠀⠀⠀⣷⠄⠀⠀⠈⠁⢀⣈⣱⣿⡆⠀⠒⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡄⠀⠀⣴⣷⣬⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣈⣉⣉⣉⣀⣠⣤⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡗⠒⢻⣿⣿⣿⡝⠛⠿⣿⠿⠋⠉⠉⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣽
⣿⡟⣿⣿⣿⣿⣿⡏⡁⠈⣻⣿⣿⣿⣿⠖⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠉⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠛⠛⢿⠟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⡇⣿⣿⣿⣿⠟⠃⠁⠈⠀⠀⠀⠀⠋⠀⢀⠃⠁⠸⣿⠛⠯⡉⢹⣿⠿⠋⠠⡏⠀⠿⠿⠃⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾
⣛⣣⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠉⠀⠀⠀⢰⣶⡖⡄⠦⠀⠈⠙⢿⣿⣿⣋⣉⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡈⠻⠀⠀⠈⠁⠀⠀⢠⡉⣻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢁⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⢶⣾⠀⠀⠀⠀⢰⣾⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢁⡘⣿⣿⣿⣿⣿⣿⣿⣯⣽
⡇⣸⣿⣿⣿⣦⡄⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣐⣉⢛⣉⣈⣁⣀⡀⣀⣀⡘⢛⣛⡉⠀⢀⣀⡀⣒⣀⣀⢀⣀⡀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣟⣺
⣯⣽⣿⣿⣿⠛⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣾⠟⢛⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡷⢺
⣷⣶⣶⠘⡄⠀⠀⠀⠀⠸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢫⣵⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢽
⣿⣿⣿⡇⠀⠤⠤⠀⠐⠂⠿⠾⠷⠾⡖⠓⢴⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠄⠐⠿⠿⡿⠿⠿⠃⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⡿⠿⣟⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠛⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⣉⣉⣍⣅⣍⣨⣝⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⣷⣾⠾⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⡿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡦⠒⠠⠽⠛⠛⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣛⣉⣭⣭⣤⣶⡆⣿
⣤⣤⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣶⣶⣦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⠭⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣠⣦⣻⣶⣄⡀⠀⠒⠚⠃⠀⠀⣿⣿⣿⣿⣿⣈⣀⣠⣤⣤⣤⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⢛⣛⣛⣉⣭⣭⣭⡬⣿
⣤⣤⣤⣴⣶⣿⣶⣾⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢻⡅⠀⠀⠀⠀⠀⠩⢶⣏⠁⣿⢸⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣇⠈⠉⠁⢀⡀⠀⠛⠙⢀⢿⣈⣉⣁⣠⣤⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⣉⣉⢉⣉⠁⠀⢼⣿⡿⠿⠿⡿⠿⠿⠟⠛⠿⠿⣿⣿⡇⠀⠀⠀⠋⠀⠖⠀⠀⠀⣷⣾⣿⣿⣿⢛⣛⣛⣛⣋⣉⣩⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣮⠀⠀⠀⠀⣷⡄⠀⠀⠀⠁⠁⣠⣱⣿⡇⠀⠚⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣆⠀⠀⣴⣷⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣁⣠⣤⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡏⠓⠲⣿⣿⣿⡍⠛⠿⣿⣿⡿⠏⠁⠘⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿
⣿⡿⣿⣿⣿⣿⣿⡏⠁⠈⣿⣿⣿⣿⣿⠖⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⢿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠉⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠀⠀⠛⠛⢿⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻
⣿⡇⣿⣿⣿⣿⠟⠃⠀⠉⠀⠀⠀⠀⠋⠁⠀⠃⠁⠰⣿⡛⢯⡉⢹⣿⠿⠋⢈⡏⠀⠿⠟⠃⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾
⣛⣣⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠈⠈⠉⠀⠀⠀⢰⣶⡖⡖⠤⠀⠈⠙⢿⣿⣿⣋⣉⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡌⠻⠀⠀⠈⠁⠀⠀⢠⡉⣻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢁⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⢷⣞⠀⠀⠀⠀⣶⣾⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⡹⣿⣿⣿⣿⣿⣿⣿⣯⣽
⡇⣸⣿⣿⣿⣦⡄⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣐⣉⢛⣉⣈⣁⣀⡀⣀⣀⡙⢛⣛⡋⠁⢀⣀⡀⣐⣀⣀⢀⣀⡀⣠⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣟⣺
⣿⣽⣿⣿⣿⠛⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢻⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣼⡿⢛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡷⢺
⣷⣶⣶⠘⡄⠀⠀⠀⠀⠸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢋⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢽
⣿⣿⣿⡇⠀⠠⠤⠀⠐⠂⠿⠾⠷⠾⡖⠓⢤⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠿⠿⡿⠿⠿⠇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⡿⠿⣟⣛⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠛⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⣉⣉⣉⣁⣉⣨⣝⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⡿⣿⣷⣶⠾⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡪⡻⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡦⠒⠠⠝⠛⠛⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣛⣋⣭⣭⣤⣶⡆⣿
⣤⣤⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣶⣶⣦⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⡭⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣁⣦⣽⣷⣤⡀⠀⠒⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣁⣀⣤⣤⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣉⣩⣭⣭⡍⣿
⣤⣤⣤⣶⣶⣶⣶⣾⣯⣭⣁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠹⡇⠀⠀⠀⠀⠀⠩⢷⣏⠁⣿⢸⣿⣿⣿⣿⣿⣿⢧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣧⠈⠉⠁⢀⣀⠀⠟⠉⠀⢿⣈⣉⣉⣀⣤⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⢉⡉⢉⣉⠉⠀⠸⣿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠀⠀⠁⠛⠀⠴⠀⠀⠀⣷⣶⣿⣿⣻⢛⣛⣛⣛⣛⣉⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡉⠀⠀⠀⢸⡤⠀⠀⠀⠀⠀⢈⣉⣸⣷⠀⠐⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣇⡀⠀⢠⣾⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣀⣠⡼⢿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⠵⠒⣾⣿⣿⣿⠛⠿⣿⣿⣿⡟⠋⠁⠿⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿
⣿⡇⣿⣿⣿⣿⣿⣏⠁⠉⣿⣿⣿⣿⣿⡖⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠁⠴⠶⠄⠁⠁⠀⠀⠀⠉⣻⣿⣿⠀⠈⠛⠛⢿⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻
⣿⡇⣿⣿⣿⣿⠛⠋⠀⠁⠀⠀⠀⠀⠋⠀⠀⠋⠁⠸⣿⠛⠯⡉⢹⣿⠿⠹⢈⡏⠀⠿⠟⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾
⣛⣣⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠈⠈⠉⠀⠀⠀⣰⣶⣖⡢⠄⠀⠈⠻⣿⣿⣿⣋⣉⣛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠻⠀⠀⠈⠀⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢶⡖⠀⠀⠀⠁⣴⣾⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⣿⣿⣿⣿⣿⣿⣿⣯⣽
⡇⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣛⣀⡀⢀⣀⣀⡀⣐⣙⢛⣉⣈⣁⣀⡀⣀⣀⡛⢛⣛⡋⠁⢀⣀⡀⣐⣀⣀⢀⣀⡀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣟⣺
⣿⣽⣿⣿⣿⠛⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣿⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣼⡿⠛⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡷⢺
⣵⣶⣶⠘⡄⠀⠀⠀⠀⠸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢛⣱⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢽
⣿⣿⣿⡇⠀⠠⠤⠀⠐⠂⠿⠾⠷⠾⡖⠓⢠⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠾⠿⡿⠿⠿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡿⠿⣟⣛⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠚⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣈⣡⣩⣨⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⣿⣿⣶⣶⠾⠶⠶⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠮⣿⣿⣿⣿⡗⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡦⠒⠠⠝⠛⠛⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣛⣋⣭⣭⣤⣶⡆⣿
⣴⣤⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣶⣶⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⡭⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣴⣼⣷⣦⣀⠀⠒⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣁⣀⣤⣤⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣉⣩⣭⣭⣌⣿
⣦⣤⣤⣶⣶⣶⣶⣾⣿⣭⣁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠚⡇⠀⠀⠀⠀⠀⠩⢷⣯⠁⣿⢸⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢣⠈⠉⠁⢀⣀⠀⠟⠙⠀⣿⣈⣉⣉⣀⣤⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⢉⡉⢉⣉⠉⠀⠰⣿⣿⡿⢿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡀⠀⠀⠘⠀⠴⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣉⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⡋⠁⠀⠀⢸⣤⠀⠀⠀⠒⠀⠌⡉⣱⣾⠀⠐⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⡀⠀⢀⣼⣅⣡⣤⣤⣤⣶⣾⣿⣿⡿⢿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣀⣠⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡧⠤⢼⣿⣿⣟⠛⠿⣿⣿⣿⠟⠋⠉⡽⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿
⣿⡟⣿⣿⣿⣿⣿⣏⠀⢉⣿⣿⣿⣿⣿⡖⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠛⠋⠉⠠⢦⡌⠉⠉⠀⠀⠀⠈⢻⣿⣿⠀⠈⠛⠛⢿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻
⣿⡇⣿⣿⣿⡿⠛⠋⠈⠁⠀⠀⠀⠀⠋⠀⢀⠋⠁⠸⣿⡛⠯⡙⢹⣿⠿⠛⢈⡍⠀⠿⠟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾
⣛⣣⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠉⠀⠀⠀⣴⣶⣔⡠⠀⠀⠙⠻⣿⣿⣿⣋⣉⣛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠛⠀⠀⠈⠀⠀⠀⢀⡉⢹⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢶⡆⠀⠀⠀⢡⣴⣾⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⣿⣿⣿⣿⣿⣿⣿⣯⣽
⡇⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣐⣙⢛⣉⣈⣀⣀⡀⣀⣀⡛⢋⣛⡋⠉⢀⣀⡀⣐⣀⣀⢀⣀⡀⢀⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣟⣺
⣯⣽⣿⣿⣿⠛⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣾⡿⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡷⢺
⣷⣶⣶⠘⡀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢛⣡⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢽
⣿⣿⣿⡇⠀⠤⠤⠀⠐⠂⠿⠾⠷⠾⡖⠓⢠⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠺⠿⡿⠿⠿⡟⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡿⠿⣟⣛⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠡⡉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣉⣡⣩⣈⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⣿⣿⣶⣶⠶⠶⠾⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣽⣽⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡦⠒⠠⠍⠛⠋⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣛⣋⣩⣭⣥⣴⡆⣿
⣤⣤⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣿⣷⣶⣶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⡭⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣓⣠⣌⣿⣦⣄⠀⠲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣁⣀⣤⣤⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⣽⣿
⣦⣦⣦⣶⣾⣿⣶⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠎⢿⠀⠀⠀⠀⠀⠩⢷⣏⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢸⡌⠉⠁⣀⣀⠀⠟⠙⠀⣿⣈⣉⣉⣀⣠⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⣉⡉⢉⣉⠁⠀⠤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠘⠁⠴⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡝⠉⠁⠀⠈⣄⠀⠀⠀⠀⠀⠈⠙⢋⣷⡄⠀⠒⢀⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⡀⠀⠀⣠⣏⣐⣠⣀⣀⣤⣴⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣈⣉⣉⣉⣉⣀⣀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣆⢠⣿⣿⣿⡿⢿⣿⣿⣿⡟⠋⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⡻⠖⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⢿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠛⠟⠛⠁⣤⡌⠉⠉⠀⠀⠀⠀⢸⣿⣿⠈⠈⠛⠛⢿⠋⠙⢿⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⡟⠛⠉⠀⠁⠀⠀⠀⠀⠋⠄⢀⠃⠁⠸⣿⠛⢯⣋⢻⣿⠿⠛⠀⡍⠀⠿⠟⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠠⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣯⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠉⠀⠀⠀⣶⣶⣖⡄⠀⠀⠛⢿⣿⣿⣿⣋⣉⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠙⠀⠀⠉⠀⠀⠀⢀⡉⠻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⢶⠂⠀⠀⠀⢡⣴⣼⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⣿⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣘⣙⢛⣉⣈⣀⣀⡀⣀⣈⡛⢛⣛⡛⠉⢀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣟⣺
⣯⣽⣿⣿⡿⠋⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢽⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣨⣿⠟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡷⢾
⣷⣶⣶⠘⡀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢻⣃⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢽
⣿⣿⣿⡇⠀⠤⠤⠀⠐⠀⠿⠾⠷⠾⡒⠓⢴⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠺⠿⠿⠿⠿⣿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠿⠿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⢉⣉⣉⣁⣉⣌⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⠿⣿⣿⣿⣶⣶⠶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣵⢵⣿⣿⣿⣯⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡆⠒⠠⠝⠛⠋⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣛⣛⣋⣩⣭⣥⣴⡇⣿
⣤⣦⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣷⣶⣶⣶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣽⠿⢣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣓⣠⣌⣿⣦⣄⠀⠲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣛⣉⣭⣭⢽⣟
⣦⣤⣴⣶⣾⣿⣶⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣴⣶⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠎⣿⠀⠀⠀⠀⠀⠩⢷⣏⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⡌⠉⠁⣀⣀⠀⠟⠉⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⢉⡉⢉⣉⠉⠀⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠃⠴⠀⠀⠀⣶⣶⣿⣿⣺⠛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡝⠋⠁⠀⠈⣇⠀⠀⠀⠠⠄⠁⠙⢛⣵⡆⠀⠒⠀⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣻⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡀⠀⠀⢠⣏⣀⣀⣀⣀⣤⣤⣾⣿⣿⣷⣶⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣈⣉⣉⣉⣉⣁⣀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⢦⢤⣿⣿⡿⠿⢿⣿⣿⣿⡿⠋⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⡿⠆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⠿⠛⠃⣠⡉⠋⠉⠀⠀⠀⠈⢺⣿⣿⠉⠉⠛⠛⠿⠋⠙⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⡟⠛⠁⠈⠁⠀⠀⠀⠀⠛⠄⢈⠁⠀⠸⣿⠛⢯⢋⢻⣿⠿⠛⢀⡈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠠⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣛⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠈⠈⠉⠀⠀⠀⣶⣶⣆⡄⠀⠈⠻⢿⣿⣿⣟⣋⣉⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠉⠀⠀⠙⠀⠀⠀⣀⡉⠻⣿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⢴⠀⠀⠀⠀⢡⣶⣽⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⣻⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣘⣙⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠉⢀⣀⡀⣀⣀⣀⢀⣀⡀⠀⣠⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣟⣺
⣯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣻⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣨⣿⠟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡷⢾
⣶⣶⣶⠘⠂⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣾⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠿⣋⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢽
⣿⣿⣿⡆⠀⠤⠤⠀⠒⠈⠿⠾⠷⠾⡒⠓⢴⠶⠶⠶⠶⠂⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠐⠲⠿⠿⠿⠿⣿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠿⠿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⡈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⢉⣉⣉⣡⣩⣌⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⠿⣿⣿⣿⣶⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡵⣿⣿⣿⣿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡆⠒⠠⠝⠛⠛⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣤⡆⣿
⣤⣤⡀⠀⠀⠘⠿⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣶⣶⣶⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣹⠿⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⢀⣌⣿⣦⣄⠀⠲⠶⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⢽⡟
⣦⣤⣶⣶⣶⣶⣶⣾⣯⣭⣂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⣶⣠⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠎⢻⠀⠀⠀⠀⠀⠩⢷⣎⠁⣿⢹⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⡌⠉⠁⣀⣀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⠉⠉⢉⣉⠉⠠⠤⢼⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠇⠤⠀⠀⠀⣶⣶⣿⣿⣺⠛⢛⣛⣛⣛⣛⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣽⠋⠉⠀⠀⣇⠀⠀⠀⠀⠀⠉⠙⢛⣵⡆⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣻⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡄⠀⠀⢀⣟⣑⣀⣀⣀⣠⣤⣾⣿⣿⣷⣾⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣢⣤⣿⣿⡿⠿⠿⣿⣿⣿⡟⠉⠉⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡋⠀⢹⣿⣿⣿⣿⡿⠂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠻⠿⠛⠃⠠⡈⠙⠁⠀⠀⠀⠀⠑⣿⣽⠉⠉⠛⠛⠿⠋⠛⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠿⠛⠁⠉⠀⠀⠀⠀⠈⠛⠄⢘⠋⠀⢺⡿⡛⢯⠑⢻⣿⠿⠛⢀⠈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣛⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠉⠀⠀⠀⣶⣤⡦⣀⠀⠈⠻⣿⣿⣿⣟⣋⣉⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠑⠄⠀⠀⣀⡙⢻⣿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡴⠀⠀⠀⠀⢥⣴⣽⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠟⠈⢼⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡀⣘⣙⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠉⢁⣀⡀⣀⣀⣀⢀⣀⡀⠀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣗⣺
⡯⣿⣿⣿⡟⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣨⣿⠟⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡧⢿
⣵⣷⣶⠈⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣟⣋⣴⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽
⣿⣿⣿⡆⠀⠠⠤⠀⠐⠈⠿⠾⠷⠾⡶⠓⣠⠴⠶⠶⠶⠂⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠐⠳⠿⠿⠿⠿⣿⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠿⣟⣓⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠡⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⢉⣉⣉⣅⣉⣌⣹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣷⣾⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⣿⣿⣿⣿⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡆⠒⠠⠝⠛⠛⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣤⡆⣿
⣤⣦⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣶⣶⣶⣤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡿⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣓⣀⣤⣿⣦⣄⡀⠲⠶⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⢀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣋⣩⣭⢽⣿
⣦⣤⣶⣶⣶⣶⣶⣾⣯⣭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⣶⣠⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⢻⡄⠀⠀⠀⠀⠩⢷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠈⣏⠉⠁⣀⣀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣠⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⠉⠉⢉⣉⠉⠥⠤⢼⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠀⠀⠠⠋⠤⠀⠀⠀⣶⣶⣾⣿⣺⠛⢛⣛⣛⣛⣛⣋⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⣹⠋⠁⠀⠈⣧⡀⠀⠀⠀⠀⠀⠙⠛⣵⡆⠀⠐⠀⣾⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣻⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⢀⣽⣙⣄⣀⣀⣤⣴⣾⣿⣿⣷⣾⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢢⡠⣿⣿⣿⡻⠿⣿⣿⣿⣿⠯⠛⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡋⠀⢹⣿⣿⣿⣿⡿⠂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠟⠛⠁⠰⠄⠉⠉⠀⠀⠀⠉⣹⣯⣯⠉⠉⠛⠛⠿⠛⠛⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠿⠛⠁⠉⠀⠀⠀⠀⠈⠛⠄⢘⠋⠁⢺⣿⠛⢯⠙⢻⣿⡿⠛⠄⡈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡧⣿
⣛⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠈⠈⠙⠀⠀⠀⣷⣤⡤⣀⠀⠈⠻⣿⣿⣿⣟⣋⣉⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠈⠑⠄⠀⠀⢀⡙⢻⣿⣿⣿⣿⣿⣿⣿⡯⣽
⡿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⠀⠀⠀⠀⢥⣴⣽⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠿⠈⢼⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡀⣘⣙⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠉⢁⣀⡀⣀⣀⣀⢀⣀⡀⠀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣗⣺
⣯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣰⣿⠿⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧⢽
⣷⣶⣦⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢟⣏⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽
⣿⣿⣿⡆⠀⠠⠤⠀⠐⠈⠿⠾⠷⠾⡖⠓⢤⠶⠶⠶⠶⠂⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠔⠛⠿⠿⠿⠿⣿⠇⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠿⣟⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠡⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⢉⣉⣉⣅⣉⣌⣹⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⣶⣾⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⡯⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡦⠐⠠⠍⠛⠛⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣤⡆⣿
⣴⣦⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⣿⣶⣶⣶⣶⣦⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣂⣤⣹⣷⣤⡀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⣽⣿
⣤⣤⣤⣶⣾⣿⣶⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢹⡇⠀⠀⠀⠀⠩⢷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣯⠉⠁⣀⣀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⢉⡉⢉⣉⠉⠀⠤⢼⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣟⠀⠀⠀⠛⠤⠀⠀⠀⣶⣶⣾⣿⣺⠛⢛⣛⣛⣛⣛⣋⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣹⠋⠁⠀⠀⣁⣀⠀⠀⠀⠀⠀⠉⠛⣽⡦⠀⠐⠂⣸⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⠀⠀⢀⣼⣉⣠⣀⣀⣤⣤⣿⣿⣿⣿⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣢⡄⣼⣿⣿⡿⠿⢿⣿⣿⣿⡿⠁⢹⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⡿⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠿⠛⠉⠀⠂⠈⠉⠉⠀⠀⠀⠘⣿⣿⠉⠉⠛⠛⠿⠛⠛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⡿⣿⣿⣿⠟⠛⠁⠉⠀⠀⠀⠀⠀⠋⠄⢈⠃⠁⠸⣿⡛⢯⢉⢻⣿⡿⠛⠁⡈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠻⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿
⣛⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠙⠁⠀⠀⣷⣦⡤⣀⠀⠈⠻⢿⣿⣿⣿⣋⣉⣛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠑⠄⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢤⠀⠀⠀⠀⢡⣴⣽⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⠿⠘⠡⣿⣿⣿⣿⣿⣿⣇⣻
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣐⣙⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠋⢁⣀⡀⣀⣀⣀⢀⣀⡀⠀⣀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣗⣺
⣯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢰⣾⡯⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢼
⣶⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡏⣿⢸⣧⡄⣿⣛⣡⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⡇⠀⠤⠄⠀⠐⠀⠿⠶⠷⠾⡒⠓⢴⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠤⠶⠀⠐⠛⠿⡿⠿⠿⣿⡇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⣉⣉⣡⣉⣬⣙⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⠿⣿⣿⣿⢶⣶⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡮⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡦⠐⠢⠭⠛⠛⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣤⡆⣿
⣤⣦⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⣿⣶⣶⣶⣶⣦⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⣻⡿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣂⣤⣹⣷⣤⣀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠐⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⡍⣿
⣶⣤⣴⣶⣾⣿⣷⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠙⡇⠀⠀⠀⠀⠩⢷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⢫⠉⠁⣀⣀⠀⠟⠛⠀⢿⣈⣉⣉⣉⣀⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⢉⠉⢉⣉⠉⠀⠤⢴⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠚⠥⠀⠀⠀⣶⣶⣾⣿⣻⠛⣛⣛⣛⣛⣛⣋⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⣩⠋⠉⠀⠁⢩⡀⡀⠀⠀⠀⠈⠈⠙⣹⡶⠀⠐⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣽⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⠀⠀⢀⣼⣉⣀⣀⣀⣤⣤⣾⣿⣿⣿⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣣⡤⣼⣿⣿⣻⠿⢿⣿⣿⣿⣿⠏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⡏⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⡿⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠻⠛⠋⠀⠀⠈⠉⠉⠀⠀⠀⠈⢻⣿⠉⠉⠛⠛⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣺
⣿⡇⣿⣿⣿⠟⠛⠉⠈⠁⠀⠀⠀⠀⠋⠅⢈⠃⠁⠹⣿⠛⢯⠋⢹⣿⡿⠛⠁⡈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿
⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠙⠃⠀⠀⣷⣶⡤⣀⠀⠈⠻⢿⣿⣿⣿⣋⣉⣛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠑⠄⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⢤⠀⠀⠀⠀⢡⣴⣼⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠈⠯⠘⠡⣿⣿⣿⣿⣿⣿⣏⣻
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣛⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠋⢁⣀⡀⣀⣀⣀⢀⣀⡀⠀⢀⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣟⣺
⣿⣼⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢰⣽⡿⠛⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢼
⣶⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣾⡛⣡⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⡇⠀⠤⠄⠀⠐⠂⠿⠾⠷⠾⡒⠓⢴⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠐⠛⠿⡿⠿⠿⣿⡟⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⣉⣉⣡⣩⣬⣙⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⣶⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣽⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡦⠐⠢⠍⠛⠛⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣤⡆⣿
⣤⣦⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⣶⣶⣶⣶⣦⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⣻⡿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣂⣤⣹⣷⣤⣀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣉⣠⣤⣤⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠐⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⣍⣿
⣦⣶⣶⣶⣾⣿⣷⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠝⣧⠀⠀⠀⠀⠩⢷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢫⡉⠁⣀⣀⠀⠞⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⣉⡉⢉⣉⠉⠀⠤⢴⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠥⠀⠀⠀⣶⣶⣾⣿⣺⠛⣛⣛⣛⣛⣛⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣭⠋⠉⠀⠀⢩⡀⡀⠀⠀⠐⠈⠉⠙⣝⣶⠀⠐⠓⢰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣽⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⠀⠀⢀⣼⣉⣢⣀⣀⣤⣶⣾⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢳⡤⣼⣿⣿⣻⠿⢿⣿⣿⣿⣿⠍⡚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⡧⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⠆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⠻⠛⠉⠀⠂⠈⠉⠉⠀⠀⠀⠈⢻⣿⠉⠉⠛⠛⢿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⡗⣿⣿⣿⠟⠛⠁⠈⠁⠀⠀⠀⠀⠋⠅⢈⠃⠁⠹⣿⠛⢯⣋⢹⣿⣿⠻⠃⡈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿
⣻⣧⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠈⠙⠃⠀⠀⣷⣶⡤⣀⠀⠈⠻⢿⣿⣿⣿⣋⣉⣛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠈⠑⠄⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢤⠀⠀⠀⠀⢡⣴⣼⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠈⠯⠊⠡⣿⣿⣿⣿⣿⣿⣏⣻
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣛⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠋⢁⣀⡀⣀⣀⣀⢀⣀⡀⠀⢀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣟⣺
⣿⣼⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢁⣭⡿⠟⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢼
⣶⣶⣶⠘⠀⠀⠀⠀⠀⠸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣺⣿⣊⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣇⠠⠤⠄⠀⠐⠂⠿⠾⠷⠾⡒⠳⢴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠐⠛⠿⡿⠿⠿⣿⡿⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠙⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⠬⠁⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⢉⣁⣉⣬⣙⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⢿⣿⢿⣿⣶⣾⠶⠶⠾⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡹⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡦⠐⠢⠭⠛⠛⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⣛⣛⣉⣭⣭⣴⡆⣿
⣴⣤⡀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣶⣶⣶⣶⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣯⣿⣿⣿⣻⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣂⣠⣼⣷⣦⣀⠲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣠⣤⣤⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⠀⣀⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⣽⣿
⣦⣤⣶⣶⣿⣿⣷⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣴⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠞⣧⠀⠀⠀⠀⠩⢷⣎⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢹⡉⠁⣀⣀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⢉⡉⢉⣉⠉⠀⠤⢴⣿⣿⠿⣿⡟⢿⣿⡿⠿⣿⣿⣿⣿⣿⠅⠀⠀⠜⠣⠀⠀⠀⣶⣶⣿⣿⣻⠛⣛⣛⣛⣛⣛⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣭⠋⠁⠀⠀⢸⣄⡀⠀⠀⠀⠀⠈⡙⣹⣶⠀⠀⠂⢠⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣧⠀⠀⢀⣬⣉⣢⣄⣀⣠⣴⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⡸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢱⡤⣼⣿⣿⣻⠿⢿⣿⣿⣿⡯⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠛⠛⠉⠀⠂⠈⠁⠁⠀⠀⠀⠀⢹⣿⠉⠉⠛⠛⠿⠋⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⡇⣿⣿⣿⠟⠛⠉⠈⠁⠀⠀⠀⠀⠋⠄⢀⠃⠁⠸⣿⠛⠏⢋⢹⣿⣿⠻⠃⡈⠀⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠠⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿
⣻⣯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠈⠙⡃⠀⠀⣷⣶⡤⣀⠀⠈⠻⢿⣿⣿⣿⣋⣉⣛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠈⠁⠄⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽
⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢤⠀⠀⠀⠀⢡⣴⣼⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠈⠯⠈⠁⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣛⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠋⢉⣀⡀⣀⣀⣀⢀⣀⡀⠀⢀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣟⣺
⣯⣼⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢠⣭⡯⠟⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢾
⣶⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣺⡿⢋⣷⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⡇⠀⠤⠄⠀⠐⠀⠿⠾⠷⠾⡒⠳⢴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠐⠛⠻⡿⠿⠿⣿⡟⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⢉⣁⣩⣬⣙⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⣶⣾⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣹⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡦⠒⠢⠍⠛⠛⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣛⣛⣋⣩⣭⣥⣴⡆⣿
⣴⣦⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣷⣶⣾⣿⣿⣶⡶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣽⠿⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣰⣦⣿⣶⣄⡲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠒⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢽⣿
⣶⣤⣴⣶⣾⣿⣷⣾⣿⣭⣄⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⣀⣀⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠊⣿⠀⠀⠀⠀⠩⢷⣏⠁⣿⢸⣿⣿⣿⣿⣿⣿⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⡍⠁⣀⣀⠀⠟⠙⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⣉⡉⢉⣉⠉⠀⠤⠤⣿⣿⡿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠂⠀⠀⠐⠳⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣩⡏⠀⠀⠀⢩⣄⠀⠀⠀⠒⠘⠀⣉⣽⣿⠂⠀⠚⣀⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡀⠀⢀⣼⣥⣥⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣈⣉⣉⣉⣉⣉⣀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡷⠶⣼⣿⣿⣿⠛⠻⣿⣿⣿⣿⢿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣻⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠛⠋⠉⠐⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠉⠉⠛⠛⠿⠋⠛⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠉⠈⠀⠀⠀⠀⠀⠛⠄⢘⠁⠀⠸⣿⠻⢏⢋⢻⣿⣿⠻⠃⠀⠈⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠠⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠀⠈⠙⡋⠀⠀⢰⣶⡤⣀⠀⠈⠻⢿⣿⣿⣟⣋⣉⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠈⠁⠄⠀⠀⢀⡙⢻⡿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣶⣶⠀⠀⠀⠀⠈⠀⠀⢸⣿⣷⢤⠀⠀⠀⠀⢡⣶⣽⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠈⠐⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣛⣀⡀⢀⣀⣀⡀⣀⣘⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠋⢉⣀⡀⣀⣀⣀⢀⣀⡀⠀⢀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣟⣺
⣯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣽⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢩⣬⡯⠟⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣶⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣺⣿⣋⣴⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⡇⠀⠤⠄⠀⠐⠀⠿⠾⠷⠾⡒⠳⢴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠐⠛⠻⡿⠿⠿⣿⡟⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⢁⣬⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⢉⣁⣭⣬⣙⣫⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⡿⣿⣿⣿⣶⣾⠶⠶⠶⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣹⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡦⠒⠠⠍⠛⠋⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣛⣛⣋⣩⣭⣥⣴⡇⣿
⣴⣦⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣾⣿⣿⣶⡶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⣽⠿⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣰⣦⣿⣶⣤⡲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠒⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣧⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢽⡯
⣦⣤⣤⣶⣾⣿⣶⣾⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣴⣶⣦⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠊⢻⠀⠀⠀⠀⠩⢷⣏⠁⣿⢸⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠈⡍⠁⣀⡀⠀⠟⠛⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⣉⡉⢉⣉⠉⠀⠤⠤⣿⣿⠟⠿⣏⠻⠿⠿⠟⠻⠿⣿⣿⣿⡄⠀⠀⠔⠳⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣭⡏⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⣈⣱⣿⠀⠀⠚⢀⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣹⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡀⠀⢠⣾⣤⣥⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣺⣈⣉⣉⣉⣉⣉⣀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠶⣾⣿⣿⣿⠛⠻⢿⣿⢿⠟⠋⠁⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⡿⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠈⠛⠛⠿⠋⠙⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠉⠈⠀⠀⠀⠀⠀⠛⠄⢘⠁⠀⠸⣿⠻⢏⢋⢻⣿⣿⠻⠋⠀⠈⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠈⠙⣛⠀⠀⢰⣶⠤⣀⠀⠈⠻⢿⣿⣿⣗⣋⣉⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠈⠁⠄⠀⠀⢀⡙⢻⡿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⣶⣶⠀⠀⠀⠀⠈⠀⠀⢸⣿⣶⢤⠀⠀⠀⠀⢡⣶⣽⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠈⠐⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣘⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠋⢉⣀⡀⣀⣀⣀⢀⣀⡀⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣗⣺
⣯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢩⣬⡯⠟⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣿⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣸⡿⣊⣴⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⡇⠀⠤⠤⠀⠐⠈⠿⠾⠷⠾⡒⠳⢴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠐⠛⠻⡿⠿⠿⣿⡿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣛⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⠬⠁⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⢉⣁⣩⣬⡙⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⢿⣿⣿⣿⣶⣶⠶⠶⠶⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡆⠒⠠⠝⠛⠋⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣛⣛⣋⣩⣭⣥⣴⢃⣿
⣤⣤⡀⠀⠀⠘⠻⠛⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣾⣿⣿⣶⡶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢼⣷⣿⣿⣿⣽⠿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣰⣦⣿⣷⣤⡲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣧⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢹⡏
⣶⣤⣴⣶⣾⣷⣶⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣴⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠊⢻⠀⠀⠀⠀⠩⢷⣏⠁⣿⢹⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⡍⠁⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⣉⡉⢉⣉⠉⠀⠤⠤⣿⣿⠿⢿⣿⠻⠿⠟⠛⠿⢿⣿⣿⣿⠅⠀⠀⠐⠳⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣩⡇⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⢀⣈⣼⣿⠀⠀⠒⢀⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣻⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡄⠀⢠⣾⣤⣤⣤⣤⣴⣶⣿⣿⣿⡿⣿⣿⣧⣺⣿⣿⣿⣿⣿⣿⣿⣺⣈⣉⣉⣉⣉⣁⣀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡯⠔⣿⣿⣿⣿⠛⠻⢿⣿⣿⠿⠛⢑⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣟⣿⠂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠉⠈⠛⠛⠟⠋⠛⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠈⠈⠀⠀⠀⠀⠀⠋⠄⢘⠉⠀⠻⣿⠛⢏⢋⢻⣿⣿⠻⠛⠀⠘⡿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣹⢽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠀⠈⠙⣛⠀⠀⢰⣦⠤⣀⠀⠈⠻⢿⣿⣿⣗⣋⣉⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠈⠁⠄⠀⠀⢀⡙⢿⡟⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣶⣶⠀⠀⠀⠀⠘⠀⠀⢸⣿⣶⢤⠀⠀⠀⠀⢡⣶⣽⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠈⠐⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣘⢛⣉⣈⣀⣀⡀⣀⣘⡛⢛⣛⡛⠛⢉⣀⡀⣀⣀⣀⢀⣀⡀⠀⠀⣠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣗⣻
⡯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢠⣬⣯⡟⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣷⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢹⡿⢋⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⠀⠤⠤⠀⠐⠈⠿⠶⠷⠾⡖⠓⣴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠐⠟⠹⡿⠿⠿⣿⣿⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣟⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⢉⣁⣉⣬⡙⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⢿⣿⣿⣿⣷⣶⠶⠶⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣺⣿⣿⣿⣿⢽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡆⠒⠠⠝⠛⠋⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢛⣛⣋⣩⣭⣥⣴⢡⣿
⣤⣄⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣾⣿⣿⣶⡶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣽⠿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣰⣦⣿⣶⣄⡲⠖⠂⠀⠀⣿⣿⣿⣿⣿⣉⣉⣀⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢹⡏
⣦⣤⣶⣶⣾⣷⣶⣿⣯⣭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣴⣶⣦⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠊⢻⠀⠀⠀⠀⠩⢷⣏⠁⣿⢹⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⡍⠀⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⢉⡉⢉⣉⠉⠀⠤⠤⣿⣿⠿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠐⠻⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣩⡏⠀⠀⠀⢸⡤⠄⠀⠀⠀⠀⢀⣉⣽⣷⠀⠀⠚⢀⣿⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣧⡀⠀⢠⣾⣥⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣺⣈⣉⣉⣉⣉⣉⣀⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠷⢖⣿⣿⣿⣟⠛⠿⣿⣿⣿⠿⠉⢉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⠂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠛⠉⠁⠀⠠⠈⠉⠀⠀⠀⠀⠀⢹⣿⠉⠉⠛⠛⠟⠋⠛⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠈⠈⠀⠀⠀⠀⠈⠋⠄⢘⠉⠀⢻⣿⠛⢏⢃⢻⣿⣿⡻⠟⠀⠘⣿⠿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⣹⢽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⠈⠈⠙⣛⠃⠀⢰⣦⠤⣀⠀⠈⠻⣿⣿⣿⣗⣋⣉⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⠁⠄⠀⠀⢠⡙⢿⣟⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠘⡀⠀⢰⣿⣶⢤⠀⠀⠀⠀⢡⣶⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠈⠸⣿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣘⢛⣉⣈⣀⣀⡀⣀⣘⡛⢛⣛⡛⠛⢉⣁⡀⣀⣀⣀⢀⣀⡀⠀⠀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣗⣻
⡯⣿⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠀⣨⣿⡿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣷⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢹⡿⢋⣴⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⠀⠤⠤⠀⠐⠈⠿⠾⠷⠾⡖⠓⢤⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠐⠛⠻⡿⠿⠿⣿⣿⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣟⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⣉⣁⣩⣬⣙⣫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⡿⣿⣿⣿⣷⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣚⣿⣿⣿⣿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡆⠒⠠⠝⠛⠛⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢛⣛⣋⣩⣭⣥⣴⢇⣿
⣤⣤⠀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣾⣿⣿⣶⡶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⡽⠿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣰⣦⣿⣷⣤⡲⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣷⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢽⡏
⣤⣤⣦⣶⣶⣷⣶⣾⣯⣭⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣴⣶⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⢻⡄⠀⠀⠀⠩⢷⣏⠁⣿⢸⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠈⣍⠁⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣀⣤⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⢉⡉⢉⣉⠉⠀⠤⠤⣿⣿⠿⡿⣿⠻⠿⠿⠿⠿⢿⣿⣿⣿⡇⠀⠀⠐⠛⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣉⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⣩⡏⠀⠀⠀⢸⣤⠄⠀⠀⠂⠀⠀⢈⣱⣿⠆⠀⠚⢀⣾⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣟⣻⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣿⣷⡀⠀⢀⣾⣭⣵⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣺⣈⣉⣉⣉⣉⣁⣠⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢶⣾⣿⣿⣟⠛⠿⣿⣿⣿⡿⠟⠊⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⢂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⣿⠉⠈⠛⠛⠟⠋⠙⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠈⠉⠀⠀⠀⠀⠈⠋⠄⢘⠉⠁⢻⣿⠛⢯⢋⢻⣿⣿⢿⠟⠂⠈⣿⠿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⢽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠈⠈⠙⣛⡇⠀⠀⣦⡤⣀⠀⠈⠻⣿⣿⣿⣗⣋⣉⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠑⠄⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⡯⣿
⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠈⠀⠀⢰⣿⣶⢤⠀⠀⠀⠀⢡⣶⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⠘⠸⢿⣿⣿⣿⣿⣿⣏⣿
⡇⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡈⣀⣘⢛⣉⣈⣀⣀⡀⣀⣈⡛⢛⣛⡛⠛⢉⣁⡀⣀⣀⣀⢀⣀⡀⠀⠀⣀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣗⣻
⣯⣿⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠀⣨⣽⣿⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣷⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢪⡾⡿⣡⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠠⠤⠀⠐⠀⠿⠶⠷⠾⡖⠓⢴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠐⠻⠺⡿⠿⠿⣿⣿⠇⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣟⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⣉⣁⣩⣨⣙⣫⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⣶⣶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢝⣿⣿⣿⣿⣹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡆⠒⠠⠝⠛⠛⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢛⣛⣋⣩⣭⣥⣴⡇⣿
⣤⣤⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣶⣾⣿⣿⣷⡶⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⡭⠿⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣴⣦⣿⣷⣦⣶⠒⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢽⡟
⣦⣤⣴⣶⣾⣷⣶⣿⣯⣭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣴⣶⣦⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠓⢹⡇⠀⠀⠀⠩⢷⣏⠁⣿⢸⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣫⠁⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣀⣤⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⢉⡉⢉⣉⠉⠀⠤⠤⢸⣿⠿⠿⣿⠛⠿⠿⠛⠿⢿⣿⣿⣿⡃⠀⠀⠀⠛⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣉⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣩⣎⠀⠀⠀⢸⣦⡄⠀⠀⠈⠁⠀⣈⣡⣿⡆⠀⠘⠂⣼⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⢠⣶⣦⣵⣤⣄⣰⣶⣾⣿⣿⣿⣿⣿⣭⣼⣿⣿⣿⣿⣿⣿⣿⣺⣈⣉⣉⣉⣉⣀⣠⡼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠶⢿⣿⣿⣿⠛⠛⢿⣿⣿⠿⠻⠋⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⠂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⠛⠛⠟⠋⠙⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⠀⠈⠋⠄⢘⠉⠀⢺⣿⠛⢯⢋⢻⣿⣿⣻⠿⠢⠈⣿⠿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠈⠈⠙⣟⡏⠀⠀⣦⡤⣀⠀⠈⠻⣿⣿⣿⣟⣋⣉⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠑⠄⠀⠀⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⡯⢿
⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠈⢂⠀⢰⣿⣶⢤⠀⠀⠀⠀⢡⣶⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⠘⠸⣿⣿⣿⣿⣿⣿⣏⣿
⡆⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡈⣀⣘⢛⣉⣈⣀⣀⡀⣀⣈⡛⢛⣛⡛⠛⢉⣁⡀⣀⣀⣀⢀⣀⡀⠀⠀⣀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣗⣺
⣯⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠀⣬⣽⢿⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣷⣶⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢪⡿⣟⣡⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠠⠤⠀⠐⠀⠿⠾⠷⠾⡖⠓⣴⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠛⠫⠾⠿⠿⣿⣿⡇⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⣟⣻⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⣭⠬⠡⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⡉⣁⣉⣬⣙⣩⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⢿⣿⣶⣶⠾⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢝⣿⣿⣿⣿⡽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡄⠒⠤⠝⠛⠛⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠾⠿⠟⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⣿⢛⣛⣋⣩⣭⣥⣴⢡⣿
⣤⣄⡀⠀⠀⠚⠿⠟⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣽⣶⣶⣿⣿⣷⣶⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢼⣷⣿⣿⣿⣽⠿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣶⣼⣿⣦⣶⠖⠂⠀⠀⣿⣿⣿⣿⣿⣈⣉⣀⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣨⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡄⠀⢀⣀⣿⣿⣿⡿⣿⢛⣛⣛⣋⣉⣭⣭⢹⡏
⣤⣤⣤⣶⣶⣶⣶⣿⣯⣽⡂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⣶⣠⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠸⣇⠀⠀⠀⠩⢷⣏⠁⣿⢹⢿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢩⡁⣀⡀⠀⠟⠙⠀⣿⣈⣉⣉⣁⣠⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⠉⡉⢉⣉⠉⠀⠤⠤⢸⣿⠿⠿⠿⡟⠻⠛⠛⠛⠿⣿⣿⣿⡧⠀⠀⠀⠚⠀⠀⠀⣶⣶⣿⣿⣻⢛⣛⣛⣛⣛⣋⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣩⣬⠀⠀⠀⠀⣷⡄⠀⠀⠈⠉⢀⣀⣰⣿⡇⠀⠐⠣⣸⣿⣿⣿⣿⣿⣿⣺⢸⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⠀⠈⣼⣷⣼⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣯⣔⣿⣿⣿⣿⣿⣿⣿⣾⣈⣉⣉⣉⣉⣉⣀⡼⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠻⢾⣿⣿⣯⡍⠛⠿⣿⣿⠿⠙⠉⡻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⢂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠉⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣻⠉⠉⠛⠛⠟⠋⠛⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⠀⠈⠛⠄⢘⠉⠀⢻⡿⡛⢿⢓⢻⣿⣿⢿⡿⠁⠈⣿⠿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣹⣽⣿⣿⣿⣿⣿⣿⣿⡗⣿
⣛⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠠⠈⠀⡀⠀⠀⠀⠃⠀⠀⠈⠈⠙⣟⣏⠀⠀⢠⡤⣀⠀⠈⠻⣿⣿⣿⣟⣋⣉⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠑⠄⠀⠀⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿
⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⠀⠀⠀⣴⣶⠀⠀⠀⠀⠙⢋⠀⢰⣾⣶⢤⠀⠀⠀⠀⢡⣴⣽⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠈⠻⠜⢸⣿⣿⣿⣿⣿⣿⣏⣿
⡆⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣀⣋⣀⡀⢀⣀⣀⡀⣀⣘⢛⣉⣈⣀⣀⡀⣀⣘⡛⢛⣛⡛⠛⢋⣁⡀⣀⣀⣐⢂⣀⡀⠀⠀⢀⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣗⣺
⣿⣽⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠈⢭⣽⡿⠟⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣵⣷⣶⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣲⣿⠟⣡⣾⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⢀⠠⠤⠀⠰⠀⠿⠾⠷⠾⡖⠓⣠⠴⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠄⠛⠛⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣟⣛⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠡⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⡉⣁⣉⣬⣙⣩⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⣷⣶⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢝⣿⣿⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡖⠂⠤⠙⠛⠛⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠾⠿⠗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⣛⣛⣉⣭⣭⣴⢰⣿
⣤⣄⡀⠀⠀⠒⠿⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣶⣶⣾⣿⣶⣶⠶⠤⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⠿⢸⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣶⣼⣿⣦⣶⡖⠂⠀⠸⣿⣿⣿⣿⣿⣉⣉⣉⣠⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢩⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⢀⣈⣿⣿⣿⡿⣿⠛⣛⣛⣛⣉⣩⣭⢹⡏
⣤⣤⣤⣶⣶⣶⣶⣿⣭⣿⡂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⣶⣠⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠊⣿⠀⠀⠀⠩⢷⣎⠁⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢸⡅⣀⡀⠀⠟⠛⠀⣿⣈⣉⣉⣉⣀⣤⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠉⠉⢉⡉⠉⠡⠤⠄⢸⡿⠏⠛⠻⡏⠛⠛⠛⠛⠻⠿⢿⣿⡧⠀⠀⠀⠚⠃⠀⠀⣶⣶⣿⣿⣻⠛⢛⣛⣛⣛⣛⣉⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⣡⣼⡀⠀⠀⠀⣶⢄⠀⠀⠈⠁⠁⣀⣠⣿⡟⠀⠐⠓⢠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⡀⢀⣾⣷⣶⣦⣤⣴⣾⣿⣿⣿⣿⡿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣁⠸⣿
⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡻⢻⣿⣿⣯⡍⠙⠻⣿⣿⠟⠁⠁⠌⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠈⢹⣿⣿⣿⣿⡿⣂⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢺⠉⠉⠟⠛⠟⠛⠻⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⣿
⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠈⢓⠀⢘⠉⠁⢺⡿⠛⣿⠕⢻⣿⣿⢿⣿⠁⠈⣹⠷⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⡧⣿
⣛⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⡃⠀⠈⠈⠈⠛⢟⣏⠀⠀⢠⡤⣀⠀⠉⠿⣿⣿⣿⣗⣋⣉⣻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠈⠁⠄⠀⠀⢀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿
⠹⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠃⠀⠀⠀⣤⣶⠀⠀⠀⠀⠙⣛⡀⢴⣾⣦⣤⠀⠀⠀⠀⣥⣴⢹⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠈⠻⠘⣽⣿⣿⣿⣿⣿⣿⣏⣿
⡄⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⣈⣀⠈⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡈⣃⣙⢛⣉⣈⣀⣀⡀⣀⣘⡛⢛⣛⡛⠛⢋⣉⡀⣀⣀⣐⢂⣀⡀⠀⠀⢀⣤⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣗⣻
⡯⣿⣿⣿⡿⠃⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠉⢍⣭⡿⠟⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣥⣷⣦⠘⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢲⣿⠟⣡⣾⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⢀⠀⠤⠀⠰⠈⠿⠶⠷⠾⠶⠓⢠⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠚⠛⠿⠿⠿⣿⣿⡟⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣟⣓⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠥⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⢉⣁⣉⣌⣙⣋⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⢿⣿⣷⣶⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⡿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡖⠠⠤⠛⠛⠛⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠾⠿⠗⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⠛⢛⣛⣋⣩⣭⣥⢸⣿
⣤⣄⠀⠀⠀⠲⠿⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣶⣶⣶⣶⣷⣶⣶⠶⠤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣿⡿⢸⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣶⣼⣿⣶⣶⠀⠀⢸⣿⣿⣿⣿⣇⣉⣉⣉⣁⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⢀⣸⣿⣿⣿⡿⡿⠟⢛⣛⣛⣋⣉⣭⢹⡏
⣤⣤⣤⣶⣶⣶⣶⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣴⣦⣀⣤⣤⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠸⣿⠀⠸⢩⢷⡞⠀⡇⣿⣿⣿⣿⣿⣿⣿⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢩⣀⣀⠀⠟⠃⠀⣇⣉⣈⣉⣉⣁⣀⣤⣼⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋⠉⣉⡉⠉⠭⢤⡄⢸⡿⠛⠉⠉⢹⠉⠉⠉⠉⠉⠛⠿⠿⢿⣂⠀⠀⠀⠚⠁⢘⣶⣶⣾⣿⡿⠟⠛⢛⣛⣛⣛⣛⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣶⣣⣼⣷⠀⠀⠄⣘⠓⠄⠀⠀⠀⣀⣤⣴⣿⣿⡀⠀⠚⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⣿⣿⣷⣶⣾⣿⣿⡿⠿⠿⢿⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣁⠸⣿
⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣏⠛⠿⠿⠟⠓⢈⠙⠻⠿⠿⠁⠀⠀⠂⠟⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⣿
⢻⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣂⠈⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿
⣾⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠘⢃⠀⢘⠉⠀⢻⡿⡛⣿⠔⣿⣿⣿⣿⣿⠀⠌⢙⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣿
⣛⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠈⠈⢛⢟⣏⡉⠀⠀⠤⣀⠀⠙⠿⣿⣿⣿⣟⣋⣛⣻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡈⠂⠀⠀⠀⢈⠻⣻⣿⣿⣿⣿⣿⣿⣿⠭⣿
⠘⡿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⠃⠀⠀⢀⣤⣄⠀⠀⠀⠀⠙⢽⡁⣤⣴⣦⡤⠀⠀⠀⠈⣭⣤⢻⣿⣿⣿⣿⣿⣷⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠘⠷⠈⣿⣿⣿⣿⣿⣿⣿⣗⣿
⠀⣶⣶⣿⣧⡀⠀⠀⠀⠀⠀⣊⣀⠉⣀⣀⡀⣀⡀⣀⣈⣋⣀⡀⢀⣀⣀⡈⣃⣙⢛⣉⣀⣀⣀⡀⣀⣘⡛⢛⣛⡛⠛⢋⣉⡀⣀⣀⡀⢛⣀⡀⣀⠀⠀⣠⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⡓⣿
⣈⣿⣿⣿⡟⠁⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠉⠉⣯⣽⠽⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛
⣭⣽⣆⠉⠀⠀⠀⠀⠀⢸⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢰⣿⡿⢫⣴⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡄⣀⠀⠠⠀⠤⠘⠿⠶⠷⠾⠶⠇⢠⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠘⠛⠳⠿⠿⣿⣿⣿⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣃⡀⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⣿⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠓⠛⠻⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣮⣿⣭⡬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⢉⢁⣉⣬⣙⣉⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⠷⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⣹⣿⣿⣿⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⡐⠠⠤⠛⠛⠛⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠾⠿⠇⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⠟⢛⣛⣋⣉⣭⣥⢸⣿
⣤⣄⠀⠀⠀⠺⠿⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⣉⣤⣶⣾⣿⣷⣾⣷⣶⡶⠤⢄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⡿⢸⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣦⣿⣶⣄⠀⢸⣿⣿⣿⣿⡇⢉⣉⣉⣁⣠⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣸⣿⣿⣿⣿⡿⠿⠛⣛⣛⣛⣉⣉⣹⡏
⣤⣤⣤⣶⣶⣶⣾⣯⣽⣟⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣴⣆⣀⣤⣤⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠈⣿⡿⢩⢿⡚⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⣈⠀⠟⠃⠀⣇⣉⣈⣉⣉⣉⣀⣤⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋⠉⣉⡉⠉⠭⢠⡄⣸⣿⣿⠁⠀⠀⣽⣄⠀⠀⠀⠈⠉⠙⠛⣛⣀⠀⠀⠠⠐⢹⣶⣶⣾⣿⡿⠿⠛⠛⣛⣛⣛⡛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣶⣣⣼⣿⣿⡄⠀⣵⣯⣬⣀⣀⠀⣤⣴⣶⣿⣿⣏⡀⠀⠐⠂⢸⣿⣿⣿⣿⡇⣿⣿⣿⠻⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠻⢿⣿⣿⣿⣿⠟⠏⠉⢻⣿⣿⣘⣿⣿⣿⣿⣿⣇⣉⣉⣉⣉⣉⣉⣁⢿⣿
⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣏⠉⠉⠉⠀⠰⠢⠉⠛⠋⠉⠀⠀⠀⠘⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿
⢻⢸⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣿
⣾⢸⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠘⠃⠀⠘⠉⠀⢻⠿⡛⣯⠎⣿⣿⣟⣿⣿⠀⠙⠙⠶⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿
⢛⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠋⢛⢟⡉⡙⠀⢀⠤⣀⠀⠙⢿⣿⣿⣿⣟⣋⠛⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠂⠀⠀⠀⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿
⠘⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⡅⠀⠀⢠⣤⡆⠀⠀⠀⠀⠙⣿⣇⣤⣴⣦⡤⠀⠀⠀⠈⣭⣬⢻⣿⣿⣿⣿⣿⣷⠸⠟⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠹⢷⠘⣿⣿⣿⣿⣿⣿⣿⣒⣿
⠀⣶⣶⣿⣦⠀⠀⠀⠀⠀⠀⣊⣀⠉⣀⣀⡀⣀⡀⣀⣘⣃⣀⡀⢀⣀⣀⡈⣛⣙⢛⣁⣀⣀⣀⡀⣀⣙⡛⢛⣛⡛⠛⢋⣉⡀⣀⣀⡀⢘⣓⡢⣄⡀⠀⢀⣤⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⡒⣿
⣬⣿⣿⣿⡟⠀⠀⠀⠀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠙⣢⣻⣯⡿⠟⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿
⣭⣿⡆⠃⠀⠀⠀⠀⠀⢹⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⡇⣿⣾⠿⣠⣶⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡀⣀⠀⠀⠀⠤⠸⠿⠾⠷⠾⠶⠇⢤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠗⠻⠛⠾⠿⣿⣿⣿⡿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⣿⣃⡀⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⢸⣿⣿⡇⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠓⠛⠻⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣶⣶⣿⣮⣿⣭⡬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⡈⡁⣉⣬⣙⣩⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⡿⣿⣷⡴⠶⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢾⣿⣿⣿⡍⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡐⠠⠌⠛⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠐⠶⠿⠇⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⡿⠟⢛⣛⣋⣉⣭⣥⢸⣿
⣤⣀⠀⠀⠀⠺⠿⠖⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⡁⣠⣴⣶⣿⣿⣿⣷⣿⣶⣶⠤⠄⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⡏⣾⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣦⣼⣶⣄⢸⣿⣿⣿⣿⡇⢉⣉⣉⣁⣠⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣛⣛⣛⣉⣉⣿⠉
⣀⣠⣤⣶⣶⣶⣾⣯⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣴⣄⣀⣤⣤⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠛⠘⣿⣯⣟⡚⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⠎⠀⠀⠀⠙⠑⠛⠃⠘⡇⣉⣉⣉⣉⣉⣀⣤⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣉⡉⠉⠍⢤⡀⣼⣿⣿⣧⠀⢀⠀⡿⡆⠀⠀⠀⠀⠈⠉⢏⣉⡀⠀⠀⠀⠤⣷⣶⣾⣗⡿⠿⠛⠛⣛⣛⣛⡛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣖⣢⣿⣿⣿⣿⣄⣰⣿⣷⣶⣤⣀⣀⣶⣶⣿⣿⢿⡁⠀⠀⠴⠄⣽⣿⣿⣿⡇⣿⣿⣿⠿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠏⠛⢿⣿⣿⣿⠟⠑⠀⠈⢺⣶⣆⢲⣿⣿⣿⣿⣇⣉⣉⣉⣉⣉⣉⣁⢿⣿
⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠃⠄⠉⠋⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿
⢹⢸⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⡂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿
⣾⢸⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠙⠂⠀⠘⠉⠀⢿⠿⢛⣏⠋⣿⣿⣟⣿⣿⠀⠹⠉⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿
⢛⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢈⠀⠀⠈⠁⠛⢛⢟⡁⣹⠀⢀⠄⣀⠀⠙⢿⣿⣿⣿⣟⡋⠛⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⣘⢻⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿
⠘⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⠀⠀⠀⢠⣤⡆⠀⠀⠀⠈⠉⣽⣏⣤⣤⣥⡤⠀⠀⠀⠈⣥⣬⢿⣿⣿⣿⣿⣿⣷⠸⠟⠛⠐⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡇⠀⠀⠀⠹⠧⢛⣿⣿⣿⣿⣿⣿⣿⣚⣿
⠀⣶⣶⣿⣦⠀⠀⠀⠀⠀⠀⣂⣀⠁⣀⣀⡀⣀⡀⣀⣉⣃⣀⡀⢀⣀⣀⡘⣛⣙⢛⣁⣀⣀⣀⡀⣀⣙⡛⢛⣛⡛⠛⢉⣉⡀⣀⣀⡀⢀⣛⡓⣦⣀⠀⢀⣠⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⢒⣿
⣤⣿⣿⣿⡟⠀⠀⠀⠀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠉⣲⣷⣷⣿⠝⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠿
⣭⣽⡆⠋⠀⠀⠀⠀⠀⢿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣷⣺⣾⡟⣋⣴⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⣀⠀⠀⠀⠄⠸⠿⠶⠷⠾⠶⠇⢤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠻⠛⠻⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣿⣃⡀⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⢸⣿⣿⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠛⠻⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⠈⡁⣉⣨⣙⣩⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⡿⢿⣷⢴⠶⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠨⣽⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡒⠠⠌⡛⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣶⡿⠆⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠟⢛⣛⣋⣩⣭⡅⣿⣿
⣤⣀⠀⠀⠐⠺⠿⠒⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣍⡁⠀⢀⣴⣾⣿⣿⣿⣿⣶⣶⣶⡤⠄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡇⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣥⣤⣌⣦⣼⣿⣿⣿⣿⡏⢉⣉⣉⣁⣠⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⢛⣛⣛⣛⣉⡉⣿⢩
⣠⣤⣤⣶⣶⣶⣾⣯⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣴⣄⣀⣤⣤⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠳⠌⣿⣿⡚⢸⡇⣿⣿⣿⣿⣿⣿⡇⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠻⡿⠛⠉⠙⠛⠿⣿⣿⣿⡿⠃⠀⠀⠀⠙⠛⠃⢸⡇⢁⣉⣉⣉⣉⣀⣤⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣙⡉⠩⠍⣠⡀⣿⣿⣿⣿⣷⠀⢠⣸⠛⠆⠀⠀⠀⠀⠀⠩⢉⣁⠀⠀⠀⠀⢀⣶⣾⣗⡿⠟⠛⢛⣛⣛⣛⡛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣖⣢⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⣶⣤⣼⣿⣿⣿⣿⢯⠀⠀⠠⠤⠀⣿⣿⣷⡇⣿⣿⣿⢿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠃⠉⢿⣿⣿⡿⠋⠂⠀⠀⢰⣶⠄⣶⣿⣿⡯⣇⣉⣉⣉⣉⣉⣉⣁⢿⣿
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠟⣻⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿
⢹⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⡂⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿
⣾⣿⣿⣿⡿⠟⠛⠉⠁⠈⠁⠀⠀⠙⡂⠀⡘⠉⠐⢿⠿⣛⢏⠋⣿⣿⣟⣿⣿⠀⠹⠋⢲⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿
⢛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠛⢻⣟⡁⣹⠀⢀⠄⣀⠀⠙⢿⣿⣿⣿⣟⡋⠛⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿
⠘⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⠀⠀⠀⢠⣤⡆⠀⠀⠀⠈⠫⣿⣏⣤⣤⣤⡄⠀⠀⠀⠈⣥⣬⣿⣿⣿⣿⣿⣿⣧⠿⠟⠛⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠹⠇⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿
⠀⣶⣶⣿⣦⠀⠀⠀⠀⠀⠐⣂⣀⠁⣀⣀⡀⣀⡀⣀⣙⣃⣀⡀⢀⣀⣀⡙⣛⣙⢛⣁⣀⣀⣀⡀⣀⣙⡛⢛⣛⡛⠛⢉⣉⡀⣀⣀⡀⢀⣛⡻⣦⣄⡀⢀⣠⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⢺⣿
⣠⣿⣿⣿⡟⠀⠀⠀⠀⣀⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠉⣰⣗⣵⣿⠟⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⢿
⣬⣽⡆⠃⠀⠀⠀⠀⠀⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡔⣿⣻⣿⡟⣃⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⠀⣀⠀⠀⠀⠄⠸⠿⠶⠷⠾⠶⠇⢤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠏⠬⠏⠻⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣟⣃⡆⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⢸⣿⣿⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠛⠻⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⢉⣁⣉⣨⣙⣩⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⡷⡴⠶⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⢿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⡀⠠⠌⡛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠆⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⡿⠟⢛⣛⣋⣩⣭⡅⣿⣿
⣤⡀⠀⠀⠐⠺⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣍⡁⠀⢀⣤⣾⣿⣿⣿⣿⣷⣶⣶⣦⡤⡀⠀⢺⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣤⣄⣲⣼⣿⣿⣿⣿⡏⢉⣉⣉⣁⣠⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⠟⢛⣛⣛⣛⣉⡉⣿⢩
⣠⣤⣤⣶⣶⣶⣾⣯⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣶⣄⣀⣤⣤⣶⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⠎⢿⣿⡋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠛⢿⠛⠉⠉⠛⠿⣿⣿⣿⣿⠇⠀⠀⠀⠘⠟⠃⢸⡏⣁⣉⣉⣉⣉⣀⣤⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠋⠉⣙⡉⠩⠉⣤⡀⣿⣿⡿⠿⣿⠀⢠⣠⡛⠇⠀⠀⠀⠀⠈⠉⢉⠁⠀⠀⠀⠀⣀⢱⣿⣷⡿⠟⠛⢛⣛⣛⣛⡛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣶⣖⣢⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣆⠀⠀⠀⢤⠀⣻⣿⣷⡇⣿⣿⣿⢿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠃⠉⠻⣿⣿⡿⠛⠉⠀⠀⢰⣶⡆⣦⣿⣿⡯⣇⣉⣉⣉⣉⣉⣉⣁⢿⣿
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣗⣺⣿
⠹⣿⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣷⡂⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠛⢿⡯⣿⣿⣿⣿⣿⣿⣿⣗⣺⣿
⣾⣿⣿⣿⡿⠟⠛⠉⠀⠈⠀⠀⠀⠙⡂⠀⡚⠉⠐⣿⢿⢛⢏⠋⣿⣿⣿⣿⣿⠀⠿⠓⢲⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⣿
⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠛⠻⣻⡉⣻⠀⢀⠀⡀⠀⠹⢿⣿⣿⣿⣟⡛⠛⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⢀⡈⢛⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿
⠘⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⠀⠀⠀⢠⣤⡆⠀⠀⠀⠈⠻⣿⣯⣤⣤⣤⡄⠀⠀⠀⠈⣥⣬⣿⣿⣿⣿⣿⣿⡇⡿⠿⠛⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠻⠆⢻⣿⣿⣿⣿⣿⣿⣿⣺⣿
⠀⣶⣾⣿⣦⠀⠀⠀⠀⠀⠐⣂⣀⠁⣀⣀⡀⣀⡀⣀⣙⣃⣀⡀⢀⣀⣀⡘⣋⣙⢋⣁⣁⣀⣀⡀⣀⣙⡛⢛⣛⡛⠛⢋⣉⡀⣀⣀⣀⢀⣛⡳⣦⣄⡀⢀⣠⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⢺⣿
⢠⣿⣿⣿⠟⠀⠀⠀⠀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠉⡢⣗⣷⣿⠝⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⢿
⣬⣽⡍⠁⠀⠀⠀⠀⠀⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡔⣷⣻⣾⡟⣃⣶⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⠀⣀⠀⠀⠀⠄⠸⠿⠶⠷⠾⠶⠅⢤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠏⠽⠋⠺⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⣿⣂⡆⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⢸⣿⣿⡇⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠛⠻⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⢈⢁⣉⣨⣙⣩⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⠷⡶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡫⡻⣿⣿⣿⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⠀⠤⢘⠻⠟⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠿⠀⠀⠀⠀⠀⠈⠉⣏⣿⣿⣿⣿⠿⠿⠛⣛⣛⣉⣭⡇⣿⣿
⣤⡀⠀⠀⠐⠾⠷⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣛⠁⠀⢀⣴⣶⣿⣿⣿⣿⣶⣶⣦⣄⣀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢇⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣷⣭⣅⣤⣰⣤⣿⣿⣿⣿⣿⠘⠉⣉⣉⣉⣀⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣛⣋⣹⡿⢩
⣀⣀⣤⣶⣶⣶⣯⣽⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣠⣤⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠳⠦⠹⣿⣟⠃⢸⢸⣿⣿⣿⣿⣿⣿⢸⡇⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠻⡟⠛⠙⠛⠻⢿⣿⣿⣿⠿⠃⠀⠀⠀⠻⠋⠀⢸⠘⢁⣉⣉⣉⣉⣁⣸⣧⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠩⢉⣁⠀⣿⣿⣿⣿⡗⠀⢄⣸⠿⡆⠀⠀⠉⠀⠉⠛⢛⢂⠀⠀⠀⢀⡀⣶⣾⣿⠿⠿⠟⠛⢛⣛⣛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣦⣤⣤⣴⣖⣠⣿⣿⣿⣿⣿⣤⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⡇⠀⠀⢠⡄⠘⣿⣿⣿⢸⣿⣿⣟⢿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠉⠙⠻⣿⣿⡿⠛⠁⠀⠐⣶⣶⠨⣼⣿⣿⣿⡈⠉⣉⣉⣉⣉⣉⡸⣿⣿
⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿
⠅⣿⣿⣿⣿⣿⡟⠉⢹⣿⣿⣿⣿⣿⡿⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⣿
⡆⣿⣿⣿⡿⠿⠃⠀⠊⠉⠉⠉⠉⠛⠀⠀⡟⠉⠘⣿⠿⣛⠯⠹⣿⣷⣿⣿⡇⠁⠿⠗⠲⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⢽⣿
⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠛⡿⣛⠉⣣⠀⢀⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢀⡛⢟⣿⣿⣿⣿⣿⣿⣿⡯⣽⣿
⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⠀⠀⠀⢠⣤⡀⠀⠀⠀⠉⠫⣿⣯⣤⣤⣄⠅⠀⠀⠀⢩⣭⡭⣿⣿⣿⣿⣿⣿⡆⡿⠿⠓⢰⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⠀⠀⠈⠿⡆⣻⣿⣿⣿⣿⣿⣿⣗⣺⣿
⢠⣥⣾⣷⡤⠀⠀⠀⠀⠀⠐⣀⣈⠁⣀⣀⡀⣀⡀⣈⣙⣃⣀⡀⢀⣀⣈⡙⣋⣛⢛⣁⣁⣀⣀⡀⣀⣛⡛⢛⣛⡛⠛⢋⣉⡀⣀⣀⡀⢘⣛⡳⣤⣀⠀⣀⣤⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣗⢺⣿
⣸⣿⣿⣿⠇⠀⠀⠀⠀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢑⣾⣵⣾⡯⠛⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠹⢿
⣭⣭⠙⠉⠀⠀⠀⠀⠈⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢜⣿⣿⢛⣠⣾⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⠀⣀⡀⠀⠠⠄⠻⠿⠾⠷⠾⠶⠁⢤⠤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠊⠟⠑⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣀⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⣿⠁⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠽⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⡬⡁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⠉⣈⣁⣉⣬⣙⣉⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⡿⢿⡿⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢝⣿⣿⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠠⠄⣘⠿⠟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣉⣭⢻⣿⣿
⣄⠀⠀⠀⠰⠶⠶⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡋⠀⠀⣠⣴⣶⣿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢸⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣠⣄⣦⣄⣿⣿⣿⣿⣿⠘⠉⣉⣉⣉⣀⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣋⢹⡏⣩
⣀⣀⣤⣶⣶⣾⣭⣿⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣤⣤⣤⣤⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠷⠌⢿⣿⡟⠃⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⠛⠛⠛⠛⠿⣿⣿⣿⣿⠚⠀⠀⠀⠘⠿⠓⠀⣿⠘⠉⣉⣉⣉⣉⣁⣸⣧⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠉⢉⣉⠀⣿⣿⣿⣿⡆⠀⢄⡿⢷⢀⠀⠈⠀⠈⠙⠛⢛⡂⠀⠀⠀⣀⢰⣶⣾⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣭⣤⣤⣴⣒⣠⣿⣿⣷⣿⣧⣴⣿⣿⣿⣶⣤⣀⣿⣶⣾⣿⡆⠁⠀⠀⢠⡀⢸⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠻⠛⠉⠛⢿⣿⣿⡿⠋⠁⠀⠰⣆⡆⢡⣿⣿⣿⣿⠘⠉⢉⣉⣉⣉⣉⡸⣿⣿
⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿
⠇⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⡯⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿
⡎⣿⣿⣿⡿⠿⠃⠐⠈⠉⠉⠉⠉⠓⠀⠀⠎⠉⠸⣿⠿⣟⠏⢹⣿⣷⣿⣿⡇⠈⠿⡖⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿
⢇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠁⠘⠛⡿⣛⠉⣧⠀⢀⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⢀⡛⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿
⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⠀⠀⠀⣀⣤⠀⠀⠀⠀⠉⢭⣿⣯⣤⣤⣄⠁⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⣿⡆⡿⠿⠛⢰⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀⠈⠿⠜⣻⣿⣿⣿⣿⣿⣿⣗⣻⣿
⢠⣤⣼⣷⡄⠀⠀⠀⠀⠀⠐⣀⣘⠁⣀⣈⡀⣀⡀⣈⣙⣂⣀⡀⢀⣀⣈⡙⣋⣛⢛⣁⣀⣀⣀⡀⣀⣛⡛⢛⣛⡛⠛⢋⣉⡁⣀⣀⡀⢘⣛⡲⣄⡀⠀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡗⣺⣿
⣸⣿⣿⣿⠇⠀⠀⠀⠀⢀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢳⣞⣷⣼⠟⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠹⢿
⣭⣭⠙⠉⠀⠀⠀⠀⠘⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢺⣿⡟⢃⣴⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⢀⡀⠀⠠⠄⠿⠿⠶⠷⠾⠶⠁⢤⠤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠨⠟⠰⠿⠿⣿⣿⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣀⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠽⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⣶⣶⣮⣿⣭⣬⡅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⢉⣉⣁⣩⣨⣙⣉⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⣿⣿⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⢿⣿⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠠⠄⡚⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢶⡶⠷⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⡿⠿⠿⠛⣛⣛⣉⣭⢹⣿⣿
⣄⠀⠀⠀⠲⠾⠶⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⡋⠀⢀⣴⣶⣾⣿⣿⣷⣶⣶⣤⣀⡀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣤⣄⣰⣄⢸⣿⣿⣿⣿⡇⠋⠉⣉⣉⣉⣠⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⠿⠿⠛⢛⣛⣛⣉⣻⡏⣭
⣀⣤⣴⣶⣶⣮⣭⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣠⣤⣦⣤⣤⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠆⢻⣿⣽⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡟⠛⠛⠛⠻⢿⣿⣿⣿⡛⠁⠀⠀⠈⠿⠿⠘⠀⣿⠙⠈⣉⣉⣉⣉⣀⣼⣧⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⡛⠩⠉⢉⣉⢸⣿⣿⣿⡗⠀⢄⡼⠿⠂⠀⠀⠁⠀⠉⠉⣁⡀⠀⠀⠀⡀⣰⣶⣶⣿⣿⠿⠿⠟⠛⢛⣛⣛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣥⣤⣤⣴⣒⣸⣿⣿⣾⣿⣤⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⡗⠃⠀⠀⠠⡄⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⠛⠉⠙⠻⣿⣿⣿⠋⠀⠀⠀⣆⣆⢀⣿⣿⣿⣿⢿⠉⢉⣉⣉⣉⣉⣉⣸⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿
⢹⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⡍⠈⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⡿⠛⠻⣿⣽⣿⣿⣿⣿⣿⣿⣿⢒⣿⣿
⣼⣿⣿⣿⠿⠿⠂⠐⠈⠉⡉⠉⠉⢋⠀⠀⠋⠉⢹⡿⢿⣛⠟⢿⣿⣷⣿⣿⡏⠸⠿⠖⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿
⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⢀⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠘⠛⠿⣟⢙⣧⠀⡠⣀⠀⠉⠿⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠐⠄⠀⠀⣈⠛⣺⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿
⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠃⠀⠀⠀⣤⣤⠀⠀⠀⠀⠙⢭⣿⣯⣤⣤⣀⠀⠀⠀⠈⢫⣭⣽⣿⣿⣿⣿⣿⣿⢸⡿⠟⠓⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠀⠀⠸⢷⠸⣿⣿⣿⣿⣿⣿⣿⣓⣿⡿
⣬⣤⣿⣦⡄⠀⠀⠀⠀⠀⠔⣀⣈⠁⣀⣀⡀⣀⡀⣉⣙⣀⣀⡀⢀⣀⣈⡛⣛⣛⢋⣈⣀⣀⣀⡀⣈⣛⡛⢛⣛⡛⠛⢋⣉⡀⣀⣀⣀⢛⣓⡂⣀⡀⣠⣴⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⡓⣿⣿
⣼⣿⣿⡿⠃⠀⠀⠀⠀⣀⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣼⣮⣶⡯⠛⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠻⣿
⣭⣍⠉⠁⠀⠀⠀⠀⢸⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣿⡿⢋⣠⣾⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⣀⡀⠀⠠⠈⠿⠿⠶⠷⠾⠶⠡⢤⠤⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠠⠟⠁⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢧⣠⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⣿⠁⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⠿⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⣬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⠉⡉⡈⣁⣉⣌⣙⣩⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⠿⢿⣷⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⢜⢿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠠⠄⡛⠟⠛⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢶⠾⠇⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⡿⠿⠟⢛⣛⣋⣩⡍⣿⣿⣿
⣀⠀⠀⠀⠲⠿⠖⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⡉⢀⣠⣶⣶⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣥⣤⣨⣦⡀⢸⣿⣿⣿⣿⡇⠋⢉⣉⣉⣁⣠⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⡿⠿⠟⠛⣛⣛⣛⡉⣿⢩⣭
⣠⣤⣴⣶⣶⣿⣭⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣤⣤⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠷⠘⣿⣯⢽⡚⠘⡇⣿⣿⣿⣿⣿⣿⡇⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⠛⠛⠛⠛⠿⣿⣿⣿⡟⠊⠀⠀⠀⠹⠇⠟⠁⠀⡇⠉⣉⣉⣉⣉⣁⣀⣿⣤⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⢛⡛⠩⠉⣉⡀⢸⣿⣿⣿⠂⠠⣀⡿⠇⠀⠀⠈⠑⠈⠉⣉⢁⠀⠀⠀⠀⠀⣶⣶⣾⣷⡿⠿⠟⠛⢛⣛⣛⡛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣤⣤⣤⣶⣂⣸⣿⣷⣿⣧⣼⣿⣿⣿⣦⣤⣠⣾⣿⣿⣿⠶⠀⠀⠀⢴⡀⣿⣿⣿⣿⡇⣿⣿⣿⠿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠛⠃⠉⠛⢿⣿⢿⡟⠋⠀⠀⠰⣬⡂⣸⣿⣿⣿⣿⣇⠉⣉⣉⣉⣉⣉⣁⢿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿
⢸⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿
⢸⣿⣿⣿⠿⠿⠀⠀⠉⠉⡉⠉⠙⠃⠀⢸⠋⠁⢻⡿⢟⣻⠌⣿⣿⣾⣿⣿⠈⢰⠿⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿
⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠈⠚⢛⢟⣋⢙⣤⠀⡤⣀⠀⠙⢿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠂⠀⠀⠀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿
⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠃⠀⠀⠀⣤⣤⠀⠀⠀⠈⢙⣽⣿⣯⣤⣤⣠⠀⠀⠀⠈⣭⣭⢹⣿⣿⣿⣿⣿⣷⢸⠿⠟⢰⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡇⠀⠀⠀⠀⠹⠷⢺⣿⣿⣿⣿⣿⣿⣿⣚⣿⣿
⣬⣴⣿⣦⠀⠀⠀⠀⠀⠀⠖⣀⣉⠀⣀⣀⡀⣀⡀⣉⣙⣀⣀⡀⢀⣀⣈⡛⣛⣛⢋⣈⣀⣀⣀⡀⣘⣛⡛⢛⣛⡛⠛⢋⣁⡀⣀⣀⣘⢛⣓⡀⣀⣀⣤⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣒⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⢀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣴⣷⣶⠟⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⢿
⣭⡍⠋⠁⠀⠀⠀⠀⢹⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣿⡟⣁⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠈⢀⣀⠀⠀⠤⠸⠿⠿⠶⠷⠾⠆⠡⢤⠤⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠤⠋⠸⡿⠿⠿⣿⣿⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢇⣠⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⡏⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠯⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣮⣿⣭⣬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣈⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⢉⢉⣉⣡⣩⣬⣙⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⢿⣿⣷⡴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⡀⠠⠌⠛⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠰⠶⠿⠆⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⡿⠿⠛⣛⣛⣉⣭⡍⣿⣿⣿
⡀⠀⠀⠐⠻⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⡁⣠⣴⣶⣿⣿⣿⣷⣶⣶⣦⠤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣤⣤⣷⣄⠀⢸⣿⣿⣿⣿⡏⠉⣉⣉⣉⣠⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⢿⡿⠿⠛⢛⣛⣛⣉⡉⣿⢩⣭
⣤⣴⣶⣶⣶⣾⣯⣽⣛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣶⣄⣀⣤⣤⣶⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠎⢻⣿⣭⣿⡛⢸⡿⣿⣿⣿⣿⣿⣿⡇⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⡟⠀⠀⠀⠘⠏⠰⠛⠃⢸⡏⢁⣉⣉⣉⣉⣀⣤⣿⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣙⡉⠩⠉⢡⡀⣼⣿⣿⡗⠀⢄⣾⢿⢀⠀⠀⠉⠀⠉⣩⡭⠀⠀⠀⠀⠠⢰⣶⣶⣿⣗⡿⠿⠛⠛⣛⣛⣛⡛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣶⣢⣾⣿⣾⣷⣤⣿⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⠃⠀⠀⠰⢆⢸⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⠛⠉⠙⠿⣿⣿⡿⠟⠀⠀⠀⣷⣗⢤⣿⣿⣿⣿⣿⣇⣉⣉⣉⣉⣉⣉⡁⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣗⣻⣿⣿
⣿⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡟⠛⢻⡯⣿⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿
⣿⣿⣿⡿⠿⠛⠀⠀⠉⠉⡁⠀⠙⡀⠀⠘⠉⠐⢿⠿⣛⣏⠊⣿⣿⣞⣿⣿⠀⠀⠤⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠛⢻⢟⡋⣹⣤⢀⠄⣀⠀⠙⢿⣿⣿⣿⣟⡋⠛⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡎⠢⠀⠀⢀⣈⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽⣿⣿
⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⠙⣿⣿⣧⣴⣤⡤⠀⠀⠀⠈⣭⣬⢻⣿⣿⣿⣿⣿⣷⠸⠿⠂⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠇⠀⠀⠀⠀⠻⠇⢻⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿
⣤⣾⣿⣦⠀⠀⠀⠀⠀⠰⠂⣀⣉⠀⣀⣀⡀⣀⡀⣉⣁⣀⣀⡀⢀⣀⣉⡛⣛⣛⢁⣀⣀⣀⣀⡀⣙⣛⡙⢛⣛⡛⠛⢉⣀⡀⣀⣀⣛⢛⣂⡀⣀⣠⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣟⣺⣿⣿
⣿⣿⣿⡟⠀⠀⠀⠀⣀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣺⣶⡿⠛⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠿⣿
⣭⡍⠋⠀⠀⠀⠀⠀⢿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢿⢋⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣧⠀⣀⣀⠀⠀⠤⠸⠿⠿⠶⠷⠾⠆⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠤⠁⠿⡿⠿⠿⣿⡏⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣂⣦⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⠃⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠿⠿⠟⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⡌⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣉⣁⣉⣌⣹⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⡶⠴⠶⠶⠶⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⢽⡿⣿⣿⣿⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⠐⠠⠌⠛⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠰⠾⠿⠆⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡿⠿⠛⣛⣛⣉⣭⡍⣿⣿⣿
⡀⠀⠀⠐⠻⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⣁⣠⣶⣾⣿⣿⣿⣶⣶⣶⡤⢄⠀⠀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣴⣬⣶⡄⠀⢸⣿⣿⣿⣿⠘⢉⣉⣉⣉⣀⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣼⣿⣿⣿⢿⡿⠿⠛⢛⣛⣛⣋⣹⣿⢩⣭
⣤⣴⣶⣶⣶⣿⣯⣽⣓⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣶⣄⣀⣤⣤⣶⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠈⣿⡟⣭⣿⠋⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⠟⠛⠛⠻⢿⣿⣿⣿⡟⠉⠀⠀⠀⠙⡇⠸⠛⠃⢸⡏⣁⣉⣉⣉⣉⣀⣬⣷⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣙⡋⠩⠍⣡⠀⣿⣿⣿⡄⠀⢀⠿⢷⠀⠀⠈⠐⠈⠉⢉⣍⡀⠀⠀⠀⠤⣳⣶⣶⣿⣿⡿⠿⠛⠛⣛⣛⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣶⣖⣢⣿⣷⣿⣧⣠⣿⣷⣾⣶⣤⣀⣾⣷⣿⣿⡯⡁⠀⠀⠶⡄⣹⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠉⠛⢿⣿⣿⡿⠃⠀⠀⠸⣦⣇⣰⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⡰⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣗⣻⣿⣿
⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⡟⠛⢻⡯⣿⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿
⣿⣿⣿⡿⠿⠃⠀⠀⠉⠉⢁⠀⠉⠀⠀⠘⠉⠘⢿⠿⣛⢏⠋⣿⣿⣟⣿⣿⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢻⣟⡉⣹⣤⢀⠄⣀⠀⠙⢿⣿⣿⣿⣟⡋⠛⢻⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠈⠢⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽⣿⣿
⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⠋⣿⣿⣧⣴⣥⡄⠀⠀⠀⠈⣭⣬⣿⣿⣿⣿⣿⣿⡷⠿⠗⠀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⠀⠀⠀⠀⠿⠂⢿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿
⣥⣾⣿⣦⠀⠀⠀⠀⠀⢰⠂⣀⣁⠀⣀⣀⡀⣀⡀⣉⣃⣀⣀⡀⢀⣀⣙⡛⣛⣋⢁⣁⣀⣀⣀⡀⣙⣛⡛⢛⣛⡛⠋⢉⣀⡀⣀⣀⣛⢓⣀⡀⣀⣠⣴⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣟⣺⣿⣿
⣿⣿⣿⠏⠀⠀⠀⠀⣀⣘⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣦⣾⡯⠛⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠿⣿
⣽⡉⠉⠀⠀⠀⠀⠀⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢿⢋⣠⣾⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⠀⣀⣀⠀⠀⠄⠹⠿⠿⠾⠷⠾⠆⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠶⠠⠄⠁⠿⡿⠿⠿⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣀⣦⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⣸⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠿⠿⠟⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⡌⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣈⣁⣉⣌⣹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⠿⣿⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠜⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠒⠠⠌⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠆⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣉⣭⢻⣿⣿⣿
⡀⠀⠀⠐⠻⠟⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣏⣁⣤⣶⣾⣿⣿⣷⣶⣶⣦⠤⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣤⣤⣱⣦⡀⠀⣿⣿⣿⣿⣿⠘⠉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣿⣿⣿⣿⢿⠿⠿⠛⣛⣛⣛⣉⣹⡏⣭⣭
⣤⣴⣶⣶⣶⣾⣯⣽⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣶⣄⣀⣤⣤⣶⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠷⠙⣿⠟⣭⣷⠃⢸⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢙⡀⠸⠋⠁⢸⡈⣁⣉⣉⣉⣉⣀⣼⣧⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣙⡉⠉⠉⣥⠀⣿⣿⣿⠄⠀⠀⣿⣦⠀⠀⠀⠂⠍⠛⠛⣋⡀⠀⠀⠠⠼⣧⣶⣶⣿⣿⠿⠿⠛⠛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣶⣖⣤⣿⣧⣿⣄⣀⣾⣿⣶⣤⣀⣀⣤⣶⣶⣿⣿⠀⠀⠀⠶⡀⣿⣿⣿⣿⣿⣸⣿⣿⣟⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠙⠻⢿⣿⣿⣿⠛⠁⠀⠸⣾⣦⣿⣿⣿⣿⣿⣿⣎⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⡟⠛⢿⡯⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⠿⠟⠃⠀⠀⠉⠉⢁⠀⢉⠀⠀⡘⠉⠘⣿⠿⣛⠏⠛⣿⣿⣿⣿⣷⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠛⠻⣿⡉⣹⣤⢀⠄⡀⠀⠹⢿⣿⣿⣿⣟⡛⠛⣿⣿⣿⣿⣿⡎⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠈⠠⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠚⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⠫⣿⣿⣧⣴⣥⡄⠀⠀⠀⠈⣥⣬⣿⣿⣿⣿⣿⣿⡇⠿⠓⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠈⠿⢖⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿
⣵⣾⣷⡄⠀⠀⠀⠀⠀⢰⠂⣈⣁⠀⣀⣀⡀⣀⡀⣉⣃⣀⣀⡀⢀⣀⣙⡛⣛⣋⢁⣁⣀⣀⣀⡀⣛⣛⡛⢛⣛⡛⠋⢉⣀⡀⣀⣈⣛⢓⣀⡀⠀⣠⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣟⣺⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣀⣘⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣶⣾⠿⠛⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⠿⣿
⣽⠙⠉⠀⠀⠀⠀⠀⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢟⢃⣰⣾⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣇⠀⣀⣀⠀⠠⠄⠻⠿⠿⠾⠷⠾⠆⠥⢤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠔⠑⠿⠿⠿⠿⣿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠿⢿⣀⣦⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⡸⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠿⠿⠟⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⡌⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣍⠉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣉⣁⣉⣌⣽⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⢿⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⢝⢿⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠒⠠⠌⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠂⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠟⢛⣛⣛⣉⣭⢻⣿⣿⣿
⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣁⣴⣶⣿⣿⣿⣿⣷⣶⡤⠤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣴⣬⣷⣦⠀⠀⣿⣿⣿⣿⣿⠈⣉⣉⣉⣁⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠁⠀⢀⣀⣀⠀⠀⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣆⣿⣿⣿⣿⢿⠿⠟⠛⣛⣛⣛⣉⢹⡏⣭⣭
⣤⣴⣶⣶⣶⣾⣯⣽⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣶⣄⣠⣤⣤⣶⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠳⢹⡏⠏⣽⣷⠃⢸⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢃⠀⠸⠛⠁⢸⣈⣁⣉⣉⣉⣁⣠⣼⣧⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣉⡉⠩⠉⢤⠀⣿⣿⣏⠀⠀⠀⣹⣦⠀⠀⠐⠒⠪⠛⠛⡋⡀⠀⠀⠠⠚⢱⣶⣶⣿⣿⠿⠟⠛⣛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⣖⣄⣿⣧⣾⡀⢀⣴⣷⣤⣤⣀⣀⣠⣴⣶⣾⣿⡁⠀⠀⠶⢀⣿⣿⣿⣿⣿⢸⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⠟⠋⠁⢹⣿⣶⣾⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣷⡂⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠻⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⠿⠟⠃⠀⠀⠈⠀⠀⠀⢉⠀⠀⡚⠉⠐⣿⢿⢛⠏⠛⣿⣿⣿⣿⣧⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢀⠀⠀⠀⢀⠀⠀⠁⠁⠛⠻⣻⡉⣻⣤⢠⠄⡀⠀⠙⢿⣿⣿⣿⣟⣉⣙⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠉⠢⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠚⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⢫⣿⣿⣧⣶⣥⡄⠀⠀⠀⠈⣥⣬⣿⣿⣿⣿⣿⣿⡇⠿⠛⢰⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠀⠀⠀⠀⠈⠿⠖⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿
⣴⣾⣷⡄⠀⠀⠀⠀⠀⢰⠂⣈⣁⠀⣀⣀⡀⣀⡀⣙⣃⣀⣀⡀⢀⣀⣙⡛⣛⣋⢁⣁⣀⣀⣀⡀⣛⣛⡛⢛⣛⡛⠉⢁⣀⡀⣀⣘⣛⢒⣀⡀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣟⣺⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣀⣘⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢶⣾⠯⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⢿⣿
⣽⠙⠈⠀⠀⠀⠀⠀⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢝⢋⣰⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣇⢀⣀⡀⠀⠠⠄⠻⠿⠿⠾⠷⠾⡆⠥⢴⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠔⠑⠿⡿⠿⠿⣿⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠿⢿⣀⣦⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⡘⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠿⠿⠟⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⠌⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣉⣁⣉⣌⣽⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣷⡶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢜⢝⢽⣿⣿⡧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠒⠠⠬⠛⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠂⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠿⠟⢛⣛⣋⣩⣭⢻⣿⣿⣿
⡀⠀⠀⠘⠻⠟⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣍⣡⣶⣾⣿⣿⣿⣿⣶⣦⠤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣽⣶⣖⠀⠀⣿⣿⣿⣿⣿⠈⣉⣉⣉⣁⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠁⠀⢀⣀⣀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⣀⣿⣿⣿⣿⢿⠿⠟⢛⣛⣛⣛⣉⢹⡏⣭⣭
⣤⣶⣶⣶⣶⣾⣯⣽⣃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣶⣄⣠⣤⣤⣶⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⢿⠀⠋⣽⣷⠃⢸⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠘⣀⡀⠸⠛⠁⢸⣈⣁⣉⣉⣉⣁⣠⣼⣧⣤⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠋⠉⣉⡉⠩⠭⢤⠀⣿⣿⡏⠀⠀⠀⣹⣦⠀⠀⠀⠒⠫⠙⠛⣋⡀⠀⠀⠘⠃⣰⣶⣶⣿⣿⠿⠛⠛⣛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣶⣖⣤⣿⣿⣿⡀⠀⣱⣿⣤⣤⣄⣀⣴⣴⣶⣾⣿⡁⢀⠐⢦⣸⣿⣿⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⠗⠃⣿⣿⣾⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡍⠁⠈⠁⠀⠀⠠⠈⠛⠛⠉⠁⠀⠀⠘⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠁⠙⣿⣿⣿⣿⣿⣷⡂⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠛⠻⡟⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⠿⠟⠃⠁⠀⠈⠈⠁⡀⠉⠀⠀⡚⠉⠐⣿⢿⣛⠯⠛⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠛⠻⣻⣁⣹⣤⢀⠄⡀⠀⠙⢿⣿⣿⣿⣟⣙⣛⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠉⠢⠀⠀⢀⡉⢻⣿⣿⣿⣿⣿⣿⣿⡯⢽⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠚⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⢫⣿⣿⣷⣶⣥⡄⠀⠀⠀⠈⣥⣬⣿⣿⣿⣿⣿⣿⡇⠿⠛⢰⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠈⠿⠖⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿
⣤⣿⣷⡄⠀⠀⠀⠀⠀⠐⠂⣀⣁⠀⣀⣀⡀⣀⡀⣙⣃⣀⣀⡀⢀⣀⣙⡛⣛⣋⢁⣁⣀⣀⣀⡀⣛⣛⡛⢛⣛⡛⠉⢁⣀⡀⣀⣘⣛⢂⣀⡀⠀⣠⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣟⣺⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣶⣾⠯⠛⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⢿⣿
⣽⡙⠉⠀⠀⠀⠀⠀⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢟⢋⣰⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣇⢀⣀⣀⠀⠠⠄⠻⠿⠿⠾⠷⠾⠆⠥⢤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠔⠐⠿⠿⠿⠿⣿⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠿⢿⣀⣦⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠘⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠿⠿⠟⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣾⣿⣮⣿⡭⠌⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⡉⣉⣉⣁⣉⣌⣽⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⢷⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⠝⣽⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠤⢜⠛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠂⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣉⣭⢹⣿⣿⣿
⠀⠀⠀⠐⠿⠿⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣥⣶⣶⣿⣷⣶⣶⣶⡤⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣴⣮⣷⣶⡆⠀⠀⣿⣿⣿⣿⣿⠘⢉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡀⣀⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣛⣉⢹⡏⣭⣭
⣤⣴⣶⣶⣶⣿⣽⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣶⣄⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠺⡇⠈⡛⡭⣷⠃⢸⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢁⣀⠀⠸⠛⠀⢸⠈⣉⣉⣉⣉⣉⣀⣼⣧⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠉⣛⠋⠩⠉⣡⠀⣿⣿⡋⠁⠀⠈⣿⣄⠀⠀⠐⠒⠪⠙⠛⡋⡀⠀⠀⠚⡀⣡⣶⣶⣿⣿⠿⠟⠛⢛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣖⣆⣿⣽⡇⠀⠀⣤⣿⣬⣌⣀⡀⣤⣶⣶⣿⣿⣇⠀⡚⠂⣼⣿⣿⣿⣿⣿⢸⣿⣿⡟⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡟⠿⣿⣿⣿⡿⠋⠓⠉⣿⣧⣾⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⠈⠁⠉⠉⠉⠀⠀⡈⠛⠁⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠹⣿⣿⣿⣿⣿⣿⡂⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⡿⠿⠃⠀⠊⠉⠉⠉⠉⡉⠀⠀⡛⠉⠘⣿⠿⣛⠯⠻⣿⣿⣿⣿⡇⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠁⠛⠻⣻⡉⣳⣤⢀⠄⡀⠈⠹⢿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠑⠠⠀⠀⢀⡙⢻⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠚⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⠫⣿⣿⣧⣤⣥⡀⠀⠀⠀⠩⣭⣭⣿⣿⣿⣿⣿⣿⡇⠿⠛⢦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡇⠀⠀⠀⠀⠈⠿⠦⣿⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿
⣬⣿⣷⡄⠀⠀⠀⠀⠀⠀⠂⣈⣁⠀⣀⣀⡀⣀⡈⣉⣃⣀⣀⡀⢀⣀⣙⡛⣛⣋⢁⣁⣀⣀⣀⡀⣛⣛⡛⢛⣛⡛⠉⢁⣀⡀⣀⣘⣛⢂⣀⡀⠀⣠⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣟⣺⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣶⣿⠝⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⢿⣿
⣭⠙⠉⠀⠀⠀⠀⠀⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠟⢃⣴⣾⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⡇⠀⢀⣀⠀⠠⠄⠻⠿⠿⠾⠷⠾⠆⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠸⠿⠿⠿⠿⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡿⠿⣀⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠈⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠽⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡌⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣈⣁⣉⣈⣽⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⢿⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⠝⢵⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣆⠂⠤⢘⡛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⡶⠿⠆⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣉⣭⢹⣿⣿⣿
⠀⠀⠀⠐⠿⠷⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣥⣶⣶⣶⣶⣶⣶⣦⠤⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣶⣽⣶⣶⠆⠀⠀⣿⣿⣿⣿⣿⠘⢉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⣀⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣛⣉⢹⡏⣭⣭
⣤⣴⣶⣶⣶⣯⣽⣟⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣄⣀⣤⣤⣴⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⢿⠀⠈⡟⠉⠁⠀⢻⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⣀⣀⠁⠀⠀⠀⢸⠈⣉⣉⣉⣉⣉⣀⣼⣧⣬⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣛⠋⠭⠉⣁⠀⣿⡿⠋⠁⠀⠙⣧⡀⠀⠀⠀⠊⠙⠛⢛⣃⠀⠀⠐⠋⠀⣧⣶⣶⣿⣿⠿⠟⠛⢛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣴⣖⣆⣟⣻⠁⠀⠀⣼⣯⣡⣀⣀⢀⣤⣴⣶⣿⣿⡀⠀⠓⢠⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⣿⣿⣿⡿⢿⣿⣿⣿⣿⠟⠹⣹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⣿⣿⣿⡇⠋⠈⠙⠉⠉⠁⠀⠈⠛⠉⠁⠀⠀⠐⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠹⣿⣿⣿⣿⣿⣿⠆⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⡿⠿⠃⠀⠈⠉⠉⠉⢉⡉⠀⠀⡞⠉⠘⡿⠿⣛⠯⠻⣿⣷⣿⣿⡇⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠘⠀⠀⠁⠁⠛⠻⣻⡉⣳⣤⢀⢄⡀⠈⠹⣿⣿⣿⣿⡛⠛⠛⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠑⠀⠀⠀⢀⡙⢻⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠚⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⢫⣿⣿⣯⣤⣥⡀⠀⠀⠀⠩⣭⡍⣿⣿⣿⣿⣿⣿⡇⠿⠃⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠈⠿⠆⣿⣿⣿⣿⣿⣿⣿⣏⣿⡟⣿
⣨⣽⣷⡄⠀⠀⠀⠀⠀⠀⠆⣈⣁⠀⣀⣀⡀⣀⡈⣙⣃⣀⣀⡀⢀⣀⣙⡛⣛⣛⢁⣁⣀⣀⣀⡀⣛⣛⡛⢛⣛⡛⠋⢁⣀⡀⣀⣛⣓⢀⣀⡀⢀⣠⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣗⣺⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣴⡿⠝⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⣿⣿
⣭⠙⠉⠀⠀⠀⠀⠀⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠛⢃⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⡇⠀⢀⣀⠀⠠⠄⠻⠿⠿⠶⠷⠾⠄⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠺⠿⠿⠿⠿⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⡿⠿⣀⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠽⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣡⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⡉⣉⣉⣁⣩⣈⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⢿⣿⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⢽⣽⣿⣿⡧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣔⠀⠤⢘⠻⠛⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣉⣭⢹⣿⣿⣿
⠀⠀⠀⠒⠿⠷⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣶⣶⣶⣶⣶⣶⣤⠤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣮⣷⣦⡶⠆⠀⠀⣿⣿⣿⣿⣿⠘⠉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⣀⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣛⣋⢹⡏⣭⣭
⣤⣴⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣄⣀⣤⣤⣴⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠊⣧⠀⠉⠛⠉⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢉⢀⣀⠀⠀⠀⠀⢹⠘⢉⣉⣉⣉⣉⣀⣼⣧⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⣛⠋⠍⢉⣉⠀⣿⡿⠛⠁⠈⢻⡄⠀⠀⠀⠉⢭⠻⠿⣟⣀⠀⠀⠘⠃⠀⣧⣶⣶⣿⣾⠿⠿⠛⠛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣖⡀⣟⡇⠀⠀⢀⣼⣋⣂⡀⠀⢠⣠⣤⣴⣾⣏⠀⢐⠃⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⢿⣷⣿⣿⣿⣿⠋⢋⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⣿⣿⣿⡘⠋⠛⠛⠛⠋⠀⠈⠙⠋⠉⠁⠀⠀⠸⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⠂⠉⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠿⢿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⣾⣿⣿⡿⠿⠓⠐⠈⠉⠉⠉⢉⠉⠀⠀⡞⠉⠈⠿⠿⣟⠧⠹⣿⣷⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠛⠻⣻⡉⣣⣤⢠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠑⠀⠀⠀⢀⡙⢻⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠀⠛⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⢫⣿⣿⣯⣤⣅⡄⠀⠀⠀⢩⣭⡍⣿⣿⣿⣿⣿⣿⡆⠿⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠈⠿⠖⣿⣿⣿⣿⣿⣿⣿⣏⣿⡟⣿
⣉⣽⣧⡀⠀⠀⠀⠀⠀⠀⠆⣈⣁⠀⣀⣀⡀⣀⡈⣙⣃⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣁⣀⣀⣀⡀⣛⣋⡛⢛⣛⡛⠋⢁⣀⡀⣀⣛⣂⢀⣀⡀⢀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣗⣻⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣬⡯⠟⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⣿⣿
⣭⠹⠉⠀⠀⠀⠀⠈⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠛⣊⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⡆⠀⢀⣀⠀⠠⠄⠿⠿⠿⠶⠷⠾⠄⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠺⠿⡿⠿⠿⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⠿⣈⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣿⣮⣿⣭⡬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣡⣭⣭⣥⣭⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣉⣡⣩⣈⣝⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⡿⢿⠷⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠌⣿⣿⣿⣿⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣖⠂⠤⠙⠛⠛⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣋⣭⢹⣿⣿⣿
⠀⠀⠀⠒⠿⠗⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣵⣶⣶⣶⣶⣶⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣶⣽⣦⣤⠶⠆⠀⠀⣿⣿⣿⣿⣿⠙⠉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣛⣋⢹⡏⣭⣭
⣤⣶⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣄⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⢻⡄⠀⠉⠛⠉⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠃⢀⣀⠀⠀⠀⠀⣿⠘⢈⣉⣉⣉⣉⣀⣼⣧⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⢉⣁⠀⣿⠿⠛⠉⠻⣏⠋⠉⠉⠉⠙⠿⠿⠿⣇⠀⠀⠀⠛⠀⠀⣧⣶⣶⣿⣾⠿⠿⠛⠛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣖⣠⠿⠀⠀⠀⢀⣟⠣⠀⠀⠀⣀⣀⣤⣼⣿⡇⠀⠒⠄⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣄⣠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣛⢻⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⣿⠿⠙⠿⠿⠛⠃⠈⠙⠻⠛⠛⠉⠀⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⢻⣿⣿⣿⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⡂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠿⢿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣰⣿⣿⠿⠿⠃⠐⠈⠉⠉⠉⠉⠉⠀⠀⡟⠉⠘⢻⠿⣛⠧⢹⣿⣷⣿⣿⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠛⠿⣻⢉⣧⣤⢠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠑⠀⠀⠀⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠛⠀⠀⠀⢠⣤⡀⠀⠀⠀⠈⢫⣿⣿⣧⣤⣄⡄⠀⠀⠀⢩⣭⡍⣿⣿⣿⣿⣿⣿⠆⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⠀⠀⠀⠀⠈⠿⠜⣿⣿⣿⣿⣿⣿⣿⣏⣿⡟⣿
⣌⣩⣧⡀⠀⠀⠀⠀⠀⠀⠆⣈⣁⠀⣀⣀⡀⣀⡈⣙⣃⣀⣀⡀⢀⣈⣙⡛⣛⣋⢁⣁⣀⣀⣀⡀⣛⣋⡛⢛⣛⡛⠉⢀⣀⡀⣘⣓⣀⢀⣀⡀⢀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣗⣿⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⢽⣽⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣿⣿
⣭⠹⠉⠀⠀⠀⠀⠘⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠛⣥⣶⣿⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⡆⠀⣀⣀⠀⠠⠄⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠴⠶⠆⠀⠀⠾⠿⡿⠿⠿⡿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⡿⠷⣀⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣡⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣉⣡⣩⣨⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⠶⠴⠶⠶⠶⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢟⢿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣔⠂⠤⢙⠛⠛⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠰⡶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣋⣭⢹⣿⣿⣿
⠀⠀⠀⠒⠿⠗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⣵⣶⣶⣶⣶⣶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣦⣷⣦⣤⠶⠆⠀⠀⣿⣿⣿⣿⣿⠙⠉⣉⣉⣉⣁⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣋⢹⡏⣭⣭
⣤⣴⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣀⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠀⠀⠉⠛⠉⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠘⠃⢀⣀⠀⠀⠀⠀⣿⠘⢈⣉⣉⣉⣉⣁⣼⣧⣭⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⢉⣁⠀⣿⡿⠟⠛⠻⡟⠛⠛⠛⢛⣻⡻⣿⡿⠇⠀⠀⠐⠃⠀⠀⣦⣶⣶⣿⣾⠿⠿⠛⠛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣖⣠⢯⠀⠀⠀⢠⡿⠂⠀⠀⠀⣀⣁⣠⣼⣿⡁⠀⠒⣠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣀⣿⣿⣾⣷⣶⣾⣿⣿⣿⣿⡟⣻⣿⣧⣾⣿⣿⣿⣿⣿⣿⢿⣈⣉⣉⣉⣉⣉⣉⡸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⡿⠛⠻⢿⡿⠿⠎⠙⠻⢿⠿⠛⠁⠐⠠⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⠛⣿⣿⣿⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⡂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠿⠿⢿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣀⣿⣿⠿⠿⠃⠐⠈⠉⠉⠉⠉⡁⠀⠀⡟⠉⠘⢻⠿⣛⠧⢹⣿⣷⣿⣿⡇⠁⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠧⣿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠈⠀⠀⠁⠘⠛⠿⣛⢉⣧⣤⢠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠙⠛⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠑⠄⠀⠀⢀⡛⢿⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠻⠀⠀⠀⣠⣤⡀⠀⠀⠀⠉⢫⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡝⣿⣿⣿⣿⣿⣿⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠈⠿⠜⣿⣿⣿⣿⣿⣿⣿⣇⣿⡟⣿
⢠⣉⣥⡀⠀⠀⠀⠀⠀⠀⠆⣈⣁⠀⣈⣀⡀⣀⡈⣉⣃⣀⣀⡀⢀⣈⣙⡛⣛⣋⢁⣀⣀⣀⣀⡀⣛⣋⡛⢛⣛⡛⠉⢀⣀⡀⣙⣂⣀⢀⣀⡀⢀⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣗⣿⣿⣿
⣾⣿⣿⠇⠀⠀⠀⠀⣀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣽⣿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣿⣿
⣭⠙⠁⠀⠀⠀⠀⠸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠛⢡⣶⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⡄⠀⣀⣀⠀⠠⠄⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠴⠶⠄⠠⠀⠾⠿⡿⠿⠿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⡿⠷⣠⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠟⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣁⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⡉⣉⣉⣡⣉⢨⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⡿⣿⡶⠰⠶⠶⠷⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢕⣝⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣖⠂⠤⢙⠻⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠴⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠚⠿⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣾⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣁⣤⣽⣶⣄⡤⠴⠆⠀⠀⣿⣿⣿⣿⣿⠛⠉⢉⣉⣉⣁⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣛⢻⡏⣭⣭
⣤⣶⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣀⣀⣤⣤⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠽⡇⠀⠀⠉⠛⠉⠉⠀⣿⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢛⠀⠀⡀⠀⠀⠀⠀⣿⠙⠊⣉⣉⣉⣉⣁⣼⣧⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠫⠭⢉⣉⢸⣿⣿⠟⠟⡟⠛⠛⠛⠛⠛⡿⣿⣿⡿⠀⠀⠀⠞⠄⠈⠀⣦⣶⣶⣿⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣒⣠⡍⠀⠀⠀⣼⠦⠀⠀⠀⠀⣈⣀⣴⣿⣗⠀⠐⢆⣸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣇⣀⠀⣴⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢽⠘⣉⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⠺⠿⣿⣿⣿⠿⠙⠻⣿⣿⠿⠁⠀⠀⡻⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⠙⢻⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠈⣭⠉⠉⠿⠿⣿⡟⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣀⣸⣿⠿⠿⠃⠐⠈⠉⠉⠉⠉⡉⠀⠀⡞⠉⠘⡿⠿⣛⡏⢹⣿⣷⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠈⠀⠀⠉⠘⠛⡿⣛⢉⣧⣤⣠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠐⠄⠀⠀⢀⡛⢻⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠛⠀⠀⠀⣤⣤⠀⠀⠀⠀⠉⢩⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠘⢿⠘⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⠀⢈⣠⡀⠀⠀⠀⠀⠀⠀⠆⣈⣁⠀⣈⣀⡀⣀⡈⣛⣀⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡀⣛⣋⡛⢛⣛⡛⠉⢀⣀⡀⣂⣀⣀⢀⣀⡀⢀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣓⣿⣿⣿
⣤⣾⣿⠃⠀⠀⠀⠀⣀⣠⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣻⡻⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠋⢠⣶⣾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣿⡄⠀⣀⣀⠀⠠⠀⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠴⠶⠀⠄⠀⠾⠿⡿⠿⠿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⡿⠧⣠⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⢁⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣉⣡⣉⣬⣝⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⣿⣿⣿⣿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣔⠂⠤⠙⠿⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠶⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠺⠿⠗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣾⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣀⣬⣷⣦⣀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣿⠛⠉⢉⣉⣉⣁⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣛⢻⡏⣭⣭
⣤⣶⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣴⣀⣀⣤⣤⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢿⡀⠀⠀⠉⠛⠉⠉⠀⣿⢾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⡟⠀⠀⡀⠀⠀⠀⠀⣿⠙⠊⣉⣉⣉⣉⣁⣼⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⢉⣁⢸⣿⡿⠟⠿⡟⠿⠿⠟⠛⢻⡿⣿⣿⡧⠀⠀⠠⠻⠄⠈⠀⣦⣶⣶⣿⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣒⣸⠁⠀⠀⠀⣷⠄⠀⠀⠈⠀⠉⣀⣢⣿⡇⠀⠒⠄⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣄⠀⠀⣾⣷⣶⣶⣶⣴⣿⣿⣿⣿⣿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⢽⠘⢉⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⡟⠞⢿⣿⣿⣿⡏⠛⠿⣿⡿⠏⠚⠉⢜⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⠉⠙⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⡿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠐⣯⠉⠉⠿⠿⣿⡟⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⢄⣠⣿⠿⠿⠃⠐⠈⠉⠉⠉⠉⠉⠂⠀⡞⠉⠘⡿⢿⣛⡯⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠈⠀⠀⠉⠘⠛⡿⣛⢉⣧⣤⣠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠙⠛⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠐⠄⠀⠀⢀⡛⢻⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠛⠀⠀⠀⣠⣤⠀⠀⠀⠀⠉⢩⣿⣿⣧⣤⣌⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠘⢿⠘⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿
⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠂⣈⣁⠀⣈⣀⡀⣀⡈⣛⣀⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡀⣛⣋⡛⢛⣛⡛⠉⢀⣀⡀⣂⣀⣀⢀⣀⡀⢀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣓⣿⣿⣿
⣤⣴⣿⠃⠀⠀⠀⠀⣀⣰⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣿⡿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⠸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢟⢠⣶⣾⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⡄⠀⣀⣀⠀⠠⠄⠿⠿⠿⠶⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠴⠦⠠⠠⠀⠾⠿⡿⠿⠿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⡿⠧⣠⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⢁⣭⣭⣥⣭⣍⡁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⠁⣉⣉⣉⣡⣉⣬⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⡿⢿⠶⠰⠶⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣔⠂⠤⠘⠻⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠒⠿⠗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣠⣬⣷⣤⡀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣿⠛⠉⢉⣉⣉⣉⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣛⢻⡏⣭⣭
⣤⣴⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣄⣀⣠⣤⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⣷⠀⠀⠀⠉⠛⠩⠿⠇⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠸⠒⠀⠀⡀⠀⢰⠦⠀⣿⠘⠊⣉⣉⣉⣉⣁⣼⣧⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⢉⣁⣿⣿⡿⠿⠻⠛⠿⠿⠟⠛⠿⡿⣿⣿⠆⠀⠀⠸⠣⠄⠈⠁⣦⣶⣶⣿⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣒⣈⠁⠀⠀⢀⡷⠀⡀⠀⠈⠉⢋⣀⣬⣿⠂⠀⠲⢠⣷⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⢀⣾⣷⣴⣶⣶⣶⣿⣿⣿⣿⡟⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⢽⠘⢉⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⡟⠳⢻⣿⣿⣯⠝⠛⠿⣿⡿⠛⠋⠈⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⠋⠉⢻⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠁⢪⣭⠉⠉⠿⠿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡒⣿⣿⣿
⠂⣄⣼⠿⠿⠃⠐⠈⠉⠉⠉⠉⢉⠀⠀⡐⠉⠘⡿⠿⣛⡯⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠈⠀⠀⠉⠘⠛⠿⣛⢉⣧⣤⢠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠐⠄⠀⠀⢀⡛⢿⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⠚⠀⠀⠀⢠⣤⠀⠀⠀⠀⠉⢭⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⠘⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⠀⠀⢠⡀⠀⠀⠀⠀⠀⡀⠀⣈⣁⠀⣀⣀⡀⣀⡈⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡀⣛⣋⡛⢛⣛⡋⠁⢀⣀⡘⣂⣀⣀⢀⣀⡀⣠⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣗⣿⣿⣿
⣤⣤⣼⠇⠀⠀⠀⠀⣀⣸⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣟⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⠸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢁⣴⣶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⡄⠀⢀⣀⠀⠠⠄⠿⠿⠿⠶⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠆⠄⠀⠰⠿⢿⡿⠿⠏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⢁⣭⣭⣥⣭⣍⡁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⢁⣉⣉⣉⣡⣩⣬⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⡿⣿⠷⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣾⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣔⠢⠤⠘⠿⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠷⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣃⣠⣽⣶⣄⡀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣿⠛⠋⢉⣉⣉⣉⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣛⢻⡏⣭⣭
⣤⣶⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣄⣀⣠⣤⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⣇⠀⠀⠀⠉⠛⠩⠿⠇⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢙⠒⠀⠀⡀⠀⢴⠦⠀⣿⠘⠚⣉⣉⣉⣉⣁⣼⣧⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⢉⣉⣿⣿⠿⠛⠿⠻⠟⠛⠛⠻⠿⢿⣿⣿⠆⠀⠀⠜⠧⠄⠈⠁⣦⣶⣶⣾⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⣤⣴⣒⡏⠀⠀⠀⢸⠇⠀⡀⠀⠀⡈⣁⣰⣼⣿⠂⠐⠢⢸⣶⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣷⣄⠀⢰⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⢽⠘⠋⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⠛⠟⢿⣿⣿⡿⠉⠛⢿⣿⡿⠋⠊⠉⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⡟⠉⠹⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⢯⣭⠉⠉⠿⠿⣿⡿⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⠃⢀⣠⠿⠿⠃⠐⠈⠉⠉⠉⠉⢉⠀⠀⠐⠉⠘⣿⢿⣛⡏⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠈⠀⠀⠁⠘⠛⠿⣛⢉⣧⣤⢠⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡎⠀⠀⠐⠄⠀⠀⢀⡚⢿⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⠚⠀⠀⠀⢠⣤⠀⠀⠀⠀⠉⢯⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠜⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⣀⣈⠀⣀⣀⡀⣀⡈⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡀⣛⣋⡛⢛⣛⡋⠁⢀⣀⡙⣂⣀⣀⢀⣀⡀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣗⣿⣿⣿
⣤⣤⣴⠇⠀⠀⠀⠀⢀⣸⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⣻⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⠸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⢠⣴⣶⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⡄⠀⢀⣀⠀⠠⠄⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⠶⠠⠄⠀⠴⠿⠿⡿⠿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠁⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⢁⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⢉⢁⣉⣉⣉⣁⢩⣬⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⡿⢿⠶⠰⠶⠷⠷⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⣿⣿⣿⣿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣔⠠⠤⢘⠿⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠴⣶⠷⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠷⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣶⣶⣦⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣻⣿⣿⡿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣬⣳⣦⡀⠀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣿⠛⠋⢉⣉⣉⣉⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣛⢻⡏⣭⣭
⣤⣶⣶⣶⣾⣭⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢤⣤⣄⣀⣠⣤⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢿⡀⠀⠀⠀⠉⠛⠩⠿⠇⣿⢾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⡓⠒⠂⠀⡀⠀⢰⠦⠀⣿⠙⠊⣉⣉⣉⣉⣁⣼⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠍⢉⣹⣿⠿⠛⠛⡟⠛⠛⠛⠛⠻⣿⣿⣿⣿⠀⠀⠠⠛⠤⠄⠈⠁⣦⣶⣶⣾⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⣤⣴⡚⠀⠀⠀⠀⡿⠂⠀⠀⠀⣀⣉⣠⣼⣿⡗⠀⠒⡄⣷⣾⣿⣿⣿⣿⣿⣿⢿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢠⣾⣿⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠘⢋⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⡏⠛⠻⣿⡿⠿⠇⠉⠛⠿⡿⠟⠉⠉⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⡟⠉⢻⣿⠋⠉⢻⣿⣿⣿⣿⢿⣿⠇⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣭⣭⠉⠉⠿⠿⣿⡿⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⡒⣿⣿⣿
⡿⠃⢄⠼⠿⠂⠐⠈⠉⠉⠉⠉⠉⡀⠀⠰⠋⠘⢿⠿⣟⡯⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠸⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⠀⠀⠁⠘⠛⠿⣛⢉⣧⡤⢠⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠀⠀⠐⠄⠀⠀⢀⡚⢻⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠘⠀⠀⠀⢠⣤⠀⠀⠀⠀⠉⣯⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⠜⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣈⣁⠀⣀⣀⡀⣀⡈⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢃⣀⣀⣀⣀⡀⣛⣋⡛⢛⣋⡉⠀⢀⣀⡒⣀⣀⣀⢀⣀⡀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣗⣿⣿⣿
⣤⣤⡠⠆⠀⠀⠀⠀⢀⣸⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣰⣶⣾⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿
⣿⡄⠀⢀⣀⠀⠠⠄⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠶⠆⠠⠀⠠⠶⠿⢿⡿⠿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⡬⠁⢉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⢁⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⣁⣉⣉⣍⡁⣭⣬⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢪⣿⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣔⠠⠤⢘⠿⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢶⣶⠷⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣭⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⣾⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠛⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⣠⣬⣷⣤⡀⠀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣷⠛⠉⢉⣉⣉⣁⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣛⣻⡏⣭⣭
⣤⣶⣶⣶⣾⣯⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢤⣦⣀⣀⣤⣤⣦⣤⣤⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠮⣷⠀⠀⠀⠀⠉⠛⠩⠿⠇⣿⣾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠘⡐⠒⠀⠀⡀⠀⢲⠶⠀⣿⠙⠊⣉⣉⣉⣉⣁⣼⣧⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠋⠭⢉⣹⡿⠟⠛⢻⡙⠛⠛⠛⢛⣻⡿⡿⠿⡆⠀⠈⠜⠃⠤⠄⠈⠀⣤⣶⣶⣿⣾⠿⠿⠿⠛⢛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⣤⣴⠂⠀⠀⠀⣸⡟⠄⠄⠀⠀⣀⣠⣤⣿⣿⡃⠐⠲⢠⣶⣿⣿⣷⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣼⣿⣿⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠈⣉⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⡟⠋⠻⣿⠿⠟⠀⠈⠛⠿⠿⠛⠉⠃⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⠋⠛⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣭⠉⠉⠿⠿⣿⡿⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⠟⠠⠀⠾⠂⠐⠈⠉⠉⠉⠉⠉⡐⠀⢰⠊⠘⢻⠿⣛⡏⢹⣿⣷⣻⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⠀⠀⠀⠈⠀⠀⠉⠘⠛⠿⣛⢉⣧⡄⠠⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠻⠀⠀⠐⠄⠀⠀⢀⡚⢻⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠘⠀⠀⠀⢠⣤⠀⠀⠀⠀⠉⢭⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⡟⠘⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣈⣁⠀⣀⣀⡀⣀⡈⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡈⣛⣋⡛⢛⣋⡉⠀⢀⣘⡒⣀⣀⣀⢀⣀⡀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠿⢿⣿⣿⣿⣓⣿⣿⣿
⣤⣤⡀⠀⠀⠀⠀⠀⢀⣹⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⣹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣽⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣴⣷⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣿⣿⣿
⣿⡄⠀⢀⣀⠀⠠⠀⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠶⠆⠠⠀⠴⠶⠿⠿⡿⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣋⢸⡏⣿⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⢁⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⣁⣉⣉⣍⢡⣭⡌⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⠿⣿⠶⠴⠾⠷⠶⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⢑⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣔⠂⠤⢙⠟⠛⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢶⡶⠷⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣋⣭⢹⣿⣿⣿
⠀⠀⠀⠚⠿⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣬⣶⣄⡀⠀⠤⠶⠆⠀⠀⣿⣿⣿⣿⣗⠛⠉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣛⣋⣿⠏⣭⣭
⣤⣶⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣤⣀⣀⣤⣤⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⣧⠀⠀⠀⠀⠉⠋⠩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢉⠐⠛⠀⢀⣀⠀⠲⠶⠀⣿⠙⢈⣉⣉⣉⣉⣁⣿⣥⣭⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠉⠭⢉⣿⠟⠋⠉⣋⡉⠉⠉⠉⠙⢿⠿⠿⢟⡀⠀⠀⠘⠃⠤⠄⠀⠀⣦⣶⣶⣿⣺⠿⠿⠛⠛⣛⣛⣛⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⠃⠀⠀⠀⣺⡋⠀⠀⠀⢀⣀⣤⣼⣿⣏⠀⠐⠣⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣼⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣈⣉⣉⣉⣉⣉⣉⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⠙⠉⠻⠿⠛⠛⠀⠈⠙⠛⠛⠛⠁⡁⢸⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣚⣿⣿⣿
⣿⣿⣿⠛⢛⠋⠉⢻⣿⣿⣿⣿⣿⣿⡷⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⠟⠄⠀⠀⠐⠈⠉⠉⠉⠉⠁⢀⠀⠀⠊⠘⠻⢿⣛⡏⢸⣿⣷⣻⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠥⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠄⡀⠀⠀⠀⠀⠀⠉⠘⠛⡿⣛⢉⣧⡄⡠⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡎⠻⠀⠀⠑⠄⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠐⠃⠀⠀⠀⣤⠀⠀⠀⠀⠉⢭⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠩⠜⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣈⣉⠀⣀⣀⡀⣀⡀⣋⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢀⣀⣀⣀⣀⡈⣛⣋⡛⢛⣉⡁⠀⢀⣙⡂⣀⣀⣀⢀⣀⡰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⠿⣿⣿⣿⣿⣓⣿⣿⣿
⣤⣤⡀⠀⠀⠀⠀⠀⣀⣹⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⣿⣿⣿
⣿⡄⠀⣀⣀⠀⠠⠀⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠶⠀⠄⠀⠶⠶⠿⠿⡿⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⡿⠧⣠⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣡⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⠉⠉⡁⣉⣉⡉⣡⣭⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⠿⢿⠶⠰⠶⠶⠶⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣟⣿⣿⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣔⠂⠤⢙⠛⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢶⡶⠷⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠛⣛⣛⣋⣭⢹⣿⣿⣿
⠀⠀⠀⠚⠿⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣼⣶⣄⠀⠀⠤⠶⠆⠀⠀⣿⣿⣿⣿⣗⠛⠉⣉⣉⣉⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣛⣋⢻⡏⣭⣭
⣤⣶⣶⣶⣾⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢤⣤⣀⣀⣤⣴⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⣇⠀⠀⠀⠀⠁⠋⠩⠿⠇⣿⢻⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢙⠐⠚⠀⢀⣀⠀⢲⠶⠀⣿⠙⢈⣉⣉⣉⣉⣀⣼⣧⣭⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠉⠭⢉⣿⠟⠉⠉⣋⠉⠉⠉⠉⠙⡿⠿⠿⣟⡀⠀⠀⠘⠃⠤⠄⠀⠀⣦⣶⣶⣿⣺⠿⠿⠛⠛⣛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⠃⠀⠀⢀⣟⠃⡀⠀⠀⣠⣠⣴⣾⣿⣇⠀⠐⠢⣰⣾⣾⣿⣷⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣈⣉⣉⣉⣉⣉⣉⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⠈⠉⠻⠟⠛⠃⠀⠉⠛⠛⠛⠋⠈⡰⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⡟⠛⠋⠉⢻⣿⣿⣿⣿⣿⣿⣷⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⡿⠧⠀⠀⠐⠈⠉⠉⠉⠉⠁⠀⠂⠀⠞⠘⠻⢿⣛⡏⢸⣿⣷⣻⣿⡇⡀⠀⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠥⣿⣿⣿
⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠉⠘⠛⡿⣛⢉⣧⡄⡠⢀⡀⠈⠻⣿⣿⣿⣿⠛⠙⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⠿⠀⠀⠑⠄⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠀⠃⠀⠀⠀⣤⠀⠀⠀⠀⠉⢭⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡝⣿⣿⣿⣿⡿⠆⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣯⡜⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣈⣉⠀⣀⣀⡀⣀⡀⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢀⣀⣀⣀⣀⡈⣛⣋⡛⢛⣉⡁⠀⢀⣙⡃⣀⣀⣀⢀⣀⡰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠿⢿⣿⣿⣿⣿⣓⣿⣿⣿
⣤⣤⡀⠀⠀⠀⠀⠀⣀⣸⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡯⣿⣿⣿
⣿⡄⠀⣀⣀⠀⠠⠀⠿⠿⠿⠾⠷⠾⠠⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠶⠀⠀⠠⠶⠶⠿⠿⡿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿
⡿⠧⣠⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢻⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣡⣭⣭⣥⣭⣉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⢉⢉⣁⣉⣉⣉⣥⣭⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣖⠠⠤⢘⠿⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢴⣶⠶⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣾⣻⣿⣿⡿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠛⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣠⣄⣦⣄⠀⠀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣷⠛⠋⢉⣉⣉⣁⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣛⢻⡏⣭⣭
⣤⣴⣶⣶⣾⣭⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣤⣤⣴⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠽⣿⠀⠀⠀⠀⠉⠛⠩⠿⠇⣿⢾⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠹⠐⠒⠂⠀⡀⠀⢲⠶⠀⣿⠙⠚⢉⣉⣉⣉⣁⣼⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠫⠭⢉⡽⠉⠀⠘⣆⠀⠀⠀⠍⠙⠛⠛⢛⣓⠀⠀⠀⠜⠂⠤⠄⠈⠁⣦⣶⣶⣿⣾⠿⠿⠿⠟⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣤⣴⣔⡁⠀⢀⣼⣭⣠⣀⣀⣀⣤⣴⣶⣿⣿⡃⠀⠐⢦⣰⣶⣿⣿⣿⣿⣿⣿⣿⢿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⠿⣟⣻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠘⠋⢉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⣩⠿⢛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⣿⡟⠋⠉⢻⣿⣿⣿⣿⣿⣿⡿⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣽⣭⣭⠉⠉⠿⠿⣿⡿⠛⠿⣽⣿⣿⣿⣿⣿⣿⣿⢒⣿⣿⣿
⣿⣿⣿⠿⠀⠀⠐⠈⠉⠉⠉⠉⠃⠀⠀⠀⠖⠈⠻⠿⣟⡏⢸⣿⣷⣻⣿⡇⡀⠀⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠁⠘⠛⡿⣛⠉⣧⡄⠠⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡙⢿⠀⠀⠐⠄⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠁⠃⠀⠀⠀⣤⠀⠀⠀⠀⠉⢭⣿⣿⣧⣥⣄⠄⠀⠀⠀⢩⣭⡽⣿⣿⣿⣿⣷⠄⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡜⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⡤⠀⣈⣉⠀⣀⣀⡀⣀⡀⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡈⣛⣋⡛⢛⣋⡉⠀⢀⣛⡒⣀⣀⣀⢀⣀⡰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠸⣿⣿⣿⣿⣿⣿⣓⣿⣿⣿
⣿⣤⡀⠀⠀⠀⠀⠀⢀⣹⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠿⣿⠧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡯⣿⣿⣿
⣿⡀⠀⢀⣀⠀⠠⠀⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠶⠆⠐⠀⠰⠶⠶⠿⠿⡿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣿⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿
⠿⠿⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⠈⣡⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⠈⡉⣉⣡⣉⣉⣉⣥⡍⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⠷⠰⠶⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣽⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠠⠄⡚⠿⠟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢴⣶⠶⠄⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣉⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠶⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣻⣿⣿⡿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣃⣨⣠⣄⡀⠀⠤⠤⠄⠀⠀⣿⣿⣿⣿⣿⠛⠛⠉⣉⣉⣉⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠿⠿⠟⢛⣛⣛⢻⡟⣿⣿
⣤⣴⣶⣶⣾⣭⣿⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣤⣤⣤⣤⣴⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⣿⡆⠀⠀⠀⠉⠛⠩⠿⠇⣿⢺⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤⣶⣾⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠹⡗⠒⠂⠀⠀⠀⢲⠦⠀⣿⠘⠚⠋⢉⣉⣉⣉⣸⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠋⠉⢉⡙⠀⢀⢠⠷⠀⠀⠀⠀⠘⠉⢩⣭⣅⠀⠀⠀⠤⠇⠤⠄⠈⠁⣤⣴⣶⣾⣾⠿⠿⠿⠿⠛⠛⡛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣭⣤⣤⣿⣤⣀⣰⣿⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⡁⠀⠰⢆⢰⣶⣶⣾⣶⣿⣿⣿⣿⢽⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⠿⠉⠙⠻⢿⠿⠟⢿⠟⢿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠘⠛⠋⢉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠚⠛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠉⢻⣿⣿⣿⣿⠿⣿⣿⠁⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⣭⠉⠉⠿⠿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿
⣿⣿⣿⡿⠿⠐⠐⠈⠉⠉⠉⠉⠋⠀⠀⠠⠐⠈⠻⠿⣟⠯⢹⣿⣷⣿⣿⡇⠀⠀⠄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠁⠘⠛⠿⣛⠉⣧⡄⠀⠀⠀⠈⠿⣿⣿⣿⣿⠙⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⣿⠀⠀⠐⠀⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠙⢭⣿⣿⣧⣥⣌⠄⠀⠀⠈⢹⣭⡽⣿⣿⣿⣿⣿⠖⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⡜⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⡤⠀⣈⣉⠀⣀⣀⡀⣀⡀⣛⣂⣀⣀⡀⢀⣈⣙⡛⣛⣛⢃⣀⣀⣀⣀⡈⣛⣋⡛⢛⣋⡉⠀⢀⣛⡒⣀⣀⣀⢀⣀⡺⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠇⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣿⣿⡧⠀⠀⠀⠀⠀⠀⢹⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠿⢿⣿⡧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⣿⣾⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡯⣿⣿⣿
⣿⡀⠀⠀⣀⠀⠀⠀⠿⠿⠿⠶⠷⠾⠀⠡⢤⠤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠶⠂⠀⠀⠶⠶⠾⠿⠿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣻⣿⣿
⣿⠧⢨⣥⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠿
⠿⢿⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣶⣮⣿⣭⠬⠅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⠁⢈⢉⣉⣅⣉⣉⣩⣥⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⠷⠰⠶⠶⠶⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠅⠩⣯⣻⣿⣿⢼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠠⠄⣘⠿⠟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢴⣶⠶⠄⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣋⢹⣿⣿⣿
⠀⠀⠀⠲⠾⠷⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢰⣯⣿⣿⡿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣉⡀⣄⠀⠀⠤⠤⠄⠀⠀⣿⣿⣿⣿⣿⠘⠛⠉⣉⣉⣉⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣛⣛⢻⡟⣿⣿
⣤⣴⣶⣶⣾⣭⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣤⣤⣤⣤⣴⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢯⣿⡇⠀⠀⠀⠉⠛⠩⠿⠇⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠟⠀⠀⠹⠗⠒⠂⠀⠀⠀⢰⠶⠀⣿⠘⠚⠋⢉⣉⣉⣉⣸⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠋⠍⣉⣽⠀⠀⢀⡿⠆⠀⠀⠀⠀⠉⠩⣭⣅⠀⠀⠀⠠⢇⠤⠄⠈⠁⣦⣴⣶⣾⣾⠿⠿⠿⠿⠛⠛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣭⣤⣤⣷⣶⣄⣴⣿⣷⣾⣶⣤⣴⣿⣿⣿⣿⣿⡀⠀⠰⢆⢰⣶⣶⣶⣿⣿⣿⣿⣿⢽⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠟⠛⠛⠈⠉⠻⠿⠿⠻⠇⠙⠵⣿⣶⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠘⠛⠋⠉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠬⠛⠛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⢹⣿⣿⣿⣿⢿⣿⣿⠅⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣭⠉⠉⠿⠿⢿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⡿⠿⠓⠐⠀⠉⠉⠉⠉⠋⠀⠀⠠⠰⠊⠻⠿⣟⠫⢹⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠈⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠙⠛⠿⣛⠉⣣⡄⢀⠀⠀⠈⠻⣿⣿⣿⣿⠙⠛⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢻⣿⡀⠀⠐⠀⠀⠀⠀⡘⢻⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡉⠘⠀⠀⠀⣠⡀⠀⠀⠀⠉⢫⣿⣿⣧⣤⣌⡁⠀⠀⠈⢹⣭⡝⣿⣿⣿⣿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⣧⠄⠀⠀⠀⠀⠀⠤⠀⣈⣉⠀⣀⣀⡀⣀⡀⣙⣃⣀⣀⡀⢀⣈⣙⡛⣛⣛⢃⣀⣀⣀⣀⡀⣛⣋⡛⢛⣉⡉⠀⢀⣛⡂⣀⣀⡀⢀⣀⡺⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⠧⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣿⣿⣿⠆⠀⠀⠀⠀⠀⢸⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡕⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡧⢿⣿⣿
⣍⠹⠉⠀⠀⠀⠀⠸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡔⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡯⣽⣿⣿
⣿⡄⠀⠀⣀⠀⠠⠄⠿⠿⠿⠶⠷⠾⠀⠡⢤⠤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⠶⠀⠀⠀⠶⠶⠶⠿⠿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣺⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠾⠿⠿
⠿⠿⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣮⣿⣭⠬⠅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⢁⣈⣉⣉⣁⣉⡉⣭⣥⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⠷⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢌⢝⢝⣿⣿⡧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠤⣘⠻⠟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠄⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣉⢹⣿⣿⣿
⠀⠀⠀⠰⠾⠷⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣷⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠟⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⢉⡂⣀⠀⠀⠤⠤⠤⠀⠀⣿⣿⣿⣿⣿⠘⠛⠉⣉⣉⣉⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠿⠿⠟⢛⣛⣛⢻⡏⣭⣽
⣀⣤⣶⣶⣶⣭⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣤⣤⣤⣤⣴⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣜⣿⡇⠀⠀⠀⠉⠛⠩⠽⠇⢿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⡿⠟⠿⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠺⡗⠒⠂⠀⠀⠁⠴⡶⠀⢸⠘⠛⠋⢉⣉⣉⣉⣸⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠋⠍⣭⢽⠀⢀⣸⠿⠀⠀⠀⠀⠋⠉⢭⣭⡃⠀⠀⠀⣀⢇⠠⠄⠈⠁⣧⣴⣶⣾⣾⠿⠿⠿⠿⠛⠛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣯⣤⣤⣶⣶⣤⣾⣿⣿⣷⣦⣤⣼⣿⣿⣿⣾⡏⠀⠀⢠⡄⢸⣶⣶⣶⣶⣿⣿⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠃⠈⠙⠿⠿⠟⠛⠋⠁⢰⣶⣆⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠋⠉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠘⠿⢛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠙⣻⣿⣿⣿⠿⣿⣿⠅⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⡍⠉⠿⠿⢿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⡿⠿⠗⠐⠀⠈⠉⠉⠉⠋⠀⠀⠠⠰⠊⠻⠿⣟⠫⠹⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠈⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠁⠁⠛⠿⣿⡉⣣⡄⢀⢀⠀⠈⠻⣿⣿⣿⣿⠙⠛⠛⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⡇⠀⠐⠀⠀⠀⠀⡘⠻⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠘⠀⠀⠀⢠⡄⠀⠀⠀⠉⣫⣿⣿⣯⣤⣄⡄⠀⠀⠀⢹⣭⡍⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠈⠙⠃⠀⠀⠀⠀⠀⠈⣿⡆⢿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⣧⡄⠀⠀⠀⠀⠀⠠⠀⣈⣉⠀⣁⣀⡀⣀⡀⣈⣃⣀⣀⡀⢀⣈⣙⡛⣛⣛⢃⣁⣀⣀⣀⡀⣛⣋⡛⢛⣉⡁⠀⢘⣓⡀⣀⣀⣀⢀⣚⡻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠅⢸⣷⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡵⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⡧⢽⣿⣿
⣭⠹⠉⠀⠀⠀⠀⠘⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡔⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⡯⢽⣿⣿
⣿⡆⠀⠀⣀⠀⠠⠄⠿⠿⠿⠶⠷⠾⠀⠡⢤⠤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠶⠠⠄⠀⠴⠶⠶⠶⠿⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣺⣿⣿
⣿⠷⣈⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠿⠿
⠿⠿⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣮⣿⣭⡬⠅⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣍⡉⠁⠉⠁⠀⠙⠋⠁⠈⡁⣈⣉⣉⣁⣉⣩⣬⠁⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⣿⠷⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠔⠝⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠤⢘⠻⠟⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠄⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠒⠿⠷⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣷⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠟⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢉⡂⡀⠀⠀⠠⠤⠤⠀⠀⣿⣿⣿⣿⣿⠘⠛⠉⣉⣉⣉⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠿⠿⠟⢛⣛⣛⢻⡏⣭⣽
⣠⣤⣶⣶⣶⣭⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣤⣤⣤⣤⣴⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡹⣿⡆⠀⠀⠀⠉⠛⠩⠽⠇⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⡛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠂⠀⠁⢿⡗⠒⠂⠀⠀⠁⠰⡶⠀⢻⠘⠛⠋⢉⣉⣉⣉⣸⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠛⠛⢩⣭⡇⠀⢀⣘⠗⠀⠀⠀⠘⠁⠩⣽⣗⠁⠀⠀⠀⡀⡂⠤⠄⠈⠁⣧⣴⣶⣾⣾⠿⠿⠿⠿⠛⠛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣭⣤⣼⣿⣶⣤⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⡁⠀⠀⣤⠀⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⢸⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠀⠉⠻⠿⠟⠛⠁⠀⠰⢴⣴⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠋⠉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⡇⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠉⢻⣿⣿⣿⠿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣭⡍⠉⠿⠿⢿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣿⣿⣿⡿⠿⠗⠐⠀⠈⠉⠉⠉⠋⠀⠀⠠⠠⠊⠻⠿⣟⠯⠹⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠈⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠛⡿⣿⡉⣣⡄⢀⢀⠀⠈⠻⣿⣿⣿⣿⠙⠛⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣿⣿⡇⠀⠐⠀⠀⠀⠀⡘⠻⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠘⠀⠀⠀⢠⡀⠀⠀⠀⠉⣫⣿⣿⣧⣤⣄⡄⠀⠀⠀⢹⣭⡝⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠀⠉⠛⠇⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⣧⡄⠀⠀⠀⠀⠀⠠⠀⣈⣉⠀⣁⣀⡀⣀⡀⣈⣃⣀⣀⡀⢀⣈⣙⡛⣛⣛⢃⣁⣀⣀⣀⡀⣛⣋⡛⢋⣁⡀⠘⢟⣃⡀⣀⣀⣀⢐⣛⡻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⣧⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⢀⣰⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡵⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⣿⣿⣿⣿⡧⢿⣿⣿
⣍⠹⠉⠀⠀⠀⠀⠘⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡔⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⡯⣽⣿⣿
⣿⡄⠀⢀⣀⠀⠠⠄⠿⠿⠿⠶⠷⠾⠀⠥⢤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠆⠤⠀⠰⠶⠶⠶⠶⠿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣺⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠋⣼⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠾⠿⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⢈⣥⣭⣭⣥⣉⠉⠁⠉⠁⠀⠙⠋⠁⢈⢁⢌⣉⣉⣅⣩⣭⡍⠁⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⠷⠰⠶⠶⠶⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠐⠗⡿⣿⣿⣿⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠤⠘⠻⠛⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢴⣶⠶⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠿⠿⠟⢛⣛⣛⣩⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠷⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⡀⢀⠀⠀⠀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣿⠛⠉⢉⣉⣉⣁⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣛⣛⢻⡏⣭⣭
⣠⣴⣶⣶⣶⣭⣽⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣠⣤⣤⣤⣤⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⡇⠀⠀⠀⠀⠉⠛⠩⠿⠇⣿⢸⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⡟⠛⠛⠿⢿⣿⣿⣿⣿⠿⠇⠀⠀⠸⡇⠐⠒⠂⠀⡀⠀⠲⠦⠀⣿⠘⠊⢉⣉⣉⣉⣁⣼⣇⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣛⠫⡽⠿⠀⢀⣸⡛⠆⠀⠀⠀⠉⠉⣭⣓⡀⠀⠀⠀⢀⠋⠀⠤⠄⠈⠀⣤⣴⣶⣾⣾⠿⠿⠿⠛⠛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣥⣤⣿⣿⣶⣿⣿⣿⢷⣶⣤⣼⣿⣿⣿⢟⡁⠀⠀⣠⠀⣭⣶⣶⣶⣾⣷⣿⣿⣿⣿⢿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠉⠉⠁⠈⠙⠿⠿⠛⠁⠀⠀⢴⣤⠄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠘⢉⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠉⠙⣿⣿⣿⣿⣿⣿⠇⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢾⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠒⣿⣿⣿
⣿⣿⣿⠿⠿⠁⠐⠀⠀⠉⠉⠉⠃⠀⠀⠠⠠⠊⠻⠿⣟⠏⢸⣿⣷⣿⣿⡇⡀⠀⠄⠀⢹⣿⣿⣿⣿⣿⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⡿⣛⠉⣧⡄⠀⢀⠀⠈⠻⣿⣿⣿⣿⠛⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⢻⣿⣿⣿⠀⠀⠐⠄⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠘⠀⠀⠀⢠⡀⠀⠀⠀⠉⢩⣿⣿⣧⣥⣄⠄⠀⠀⠀⢩⣭⡝⣿⣿⡿⢿⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡏⠀⠉⠛⠿⠀⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣈⣉⠀⣁⣀⡀⣀⡀⣘⣀⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡈⣛⣋⡉⢁⣀⡀⣿⢗⣀⡀⣀⣀⣒⢛⣛⡻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⡇⢸⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠜⢸⣿⡇⣿⣯⡿⢸⣯⡵⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠿⣿⣷⣿⣿⣿⡧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⣿⣿⣿
⣿⡀⠀⢀⣀⠀⠠⠀⠿⠿⠿⠶⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠶⠆⠄⠄⠰⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣿⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠾⠿⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⠁⣨⣥⣭⣭⣅⡉⠉⠁⠉⠁⠀⠙⠋⢡⣈⣡⣬⣉⣍⣡⣭⠉⠈⠁⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠐⣗⣟⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠤⠘⠻⠛⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⡶⠷⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣋⣩⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣾⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡋⢑⢀⡀⠀⠀⠀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣏⠛⠉⢉⣉⣉⣀⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣋⢻⡏⣭⣭
⣠⣴⣶⣶⣶⣯⣽⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣠⣤⣤⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⢿⣿⠀⠀⠀⠀⠀⠉⠛⠩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⣿⠛⠛⠻⠿⣿⣿⣿⣿⡿⠥⠀⠀⠸⣿⠀⠐⠒⠀⠀⣀⠀⢲⠦⠀⣿⠙⠈⣉⣉⣉⣉⣁⣼⣧⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⣛⠿⠿⠂⠀⣠⡟⠃⠀⠀⠀⠘⠈⢭⣽⡃⠀⠀⠀⠀⢈⠉⠀⠤⠄⠈⠀⣤⣶⣶⣿⣾⠿⠿⠟⠛⢛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣥⣿⣿⣶⣾⣿⣿⣿⣶⣤⣤⣾⣿⣿⣿⠏⠀⠀⢀⡄⢸⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⢿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠁⠀⠙⠿⠿⠿⠛⠁⠀⠀⣦⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠈⢉⣉⣉⣉⣉⣉⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡿⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠉⠉⠉⢿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣭⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⠿⠿⠁⠐⠠⠀⠈⠉⠉⠃⠀⠀⠀⠠⠊⠻⠿⣛⠏⢸⣿⣷⣻⣿⡇⠀⠀⠄⠀⢹⣿⣿⣿⣿⣿⣧⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⡿⣛⢉⣧⡄⠀⢀⠀⠈⠻⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠹⢿⣿⣿⣿⠀⠀⠐⠄⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠘⠀⠀⠀⢠⠀⠀⠀⠀⠉⢩⣿⣿⣧⣤⣄⠄⠀⠀⠀⢩⣭⡝⣿⡿⠟⣧⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠀⠀⠙⠻⠿⠀⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣈⣉⠀⣀⣀⡀⣀⡀⣈⣀⣀⣀⡀⢀⣈⣙⡛⣛⣛⢁⣀⣀⣀⣀⡈⣛⣉⡁⢀⣀⡛⣿⢆⣀⡀⣀⣐⣛⢛⣛⡻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢻⡇⢸⣿⣿⣿⣿⣿⣿⣓⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⢀⣀⡸⣿⣟⢣⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠊⢸⣿⡇⣿⣯⡿⢸⣯⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢿⣿⣷⣿⣿⣿⡧⣿⣿⣿
⣍⠉⠁⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡯⣿⣿⣿
⣿⡀⠀⢀⣀⠀⠠⠀⠿⠿⠿⠾⠷⠾⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠷⠠⠤⠀⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⣿⣿⣿
⡿⠧⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠓⠻⠿⠿
⠿⠿⠿⠿⠃⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⢁⣬⣥⣭⣭⣁⠉⠉⠁⠉⠁⠀⠙⠋⢁⣈⣡⣬⣉⣉⣥⡍⠉⠈⠁⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⠿⣿⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢑⣹⣻⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠤⣘⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢶⡶⠷⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠿⠿⠛⢛⣛⣋⣍⢹⣿⣿⣿
⠀⠀⠀⠲⠿⠷⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠟⡐⢄⠀⠀⠀⠀⠀⠤⠴⠆⠀⠀⣿⣿⣿⣿⣇⠛⠉⣉⣉⣉⣁⣤⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⠿⠟⠛⣛⣛⣛⣿⠋⣭⣭
⣤⣶⣶⣶⣾⣭⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣀⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡝⣿⣗⠒⠂⠀⠀⠀⠀⠉⠛⠩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⡟⠟⠿⠿⢿⣿⣿⣿⣿⣿⠏⠀⠈⠸⡟⠀⠀⠐⠒⠀⢀⡀⠀⠲⠦⠀⣿⠙⠈⣉⣉⣉⣉⣁⣿⣤⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⣿⣿⠀⠠⣀⡿⠆⡀⠀⠀⠙⠛⢛⣛⡃⠀⠀⠀⠀⡀⠈⠉⠀⠤⠄⠈⠀⣤⣶⣶⣿⣾⠿⠿⠟⠛⢛⣛⣛⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣦⣼⣿⣿⣶⣤⣄⣠⣶⣶⣾⣿⡟⠀⠀⢀⡀⢸⣶⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠋⠙⠻⣿⣿⠿⠟⠁⠀⢢⣤⡄⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠈⣉⣉⣉⣉⣉⣉⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢟⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣚⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠉⢹⠋⠙⢿⣿⣿⣿⣿⠏⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢾⣿⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣭⣭⣭⠉⠉⠿⠿⣿⡿⠛⠻⣽⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿
⣿⣿⣿⡿⠿⠁⠐⠈⠀⡀⠉⠉⠃⠀⠀⠀⠀⠊⠻⠿⣟⡏⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⡶⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠸⠅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⡿⣛⠉⣧⡄⠠⢀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠘⠿⢿⣿⣿⣿⠀⠀⠐⠄⠀⠀⢀⡘⢻⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⢭⣿⣿⣧⣥⣄⠄⠀⠀⠀⢩⣭⡽⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠉⠙⠿⣿⠀⠀⠀⠀⠀⢀⠨⣿⡔⣿⣿⣿⣿⣿⣿⣿⣗⣿⡿⣿
⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣉⠀⣀⣀⡀⣀⡀⣈⣀⣀⣀⡀⢀⣈⣛⡛⣛⣛⢁⣀⣀⣀⣀⡈⣋⣁⡀⢀⣙⡓⣤⢀⣀⡀⣀⣚⣛⢛⣛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢻⡇⢹⣿⣿⣿⣿⣿⣿⣓⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡸⣿⣟⢳⣿⢹⡇⣿⣿⣿⣿⣿⣯⡁⢸⣿⣿⣿⣿⢹⡏⢹⡏⢹⣿⡅⣿⣿⡿⢿⣿⡛⠀⢸⣿⡇⣿⣯⡿⢸⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⣿⣿⣷⣿⣿⣿⡧⣿⣿⣿
⣍⠋⠅⠀⠀⠀⠀⢸⣿⣿⡷⣶⣿⡟⣿⣼⡇⣿⢻⣿⣿⣿⣧⡄⠀⣿⣿⠹⣿⣼⡇⢸⡇⢸⣿⣄⣿⣿⣿⢶⣿⣿⠀⣿⡿⣿⣿⡇⣿⢸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡯⣿⣿⣿
⣿⡀⠀⢀⣀⠀⠠⠀⠿⠿⠿⠶⠷⠶⠀⠥⢤⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠢⠀⠀⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣇⣿⣿⣿
⡿⠇⣨⣤⡄⣾⣿⣷⢸⣇⣿⣿⣿⠃⣸⣿⡇⣿⣿⡇⣿⡛⢸⣟⣿⠀⠘⣿⡟⢹⣇⣿⢰⣿⣷⢸⣷⣿⡇⢰⣿⣿⡞⢻⡟⢻⣿⣿⡇⣿⡛⢸⣟⣿⢸⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠿⠿⠿
⠿⠿⠿⠿⠇⣿⣧⣶⢸⡟⣿⣿⣿⣁⣿⣽⣇⣿⡟⠁⣿⣋⢸⡏⣿⠀⠀⣿⡇⢸⡟⣿⢸⣯⣿⣸⡿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣉⢸⡏⣷⢨⡝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣿⣮⣿⣭⠬⠁⠉⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠈⠁⠉⠀⠀⠉⣡⣬⣥⣭⣍⡁⠉⠉⠁⠉⠁⠀⠙⣋⣡⣈⣡⣨⣉⣭⡅⠉⠉⠈⠁⠉⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣿⠿⢿⠷⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠐⠪⢿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣄⢀⣴⣷⣀⣴⣦⣤⣿⣿⡇⣀⣠⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⡀⠈⠀⠀⡀⡖⢢⣪⣀⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣿⡗⣢⣯⣯⣽⣷⣾⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣯⢿⣿⣿⣿⣿⣿⢻⣿⡟⣿⣿⣿⣿⣿⣇⣿⢛⣿⣻⡟⣯⣝⢫⡝⣽⠻⣫⣭⣻⣭⣭⢑⣭⣝⢊⣭⡉⣭⣤⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣹⣷⣾⣿⡿⣿⣿⣿⡆⣿⠀⣿⣿⣿⡷⢾⣿⣿⢸⡼⣿⢱⣿⣿⢸⡇⣿⢰⣻⣮⣽⣿⣿⢸⡇⣿⢸⣿⣿⢸⡇⡄⠁⠀⣠⣄⠀⠀⠀⠀⠀⠃⠀⢀⡴⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣿⣿⣿⣧⣿⣦⣿⣿⣿⣷⣾⣧⣿⣾⣷⣿⣾⣻⣿⣼⣷⣿⣶⣿⠾⠛⠿⠿⠚⢷⣿⣜⣿⣿⣾⣧⣶⣶⣶⣶⣶⡆⠀⠀⠀⢀⣴⣾⣾⣿⣦⠀⠀⠀⠀⠀⠘⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣾⣿⣿⣿⣿⣿⣏⣃⣾⡿⠀⠀⢠⡠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣧⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⢀⠀⢴⣿⣟⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣨⣄⠀⢀⢠⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠘⣷⣿⣿⣿⣿⣿⡇⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠸⢉⣿⣿⠆⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢿⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⠟⠛⠉⠀⠀⠈⢿⣟⣟⣿⡿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⢗⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⠻⠿⣿⡿⠿⠿⠏⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⢿⣿⣼⣿⣿⣿⠃⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠘⢿⣷⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⣶⢿⢿⣿⡿⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠉⠉⠀⢀⡠⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⢻⠁⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⣀⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⡿⢉⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠿⡟⢿⣿⣿⣿⡿⠛⠃⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣧⣸⣿⣿⣿⠁⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠐⢿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⢶⡾⢿⣿⣿⣿⢿⣿⣽⢳⡿⣿⣿⢷⣶⣶⡆⣶⢶⣴⡆⣶⣴⡆⣶⣶⣰⡶⣦⣤⣶⣲⣿⣏⣾⡏⣷⣶⡆⣶⣶⣶⢰⡶⣶⣶⣶⢰⣶⡆⣶⠀⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢹⡇⢸⣿⣿⣿⣛⠋⣿⢨⣅⣿⣿⢸⣿⣿⡇⣿⠛⢹⡇⣿⢿⡇⣿⣿⢯⡟⣿⠉⣿⢹⣿⢻⣯⣿⣿⣿⡇⣿⣿⣿⢸⣟⣻⣿⣿⢨⣿⡆⣿⠀⣙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢀⢈⡁⣈⠍⣉⠉⠉⣀⡈⢉⣉⡭⣉⡭⢭⡭⣁⡩⢸⣮⡥⢭⣈⡡⣭⢭⡮⣭⡩⡶⢉⡭⠭⣈⡡⠍⣉⠩⣁⢉⡉⣉⡈⠉⣉⠉⣉⣈⢉⡁⢉⡀⢙⡃⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⢸⣧⣿⣾⣿⡇⠀⣿⣿⢾⣿⡹⣯⡛⢸⡿⣯⣛⠉⣿⠁⡌⣿⠉⣿⣿⣿⣿⡁⢵⣿⣿⢸⡏⠿⢸⡿⠷⣿⢸⡇⣿⣿⢸⣿⡇⢹⡏⣽⣷⣿⣿⢸⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⢸⡏⣿⢻⣿⠇⠀⣿⢿⣿⣯⡴⣮⡿⢸⡗⣮⣿⠀⣿⠀⠀⣿⠀⣿⢿⡿⣿⡄⡘⣿⡿⠸⣧⡿⢸⣿⡟⢿⣼⠇⣿⠀⣾⢿⣇⢸⡇⢿⡟⣿⡿⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3880

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/campinos-rigging/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/campinos-rigging/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_[Teaser]_Thanking_and_Rewarding_My_Rigga’_in_Riga⠀✐


Posted in Europe, Patents at 6:17 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Campinos_on_Riga⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Latvian_votes⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Chubby_orangutan:_My_staff_hates_me_and_I_wonder_why...⦈_


Summary: The EUIPO-EPO den of nepotism (misuse of EU funds/jobs by António
Campinos) is still fully operational, as we shall see tomorrow morning at
around 6AM GMT


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

                    ䷩ 𝚕𝚒𝚗𝚎 4077

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✐ Challenging_David_Kappos,_Seeking_Accountability_Over_His_Corporate_Legacy_as
IBM/Microsoft_‘Mole’_Inside_the_U.S._Patent_and_Trademark_Office⠀✐


Posted in Deception, IBM, Microsoft, Patents at 5:21 pm by Dr. Roy Schestowitz


August (background): U.S._Patent_and_Trademark_Office_Has_a_Deep_Revolving
Doors_Crisis_(Former_Officials_Cashing_in_as_Lobbyists_and_Private_Sector
Actors)


               🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Kronborg Castle and fortress⦈
           Castles and fortresses of lawyers won’t turn in their own


Summary: David Kappos is still active, he’s still lobbying for software patents
(IBM and Microsoft pay him to do this), so we’re reporting him for conflict of
interest (DC Bar, California Bar, and the New_York_State_Bar_Association)


THE other day we wrote about a bar_complaint_against_Kappos, filed by a GNU/
Linux user who was appalled by the Office requiring Microsoft formats,
operating systems and so on. What made this more severe is the close ties —
ongoing ties — between IBM and Kappos, who was at one point the head of the
U.S. Patent and Trademark Office (USPTO) along with someone from Microsoft.
Nowadays Kappos is a lobbyist of both IBM and Microsoft, lobbying_in_favour_of
software_patents_for_the_most_part (even exploiting the pandemic to push that
nefarious agenda, as if patents on software will miraculously make a virus go
away).


“Nowadays Kappos is a lobbyist of both IBM and Microsoft, lobbying in favour of
software patents for the most part (even exploiting the pandemic to push that
nefarious agenda, as if patents on software will miraculously make a virus go
away).”Earlier this week we received an update about this bar complaint against
Kappos. The interesting part seems to be the persistent insistence that
proprietary systems should be used. As our reader explained: “I’m trying to
file electronically with the DC Bar, and the complaint form has 5 sections, and
it won’t allow me to advance past the 3rd section: Complaint Information. Most
likely, the website doesn’t work, because they don’t want to receive any
complaints. Or, maybe it knows I’m using Linux. So, I can print out a form and
file_through_the_post.”


“New York actually has a_rule [PDF] about “prolong[ing] the proceeding or…caus
[ing] needless expense.” Which is exactly what Kappos did. RULE 3.2. Delay of
Litigation – In representing a client [he was representing IBM while at the
USPTO, and Microsoft, too], a lawyer shall not use means that have no
substantial purpose other than to delay or prolong the proceeding or to cause
needless expense.”


“New York has an on-line form you can complete and scan and then submit by e-
mail, but they also require a_paper_submission.” [PDF]


“Last week, as we’ve mentioned here before, a complaint was successfully filed
in California (after the rules had been studied).”“Given that the US system is
so decrepit, and still relies on paper and post, it might be interesting to see
how the lawyers deal with Kappos, and his “anti-paper, anti-post” dictatorship
at the USPTO. Of course, lawyers protect themselves, so I don’t really expect
them to do anything.”


Last week, as we’ve mentioned here before, a complaint was successfully filed
in California (after the rules had been studied). But they managed to find a
convenient formality by which to toss it out. Ignoring all substance.


“It didn’t take California long to come up with a reason to protect Kappos,”
our reader said. “They used the statute of limitation excuse, saying they can’t
investigate things that are more than five years old. They were so fast because
they would only have to read the first page of my complaint to see that
Kappos’s confirmation hearing was in 2009, and they probably stopped reading
there.”


“We’ll try to document all those endeavours.”“Maybe I’ll try to argue with
them. When I file complaints with New York and Washington, DC, I’ll make some
changes to try to eliminate the statute of limitation issue. Won’t work, but
why stop now.”


These complaints help make a point and, shall they not be successful among the
“protectors”, in the public arena they can help sway opinion. We’ll try to
document all those endeavours.


Of course here in Europe we have an issue with EPO immunity; the US doesn’t
work the same way and Directors — both past and present — get sued all the
time, including Michelle Lee quite recently. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠐⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠀⠀⠐⠊⠉⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠀⠐⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠙⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠁⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠈⠛⠃⠀⠀⠘⢿⠿⠿⠿⠀⠀⠉⠉⠀⠀⠀⠀⢰⣶⣶⡆⡂⣴⣤⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠄⠀⠀⠀⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⣳⢻⣏⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠙⠗⠘⠲⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠠⠤⢀⣁⠉⣉⣉⣁⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⢘⠈⠨⣾⣿⣶⣿⣿⢿⣿⠋⠉⣿⡇⣿⣿⠉⣹⣿⣿⣿⣩⢹⠉⣿⣿⣿⡏⠩⣷⣿⣶⣾⡟⠲⣶⣶⣶⣶⣶⠖⠒⣶⣶⣶⡖⠲⣦⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠙⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣭⣙⣻⣻⣿⣿⣾⣿⠀⠀⠿⠇⠿⠿⠰⠾⠿⠿⠿⠆⠸⠀⠟⠿⠿⠧⠬⠿⠿⠿⠿⠫⠭⠿⠿⠿⠿⠿⠀⠀⠿⠟⠿⠃⠀⢿⣿⣿⣿⣿⡇⢯⠿⠿⠿⢿⣿⣟⣛⣻⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠉⠈⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠓⠛⠒⠓⠻⠿⡶⠷⡰⠖⡟⣿⠿⠿⠓⠚⠋⠛⠛⠛⠛⠓⠒⠚⠃⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 4209

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/corporate-uspto/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/corporate-uspto/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_12_Years_of_Corporate_Deplorables_Running_the_USPTO⠀✐


Posted in America, Google, IBM, Patents at 5:42 pm by Dr. Roy Schestowitz


In the EPO (Europe), the regime is an aggressive dictatorship of corporations
and litigation giants, served by António_Campinos and Benoît_Battistelli; in
the US, it’s the corporations themselves


            🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇PragerU Reagan: Kappos, Lee, Iancu⦈
                         Where are the civil servants?


Summary: It’s hard to swallow the idea (myth, fiction) that the U.S._Patent_and
Trademark_Office protects the ‘small person’ when it’s run by Mr. Iancu, an old
Trump associate (protecting a high-profile fraud), preceded by Mr._Kappos
(Microsoft and IBM lobbyist) and Michelle Lee (Google)


⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣽⣿⣿⣯⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠶⣶⣾⣷⣶⠶⠶⣶⣶⡶⠶⢾⣶⡶⠶⠶⠶⢿⡿⠶⠶⠶⢶⣾⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣟⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣤⣄⡈⠙⢻⣿⣿⠟⠉⣀⣴⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⣿⣿⣿⣿⠶⠶⣶⣶⡶⠾⢿⣿⡷⠶⢾⣷⠶⠶⣾⠷⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⡷⣾⣿⣿⣦⣾⣿⣿⣿⣿⣿⡇⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣿⣟⣻⣿⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣭⣾⣿⣿⣿⣷⣭⣭⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠀⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⢟⣻⢿⣛⠿⣟⣛⡿⢿⣛⣛⡿⢿⣛⣛⠿⡿⣟⣛⡿⣿⢟⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢸⣿⣼⡟⣄⣿⣿⡇⢸⣿⢻⣿⢸⣿⢻⣿⢸⣿⢹⣿⠠⣿⡛⠿⢼⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⢹⣿⣸⣷⢸⣿⠿⣟⢸⣿⠿⣟⢸⣿⢸⣿⠀⣙⢿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⣩⣽⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢸⣿⢹⣿⣸⣿⢻⣿⢸⣿⢸⣿⢸⣿⢸⣿⡼⣿⣼⡿⣀⢿⣧⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣿⣶⣷⣶⣿⣿⣷⣶⣿⣿⣿⣷⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⡟⢩⣽⡛⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⢝⠒⣋⣴⣿⣿⣿⣿⣿⣿⣿⡓⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣾⣷⢿⣩⣝⢋⣩⣭⣀⣊⢕⣊⣍⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡑⣶⢻⣿⣩⣘⣵⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠉⠉⠉⠙⣿⣿⣿⠛⠛⠛⠻⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⠼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⣠⣶⡆⢸⣿⣏⣴⣶⢞⡻⣿⣿⣿⣿⣿⣶⠶⢶⣦⣤⡘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⣿⣿⣷⣸⣿⣿⣿⣷⠁⠈⣼⣿⣿⣿⣿⡑⠉⢱⢻⣿⣿⣿⣇⣼⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⠛⠟⠛⠛⠛⠛⠛⠛⢿⣦⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣴⣶⣶⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡇⠀⣿⡟⠃⢸⣿⠛⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⡆⣿⡷⠆⢸⣿⠶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⡅⣿⣧⣭⢸⣿⣬⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠓⠒⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣤⡄⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠷⠶⢶⣶⣶⣾⣿⣿⣿⣿⣿⣧⡉⠰⣿⣄⢼⣧⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣧⣤⣤⣤⣤⣧⣤⣤⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣾⣿⣿⣍⣿⣿⣿⡜⢿⣤⡀⠹⣿⡞⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡴⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣶⣯⣽⣿⣿⣿⣇⠈⢿⣷⡀⠹⣷⣿⣯⣯⣃⣾⣿⣿⡇⠀⠀⠀⣠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡿⠿⠀⣾⣿⣿⣿⢿⣦⠁⢻⣿⡄⢘⡿⢬⠠⢼⣿⣿⣿⡇⠀⠀⠀⠉⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣿⣶⡇⠙⠻⢿⣿⠈⣿⠇⠀⠁⠀⢸⣿⢂⣾⡄⠈⠉⢿⡇⠀⠀⢀⣀⣇⠀⢀⢀⣀⣇⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠁⣉⣿⣿⣿⡟⠉⠁⣀⣤⣬⣹⣷⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⢿⣆⠈⠀⠀⠀⠀⠘⣿⠈⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⡁⣴⣶⣶⣶⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⢀⣴⣾⣿⣿⣿⣿⣷⡾⣫⢟⢿⣿⣿⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⠿⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣤⣄⠸⣿⣧⣿⡏⡞⠁⢹⣿⣿⣿⣷⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⢘⣤⣼⣶⣶⣶⣶⣷⣾⡂⠉⠉⠱⡟⠻⡛⠻⠖⠒⠂⠀⡼⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣦⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢺⡛⢛⠅⠀⠀⠁⠀⠃⡆
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣦⡎⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠲⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠘⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠛⠏⠐⢿⣿⠿⠿⠿⢿⡏⠙⠻⣷⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠨⠋⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⡀⣿⣷⢸⣿⢰⣿⢻⣷⡀⣿⡇⣿⡇⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢸⣿⡇⠀⠀⠀⠀⠀⣿⡇⣸⡏⣿⡇⣿⣿⣿⣿⢸⣿⠈⠛⠁⣿⡇⣿⡇⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣭⣉⣥⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⣿⡇⣿⡟⢿⣧⣿⡇⢿⣿⠸⣿⣸⣿⠃⣿⣇⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠈⠉⠈⠁⠈⠁⠀⢨⣭⣷⣿⣶⣭⣥⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4297

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/epo-patent-colonialism/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/epo-patent-colonialism/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ What_Patent_Colonialism_Looks_Like⠀✐


Posted in Europe, Patents at 5:35 am by Dr. Roy Schestowitz


Video_download_link | md5sum cf17c93e680a84cccc8c31943db94c1a


http://techrights.org/videos/epo-africa-baltic.webm


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Nibbles eat whole orange: Needs to 'put food on the table';
Swallows the whole market⦈ Summary: This video discusses the latest two “news”
items from the EPO (first in about a month!) and part_19_of_the_current_series,
which ends tomorrow


THE rationale for patent law is well documented. The original purpose of
patents was explained very clearly. But has patent law been warped in favour of
litigation profiteers? Or only their largest clients? Are we still rewarding
actual scientists? To encourage disclosure rather than feed opportunistic
patent_trolls_with_trivial_so-called_'inventions'?


“It’s hard not to feel like some of the existing system has been co-opted by a
shameless agenda of corporate subjugation and maybe colonisation, in effect
offering generous financial rewards to facilitators in their home countries,
enabling foreign occupation (by monopolistic/multinational corporations) and
elimination of domestic competition.”What good are patent offices in nations
that barely have any patents and sometimes lack basics like foods? Patents are
not edible, are they? It’s hard not to feel like some of the existing system
has been co-opted by a shameless agenda of corporate subjugation and maybe
colonisation, in effect offering generous financial rewards to facilitators in
their home countries, enabling foreign occupation (by monopolistic/
multinational corporations) and elimination of domestic competition. Who does
today’s EPO work for? In the case of ‘ViCo’ (especially_G_1/21) we’ve seen that
even the rule of law isn’t being respected because ad hoc shortcuts are chosen
instead; for no reason other than to protect litigation zealots, not science. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠫⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠉⠛⠛⠻⠛⠫⢿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠴⠶⠒⠒⠒⠒⠒⠂⠂⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⢂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⡾⠏⠀⠀⠀⣀⣤⣶⣾⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣠⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⡟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠛⣛⣛⣛⣛⣉⣉⣙⣉⣛⣛⣛⠃⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠟⠛⠿⠟⠿⠿⠿⠿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡆⠀⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠿⣖⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⢥⣒⠮⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠂⠘⢷⣄⠀⠀⠀⠀⠉⠙⠉⠙⠉⠁⠀⠂⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠐⣾⣿⡿⠀⠿⡿⢿⣿⣿⣿⠟⢛⣥⣟⣩⠴⠛⢋⣀⣤
⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠉⠐⠀⡀⠀⠀⠀⢀⡀⣀⣀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠞⣷⣄⠛⠛⠛⢠⣾⠟⢛⣡⣶⣶⣿⠿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠁⠀⠄⢀⣤⣬⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣄⡀⠀⠀⠀⠀⠀⠈⠉⠅⠀⠀⠈⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⠐⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⡖⣶⣤⡤⣄⣤⣠⢤⣴⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⠀⠀⢀⣴⣶⣾⡆⠀⠀⠠⠤⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠈⢿⣿⣿⣿⣿⣟⠣⣹⣿⣿⣿⠁⠸⠟⢿⣿⣿⣿⡿⠀⠙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⢿⠷⠾⠿⢿⠿⠿⠿⠿⠿⠿⠧⠄⣴⠆⠤⠶⠺⣿⣿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢷⠤⠀⠈⠛⠿⠿⠿⠧⠙⠿⣿⣿⣿⣧⡁⠀⠻⣿⣿⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⠀⣿⡇⣿⣿⠿⠇⣿⣿⠿⠀⣿⡿⢿⣶⠈⣶⡿⢿⣶⢹⣇⠿⢿⣿⠿⠇⣶⡿⢿⣦⢹⣏⢸⡇⣿⡇⣿⣿⢿⣦⢸⣿⡇⣿⣿⠸⢿⣿⡿⠇⠙⢿⣿⣿⣷⣶⠀⠈⠻⣿⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣿⡇⣿⣿⣤⡁⣿⣿⣬⠀⣿⡇⢸⣿⡇⢿⣷⣬⡉⢾⣿⡇⢸⣿⠀⠀⣿⡇⢸⣿⢸⣿⣬⣥⣭⡄⣿⣿⣼⣿⢸⣿⡇⣿⣿⠠⢸⣿⡇⣀⠀⠀⠈⠙⠻⠽⢅⣀⠑⠻⢿⣻⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⡇⣿⣿⠉⠄⣿⣿⠩⠀⣿⣇⢸⣿⡇⣤⡌⢻⣿⠈⣿⡇⢸⣿⠀⠀⣿⡇⢸⣿⢸⣿⣿⣿⣿⡇⣿⣿⢩⣥⢸⣿⡇⣿⣿⢰⢸⣿⡇⣿⣿⣷⣶⣦⣥⣤⣀⣀⣀⡀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠇⠸⠿⠇⠿⠿⠿⠇⠿⠿⠿⠇⠿⠿⠿⠟⣠⡻⠿⠾⠟⣰⣿⣇⠸⠿⢀⣇⠻⠷⠿⢟⣼⣿⣿⣿⣿⡇⠿⠿⣸⣿⣌⠻⠷⠿⢋⣼⠸⠿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠛⠛⠻⠿⠛⡛⠻⢿⡿⠛⣛⠻⠿⠟⠛⠛⠿⢿⣿⣿⠿⢛⡛⠻⡿⠟⠻⠿⠛⠿⣿⠿⠛⠛⠛⠿⠟⠻⠿⠛⠿⠟⠛⠛⠿⣿⠿⠛⠛⠛⠿⠿⠛⠛⠿⡿⠛⠛⠿⢿⡿⠿⠿⣿⠿⠛⠛⠿⠿⠿⠻⢿⣿⣿⣿
⣿⡇⢸⣿⠿⠇⣼⣿⢻⣿⡄⣼⣿⢻⣿⡆⢸⣿⠻⣿⡆⢿⡏⣾⣿⢻⣿⡄⣿⣿⡀⣿⡇⣿⡸⢿⣿⡿⠇⣿⣿⢸⣿⡇⢹⣿⠿⢇⣿⡸⢿⣿⡿⠇⢸⣿⣿⡇⠈⣿⡟⢿⣷⠀⣿⣿⢸⢸⣿⡿⠇⣿⡇⣿⢸⣿⣿⣿
⣿⡇⢸⣿⣦⡆⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⢸⣿⠀⣿⡇⢸⡇⣿⣿⢸⣿⡇⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⡇⣿⣿⣾⣿⡇⢸⣿⣶⡌⣿⣿⢸⣿⡇⡇⣾⡿⢿⣧⠀⣿⣧⣾⣟⠀⣿⣿⢸⢸⣿⣧⡆⣶⣶⣶⣾⣿⣿⣿
⠺⠇⢸⣿⡅⠀⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⢸⣿⢀⣿⡇⢸⡇⣿⣿⢸⣿⡇⣿⡇⢿⣿⡇⣿⣿⢸⣿⡇⡇⣿⣿⢸⣿⡇⢸⣿⡀⠺⣿⣿⢸⣿⡇⠁⣿⣷⣾⣿⠀⣿⡇⣸⣿⠀⣿⣿⠘⢸⣿⡇⠲⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠛⠂⢃⠘⠻⠿⠛⣠⡘⠻⠿⠛⣁⠘⠛⠛⠛⣣⣿⣧⡙⠻⠿⢛⣀⠛⢃⡘⠛⢃⣿⣿⡘⠛⢃⣇⠛⠛⡘⠛⢃⠚⠛⠛⢃⣿⣿⡘⠛⢃⡐⠛⢃⡘⠛⠃⠛⠛⠛⣛⣀⠛⠛⠛⡘⠛⠛⢃⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣶⣾⣿⣿⣷⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⣠⠂⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠃⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠛⠿⠻⢿⣿⣻⣿⣿⢿⣿⣿⡿⠟⢒⡢⣄⠀⢠⠀⠄⠤⠉⠙⠛⠻⢿⣿⣛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢁⢠⠼⠾⡉⡍⣿⣰⠀⣼⠴⠀⠀⡀⠀⠆⢈⠻⠿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⡒⡰⣿⠸⠿⣟⣿⡃⢻⠀⠈⠀⠀⠰⣦⣄⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠕⣠⣶⣶⣦⠀⢨⣷⡌⠀⠀⠀⡈⠁⠈⠻⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣾⣿⡏⢿⡿⠠⢸⡯⢷⣀⡀⠀⠤⠀⠀⠂⠘⣾⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢋⠩⢴⣒⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⢠⣿⣿⣿⣷⢀⣤⡌⣠⢢⣧⣿⣿⣴⠀⠀⠀⡀⠀⢿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢤⣾⣿⣆⠹⣿⣿⣿⣿⣿⣿⠿⢿⣯⣗⣫⡵⠿⠛⣋⣩
⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢀⢸⣿⣿⣿⠇⠘⡿⠟⠿⠘⠩⠉⠹⠁⠀⠁⠀⣵⠀⢻⣿⢻⢿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠁⠀⠐⠠⣏⡉⣷⣿⣬⡛⠿⡿⠛⣫⣶⠿⠟⣭⣥⣶⣾⣿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠂⢙⣛⠋⠀⠰⠃⡁⡀⠀⠀⢀⢀⡀⢀⣴⠆⢰⠈⠀⠙⠟⢸⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⡀⠀⠀⠈⠛⠁⠉⠛⢙⠀⠀⠀⠉⠁⠐⠛⠛⠋⠉⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠌⢡⠜⢼⡇⢸⡇⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣷⣶⣶⣶⣶⣶⣤⣄⣀⣀⣠⢤⣤⣀⣀⣀⣀⣀⣠⣤⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠐⠠⠈⠁⠈⠑⠒⠈⠀⣀⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⢿⢿⣶⣶⣶⣶⡎⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠆⠀⠐⠀⢐⡡⢄⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣀⠉⠛⢿⣿⣿⣿⣌⢿⣿⣿⣿⣷⡌⢀⢹⣿⣿⣿⣇⠈⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣤⣄⣂⣘⣂⣒⡀⠀⠕⣀⣠⢑⣀⣠⣤⣥⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⡠⠍⡛⠿⣿⣿⣟⢿⣿⣿⣿⣾⡠⣘⣻⣿⣿⣿⣌⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣥⣶⣬⡍⣭⣭⠉⣤⣬⢁⣬⡅⢩⣭⣥⡍⠋⣭⡄⡿⢩⣭⠙⡟⣩⣴⣦⣍⢩⣭⡍⣡⣤⡍⣥⣤⢉⣤⣶⣬⡙⣶⣶⣤⣌⠍⠑⠈⠙⠻⢿⣟⣢⡙⠿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠛⢃⢸⣿⢰⣿⣿⢸⣿⡇⣸⣿⣿⡇⠀⣿⡇⡇⢸⣿⠀⠁⣿⡇⢸⣿⠈⣿⡇⣿⣿⡇⣿⡿⢸⣿⣌⠛⢃⣿⣿⣿⣿⣿⣶⣮⣥⣔⣒⣀⡈⠉⠁⠀⠉⠙⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣙⡻⣿⣆⢸⣿⣾⡟⣿⣼⣿⠁⣿⣏⣸⣿⠀⣿⡇⡇⢸⣿⠀⠀⣿⡇⢸⣿⠀⣿⣧⣿⢻⣧⣿⡇⢀⣙⠿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣧⣿⡟⠀⣿⣿⡇⢻⣿⣿⢀⣿⡟⢻⣿⡄⣿⣷⣤⢸⣿⣦⡄⢿⣧⣼⡿⠀⢿⣿⣿⠸⣿⣿⡇⠸⣿⣤⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣥⣶⣷⣤⣤⣶⣦⣤⣴⣶⣤⣴⣦⣤⣴⣤⣤⣴⣦⣤⣤⣶⣶⣬⣥⣶⣿⣶⣤⣴⣶⣤⣤⣾⣷⣦⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⢰⣶⣶⣶⡆⣶⣶⢰⣶⡆⢰⣶⣶⡆⣿⢰⣶⡄⣶⣶⠀⣶⣶⢰⣶⠀⣶⡆⢉⣴⡶⣶⡌⢱⣶⡆⡏⣶⣶⣶⡎⣿⢱⣶⣶⠀⣶⣶⡆⢁⣶⣶⡆⠃⣶⣶⣶⣮⠉⣶⣶⢠⣶⠆⣶⣶⣶⢰⣶⣶⣶⡆⣻⣿⣿
⣿⣿⣿⣦⢸⣿⡇⠀⣿⣿⣼⣿⡇⢸⣿⣀⡒⣿⠸⣿⡇⣿⣿⣆⣿⡇⢸⣿⣤⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⡇⣿⣿⣀⠺⣿⢸⣿⣿⣧⡿⣿⡇⢸⣿⢻⣿⠀⣿⣿⣸⣿⠀⣿⣿⣾⡟⡀⣿⣿⣐⢲⢸⣿⡇⣶⣿⣿⣿
⢿⣿⣿⡟⢸⣿⡇⠀⣿⣿⢹⣿⡇⢸⣿⠛⣡⣿⡀⣿⣿⣿⢻⣿⣿⡇⢸⣿⠛⣿⡇⢸⣿⡇⣿⣿⢸⣿⡇⠇⣿⣿⠛⣠⣿⢸⣿⣿⣿⡇⣿⡇⣼⣿⣸⣿⡀⣿⣿⢹⣷⠀⣿⣿⣿⣧⠀⣿⣿⢛⣼⢸⣿⡇⣿⣿⣿⣿
⡉⠈⠈⠁⢸⣿⡇⠀⣿⣿⢸⣿⡇⢸⣿⣶⡆⣻⡇⣿⣿⡏⢸⣿⣿⠀⢸⣿⠀⣿⡇⠘⢿⣧⣿⠏⢸⣿⣷⡆⣿⣿⣶⡆⣿⢸⣿⠇⣿⠃⣿⡇⣿⣿⢹⣿⡇⣿⣿⢸⣿⠀⣿⣿⢸⣿⡆⣿⣿⣶⡎⢸⣿⡇⣿⣿⣿⣿
⣿⣿⣷⣶⣦⣤⣀⣀⠀⠤⠶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4415

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/irc-log-090921/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/irc-log-090921/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_September_09,_2021⠀✐


Posted in IRC_Logs, Site_News at 2:04 am by Needs Sunlight


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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
 QmcLJzAhrgmyjZz1yoHJFL1oyrZN7Y6tec5a9hhzyG38NU #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmPcBiWEJGd3sHnoWuJynXqceTRc2Powjc6s2iWKDGZ6ws (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmWnjK3TNZpHoikxfsCpYXf2LshGGJ9FdMxYPunBWHLa2S social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmXDeNCPoKgqUQEMXM6iwy7oise46JGbBDbzvJTdPv4Hr5 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmPABDbzhQ1jjiUECPPVUg6g9Kjs1o5RhNKhk42foCXbTG #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmX8VubGFjzWTc9ZGE7D4ahzUZQBB7oof8biygAAaDNbhZ (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRykMocs5jvcisWuaknXWbagbdkFLwEBsKF9A934LVMEs #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmPuydiP6UXyCcgnVwdkK7xfXNhbKJYRJeoUa1w5qieE7J (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmcMxMu1mpdqgj3DsyKreqYUhQWgSSuXM2hkpD8u5qhFQx



                    ䷩ 𝚕𝚒𝚗𝚎 4532

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/09/10/rigging-epo-and-euipo/#comments
    Gemini version at gemini://gemini.techrights.org/2021/09/10/rigging-epo-and-euipo/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO_and_EUIPO_Aren’t_Democratic_Institutions⠀✐


Posted in Europe, Patents at 5:58 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Self-Appointed_“Select_Committee”;_Competition/election⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I'm_done_with_EUIPO_for_now;_Team_Battistelli_will_'fix'_the
EPO_election_for_me⦈_


Summary: How António_Campinos and Benoît_Battistelli rigged_the_election at the
EUIPO and EPO


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣤⡀⣤⡄⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣭⠉⠁⠉⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤
⣿⠃⠀⠀⠀⠀⢀⡀⠀⡀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⠿⠿⡿⠿⣿⣿
⡏⠀⠸⣾⣿⣿⣷⢳⣿⢻⣿⡄⣿⣿⣸⣿⣿⢸⣿⢿⣷⢸⣿⠿⠻⢿⣿⠿⢸⣿⠸⢿⣿⠿⣿⣿⢰⣿⢻⣿⡄⣿⣇⣿⡇⠀⣸⡏⣿⣿⠿⢸⣿⠀⢸⣿⡿⠇⣾⡟⣿⡆⠿⣿⡿⠇⣿⡇⣾⣿⣿⣧⢸⣿⣼⣿⢸⣿
⠃⠰⠇⣿⣿⣿⣿⢸⣿⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⣾⠿⢸⣿⠶⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣿⡇⢠⣿⠁⣿⣿⠶⢸⣿⠀⢸⣿⡷⢆⣿⡇⣛⡋⠀⣿⡇⠀⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿
⠁⠀⢠⢿⣿⣿⡿⣸⣿⣼⣿⠃⣿⣿⣿⢸⣿⢸⣿⡇⠀⢸⣿⣤⡄⢸⣿⠀⢸⣿⠀⢸⣿⠀⣿⣿⠸⣿⣼⣿⠇⣿⡿⣿⡇⣼⡇⠀⣿⣿⣤⢸⣿⣤⢸⣿⣧⡌⣿⣧⣿⡇⠀⣿⡇⠀⣿⡇⢿⣿⣿⡿⢸⣿⢻⣿⢸⣿
⠀⠀⠸⣷⣿⣿⣾⣿⣿⣿⠇⠀⠉⠀⢉⡈⠉⠨⠽⠀⠐⠈⠉⠉⠁⠈⠉⠀⠈⠉⠀⠈⠉⠀⠈⠉⠀⠈⠉⠁⠀⠉⠁⠉⠁⠉⠀⠀⠉⠉⠉⠈⠉⠉⠈⠉⠉⠁⠈⠉⠉⢰⡀⠉⠁⢀⣭⡇⠀⠉⣽⣾⣾⣿⣾⣿⣾⣿
⠀⠀⠀⢸⣿⣿⡟⠁⠁⠀⠀⠀⠀⠀⣘⡓⠀⣀⣠⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⣼⣿⣿⣤⠀⠀⠀⠀⠀⠀⡀⠛⠀⣀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣤⣾⣿⣿⣿⣿⣧⠀⠀⠀⢀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣯⣽⣿⣿⣿⣿⣿⣿⡄⠀⢀⣿⡄⠀⠀⠀⣾⣿⠟⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠛⠿⣯⢸⣿⣇⣠⣾⣿⠀⠀⠀⣤⣟⣃⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿
⣿⣿⠀⠀⠀⢀⠀⢸⣧⢿⣿⣿⡌⠀⢼⣿⣿⣿⡇⠀⢠⡀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⣿⣿⣿⣿⣿⣿⡇⠀⣶⣿⣿⣷⡆⠀⠠⢿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡿⠛⠉⠀⠀
⣾⣿⡆⠀⠀⠈⠀⠀⠀⠠⠉⠉⠀⠀⣿⣿⣿⣿⣧⣴⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣾⣿⣷⣦⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠁⠀⠀⠀⠀⠀⠓⠒⠂⠁⠀⠀⠻⠟⠛⠩⢭⣽⣿⠇⢸⣿⣿⣿⣿⣿⠀⣤⣴⣤⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠁⠈⣿⣿⣿⣿⣷⣿⡀⢘⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⠁⢸⣿⣿⣯⣭⣤⡄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠃⠀⣶⠝⠻⣿⡿⢽⣇⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡇⠨⠛⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠈⣡⣾⣿⣿⣿⣿⣿⣶⡿⠿⠿⢀⣤⣶⣾⣿⣬⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⠄⠀⠀⠸⠿⠂⠐⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠀⣠⣤⣤⣦⣤⣤⣄⣀⡀⢠⣴⣶⣄⢠⣤⣤⢤⣤⡄⢠⣤⣤⡄⠀⠀⢠⣤⣤⡀⣤⣤⣤⡄⣤⣤⣤⡄⣠⣴⣦⣄⢠⣤⢠⣤⡄⣬⣿⣿⣿⣿⣿⣭⣽⡟⣯⣭⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣹⣿⣿⣿
⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⣿⣜⡛⢸⣿⣥⢸⣿⡇⢸⣿⣧⡄⠀⠀⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣸⣿⣿⣿⣿⣿⢸⣿⢸⣿⣷⣿⡇⢾⣿⣇⣿⣿⣧⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿
⣿⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⠀⢤⣭⢻⣿⢸⣿⠉⢸⣿⡇⢸⣿⡏⠙⠛⠛⣿⣿⣿⣧⣿⣿⠉⠁⣿⣿⠉⠁⣿⣿⣿⣿⢸⣿⢸⣿⢿⣿⡇⢸⣿⣿⣿⣿⡯⠇⣿⡇⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠻⠿⠛⢘⣛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠛⠛⠛⠀⠀⠛⠛⠀⠀⠙⠻⠿⠋⠘⠛⠘⠛⠈⠛⠃⠘⠛⢻⣿⣛⣛⣃⣛⣛⣛⣫⣿⣿⡿⠃⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⣿⡿⣻⢛⣟⣿⣭⣥⠠⣤⣤⡄⣤⣬⠉⣤⣤⣤⢀⣤⣤⣄⢠⣤⣤⣤⠀⠀⣠⣤⣤⡀⢀⣤⣤⡄⢠⣤⣄⣠⣤⡄⣤⣤⡄⣤⣤⡄⣤⡄⣽⣿⣿⣿⣿⣿⣿⢻⣭⣭⢻⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⢠⣿⣇⠿⠻⠿⣿⣟⡛⠃⣿⣏⡁⣿⣿⡦⣿⣿⣉⢸⣿⢸⣿⡎⢹⣿⠉⠀⢰⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣧⣿⣿⡇⣿⡇⢹⣿⡏⠿⢹⣿⠉⢸⣿⣉⢸⣿⣏⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣶⣿⣷⣾⡆⢠⣭⣿⣿⡆⣿⡟⠃⣿⣿⠿⣿⣿⠛⢸⣿⢠⣤⡄⢸⣿⠀⠀⢸⣿⡇⣤⡄⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⡟⣿⣿⣿⡇⣿⡇⢸⣿⡇⠀⢸⣿⠀⢸⣿⠛⢸⣿⡟⠃⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⡈⠻⠿⠿⠃⠿⠿⠿⢿⣿⣿⢿⣿⡿⠘⠿⠾⠟⠀⠸⠿⠀⠀⠀⠻⠷⠿⠃⠙⠿⠿⠏⠸⠿⠸⠏⠿⠇⠿⠇⠿⠿⠿⠇⠿⠇⣜⠿⢇⡀⠸⠿⠀⠸⠿⠿⠿⠿⠿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣟⢿⢿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠈⠙⠃⠈⠿⣿⡀⣤⣦⠘⠀⣠⣶⣿⣶⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠄⡀⠀⠉⠿⠟⠿⠞⠀⣿⣿⣿⣿⡇⢀⣾⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠈⠁⠿⢷⠆⣴⣀⠀⢰⣿⣿⣷⢿⡷⣿⣿⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⣤⣴⣾⣿⣿⡶⠿⠿⠿⠿⠿⠿⠇⢸⣿⣿⣿⣿⢀⣀⠀⢈⣿⣿⣿⣿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠹⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠘⠛⠛⣿⠀⢸⣿⣿⣿⣿⡏⠘⣿⢾⣽⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⡇⠀⡱⢿⣿⣟⣿⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣶⣧⠀⠀⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣫⣤⠉⠾⠏⠻⣷⣦⣤⣶⣀⣀⣀⣀⣀⠀⠀⢀⣴⡿⠻⣿⣿⣤⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠻⠋⠀⠀⠀⠀⠈⠛⢛⣛⠛⡛⠛⠛⠿⣷⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠋⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⡿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣀⣤⣶⣶⣶⣶⣦⣤⣀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⡇⣾⣿⡆⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢰⡆⣿⡿⣷⡟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⡇⣿⡇⣿⠇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣾⣿⣯⣵⣯⣶⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡏⣶⡶⢶⣮⢣⣶⢳⣦⠁⣶⡄⣶⡆⣶⡶⠆⣿⢰⣶⢰⣶⡆⣶⡆⣶⡆⠶⣶⡶⠆⣶⡆⣶⡎⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠿⠛⠉⢁⣀⣤⣤⣤⠀⠈⣽⣿⣿⣿⣿⢿⠀⠀⠀⠈⠛⠉⠉⠉⠙⠻⣿⡇⠀⠀⢸⡇⣿⡇⢸⣿⢸⣿⢸⣿⠀⣿⣷⣿⡇⣿⣧⡍⣿⢸⣿⣸⣿⣧⣿⠃⣿⡇⡇⣿⡇⡇⣿⣷⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⡧⠀⠉⣀⣤⣶⣿⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⠙⡇⠀⠀⢸⡇⣿⣇⣼⣿⢸⣿⣸⣿⠀⣿⢹⣿⡇⣿⣇⡚⣿⡎⣿⣿⠸⣿⣿⠀⣿⡇⡇⣿⡇⡇⣿⡇⣿⡇⣿⣿
⣿⣿⣿⣿⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢠⣿⣿⣿⣿⠿⠀⠀⢀⠀⠀⠀⠽⠟⢿⣿⠧⠀⠁⠀⠀⢸⣷⣭⣭⣭⣵⣷⣭⣭⣵⣦⣭⣤⣭⣥⣭⣭⣥⣿⣧⣭⣭⣦⣭⣭⣦⣭⣵⣧⣭⣵⣧⣭⣥⣭⣵⣿⣿
⣿⣿⣿⣿⣿⠀⢾⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡿⡀⠀⢠⡈⣄⡀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⠶⢰⣶⢰⣶⢱⣶⠀⣶⡶⣾⡙⣵⡶⣶⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⠈⠁⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣷⡀⢄⣿⣿⣷⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⡌⢸⣿⢸⣿⢸⣿⠀⣿⣧⣿⠇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡄⢹⠇⢸⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣐⢸⣿⢸⣿⢸⣿⠀⣿⡇⣶⡆⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠛⣾⣇⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣭⣬⣝⣛⣥⣮⣭⣤⣭⣥⣿⣷⣭⣛⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⣿⣿⢩⣵⢶⣍⢻⣿⣯⣭⢻⡿⣽⣏⢹⡏⢫⣵⢶⣍⢹⣿⢹⣿⡏⣿⡏⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣤⢸⣿⢸⣿⢸⣿⣼⡿⢸⡇⣿⣿⣼⡇⢸⣿⢸⣿⢸⣿⢸⣿⡇⣿⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⢩⢸⣿⢸⣿⢸⣿⢸⣿⢸⡇⣿⡟⣿⡇⢸⣿⢸⣿⠀⣿⣾⠻⣿⣿⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣘⣛⣾⣮⣛⣛⣣⣜⣛⣘⣛⣼⣷⣛⣣⣝⣃⣮⣛⣛⣫⣦⣛⣛⣤⣛⣛⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣠⣄⣶⣶⣶⣶⣶⣦⣤⣄⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⢶⠖⣶⠒⢰⣶⢰⣶⢰⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣿⣁⣿⢼⣼⡟⡟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣮⣿⡿⠟⠛⠋⢉⣉⣉⣉⡉⠉⠛⠛⠿⣿⣿⣽⣆⠈⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠿⠿⠿⠮⠶⠯⠭⠽⠾⠽⠵⠷⠿⠿⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⡏⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠉⣿⣿⡦⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣹⠇⣾⣿⠈⣿⢉⢹⡏⣿⠸⣏⡃⢹⡏⢸⣏⢸⡇⢸⡇⢸⡇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⢠⣾⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⡆⠸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣼⠇⣿⢺⡄⣿⢸⢸⡇⣿⠰⣮⡷⢸⡇⢸⣧⢸⣧⢸⣧⢸⡇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⣿⡀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠿⠟⠁⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣷⣿⣶⢛⢓⡛⣓⢛⡒⣚⠟⣚⣷⣶⣷⣶⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣷⣦⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀⣀⠀⠀⢀⣼⣿⣿⡟⠀⠿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⣿⣿⢸⡇⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡗⠀⣤⡀⠹⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠿⡸⢟⡸⢇⠿⠆⠿⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⢠⣾⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡿⠇⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡭⣭⠭⣭⢩⣭⡍⡍⠫⣭⠭⣭⢩⡍⣭⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢸⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠂⣿⢸⣿⡅⣶⡇⣿⠀⣿⢺⡇⣿⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠛⠉⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⠿⠃⠀⠄⠀⢠⣾⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣤⣛⣘⣫⣣⣿⣷⣛⣤⣛⣘⣣⣛⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠐⠀⠀⠈⠋⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡖⢰⡖⡆⣾⢳⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠁⠀⠒⠠⠄⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢸⡏⡅⣿⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠶⡶⠶⠶⠿⢾⠷⠾⠿⢿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⢿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⢸⣏⣹⡇⢸⣏⢱⡏⠿⠈⣿⠁⡇⣾⢹⡇⣿⣼⢸⢸⣏⢸⡏⣷⣿⣹⠇⡇⣿⣼⣿⢸⣏⢸⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⡸⠧⠼⠧⠼⠧⠜⢧⡿⡀⠿⠀⠇⠻⣼⠇⠏⠿⢸⠸⠇⡸⣧⠟⠿⠸⠇⡇⠇⠟⠿⠸⠧⢹⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 4654

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Gemini_version_available_♊︎


✐ [Meme]_‘Open_Source’_Study/Report_From_the_European_Commission_Promotes
Software_Patents_in_Europe⠀✐


Posted in Deception, Europe, Free/Libre_Software, Patents at 6:08 am by Dr. Roy
Schestowitz


Related: OpenForum_Europe_(IBM_et_al)_and_Linux_Foundation_Are_Boosting_and
Cooperating_With_Enemies_of_Software_Freedom


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Garfield_cat:_'Open_Source'_Study/Report_From_European
Commission_Promotes_Software_Patents⦈_


Summary: OpenForum Europe and a German patent troll have issued this_report,
which on the surface looks like advocacy regarding (or for) software freedom…
until one looks more closely (in a nutshell, it promotes European_software
patents as a beneficial thing and pretends that only source code controlled by
Microsoft in proprietary software (GitHub) actually counts or exists at all — a
common fallacy promoted by the GPL-violating monopolist)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇An_image_of:_Study_about_the_impact_of_open_source_software
and_hardware_on_technological_independence,_competitiveness_and_innovation_in
the_EU_economy⦈_


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⢹
⣟⣿⣯⣯⣽⣭⣏⡟⣽⣫⢏⣽⠛⡝⣯⢹⣿⢩⣯⣯⣽⢭⡟⣝⣿⡭⣿⣯⣹⢹⢫⣻⣿⣽⣿⣯⣽⣿⣽⢫⣻⣿⣭⡯⢻⣭⡇⢏⢻⣿⣽⣿⣱⡎⣧⡞⣷⡺⣿⣏⣽⣭⡟⣽⢫⡟⢹⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢸
⣿⣇⣯⣩⣷⣿⣺⣿⣏⣼⣙⣷⣟⣯⣿⣻⣺⣿⣽⣿⣷⣽⣺⣇⣿⣎⣤⣿⣸⣿⣷⣿⣟⣺⣗⣟⣽⣾⣿⣟⣮⣻⣗⣯⣸⣿⣿⣿⣿⣟⣿⣾⣇⣗⣻⣇⣯⣞⣆⣿⣾⣸⣇⣏⣸⣿⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⡿⠿⠿⠿⢿⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢩⣭⡍⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣾⣿⣷⠻⢿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣟⣻⣿⣿⣻⣿⣿⣿⣿⢯⣿⢿⣿⣿⣿⡆⣾⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⢸⣿⡇⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣽⣤⣽⣾⣷⣿⣿⡝⠹⣿⣿⡿⣛⡟⢣⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣤⣸⣿⣇⣄⣠⣠⣤⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢩⣍⣽⣻⡹⣿⡿⠿⠿⠗⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣾⢸⣷⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣾⡷⢎⡭⣍⡉⠉⠉⠉⠉⠉⠉⢸
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⣛⣓⣛⣛⣛⣀⣀⣒⣛⣛⣸
⣿⢿⡿⡿⢿⢿⡿⣿⣿⡿⣿⢿⣿⡿⣿⢻⣿⣿⢿⠿⡿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣿⢿⡟⣿⣿⣿⣿⡿⣿⣿⢿⣿⢻⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⢿⢿⡿⣿⢿⣿⡿⡿⣿⣟⣶⣶⣶⢸
⣿⣼⣷⣿⣮⣼⣧⣯⣿⣽⣮⣽⣿⣿⣿⣼⣯⣽⣾⣿⣧⣯⣷⣭⣿⣯⣽⣿⣿⣯⣿⣿⣭⣿⣇⣷⣬⣷⣯⣿⣼⣷⣯⣼⣿⣭⣿⣿⣿⣮⣽⣼⣼⣿⣯⣿⣿⣽⣿⣧⣿⣬⣷⣿⣾⣾⣧⣿⣼⣿⣇⣷⣬⣼⣿⣿⣿⢸
⣿⣿⣩⡏⡯⣽⣍⡟⣽⣽⣿⣿⡏⣽⣿⣯⢻⣭⣯⣽⠉⣿⢫⢻⡝⣿⣿⢹⣩⡟⣝⣿⣯⢽⣭⣯⢹⣿⣭⣿⡟⡝⢹⣿⢹⣭⡟⣽⣿⣯⢻⣭⣯⣽⢻⡇⢯⢻⡏⢫⢻⣭⣿⣟⡻⡍⣽⢨⢻⣯⡟⣝⢫⢹⣾⣿⣿⢸
⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣸⣿⣿⣸⣿⣿⣾⣗⣿⣰⣳⣿⣿⣻⣇⣿⣾⣿⣾⣏⣻⣺⣗⣿⣸⣸⣇⣿⣿⣻⣿⣺⣾⣟⣿⣿⣺⣇⣿⣸⣗⣿⣸⣰⣝⣿⣸⣅⣿⣗⣿⣛⣷⣿⣸⣷⣇⣿⣷⣝⣿⣸⣛⣿⣧⣿⣹⣿⣸⣿⣼⣸⣗⣿⣿⣿⣿⢸
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⢻⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠟⣛⡻⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣳⣿⣿⣿⣿⠙⢫⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡻⣯⣽⠿⣿⢝⡝⣿⣿⣿⣳⣿⣿⣿⣿⣿⡗⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣎⣘⣿⣿⣟⣭⡏⢹⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣶⣶⣼⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⢰⢶⣾⣽⣞⣿⣟⣻⣛⣋⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⠿⠿⢿⣿⣸⢷⡿⢸⣿⣿⣿⣧⠿⢿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⢻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⣫⡖⣦⣄⣀⠀⠀⠀⣀⣠⢸
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡤⠭⠭⠭⠭⠭⠥⠤⠭⠭⠭⢼
⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣸⣧⣷⣿⣜⣾⣧⣃⣝⣺⣱⣝⣺⣟⣻⢘⣄⣿⣿⣜⣇⣇⣼⣿⣞⣧⣿⣟⣿⣸⣛⣿⣟⣻⣻⣿⣟⣻⣾⣿⣟⣹⣿⣳⣿⣿⣿⣜⣻⣸⣿⣿⣿⣿⣸⣨⣓⣟⣹⣛⣿⣿⣟⣻⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡿⢻⣿⠭⡟⣿⣿⣏⢟⢻⡻⣿⢿⢿⣿⣿⣿⣿⣟⠭⣟⣿⢿⡻⡻⣟⣿⣿⣿⢟⠿⡋⣿⣿⡿⣿⣿⡿⣻⣿⣿⡿⣿⣿⡿⣻⢟⡿⣿⣿⠋⣿⢟⣿⣿⢛⡿⣻⣿⡿⣻⣿⢟⡏⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣷⣾⣿⣭⣷⣭⣿⣿⣾⣶⣭⣿⣿⣾⣿⣯⣽⣿⣿⣭⣿⣯⣿⣵⣽⣯⣾⣯⣿⣾⣶⣵⣿⣯⣿⣾⣯⣷⣿⣿⣽⣷⣯⣽⣯⣽⣿⣷⣯⣿⣶⣿⣭⣯⣿⣮⣯⣽⣽⣷⣿⣿⣬⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⢛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢿⡿⠿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣴⣴⣜⡝⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡿⢿⠿⣿⣿⣿⠎⣾⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠿⢸⣿⠀⠿⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⢾⠛⠿⣪⣏⣿⣿⠧⣿⣷⢾⣶⣿⣿⣿⡛⣼⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣷⣬⣭⣿⣿⣿⣷⣀⣾⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣾⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⣸⢳⣿⣾⣿⣿⣿⣿⢭⣿⣯⢻⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣛⢛⣻⣿⣬⣻⣟⣸⠿⠿⠟⠟⠸⠞⠿⠿⠿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢵⣏⣷⣦⣤⡀⠀⣀⣠⣤⢸
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡟⡏⣭⡚⣭⣍⣝⠟⢟⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢛⣛⡛⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢟⠻⡿⡻⢿⣿⣧⣾⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣤⣤⣆⣉⣼⣿⣿⣿⡏⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⢸⣿⡇⠛⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣫⣉⣛⣍⣮⣿⣯⡻⠿⢿⣿⣿⣿⣿⡿⠿⢏⣵⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣛⣻⢵⣿⣿⣿⣿⣿⣮⣿⣸⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢻⣿⣿⣯⣿⣿⣿⣿⣷⣿⣛⢻⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⢩⣍⣭⣿⣶⣽⣧⡽⣛⡛⠛⢻⠇⠿⠸⠓⠛⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠵⠾⠯⠿⠿⠿⠻⠋⠺⠧⠿⠷⠶⠄⠀⠤⠶⠶⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻
⣿⣽⣽⣹⢿⣹⢿⣿⣻⣿⣻⣻⣟⣿⣿⣻⡟⣿⢹⣻⣟⣿⢿⣿⡿⡟⣿⣯⣿⡟⢹⢹⣿⢻⠋⡟⣿⣿⢻⣿⠿⣿⡟⣿⠻⣟⡿⢿⣿⡻⣿⣻⡟⣿⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⢾⣾⣾⣾⣿⣾⣿⡾⣿⣾⣿⣷⣿⣿⣾⣷⣿⣾⣾⣿⣿⣿⣿⣿⣷⣿⣷⣿⣷⣿⣾⣿⣾⣶⣷⣿⡿⣾⣿⢾⣿⣿⣾⣾⣿⣿⣾⣿⣿⣿⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣸⣿⣿⢿⡱⣹⣿⣿⣿⣿⣏⣿⠽⣿⣇⣧⣿⡹⣽⣿⣏⢏⣿⢿⢿⡯⢿⢿⣏⡿⢿⠟⡿⣻⣿⢿⣿⣿⡿⢸⣉⠯⣿⡿⣿⠹⡏⢏⣹⡹⣙⠎⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡿⢿⢿⣿⣿⠿⣿⣿⢿⡿⡿⣿⢿⡿⣿⣿⠿⣿⣿⡿⣿⣿⡿⡿⣿⣿⡿⣿⢿⣿⣿⢿⡿⢿⢿⡿⣿⣿⢿⣿⣿⢿⠿⡿⡿⣿⣿⢳⠿⣿⣿⣻⣻⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣴⣿⣿⣿⣯⣿⣼⣿⣯⣿⣴⣧⣿⣿⣿⣿⣿⣧⣧⣵⣼⣧⣼⣼⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣿⣽⣯⣿⣷⣿⣿⣼⣿⣿⣿⣽⣽⣿⣾⣿⣼⡿⣿⣿⣿⣿⣽⣛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⢻⣿⣿⣿⣿⣯⣿⣿⣻⣯⣿⢿⣟⣿⢻⢻⡏⣿⡏⣿⣿⣿⣟⣿⣿⡟⣿⣿⣿⣟⣿⢻⡟⡟⣿⡻⡿⢹⠛⡟⣿⢻⡟⣿⢻⣿⣿⢻⣿⣿⣽⣿⣟⣿⢿⢻⣾⣿⣿⣿⣇⠀⠈⠉⠺⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⡷⠿⠿⠷⠾⠶⠷⠷⠾⠿⠷⠷⠾⠷⠾⠾⠾⠿⠶⠷⠿⠿⠶⠷⠾⠿⠶⠿⠿⠿⠿⠿⠾⠿⠾⠷⠷⠾⢿⡿⢾⣿⢾⣷⡿⣿⣶⠿⠷⠷⠿⣾⣶⣿⣿⣷⣿⣿⡿⣋⣑⣤⢖⣫⣵⡄⠈⢳⠱⣵⣦⢻⣿⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⢸⣿⡇⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⢶⣾⡿⣱⣟⣿⣿⣿⣴⣆⢳⣿⣽⣏⢿⣿⣿⣿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣟⡸⠿⣫⣺⣧⣿⢃⣤⣽⣿⣿⣸⣿⣽⣿⣿⢙⡿⢿⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⢻⣿⣿⡿⠙⣿⣿⣿⢷⣿⣟⣹⣻⣗⣬⣟⣷⣿⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢪⣿⣧⠶⣛⣯⣭⣟⣾⡯⡉⠉⠉⠉⠉⠉⠉⠉⢸
⣷⣶⣦⣎⣰⣄⣦⣔⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣏⣸⣟⣶⣶⣿⣿⣿⣿⣿⣷⣿⣿⣷⣀⣀⣐⣒⣛⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡔⠘⠐⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⡄⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣇⣀⣀⣈⣘⣈⣀⣀⣀⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢹⣿⣶⣿⠀⣿⣿⣿⣷⣟⣷⣿⣶⣟⣻⡃⢼⣻⢿⠃⢿⣩⣷⣟⣶⣿⢾⢻⡄⣽⣺⢼⣻⢼⣸⣾⢳⣛⣾⣷⠠⣟⣯⣞⣷⣿⣿⢷⢷⢷⣿⣼⢳⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⣠⠀⡇⢠⢀⡀⢀⢀⣠⡀⡀⡀⣀⢀⡀⣈⠃⠀⡀⠀⡀⠀⣀⢀⠀⢀⢀⣄⠀⢀⠀⣀⢠⡀⡀⠀⣀⢠⢀⡀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠿⠽⢿⢿⠀⡿⢻⢼⠿⡯⢻⣽⢻⢿⠿⡿⢿⠹⣿⠇⠺⡽⢿⢹⠀⢿⢿⡿⢯⠽⠯⣿⠿⠿⣽⠿⠿⡽⢺⣽⢿⢿⡭⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⣀⣠⣄⣀⣀⣀⢀⣀⣀⡀⣀⡦⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣤⣤⣤⣤⡀⣀⣀⣀⣀⣀⣈⣉⣀⣀⡀⢀⣀⣀⣀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠾⠿⠿⣿⠾⠻⠟⠇⠟⠷⠟⠿⠻⠟⠟⠶⠻⠟⡶⠈⠷⠞⠷⠻⠻⠿⢻⠾⠻⠿⠿⠿⠿⠿⠹⠛⠿⠻⠿⠿⠿⠻⠗⠿⠗⠰⠿⠿⠸⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣄⣤⣄⣄⣄⣤⣴⣴⣢⣤⣠⣤⠀⣶⣤⣄⠠⡦⣦⣄⣤⡄⢰⣖⣲⡆⣶⢀⣤⣀⣤⣠⣤⣠⣤⣠⣤⣤⣤⣄⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠓⠋⠙⠙⠛⠛⠚⠛⠚⠙⠘⠀⠛⠛⠛⠀⠓⠃⠛⠛⠃⠘⠓⠊⠓⠋⠈⠛⠛⠓⠛⠚⠙⠘⠙⠚⠛⠛⠛⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢂⠀⠀⣀⡀⠠⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣮⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⠀⠉⢻⣷⣤⣦⣦⡆⠀⣖⣴⢦⢠⡔⡆⡤⠀⣲⢴⣢⣢⡔⢦⣶⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠉⠁⠉⠈⠀⠉⠉⠁⠁⠈⠈⠉⠉⠀⠉⠁⠈⠉⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⢿⣶⣶⣿⣿⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡤⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⢀⢤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣒⡒⠒⡒⢂⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿
⠀⠀⠀⠀⠀⠜⠛⠋⠉⠉⠻⢿⣧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡄⠐⠂⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣄⣀⠀⠀⠀⠀⠀⠈⣤⣤⣤⣤⣤⣴⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⡛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣄⡀⠈⠛⠛⠳⠤⠤⢀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣴⣷⡀⠀⠀⠀⠈⢆⡀⠠⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠈⠉⣉⣉⣁⡒⠤⠀⣤⠴⠶⢶⡒⠦⠴⠆⡐⠒⠒⠂⠀⣀
⣿⣿⣿⣷⣶⣤⣤⣄⣀⠈⠒⢤⣀⡀⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠶⠦⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠉⠙⠛⠶⠶⢤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿
⡿⠿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣄⣠⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⢿⣿⣿⣿⡿⢟⣛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠓⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠁⠀⠀⠀⢡⡼⠿⢷⣿⣿⣿⣶⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣴⣶⣶⣷⣠⡤⠄⠀⢀⣩⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣴⣿⣿⣧⣄⣀⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⣈⠶⠛⠋⠉⠉⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠙⣻⣿⣿⣿⣿⣿⣿⡿⠟⢿⠷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠒⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣷⣾⣿⣿⣍⡉⠙⠻⣿⣿⣟⣐⣻⣻⡛⠛⠛⠋⠛⠃⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⢼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠉⠛⠉⠋⠉⠉⠉⠂⠀⠦⠴⠿⠶⠰⠦⠶⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣶⣾⣶⡞⠉⠀⢸⣿⣿⣿⣿⣿⢨⡏⣽⢓⢹⢹⢹⢹⡎⡇⡎⡏⡮⣳⣾⢑⣹⢱⡇⠀⣿⣿⣿⣿⣽⢫⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣛⡉⣟⣛⣛⣀⣠⠤⠖⣒⣺⣿⣿⣿⠿⠿⠿⠿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣶⣾⣿⣿⣿⣷⣿⣾⣿⣿⣷⣾⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣤⡄⣀⠀⠐⠒⠲⠶⣶⠦⠬⣈⡀⠁⠁⠀⢈⡠⠴⠚⠋⢹⣿⣿⠋⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠑⠢⣈⠉⠁⠀⠒⠂⠬⠁⢒⠀⠅⠀⠀⠁⠠⠤⠀⠒⠺⠿⠋⠛⠋⠉⠉⠉⠉⠁⠁⠈⠀⠙⠋⠋⠙⠛⠿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⠉⠑⠲⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠲⠤⠤⠤⣤⡤⠄⢠⣀⠀⠀⠀⠈⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠛⠲⢤⣄⣀⠀⠀⠈⠉⠑⠒⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4816

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/9/2021:_liveslak-1.3.10_and_PipeWire_0.3.35⠀✐


Posted in News_Roundup at 1:00 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⠀➾


                # ⚓ System76_Updates_The_15″_Pangolin_with_Ryzen⠀⇛


                       System76 announced they’re updating the Ryzen-
                       powered Pangolin laptop to meet today’s need for
                       more power.


                       System76 is not just one of the most popular makers
                       of Linux-only hardware, they’re also really good at
                       pushing all of the boundaries and reinventing all
                       of the wheels. This latest move might not push or
                       reinvent, but it certainly gives consumers options
                       for more mobile power.


                       But this isn’t news, right? The Pangolin was
                       already available with an AMD Ryzen processor. This
                       is a situation where out with the old, in with the
                       new applies, because the company is upping the
                       Ryzen ante by offering the 15″ Pangolin with a
                       Ryzen 7 5700U CPU.


                # ⚓ AlmaLinux_8.4_on_my_IdeaPad_3_–_Decent,_with_a_snag_or
                  two⠀⇛


                       All in all, my AlmaLinux 8.4 experiment on the
                       IdeaPad 3 went well. Very nice considering this
                       being a relatively new device, with some relatively
                       new hardware in it (not innit, guv), plus the fact
                       AlmaLinux 8 is a conservative server distro with a
                       somewhat older kernel. In that regard, I had a
                       good, fast, stable experience. Solid speed, no
                       errors, pretty looks. Very desktopy, very
                       accessible. Triple boot, no issues and all that.


                       The Wireless card issue can be a dealbreaker for
                       many, though. Having to customize the system is
                       also a tricky one, ergonomics and all that. But, at
                       the end of the day, I had a very stylish,
                       functional system, and now I can focus on some
                       extra tweaking and testing. Can I call this: How to
                       turn AlmaLinux into a perfect desktop? Well,
                       almost. ‘Tis a good, promising start. Now, from a
                       pure usability perspective, this ain’t it, but
                       then, this also isn’t a desktop per se, which
                       explains my chipper and forgiving attitude.
                       Definitely worth exploring, and stay tuned for more
                       solid fun and nerdology.


          o § Audiocasts/Shows⠀➾


                # ⚓ The_5_things_holding_back_the_Librem_5_–_Invidious⠀⇛


                       The Librem 5 is very, very close to being the only
                       phone I carry around with me. But there are five
                       things holding it back. Let’s talk about them.


                # ⚓ Adventurous_Build_|_Self-Hosted_53⠀⇛


                       We chat with Matt from Adventurous Way about the
                       home automations that have improved his quality of
                       life, the clever way he manages their off-grid rig,
                       and the new smart home project he’s just kicking
                       off.


          o § Kernel Space⠀➾


                # ⚓ Looking_back_on_30_years_of_Linux_history_with_Red_Hat’s
                  Pete_Zaitcev⠀⇛


                       The Linux kernel and the second version of the GNU
                       General Public License (GPLv2) turned 30 this year.
                       As part of that major milestone we asked Red
                       Hatters who have been using or contributing to
                       Linux since the early days about their experiences.
                       What was it like contributing to Linux, what was it
                       like using it? Could you imagine that Linux would
                       have the impact it’s had on the world up until now?


                       Today we’re talking to Pete Zaitcev, who has been
                       contributing to Linux since the early 1990s,
                       joining Red Hat in 2001. Pete now works as a
                       Principal Software Engineer in Red Hat’s R&D
                       OpenStack Platform team.


                       [...]


                       A: I do not remember what my first proper
                       contribution was. I think it must have been a patch
                       to fix pseudo-DMA in floppy.c in August 1995.
                       Nobody cared who you were as long as the code was
                       good. My first attempt was to make a raster
                       console. It was required for SPARCstation, which
                       did not have a text mode. The prime customer for
                       that was David “DaveM” Miller, the leader of the
                       port to SPARC. However, my code was over-engineered
                       for what was needed. Although he accepted it in the
                       Sparclinux tree initially, DaveM eventually ripped
                       it out and replaced it with the raster console
                       developed by Geert Uytterhoeven for Amiga. I
                       remember being very disappointed. I wasn’t sure
                       Dave even made the right call. Thereafter I stuck
                       with minor fixes here and there.


                # ⚓ The_most_popular_AMD_Ryzen_CPUs_are_finally_getting
                  optimized_Linux_support⠀⇛


                       The latest AMD driver has posted patches to the
                       Linux kernel that’ll enable users to get better per
                       watt performance from their AMD Zen-based CPUs.


                       According to Phoronix, the drivers currently
                       support processors powered by the Zen 3
                       microarchitecture, such as the Ryzen 5000 desktop
                       processors, as well as the Epyc server processors.


                       “We would like to introduce a new AMD CPU frequency
                       control mechanism as the “amd-pstate” driver for
                       modern AMD Zen based CPU series in Linux Kernel,”
                       wrote Rui Huang, senior member of the technical
                       staff at AMD.


                # ⚓ Ext4_vs_XFS_–_Which_Filesystem_Should_You_Use⠀⇛


                       Users running a Linux system hardly pay attention
                       to the underlying filesystem. In fact, during the
                       installation of Linux, there’s a tendency to often
                       go with the default filesystem listed without
                       exploring other available options. For windows,
                       things are a lot easier since NTFS is the dominant
                       filesystem. With Linux, there are numerous
                       filesystems at your disposal. These include the
                       Ext4, XFS, ZFS, and BTRFS.


                       The most widely used filesystems are Ext4 and XFS,
                       with the latter being the default filesystem in
                       RHEL-based distros and Ext4 being the standard
                       filesystem in Debian and Ubuntu distributions. When
                       choosing a filesystem some of the factors that need
                       to be considered include scalability, stability,
                       and data integrity.


                # ⚓ Linux_Kernel_5.15_Will_Have_Improved_NTFS_File_System
                  Support⠀⇛


                       The Paragon’s NTFS driver was merged by Linux
                       creator Linus Torvalds earlier this month, bringing
                       reliable read and write functionality for this
                       filesystem to the kernel.


                       The last month, Linus Torvalds, the creator of
                       Linux, made it known to Paragon Software that it
                       should really submit a pull request for its read-
                       write NTFS driver to be included in the awaited
                       version 5.15 release, for which the merge window is
                       still open at the time of writing this.


                # ⚓ Linux_5.15_Readies_More_Code_For_Compile_&_Run-Time
                  Detection_Of_Buffer_Overflows_–_Phoronix⠀⇛


                       Last week a number of patches were merged in the
                       quest to provide the kernel with comprehensive
                       compile-time and run-time detection of buffer
                       overflows. Another patch series was sent out today
                       while still for this cycle they are expected to
                       enable the compiler warnings around array-bounds
                       and zero-length-bounds.


                       Kees Cook sent in the second batch of overflow
                       updates for Linux 5.15. This latest batch has tree-
                       wide changes to replace open-coded flex arrays in
                       unions, replacing zero-element memcpy()
                       destinations with flexible arrays, and a variety of
                       other improvements to improve the Linux kernel’s
                       buffer overflow detection and trying to make it an
                       issue of the past.


                # § Graphics Stack⠀➾


                      # ⚓ AMD_Just_Squeezed_More_Workstation_Performance_Out_Of
                        Its_RadeonSI_Driver_–_Phoronix⠀⇛


                             While Vulkan is quickly taking over as the
                             dominant graphics API for Linux gamers
                             especially with the likes of DXVK and VKD3D-
                             Proton mapping Direct3D atop Vulkan, OpenGL
                             remains widely used by workstation software.
                             It’s also for workstation software where
                             AMD’s “PRO” closed-source OpenGL Linux driver
                             has traditionally competed well (and
                             outperformed) the open-source Mesa driver.
                             But with all the recent changes, that’s
                             either a matter of the past or close to not
                             being relevant with the latest Mesa
                             enhancements.


          o § Benchmarks⠀➾


                # ⚓ Ubuntu_21.10_Performance_Still_Pushing_Ahead_Of_Windows_10,
                  Latest_Windows_11_Build⠀⇛


                       With less than one month out from the official
                       release of Microsoft Windows 11, I was curious to
                       run some fresh benchmarks of the latest Windows 11
                       Insider Preview build against Windows 10 21H1 to
                       see how the performance is looking. Of course, also
                       to see how Windows 11 is shaping up against Ubuntu
                       21.10 also due for release in October.


          o § Applications⠀➾


                # ⚓ Input_mapping_tool_AntiMicroX_3.1.7_is_out_with_improved
                  Wayland_support⠀⇛


                       AntiMicroX (a continuation of AntiMicro) for
                       mapping gamepad keys to keyboard, mouse, scripts
                       and macros has a new release out with version
                       3.1.7.


                       Thankfully for people who have moved from classic
                       X11 over to Wayland – you’re in luck. This version
                       brings on Wayland support for keyboard emulation!
                       This was achieved by moving from xtest to uinput
                       when wayland session is detected, and they’ve added
                       some new udev rules too. That’s the biggest change
                       with the rest being general bug fixes and
                       improvements.


                # ⚓ Cozy_–_modern_audio_book_player⠀⇛


                       Linux offers a huge array of open source music
                       players. And many of them are high quality. I’ve
                       reviewed the vast majority for LinuxLinks.


                       Cozy is different to the music players we’ve
                       covered. While it plays music the software is
                       geared to playing audio books. Cozy is free and
                       open source software. It’s written in Python.


                       Let’s see how it fares.


                # ⚓ OpenSnitch_Application_Firewall_1.4.0_Adds_eBPF_And
                  nftables_Support,_Allow/Block_Lists⠀⇛


                       OpenSnitch, a Linux port of the Little Snitch
                       application firewall for macOS, had a major new
                       release today. The latest OpenSnitch 1.4.0 adds the
                       ability to use eBPF to intercept processes,
                       nftables support, allow/block lists, GUI
                       improvements, and more.


                       The application is made of a daemon (written in Go)
                       and a GUI (PyQt5); a tray icon is also available
                       which you can use to open the OpenSnitch GUI,
                       disable the firewall or close it. While running,
                       OpenSnitch monitors outbound connections that your
                       applications are trying to make, preventing or
                       permitting their connection based on a set of rules
                       (the user is prompted to allow or deny access when
                       no existing rules are found).


                       It’s worth noting that the first time you run this
                       application-level firewall for Linux, it will
                       display many dialogs to allow or deny connections.
                       That’s expected since every process that tries to
                       make outbound connections is shown in a new popup
                       by OpenSnitch. But once you allow or deny your most
                       used applications, the application will remember
                       your preference, and it won’t bother you again.


                # ⚓ YOGA_Image_Optimizer_–_Graphical_Tool_to_Convert_&_Compress
                  PNG,_JPEG,_WebP⠀⇛


                       YOGA Image Optimizer is a graphical tool to batch
                       convert photos into JPEG, PNG and WEBP, and
                       compress file sizes while having equivalent
                       quality.


                       It’s a free and open-source tool based on YOGA
                       command line tool, which can also convert and
                       optimize 3D models from various formats to glTF and
                       GLB.


                # ⚓ PipeWire_Media_Server_0.3.35_Released⠀⇛


                       The release of the project has PipeWire 0.3.35 been
                       published , which develops a new generation
                       multimedia server to replace PulseAudio. PipeWire
                       has enhanced video streaming capabilities over
                       PulseAudio, low latency audio processing, and a new
                       security model for device and stream access
                       control. The project is supported in the GNOME and
                       already the default used in Fedora Linux. The
                       project code is written in C and is distributed
                       under the LGPLv2.1 license.


          o § Instructionals/Technical⠀➾


                # ⚓ MAKE_MORE_with_Inkscape_–_Ink/Stitch_–_Fedora_Magazine⠀⇛


                       Inkscape, the most used and loved tool of Fedora’s
                       Design Team, is not just a program for doing nice
                       vector graphics. With vector graphics (in our case
                       SVG) a lot more can be done. Many programs can
                       import this format. Also, Inkscape can do a lot
                       more than just graphics. The first article of this
                       series showed how to produce GCode with Inkscape.
                       This article will examine another Inkscape
                       extension – Ink/Stitch. Ink/Stitch is an extension
                       for designing embroidery with Inkscape.


                # ⚓ Setup_Lamp_in_Slackware_15.0_–_Unixcop⠀⇛


                       So Slackware is already in release candidate
                       available, this release is coming with many changes
                       on the core and on the packages, we will explain to
                       you to Setup LAMP stack Slackware 15.0 Server.


                # ⚓ 3_must-know_Linux_commands_for_text_manipulation⠀⇛


                       Sysadmins use an untold number of command-line
                       tools, and you probably regularly use the three
                       discussed in this article: grep, sed, and awk. But
                       do you know all the ways you can use them to
                       manipulate text? If not (or you’re not sure),
                       continue reading.


                # ⚓ A_nightmare_of_confcalls_and_microphones⠀⇛


                       I had this nightmare where I had a very, very
                       important confcall.


                       I joined with Chrome. Chrome said Failed to access
                       your microphone – Cannot use microphone for an
                       unknown reason. Could not start audio source.


                       I joined with Firefox. Firefox chose Monitor of
                       Built-in Audio Analog Stereo as a microphone, and
                       did not let me change it. Not in the browser, not
                       in pavucontrol.


                       I joined with the browser on my phone, and the
                       webpage said This meeting needs to use your
                       microphone and camera. Select *Allow* when your
                       browser asks for permissions. But the question
                       never came.


                # ⚓ How_to_format_a_harddisk_partition_with_BTRFS_on_Ubuntu
                  20.04_–_VITUX⠀⇛


                       Btrfs or commonly pronounced as b-tree FS or butter
                       FS is a COW (copy-on-write) based disk storage
                       format and filesystem. In btrfs, all characters
                       except / and Null are applicable for creating the
                       files featuring self-healing and the capability of
                       spanning multiple volumes. It was initially
                       developed by Oracle in 2007 and developed by
                       multiple companies such as Redhat, Linux
                       Foundation, Facebook, suse, etc.


                       Many features like sub volume file-system, extended
                       base file-system, mks skinny-metadata, ability to
                       link lost files to lost and found, etc. make it a
                       powerful file system compared to others. In this
                       article, I will show you how to create a disk
                       partition and format it with Btrfs file system on
                       Ubuntu 20.04 LTS.


                # ⚓ How_To_Install_Trimage_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Trimage on Ubuntu 20.04 LTS. For those of you who
                       didn’t know, Trimage is a cross-platform GUI and
                       command-line interface to optimize image files for
                       websites, using optipng, pngcrush, advpng and
                       jpegoptim, depending on the filetype (currently,
                       PNG and JPG files are supported). It was inspired
                       by imageoptim. All image files are losslessy
                       compressed on the highest available compression
                       levels, and EXIF and other metadata are removed.
                       Trimage gives you various input functions to fit
                       your own workflow: A regular file dialog, dragging
                       and dropping and various command-line options.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Trimage image compressor on
                       Ubuntu 20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ How_To_Install_Sublime_Text_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Sublime Text on Debian 11. For those of you who
                       didn’t know, Sublime Text is a cross-platform text
                       editor written in C++ and python and developed for
                       individuals who are looking for an effective yet
                       minimalist tool for shuffling code around. Not only
                       does it supports many languages, but you can also
                       even extend the functionality using plugins.


                       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 Sublime Text 4 on a Debian 11
                       (Bullseye).


                # ⚓ How_To_Install_Anaconda_on_Debian_11_–_TecAdmin⠀⇛


                       Anaconda is an open-source platform written with
                       Python programming language. It was built by data
                       scientists, for data scientists. Anaconda contains
                       a large variety of packages and repositories. It is
                       important in its functionality as it provides
                       processing and computing data on a large scale and
                       also to program in python language. The Anaconda is
                       a good platform to program python applications.


                       This article helps you to install Anaconda on your
                       Debian 11 (Bullseye) Linux system with easy
                       instructions.


                # ⚓ How_to_Install_MERN_Stack_for_JS_based_applications_on
                  Debian_11⠀⇛


                       MERN stack consists of four key technologies
                       MongoDB, Express, React, and Node. It is specially
                       designed for easier and faster deployment of full-
                       stack web applications. It is one of the most
                       popular and user-friendly development structures
                       that helps you to improve your applications to a
                       great extent. The MERN stack allows you to build a
                       3-tier architecture (frontend, backend, database)
                       entirely using JavaScript and JSON.


                       In this tutorial, we will show you how to install
                       the MERN stack on Debian 11.


                # ⚓ How_to_Install_Vivaldi_Browser_on_Debian_11_–
                  LinuxCapable⠀⇛


                       Vivaldi is a freeware, cross-platform web browser
                       developed by Vivaldi Technologies. It had grown
                       from the downfall of Opera with many disgruntled
                       when it changed from the Presto layout engine to a
                       Chromium-based browser, the platform that angered
                       traditional Opera users. Since then, Vivaldi has
                       become one of the most popular alternative Internet
                       Browsers amongst the big three Chrome, Firefox, and
                       Edge.


                       Vivaldi promotes itself as a leading browser with
                       faster navigation, clever bookmarking, smarter
                       browsing, extensive tab management, and a more
                       visual style approach to browsing than its
                       competitors.


                # ⚓ How_to_Set_JAVA_HOME_in_Ubuntu_Linux_Correctly⠀⇛


                       If you are running Java programs on Ubuntu using
                       Eclipse, Maven or Netbeans etc, you’ll need to set
                       JAVA_HOME to your path. Otherwise, your system will
                       complain that “java_home environment variable is
                       not set”.


                       In this beginner’s tutorial, I’ll show the steps to
                       correctly set Java Home variable on Ubuntu. The
                       steps should be valid for most other Linux
                       distributions as well.


                # ⚓ How_to_Change_WordPress_Site_URL_via_phpMyAdmin⠀⇛


                       Changing the WordPress site URL is an inevitable
                       activity. A growing WordPress site or one under
                       active development and testing introduces new URL
                       routes to make it more flexible, dynamic, and
                       easily explorable to the targeted internet users.


                       One reason to remove this issue of changing
                       WordPress site URLs from your bucket list is the
                       fact that your WordPress site developer might not
                       always be on speed dial.
                       When a WordPress site changes its domain name, the
                       domain name change does not automatically integrate
                       with the already configured site URLs.


                # ⚓ 3_Ways_to_install_Slack_Ubuntu_20.04_LTS_(Focal_Fossa)_–
                  Linux_Shout⠀⇛


                       Slack is a group collaboration tool designed for
                       teams that work in different locations. Primarily
                       used for communication in teams, as the service can
                       be perfectly integrated into the workflow. Users
                       can link Slack with many other services, for
                       example with cloud services such as Dropbox or with
                       social networks. So Slack becomes the focal point
                       of the action. At its core, Slack is instant
                       messaging software. In addition to direct
                       messaging, Slack enables communication “channels”
                       that can be organized by project, customer, team,
                       or any other way your company deems appropriate for
                       separate conversations. Channels are structured
                       according to the concept of a chat room: All
                       channel participants can take part in the
                       conversation and the messages appear in real-time.


                       Well, communication using Slack is possible both
                       between individuals and in groups. It comes with a
                       free plan suitable for small teams. You can use
                       this plan for as long as you want, but there are
                       limitations.


                # ⚓ How_to_install_and_use_wget_on_CentOS_6,_7_and_8⠀⇛


                       If you try to download something with wget on
                       CentOS 6/7 or 8 you will get the error : bash:
                       wget: command not found or bash: /usr/bin/wget: no
                       such file or directory and this is because wget is
                       not installed on your system, so to solve this
                       issue you need to install wget first then you can
                       use it to download anything you want.


          o § Games⠀➾


                # ⚓ Valve_rolls_out_big_Steam_client_update_with_new_Downloads
                  Page_&_Storage_Management_|_GamingOnLinux⠀⇛


                       After being in Beta since the end of July, Valve
                       has now released a big update to the stable version
                       of the Steam client for everyone which has the new
                       Downloads Page & Storage Management.


                       The new Downloads Page is actually a big
                       improvement overall. Allowing you to drag and drop
                       games around in the list. It now also correctly
                       shows the total progression based on the
                       downloading and disk allocation.


                # ⚓ Open_source_in_games:_How_to_save_your_studio_time_and
                  effort_|_GamingOnLinux⠀⇛


                       At the Game Developers Conference 2021, multiple
                       developers from Red Hat attended and gave a talk
                       titled “Open source in games: How to save your
                       studio time and effort”. GDC 2021 was held back in
                       July but only recently Red Hat put their
                       presentation video up so now everyone can view it.


                       For most normal gamers it probably won’t be a
                       hugely relevant talk but for developers it could be
                       an interesting one. The main thing is that Linux
                       had a presence at such a huge industry event.


                # ⚓ PS4_emulator_Spine_gets_a_new_demo_release_|
                  GamingOnLinux⠀⇛


                       Spine is an upcoming PlayStation 4 emulator that’s
                       currently closed-source while it’s under heavy
                       development. It’s also currently only available for
                       Linux. Well-known PlayStation “scener” Nagatoro
                       announced the new demo on Twitter along with a
                       download link.


                       What’s interesting is that the PS4 was the
                       generation to come back to x86 CPUs, instead of the
                       Cell style found in the PS3. This makes the
                       emulator a bit more like the Wine compatibility
                       layer and less like a full emulator, the developers
                       even announced it originally as it being “Wine-
                       like”.


                # ⚓ Tux_and_Fanny_is_the_most_completely_bizarre_adventure_and
                  it’s_out_now_|_GamingOnLinux⠀⇛


                       Ever heard of Tux and Fanny? It’s originally an
                       incredibly strange 2019 animated film by Albert
                       Birney who has teamed up with Ghost Time Games
                       (Jettomero, Test Tube Titans) to make an adventure
                       game out of it.


                       The film was so weird that it’s gained a small cult
                       following. I cannot express in clear enough wording
                       just how completely odd it is. Tux and Fanny
                       matches up well with a lot of the early classic
                       flash animations, it leaves that strange lasting
                       impression.


                # ⚓ Valve_Releases_Major_Steam_Client_Update_with_New_Downloads
                  Page,_Linux_Improvements⠀⇛


                       The biggest new feature of the new Steam Client
                       update is a brand new downloads page that’s easier
                       to use and has a new design. The new download page
                       now displays the total progress, including disk
                       allocation process, when downloading or updating a
                       game, as well as a faded progress bar and percent
                       completed for partially completed downloads or
                       updates.


                       In addition, the new downloads page will now
                       display a new icon next to a game’s title with a
                       tooltip showing the type of content included in the
                       update (e.g. Downloadable Content, Game Content,
                       Shader Pre-caching, or Workshop Content). Moreover,
                       users will now be able to re-order the download
                       queue using drag and drop, as well as to launch a
                       game or suspend download throttling from the
                       context menu of the actively downloading game.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Get_more_out_of_the_window_title_with_Konsole⠀⇛


                             If you use git on a regular basis, you should
                             look at using git-prompt; there is a file
                             called git-prompt.sh that is shipped with
                             git, the location in your setup varies
                             depending on the Linux distribution you’re
                             using, for example in OpenSuse it’s /etc/
                             bash_completion.d/git-prompt.sh. The file is
                             of course available in the upstream git repo.


                             Following the instructions from the top of
                             that file should give you a very useful
                             addition to the prompt of your shell (the
                             file has instructions for BASH and ZSH).
                             However that is not what this blog post is
                             about; this post is about making the Konsole
                             window title more useful, and by that I mean
                             use the window title to show the current dir
                             path and the info from git-prompt.


                      # ⚓ kdenlive_/_mlt_status_in_Debian_Bullseye⠀⇛


                             Debian 11 (Bullseye) comes with the mlt
                             framework 6.24.0 and kdenlive 20.12.3.
                             Unfortunately it was already too late
                             (freeze) to build mlt with enabled OpenCV
                             features, this are also required to use the
                             motion tracker features, which are now still
                             missing in the pure stable release.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ GNOME_41_RC1_Download_with_fixes_beta_bugs⠀⇛


                             The beta version for GNOME 41 from August
                             25th is now followed by a release candidate
                             GNOME 41 RC1 (Download). Release manager
                             Javier Jardón announced this on the GNOME
                             mailing list . The stable release of GNOME 41
                             is scheduled for September 22nd.


                      # ⚓ Cleaning_up_header_bars⠀⇛


                             Making the style feel lighter and reducing
                             visual noise is a major goal for the style
                             refresh we’re doing for libadwaita. While
                             we’ve done lots of smaller changes and
                             cleanups across the stylesheet to bring us
                             closer to that goal, this is probably the
                             highest-impact part of it due to how
                             prominent header bars are in GNOME apps.


                             This is not a new idea either — pretty much
                             everyone else is doing it, e.g. macOS,
                             Windows, iOS, Android, elementary OS, KDE.


                             In fact, we’ve been doing this for a long
                             time in view switchers. So this just extends
                             it to the whole header bar.


                             However, if applied carelessly, it can also
                             make certain layouts ambiguous. For example,
                             a text-only button with no background would
                             look exactly same as a window title. To
                             prevent that, we only remove background from
                             buttons that we can be confident won’t look
                             confusing without it — for example, buttons
                             containing a single icon.


                             While we avoid ambiguous situations, it also
                             means that apps will need changes to have
                             consistent buttons. In my opinion this is a
                             better tradeoff: since the API is not stable
                             yet, we can break behavior, and if an app
                             hasn’t been updated, it will just get
                             inconsistent look and not accessibility
                             issues.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ Linux_Release_Roundup_#21.37:_Lakka_Linux_3.4,_Tails
                        4.22,_GhostBSD_21.09.06,_and_More_New_Releases⠀⇛


                             In the Linux Release Roundup series, we
                             highlight the new distribution and
                             application version releases in the last few
                             days. This keeps you informed of the latest
                             developments in the Linux world.


                             ⚓  Lakka Linux 3.4⠀⇛


                             The retro gaming OS now runs on the latest
                             Retroarch 1.9.9. It has received many new
                             features, including AMD’s Fidelity FX, Mesa
                             21.2.1, and new console cores.


                             To know more, you can check out our original
                             coverage.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ KDE_Gear,_Plasma,_systemd_Update_in_Tumbleweed⠀⇛


                             There was one openSUSE Tumbleweed snapshot
                             this week out of five that brought an
                             enormous amount of package updates for those
                             using the rolling release.


                             Snapshot 20210904 brought updates for
                             systemd, GTK4, Mesa, KDE’s Plasma and Gear
                             and many other packages.


                             The most recent snapshot to be released was
                             20210908; it updated fuse3 3.10.5 and made
                             various improvements to unit tests more
                             robust for the Filesystem in Userspace
                             package. The mpg123 1.29.0 update added
                             an–enable-runtime-tables. An update of yast2
                             4.4.17 provided some maintenance for the
                             systemd package that arrived earlier in the
                             week. A few other packages like glslang
                             11.6.0, libstorage-ng 4.4.36 and pinentry
                             1.2.0 were also updated in the snapshot.


                             Snapshot 20210907 updated seven packages. The
                             package manager zypper 1.14.49 made a change
                             to avoid calling su as it can be too
                             restrictive for sudo user umask. The package
                             manager library libzypp also had an update to
                             version 17.28.3, which had a policy
                             modification for avoid the breaking of a
                             single rpm transaction. The AV1 decoder
                             package dav1d 0.9.2 had some Streaming SIMD
                             Extensions 3 and SSE4 optimizations for
                             x86_64. Other packages updated in the
                             snapshot were geoclue2 2.5.7, mozilla-nss
                             3.69.1, supermin 5.2.1 and an update to
                             plymouth.


                # § Slackware Family⠀➾


                      # ⚓ liveslak-1.3.10_and_new_ISO_images_for_Slackware_Live
                        Edition⠀⇛


                             The previous batch of ISOs for Slackware Live
                             Edition is already a few months old, so I
                             decided to generate new images.
                             The ISO files are based on Slackware-current
                             of “Wed Sep 8 18:07:38 UTC 2021” and using
                             the liveslak-1.3.10 scripts, where
                             passwordless login is a new feature.


                             Slackware-current has the label “15.0 Release
                             Candidate 1” since August 16th but
                             considering the amount of non-trivial updates
                             since that date, I wonder whether the phrase
                             “release candidate” has any relevance here.
                             No sign that we are anywhere nearer to a
                             final 15.0 release.


                             Let’s hope for the best, and in the meantime
                             fresh ISOs for the Slackware Live Edition can
                             be obtained at download.liveslak.org .


                             I refreshed he ‘bonus‘ section as well. There
                             you find several squashfs modules you can use
                             with your persistent liveslak USB stick. Copy
                             these module into the ‘addons’ directory on
                             the USB drive. They expand the functionality
                             of the Live OS and allow me to keep the ISO
                             file size within reasonable bounds.
                             Among these you’ll find the binary nvidia
                             driver (already contained in the CINNAMON,
                             DAW and MATE ISOs by the way); Wine 6.12,
                             multilib, the DAW package collection, and a
                             set from my own repository (chromium,
                             libreoffice, veracrypt, vlc etc).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Sumo_Logic’s_Continuous_Intelligence_Platform_Now
                        Available_On_Red_Hat_Marketplace⠀⇛


                             Sumo Logic and IBM have expanded their
                             alliance to announce the availability of Sumo
                             Logic’s Continuous Intelligence Platform on
                             Red Hat Marketplace, the open cloud
                             marketplace for enterprise customers that
                             offers a simpler way to buy and deploy
                             certified container-based software.


                      # ⚓ When_everything_is_in_the_cloud,_does_the_OS
                        matter?⠀⇛


                             With applications running in the cloud, it’s
                             easy to focus on the cloud services without
                             ever thinking of the underlying operating
                             system — or even needing to think about it.
                             It almost seems quaint, to think about
                             standard operating environments, base images,
                             and compatibility like it’s 2010.


                             When all of your innovation and future
                             projects are in the cloud, does the operating
                             system really matter anymore?


                      # ⚓ Remi_Collet:_PHP_version_7.4.24RC1_and_8.0.11RC1⠀⇛


                             Release Candidate versions are available in
                             testing repository for Fedora and Enterprise
                             Linux (RHEL / CentOS) to allow more people to
                             test them. They are available as Software
                             Collections, for a parallel installation,
                             perfect solution for such tests, and also as
                             base packages.


                             RPM of PHP version 8.0.11RC1 are available as
                             SCL in remi-test repository and as base
                             packages in the remi-php80-test repository
                             for Fedora 33-34 and Enterprise Linux.


                             RPM of PHP version 7.4.24RC1 are available as
                             SCL in remi-test repository and as base
                             packages in the remi-test repository for
                             Fedora 33-34 or remi-php74-test repository
                             for Enterprise Linux.


                      # ⚓ 5_tips_for_recruiting_an_open_source_job_candidate⠀⇛


                             This is one of those more open-ended posts in
                             that I don’t have any good answers, but I’ve
                             got a bunch of questions. I’d love to have
                             feedback, comments, and thoughts if you have
                             any.


                             Recently, it was “results week” in the UK.
                             Here, there are two major sets of exams that
                             most students take: GCSEs and A levels. The
                             former generally are taken by 16-year-olds,
                             with around 8-12 in total, and the latter by
                             18-year-olds, with 2-4 in total (3 being the
                             strong median). A level results are one of
                             the major criteria for entry into
                             universities, and GCSE results typically
                             determine what A levels students will take,
                             and therefore have an impact on university
                             course choice in the future.


                      # ⚓ Call_for_Projects_and_Mentors_for_Outreachy_December-
                        March_Cohort⠀⇛


                             Fedora will be participating in the upcoming
                             round of Outreachy (December 2021-March 2022)
                             and we are looking for more projects and
                             mentors!


                             Being a community of diverse people from
                             various backgrounds and different walks of
                             life, the Fedora Project has been
                             participating as a mentoring organization for
                             Outreachy internships for years. The
                             Outreachy program is instrumental in
                             providing a rich experience in working with
                             free and open-source software. Fedora is a
                             proud participant.


                      # ⚓ Moving_Forward_After_CentOS_8_EOL⠀⇛


                             The Linux community was caught unprepared
                             when, in December 2020, as part of a change
                             in the way Red Hat supports and develops
                             CentOS, Red Hat suddenly announced that it’s
                             cutting the official CentOS 8 support window
                             from ten years – to just two, with support
                             ending Dec 31, 2021.


                             It created a peculiar situation where CentOS
                             7 users that did the right thing and upgraded
                             quickly to CentOS 8 were left using an OS
                             with just a year’s official support remaining
                             – while users of CentOS 7 still get full
                             support until June 30, 2024.


                             Worse, the fact that stable releases of
                             CentOS were discontinued in exchange for the
                             rolling-release CentOS Stream means that to
                             secure their workloads most CentOS 8 users
                             have to opt for an entirely different Linux
                             distribution, with just a year to choose,
                             evaluate and implement an alternative.


                      # ⚓ 5_must-read_Harvard_Business_Review_articles_|_The
                        Enterprisers_Project⠀⇛


                             Each month, through our partnership with
                             Harvard Business Review, we refresh our
                             resource library with five new HBR articles
                             we believe CIOs and IT leaders will value
                             highly. Check out the curated pieces below,
                             available to readers through the end of the
                             month.


                      # ⚓ 6_IT_hiring_pitfalls_to_address_now_|_The
                        Enterprisers_Project⠀⇛


                             In terms of IT jobs, it’s largely a
                             candidate’s market. If the predicted post-
                             pandemic turnover tsunami hasn’t hit your
                             organization yet, it may soon. The hybrid
                             work options that the pandemic created means
                             that as an IT leader, you may have more open
                             roles – and a tougher time filling them.


                             That points to the need to step up retention
                             efforts. But there are also IT hiring
                             practices that need rethinking. Fine-tuning
                             your recruiting approach can improve your
                             ability to attract and retain top IT talent.


          o § Devices/Embedded⠀➾


                # ⚓ Musical_Cyberdeck_is_Part_Synth,_Part_MIDI_Controller,_and
                  All_Cool⠀⇛


                       When a new project type starts to get a lot of
                       exposure, it’s typically not long before we see
                       people forking the basic concept and striking out
                       in a new direction. It happened with POV displays,
                       it happened with Nixie clocks, and now, it seems to
                       be happening with cyberdecks. And that’s something
                       we can get behind, especially with cyberdecks built
                       to suit a specialized task, like this musical
                       cyberdeck/synth.


                       Like many musicians, [Benjamin Caccia] felt like he
                       needed a tool to help while performing with his
                       band “Big Time Kill.” He mainly needed to trigger
                       track playbacks on the fly, but also wanted
                       something to act as a mega-effects pedal and
                       standalone synth. And while most of that could be
                       done with an iPad, it wouldn’t look as cool as a
                       cyberdeck. The build centers around a Raspberry Pi
                       4 and a 7″ LCD display. Those sit on top of a 25-
                       key USB MIDI keyboard and a small mixer. Alongside
                       the keyboard is a USB keypad, which has custom
                       mappings to allow fast access to buried menu
                       functions in the cyberdeck’s Patchbox OS.
                       Everythign was tied together on a 3D-printed frame;
                       the video below shows it in action, and that it
                       sounds as good as it looks.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ EU_Begins_Antitrust_Investigation_Into_Google
                        Assistant_on_Android_–_Voicebot.ai⠀⇛


                      # ⚓ [Updated]_Want_to_disable_Tab_Groups_in_Chrome_on
                        Android?_Here’s_how⠀⇛


                      # ⚓ How_to_unlock_Android_phone_without_password_–
                        Phandroid⠀⇛


                      # ⚓ How_to_use_Android_12′s_new_one-handed_mode⠀⇛


                      # ⚓ Motorola_Android_11_update:_List_of_eligible_devices
                        &_release_date⠀⇛


                      # ⚓ The_Best_Android_Games_On_Sale_This_Week_–_KOTOR,
                        Titan_Quest,_Cyberlords_–_Arcology_and_More_–_Droid
                        Gamers⠀⇛


                      # ⚓ The_Best_Games_On_Android_For_18+_–_TechFinancials⠀⇛


                      # ⚓ Renault_joins_Volvo,_Polestar_in_offering_Google’s
                        Android_Automotive_in_production_vehicle_|_Automotive
                        News_Europe⠀⇛


                      # ⚓ An_innovative_ROUND_Android_smartphone_–_The_Cyrcle
                        Phone_2.0_-⠀⇛


                      # ⚓ SOVA:_New_Android_Banking_Trojan_Emerges_With_Growing
                        Capabilities⠀⇛


                      # ⚓ SOVA,_Worryingly_Sophisticated_Android_Trojan,_Takes
                        Flight_|_Threatpost⠀⇛


                      # ⚓ iOS_vs._Android_Security_–_4_App_Development_Experts
                        Share_Insights_[DesignRush_QuickSights]_|_News_|
                        wfmz.com⠀⇛


                      # ⚓ Google_Pay_on_Wear_OS_now_works_in_10_new_countries⠀⇛


                      # ⚓ Google_Assistant_Driving_mode_is_replacing_Android
                        Auto_on_phones_—_are_cars_next?_|_Android_Central⠀⇛


                      # ⚓ Renault_joins_Volvo,_Polestar_in_offering_Google’s
                        Android_Automotive_in_production_vehicle_|_Automotive
                        News_Europe⠀⇛


                      # ⚓ Google’s_made-for-India_cut_of_Android_and_the_one
                        phone_that_runs_it_delayed_by_chip_shortages,_testing_•
                        The_Register⠀⇛


                      # ⚓ Handheld_announces_new_version_of_the_NAUTIZ_X6
                        ultra-rugged_Android_phablet⠀⇛


                      # ⚓ Azulle_Ally_is_a_$150_Android_mini_PC_with_Snapdragon
                        450_–_Liliputing⠀⇛


                      # ⚓ Android_12′s_Material_You_Clock_app_works_on_older
                        versions_(APK_Download)⠀⇛


                      # ⚓ 6_Must-Have_Android_Apps_for_Cyclists⠀⇛


                      # ⚓ Top_10_Best_Investment_Android_Apps_–_2021⠀⇛


                      # ⚓ Top_3_Android_Antivirus_Software_With_VPN_In_2021⠀⇛


                      # ⚓ Fake_Cryptomining_Apps_Stole_Over_$350K_From_Android
                        Users⠀⇛


                      # ⚓ Tips_for_playing_your_favorite_shooters_on_an_Android
                        phone_–_9to5Google⠀⇛


                      # ⚓ TIM_Deploys_Technicolor’s_Next-Gen_Android_TV_Set-Top
                        Boxes⠀⇛


                      # ⚓ Bharti_Airtel_Android_DTH_Box_Might_Be_the_Best_In
                        India⠀⇛


                      # ⚓ How_To_Create_A_Logo_On_Android_Using_Logo_Maker_Apps
                        And_Online_Tools⠀⇛


                      # ⚓ Snapchat_Dark_mode_for_Android_phones:_Here’s_how_to
                        get_the_feature⠀⇛


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


                # ⚓ Building_an_open_source_community_health_analytics
                  platform⠀⇛


                       Rochester Institute of Technology (RIT) has made
                       considerable strides in increasing its presence in
                       the open source world lately. RIT’s Free and Open
                       Source Software and Free Culture minor is the first
                       of its kind in academia. For example, its open
                       source programs office, Open @ RIT, has begun
                       helping RIT faculty and staff fellows build and
                       maintain communities for their open source
                       projects.


                       These strides are driven by the students, faculty,
                       and staff at RIT. Already, a growing number of
                       people at the university are heading their own open
                       projects. However, running an entirely open source
                       project can be cumbersome. Much of this comes from
                       maintaining a community for the project and
                       managing data such as the project’s code, issue
                       tracking, and repositories.


                # ⚓ An_xrdesktop_summer_of_code⠀⇛


                       This summer, Christoph Haag and I had the pleasure
                       of taking part in Google Summer of Code (GSoC) as
                       mentors for xrdesktop, the Open Source project
                       bringing the Linux desktop to VR on SteamVR &
                       Monado. Our students, Remco and Manas, were both
                       able to finish their projects and submit merge
                       requests. Kudos!


                       As our tools of choice, C/GObject and Vulkan were
                       used in both projects, maintaining our goal of
                       keeping xrdesktop low level and thus providing a
                       performant XR experience.


                       Contributions like these support our vision with
                       projects like xrdesktop and Monado to provide a
                       fully open source XR stack that enables complete
                       control and independence for end users and product
                       builders alike.


                # ⚓ Briar:_The_right_open-source_messenger_for_activists⠀⇛


                       Briar is an open-source mobile massager application
                       with enhanced security for Android systems. It is
                       designed to protect its users from surveillance and
                       authority tracking.


                       With Briar, you don’t need to worry about messages
                       encryption as it uses a peer-to-peer encryption for
                       all messages and forums.


                       The app can work seamlessly even with or without
                       internet as it can sync the messages between
                       devices using Bluetooth, Wi-Fi or Tor network.


                       Using Briar messenger you don’t need to worry about
                       denial of service, metadata surveillance, message/
                       content surveillance, takedown and internet
                       blackouts.


                       Currently, the application works in the background,
                       and asks for some permission to run as camera
                       access, location access and Bluetooth access.


                # ⚓ Schedule_Finalized_for_Practical_Open_Source_Information
                  [Ed: BBB is good. Having said that, OSI’s Practical Open
                  Source itself is quite_the_farce with talks_for_sale]⠀⇛


                       We’d also like to point out several details
                       regarding event administration. We will be using an
                       instance of the open source web conferencing
                       system, BigBlueButton, to stream our talks and
                       panels at POSI, with hosting courtesy of our in-
                       kind sponsors at Blindside Networks.


                # ⚓ The_Apache_News_Round-up:_week_ending_10_September_2021⠀⇛


                       We’re wrapping up another great week with the
                       following activities from the Apache community…


                # § Programming/Development⠀➾


                      # ⚓ 5_Programming_Languages_you_must_know⠀⇛


                             Once upon a time, a few people were thought
                             to be software engineers with cutting-edge
                             coding skills. Currently, a good command of
                             many programming languages is required for a
                             variety of IT jobs. If you want to advance in
                             your career or change careers completely, you
                             may be considering which programming language
                             to study.


                             Given that learning a language will take time
                             and money, you must choose wisely. A few
                             considerations, for example, the difficulty
                             level you’re willing to learn, the
                             information you already have that corresponds
                             to your present coding talents, or your
                             motivation for learning a top programming
                             language, all play a role in your decision.


                      # § Python⠀➾


                            # ⚓ Five_things_to_know_before_learning_Python_|
                              Red_Hat_Developer⠀⇛


                                   Getting started with a new programming
                                   language can be challenging. Whether
                                   you’re a beginner or a grizzzled
                                   veteran, there are a number of larger
                                   context questions to answer that go
                                   beyond simply learning the language’s
                                   syntax. This article provides a high-
                                   level overview of five important things
                                   to keep in mind as you begin your
                                   journey into Python. You won’t learn
                                   the specifics of the language here, but
                                   you’ll gain a general picture of how
                                   Python works.


          o § Standards/Consortia⠀➾


                # ⚓ Six_Standards_Recommendations_for_the_Biden
                  Administration⠀⇛


                       Adopting an enlightened standards policy could
                       greatly advance the national interest in the area
                       of information and communications technology (ICT)
                       standards. And at no time in recent memory has the
                       need to do so been more urgent, as trade tensions
                       with China sustain rather than abate. Absent a
                       change in direction in policy, there is the
                       potential for standards wars between East and West
                       in areas such as 5G technology.


                       Maintaining a healthy standards development
                       ecosystem domestically is equally important, as
                       standards setting organizations (SSOs) annually
                       create hundreds of standards that are referenced
                       into law, at great savings in time and tax dollars
                       when compared to the costs of drafting regulations
                       within the government.


                       [...]


                       With the exception of specific treaty obligations,
                       international adoption of standards is entirely
                       voluntary and market driven. Competing standards
                       can, and often have, been used as competitive
                       weapons, both to exclude or burden foreign products
                       or to avoid licensing costs associated with
                       “standards essential patents” (SEPS). While both
                       the US and China are signatories of the World Trade
                       Organization Treaty on Technical Barriers to Trade
                       (TTBT), which bars signatory nations from adopting
                       local standards where suitable global standards
                       have become widely adopted, this did not prevent
                       China from launching its own wireless standard
                       (WAPI) in competition with Wi-Fi a decade and a
                       half ago, alleging that the Wi-Fi standard
                       developed by the IEEE provided insufficient
                       security.


                       The WAPI standard was encumbered by many SEPS owned
                       by Chinese companies (as, indeed, the competing Wi-
                       Fi standard was encumbered by SEPS owned by Western
                       companies). Licenses to those standards were
                       available only to certain Chinese companies. China
                       also developed its own 4G standard (CDMA) in
                       competition with two Western contenders. With the
                       largest population in the world, China was able to
                       use its competing standards to the benefit of its
                       domestic vendors. It has every incentive to do the
                       same now if trade tensions between the US and China
                       do not lessen.


                       Significantly, Huawei is recognized as owning more
                       5G patents than any other company in the world. It
                       is also believed to have been a member of c. 400
                       SSOs, many of which ejected Huawei or suspended its
                       participation after it was placed on the Entity
                       List. The intellectual property rights (IPR)
                       policies of virtually all of these SSOs require
                       participants to either license their SEPS on
                       “reasonable and non-discriminatory” (RAND) terms,
                       or to disclose them so that an attempt can be made
                       to revise the related standards to avoid
                       infringement. But this obligation only attaches to
                       companies participating in the working groups that
                       create the standards.


    * § Leftovers⠀➾


          o ⚓ EFB_Tampering._The_Human_Factor⠀⇛


                 Like most people, pilots want to expedite things and
                 generally make their work easier. A common conception
                 about aviation is that it’s a leading industry with
                 technology at its forefront. While this is generally true
                 some of the systems in use today are rather dated (to put
                 it mildly). A great example is the method that pilots use
                 in poor visibility to “find” the runway; their Instrument
                 Landing System (ILS), a technology invented in 1929.


                 [...]


                 The ILS is used on aircraft to help pilots navigating to
                 the runway on approach / landing in both a horizontal and
                 the vertical sense. Whilst there have many improvements
                 to ILS technology since its conception, the fact remains
                 that the ILS was invented in the 1920s and became
                 approved and adopted by ICAO in 1949. To this very day,
                 it remains the most accurate method available to
                 commercial pilots when it comes to navigating to the
                 runway.


          o § Hardware⠀➾


                # ⚓ Habana_Labs_Opens_Up_The_Code_To_Their_AI_Compiler,
                  SynapseAI_Core⠀⇛


                       Intel-owned Habana Labs now has the most open
                       software stack among AI accelerators! While Habana
                       Labs has long provided an open-source, upstream
                       kernel driver for their Gaudi AI training and Goya
                       AI inference accelerators, the user-space portions
                       including their code compiler and run-time library
                       have been closed-source. This has been a thorn for
                       upstream kernel developers and their standards, but
                       now Habana Labs has open-sourced their user-space
                       components too.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ SPDX_becomes_internationally
                                          recognized_standard⠀⇛


                                               In use for a decade as the
                                               de facto standard for
                                               communicating software
                                               bills of materials, The
                                               Linux Foundation has
                                               announced that the Software
                                               Package Data Exchange
                                               (SPDX) specification has
                                               been published as ISO/IEC
                                               5962:2021 and recognized as
                                               the open standard for
                                               security, license
                                               compliance and other
                                               software supply chain
                                               artifacts.


                      # § Security⠀➾


                            # ⚓ HAProxy_urges_users_to_update_after_HTTP
                              request_smuggling_vulnerability_found⠀⇛


                                   Users of HAProxy 2.0 and earlier
                                   versions are being urged to push
                                   through updates after a vulnerability
                                   was found that could allow “an attacker
                                   to bypass the check for a duplicate
                                   HTTP Content-Length header, permitting
                                   a request smuggling attack or a
                                   response-splitting attack.”


                            # ⚓ Security_updates_for_Friday⠀⇛


                                   Security updates have been issued by
                                   Debian (firefox-esr, ghostscript, ntfs-
                                   3g, and postorius), Fedora (java-1.8.0-
                                   openjdk-aarch32, libtpms, and salt),
                                   openSUSE (libaom, libtpms, and openssl-
                                   1_0_0), Red Hat (openstack-neutron),
                                   SUSE (grilo, java-1_7_0-openjdk,
                                   libaom, libtpms, mariadb, openssl-
                                   1_0_0, openssl-1_1, and php74-pear),
                                   and Ubuntu (firefox and ghostscript).


                            # ⚓ WordPress_Releases_Security_Update⠀⇛


                                   WordPress 5.4-5.8 are affected by
                                   multiple vulnerabilities. An attacker
                                   could exploit these vulnerabilities to
                                   take control of an affected website.


                                   CISA encourages users and
                                   administrators to review the WordPress
                                   Security and Maintenance Release and
                                   upgrade to WordPress 5.8.1.


                            # ⚓ New_ChaChi_malware_variant_designed_to_target
                              Linux_systems [Ed: More of that very typical_FUD
                              trying_to_blame_Go_and_Google because people can
                              write malicious software in some particular
                              language. It also blames “Linux” even though it’s
                              not clear how the malicious programs get there in
                              the first place and what that has to do with
                              Linux.]⠀⇛


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Surveillance_state_incoming_with
                                    Australia’s_“hacking”_bill_–_Access_Now⠀⇛


                                         Imagine that the data on your
                                         devices could not only be
                                         collected and copied, but also
                                         added to and modified (data
                                         disruption warrant). To make
                                         matters worse, imagine if any or
                                         all of your online accounts could
                                         be controlled by law enforcement
                                         without your knowledge, and you
                                         could potentially also be locked
                                         out of those accounts (account
                                         takeover warrant). Further, any
                                         network you interact with and all
                                         your electronic communications,
                                         whether on email, social media,
                                         or messaging platforms, could be
                                         intercepted (network activity
                                         warrant). Not only would all of
                                         this be done without your consent
                                         or knowledge, but the fact of
                                         access by law enforcement could
                                         also be concealed. This is how
                                         three new warrants under the
                                         Identify and Disrupt bill, or the
                                         hacking bill, jeopardise people’s
                                         data, privacy and security in
                                         Australia.


                                         Indeed, any device, online
                                         network or account, including
                                         social media profiles, used by
                                         people in Australia, could now be
                                         susceptible to hacking by
                                         Australian law enforcement
                                         agencies. The Identify and
                                         Disrupt Bill confers hacking
                                         powers on the Australian Federal
                                         Police (AFP) and the Australian
                                         Criminal Intelligence Commission
                                         (ACIC), enabling them to add,
                                         copy, delete or modify data,
                                         control online accounts and
                                         access communications data,
                                         through a data disruption
                                         warrant, an account takeover
                                         warrant, and a network activity
                                         warrant.


                                  # ⚓ ProtonMail_Now_Keeps_IP_Logs⠀⇛


                                         After being compelled by a Swiss
                                         court to monitor IP logs for a
                                         particular user, ProtonMail no
                                         longer claims that “we do not
                                         keep any IP logs.”


                                  # ⚓ ProtonMail_deletes_‘we_don’t_log_your_IP’
                                    boast_from_website_after_French_climate
                                    activist_reportedly_arrested_•_The
                                    Register⠀⇛


                                         Encrypted email service
                                         ProtonMail has become embroiled
                                         in a minor scandal after
                                         responding to a legal request to
                                         hand over to Swiss police a
                                         user’s IP address and details of
                                         the devices he used to access his
                                         mailbox – resulting in the
                                         netizen’s arrest.


                                         Police were executing a warrant
                                         obtained by French authorities
                                         and served on their Swiss
                                         counterparts through Interpol,
                                         according to social media rumours
                                         that ProtonMail chief exec Andy
                                         Yen acknowledged to The Register.


                                  # ⚓ Neutron:_A_Libre_Mail_server_for_Proton
                                    Webmail_client⠀⇛


                                         ProtonMail is an open-source
                                         webmail client distributed and
                                         licensed under GNU “General
                                         Public License” version 3.


          o § Defence/Aggression⠀➾


                # ⚓ Bob’s_9/11_post_from_20_years_ago_—_To_a_Man_With_a
                  Hammer⠀⇛


                       The point of terrorism is to leverage the efforts
                       of a small group in an attempt to modify the
                       behavior of a much larger group.


                       [...]


                       “To a man with a hammer, everything looks like a
                       nail,” wrote Mark Twain. In the current, context
                       this means that the organizations charged with
                       reacting to this catastrophe will do so by doing
                       what they have always done, only more of it.
                       Congress, which controls the budget and passes
                       laws, will want to pass laws and to allocate more
                       money, lots of money, forgetting completely about
                       any campaign promises. The military, which is the
                       nation’s enforcer, will want to use force, if only
                       they can find a foe. The intelligence community,
                       which gathers information, will want to be even
                       more energetic in that gathering, no matter what
                       the cost to the privacy of the millions of us who
                       aren’t thinking of terrorist acts. And agencies
                       like the Federal Aviation Administration, which
                       regulate, will want to create more stringent
                       regulations. Now here is an important point to be
                       remembered: All these parties will want to do these
                       things WHETHER THEY ARE WARRANTED OR USEFUL OR NOT.


                       In 1956 two airliners collided over the Grand
                       Canyon and the regulatory response was today’s air
                       traffic control system. The FAA felt that by
                       keeping most planes under positive control —
                       telling them where to go and when — they could
                       avoid future collisions. Yet collisions continue to
                       happen. In 1978 a Pacific Southwest Airlines plane
                       smashed into a small Cessna over San Diego despite
                       the fact that both planes were flying under
                       instrument rules and were under positive control.
                       The FAA response that time was to carve up even
                       more finely the sky over nearly every metropolitan
                       area, controlling the airspace even more
                       stringently with the intent of keeping instrument
                       and visual traffic apart. There was no visual
                       traffic in the San Diego accident, yet we still
                       live with rules that arose from that accident even
                       though those rules would not have prevented it.


                       So how will the FAA react this time? They will do
                       what they have always done, pass new and stricter
                       rules, and they will do so because it makes them
                       feel better, not because it will actually help.


                       [...]


                       Why, I find myself thinking, can’t we build a
                       system that takes over control of the autopilot,
                       locks out flight crew and hijackers alike, and
                       lands the plane at the first sign of trouble. Well,
                       we could, but it opens a whole new area of
                       vulnerability — hijacking autopilots. Forget I said
                       anything.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Uganda_charges_lawmakers_allied_to_opposition_leader_with
                  murder⠀⇛


                       Ugandan prosecutors on Tuesday charged two
                       lawmakers allied to opposition leader Bobi Wine
                       with the murder of three people, following a spate
                       of unsolved killings that have stoked widespread
                       public alarm.


                       Wine’s opposition National Unity Platform (NUP)
                       dismissed the prosecution of the two MPs, Muhammad
                       Ssegirinya and Mr Allan Ssewanyana, both NUP
                       members, as a politically motivated attempt by
                       authorities to smear the party.


                       Appearing at a court in Masaka town in central
                       Uganda, south of the capital Kampala, the two were
                       charged with the three murders and remanded in
                       prison, Joel Ssenyonyi, a fellow NUP lawmaker and
                       the party’s spokesperson, told Reuters.


                # ⚓ ‘Incredible_fear’_among_women_across_Afghanistan_-U.N.
                  official⠀⇛


                       A lack of clarity on the Taliban’s position on
                       women in Afghanistan has generated “incredible
                       fear” across the country, a senior U.N. official
                       said on Wednesday, warning there were daily reports
                       of curbs on the rights of women.


                       Alison Davidian, deputy head of UN Women in
                       Afghanistan, said some women were being prevented
                       from leaving home without a male relative, women in
                       some provinces were forced to stop work, protection
                       centers for women fleeing violence had been
                       targeted and safe houses for rights activists were
                       at full capacity.


          o § Civil Rights/Policing⠀➾


                # ⚓ Brazil’s_Restrictive_New_Social_Media_Rules_Could_Be_an
                  Omen_For_the_Future_of_the_Internet⠀⇛


                       Brazilian President Jair Bolsonaro signed a decree
                       on Monday that temporarily bans social media
                       platforms from removing many types of content,
                       including misinformation about COVID-19 and the
                       country’s upcoming presidential election.


                       Brazil’s new rules appear to be the first in the
                       world to make certain types of content takedowns
                       illegal under national law, even as other national
                       governments around the world implement rules that
                       force social media companies to take down more
                       types of content proactively.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ IFF_wrote_to_the_Haryana_Government_urging_restraint_on
                  internet_shutdowns⠀⇛


                       Between September 7, 2021 and midnight of September
                       9, 2021, internet services were suspended in four
                       districts of Haryana due to ongoing farmers’
                       protests. The order has been circulating on social
                       media, but is not available on the Government
                       websites. The order does not lay out a factual
                       justification for why the internet suspension is
                       required, and does not justify the geographical
                       extent of the suspension either. We wrote to the
                       Haryana government to officially publish all orders
                       related to the current internet shutdowns in the
                       state and proactively publish any subsequent
                       internet shutdown orders in compliance with the
                       Supreme Court of India’s judgment in Anuradha
                       Bhasin v. Union of India (2019).


                # ⚓ Why_you_should_be_more_concerned_about_internet_shutdowns⠀⇛


                       Deliberate internet shutdowns enacted by
                       governments around the world are increasing in
                       frequency and sophistication, according to a recent
                       report. The study, published by Google’s Jigsaw
                       project with the digital rights nonprofit Access
                       Now and the censorship measurement company Censored
                       Planet, says internet shutdowns are growing
                       “exponentially”: out of nearly 850 shutdowns
                       documented over the last 10 years, 768 have
                       happened since 2016.


                       India’s government has shut off the internet more
                       than any other—109 times in 2020 alone—and data
                       shows that shutdowns are most common around
                       elections and times of potential civil unrest,
                       leading to claims that it has become a tactic to
                       suppress dissent. But while they are becoming more
                       prevalent, shutdowns are also getting more subtle,
                       using tactics like throttling a URL to dramatically
                       slow its function, blocking particular internet
                       addresses, and restricting the use of mobile data.


                       MIT Technology Review sat down with Dan Keyserling,
                       the chief operating officer of Jigsaw, to discuss
                       the growing phenomenon.



                    ䷩ 𝚕𝚒𝚗𝚎 6790

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.10.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_10/9/2021:_Firefox_Ads_and_Sci-Hub_Turns_10⠀✐


Posted in News_Roundup at 9:50 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Applications⠀➾


                # ⚓ Best_Linux_Text_Editors:_The_20_Text_and_HTML_Editors
                  Reviewed⠀⇛


                       From jotting down your latest thoughts to writing
                       your most recent program, a text editor is a go-to
                       solution for Linux enthusiasts. Text editors are
                       perhaps the most used software in Linux systems.
                       They are used to modify system configs, administer
                       system resources, and other critical areas. So,
                       your choice of Linux text editor should be capable
                       enough to get the job done.


                # ⚓ Top_15+_Fast_and_Secure_Remote_Desktop_Clients_for_Linux⠀⇛


                       As you are a developer or administrator or even a
                       traveler, you might want to access the remote
                       desktop to perform any task, including mounting
                       remote directories, cleaning remote databases, or
                       even backing remote servers. In this situation, the
                       remote desktop clients help to communicate with the
                       remote RDP server for easy access. There are many
                       remote desktop protocols available for performing
                       the task of remote system access. It’s a
                       communication between the server and client
                       software.


                       Linux has the default SSH remote access tool to
                       perform this sort of job, but as it’s done through
                       the terminal, so many users do not feel comfortable
                       using it. Besides using the terminal, you can also
                       use GUI based remote desktop client for your Linux
                       system.


          o § Instructionals/Technical⠀➾


                # ⚓ Figuring_out_the_container_runtime_you_are_in_–_/home/
                  liquidat⠀⇛


                       Containers are pretty good at keeping everyone and
                       everything inside their boundaries – thanks to
                       SELinux, namespaces and so on. But they are not
                       perfect. Thanks to a recent Azure security flaw I
                       was made aware of a nice trick via the /proc/ file
                       system to figure out what container runtime the
                       container is running in.


                # ⚓ Helpful_tips_to_improve_Linux_system_performance_|_FOSS
                  Linux⠀⇛


                       We all detest when a running Linux system becomes
                       slow or sluggish over time. You might have invested
                       in powerful PC hardware but find it getting slow
                       when you run multiple applications. Linux systems
                       are known for their resilience and speed of
                       processes. However, sometimes processes or services
                       take longer to execute than expected.


                       The reasons can range from system applications
                       consuming your RAM, many unnecessary applications
                       consuming system resources, poorly configured
                       systems, or inefficient hardware resources that
                       cannot handle increasing demand.


                # ⚓ How_to_install_World_Painter_on_a_Chromebook⠀⇛


                       Today we are looking at how to install World
                       Painter 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.


                # ⚓ Install_Prometheus_and_Node_Exporter_on_CentOS_/_RHEL_8_–
                  Unixcop⠀⇛


                       Prometheus is a free software application used for
                       event monitoring and alerting. It records real-time
                       metrics in a time series database built using a
                       HTTP pull model, with flexible queries and real-
                       time alerting. The project is written in Go and
                       licensed under the Apache 2 License, with source
                       code available on GitHub, and is a graduated
                       project of the Cloud Native Computing Foundation,
                       along with Kubernetes and Envoy.


                # ⚓ How_to_install_Olive_Video_Editor_on_Linux_Lite_5.4_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       Olive Video Editor on Linux Lite 5.4. Enjoy!


                # ⚓ How_To_Setup_Chrooted_SFTP_In_Linux⠀⇛


                       This guide explains how to setup Chrooted SFTP in
                       Linux in order to restrict SSH user access to home
                       directory or any particular directory. To put this
                       in other words, we are going to force the users to
                       a specific directory and set their shell to /bin/
                       nologin or some other shell that denies access to a
                       ssh login. Once the chrooted SFTP is configured,
                       the users can only access their assigned home
                       directory, but not the entire filesystem


                # ⚓ How_to_access_clipboard_using_xclip_in_Ubuntu⠀⇛


                       A clipboard is non-permanent storage on your
                       computer for data that the user wants to copy from
                       one path to another. Later, you can also paste that
                       data stored in the clipboard to somewhere else as
                       well. Until logging off of the system or cutting/
                       copying something, the data on the clipboard is
                       saved. This might be a word selection, a picture, a
                       file, or any other form of data.
                       You can also clip text from one section of a
                       document and paste it into another portion of the
                       document or somewhere else in a word processing
                       program. The selected information will be copied
                       and kept in the clipboard till you paste it
                       somewhere. Xclip is a great tool that is used as a
                       clipboard in Ubuntu OS. This article is focussing
                       on how you can install and use Xclip clipboard.
                       Let’s begin:


                # ⚓ How_to_automount_USB_Drive_in_Ubuntu⠀⇛


                       USB (Universal Serial Bus) is a device which is
                       used as a medium of communication between two
                       peripherals, laptops and personal computers. We can
                       save data on USB from one computer and can copy it
                       to another computer by just using a plugin. When
                       USB is plugged into a computer it is mounted by the
                       operating system installed on that machine. By
                       default the USB is automatically mounted by the
                       operating system installed in a machine but
                       sometimes because of some issue like USB storage
                       device configurations are missing the USB devices
                       are not automatically mounted when they are plugged
                       in. In this case, we have to configure the USB
                       storage devices so that they can be automatically
                       mounted when the system is plugged in. Two methods
                       to auto mount the USB drive on Ubuntu are going to
                       be discussed in this post.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Privacy-Screen_DRM_API_With_Intel_Support_Ready_Now
                        That_GNOME_Is_Prepared_To_Use_It⠀⇛


                             Over the past two years we have seen work
                             around bringing up privacy screen support on
                             Linux whereby an increasing number of laptops
                             can reduce the amount of visible light when
                             viewed at wide angles to try to block the
                             screen contents from anyone potentially
                             snooping at the screen. Ready to go now is
                             the DRM/KMS user-space interface and the
                             Intel graphics driver support now that there
                             is a user-space “client” ready.


                             In recent times there has been Lenovo
                             PrivacyGuard work for Linux and Dell privacy
                             support. As part of enhancing the Lenovo
                             ThinkPad support there has also been a patch
                             series by Hans de Goede working on the
                             necessary changes from the DRM/KMS driver
                             side, coming up with a common user-space
                             interface via KMS properties for indicating
                             it, and getting it implemented for the Intel
                             i915 driver.


                             [...]


                             Thus the thinkpad_acpi driver will likely
                             need to be pulled into the initrd images of
                             distribution kernel builds if not already
                             done so.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ New_IBM_Power_E1080_server_promises_dramatic
                        increases_in_energy_efficiency,_power⠀⇛


                      # ⚓ Quarkus_for_Spring_Developers_|_Red_Hat_Developer⠀⇛


                             Java can be clunky and slow. Learn how to
                             optimize Java for today’s compute and runtime
                             demands with Quarkus—a Kubernetes-native
                             platform.


                      # ⚓ Red_Hat_to_help_bring_climate_impact_data_to_global
                        finance_industry [Ed: Red Hat is greenwashing_with
                        Microsoft while the servers pollute the planet; we’re
                        meant to think that the very worst culprits are the
                        solution]⠀⇛


                             Enterprise open source giant Red Hat has
                             joined OS-Climate (OS-C), a Linux Foundation-
                             backed initiative that’s setting out to
                             harness open source collaboration and big
                             data to push “global capital flows” into
                             climate change mitigation and resilience
                             initiatives.


          o § Devices/Embedded⠀➾


                # ⚓ Remembering_Intel_740_|_Custom_PC_#218⠀⇛


                # ⚓ Beelink_LZX_–_A_Zhaoxin_KX-6640MA_based_x86_Mini_PC_you_may
                  never_see_–_CNX_Software⠀⇛


                       The mini PC comes with Windows 10 operating system,
                       but it also supports the Unity Operating System
                       (UOS) and Kylin both of which are Linux
                       distributions for the Chinese market.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Mikron_MIK32_–_Made_in_Russia_32-bit_RISC-V_MCU
                        offers_features_similar_to_STM32L0_MCU_–_CNX_Software⠀⇛


                             The Mikron MIK32 is a 32-bit RISC-
                             V microcontroller made in Russia with
                             features similar to an STMicro STM32L0
                             Cortex-M0+ MCU that shows how RISC-V open-
                             source architecture can help lower the
                             barrier to entry, and let more companies
                             design their own chips.


                             The MIK32 microcontroller features CPU IP
                             from Syntacore based in Saint Petersburg
                             following the RV32IMC profile. Clocked a 32
                             MHz, the MCU comes with I2C, UART, SPI, ADC,
                             DAC interfaces, as well as various timers, an
                             interrupt controller, and more.


                      # ⚓ Wio_Lite_AI_–_An_STM32H725A_Cortex-M7_board_for_AI
                        vision_applications⠀⇛


                             Wio Lite AI is another development board from
                             Seeed Studio’s “Wio Lite” family. The board
                             is based on STMicro STM32H725A Cortex-M7
                             microcontroller with a dual-band WiFi and
                             Bluetooth module, as well as camera & display
                             interfaces for connected AI vision
                             applications.


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


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Feel_good_when_you_get_online_with_Firefox⠀⇛


                # § CMS⠀➾


                      # ⚓ Top_10_Open_Source_Affiliate_Management,_Marketing
                        Programs_For_2021⠀⇛


                             On this article, I’m going to show you 10
                             open source different affiliate platforms
                             that you can consider promoting if you’re
                             looking to make money with affiliate
                             marketing.


                             The affiliate is the person that is the
                             connector between the enterprise and the
                             consumer.


                             Basically, the affiliate is the middle person
                             between the company and consumers. They work
                             independently as an affiliate, so he has no
                             boss he’s basically they are a boss because
                             he has no boss.


                             Affiliate it’s simple to find consumers and
                             here’s the key who are interested in the
                             company’s product then affiliate will tell


                # § Openness/Sharing/Collaboration⠀➾


                      # § Open Access/Content⠀➾


                            # ⚓ Sci-Hub_Celebrates_10_Years_Of_Existence,_With
                              A_Record_88_Million_Papers_Available,_And_A_Call
                              For_Funds_To_Help_It_Add_AI_And_Go_Open_Source⠀⇛


                                   To celebrate ten years offering a large
                                   proportion of the world’s academic
                                   papers for free — against all the odds,
                                   and in the face of repeated legal
                                   action — Sci-Hub has launched a funding
                                   drive:


                # § Programming/Development⠀➾


                      # ⚓ What_they_don’t_tell_you_when_you_translate_your
                        app⠀⇛


                             I recently had the privilege of helping a
                             client with localization efforts for their
                             website. There are some things I did not run
                             into in my web research that I learned in
                             actually doing the work, things that I feel
                             are worth capturing and sharing: [...]


                      # ⚓ How_to_add_elements_into_an_array_in_JavaScript⠀⇛


                             Arrays are data structures which are used to
                             keep multiple values in a variable. A single
                             JavaScript array can have multiple element
                             types stored in it. It can be modified even
                             after it has been declared and initialized.
                             JavaScript arrays offer a lot of built-in
                             methods which can be used to access and
                             manipulate data stored inside them.


                             In this how-to guide we will discuss four
                             different methods which can be used to add
                             elements into JavaScript arrays.


                      # ⚓ Dirk_Eddelbuettel:_RcppSMC_0.2.5_on_CRAN:_Build
                        Update⠀⇛


                             A week after the 0.2.5 release bringing the
                             recent Google Summer of Code for RcppSMC to
                             CRAN, we have a minor bug-fix release
                             consistently, essentially, of one line.
                             “Everybody’s favourite OS and toolchain” did
                             not know what to make of pow(), and I
                             seemingly failed to test there, so shame on
                             me. But now all is good thanks to proper use
                             of std::pow().


                             RcppSMC provides Rcpp-based bindings to R for
                             the Sequential Monte Carlo Template Classes
                             (SMCTC) by Adam Johansen described in his JSS
                             article. Sequential Monte Carlo is also
                             referred to as Particle Filter in some
                             contexts. The package now features the Google
                             Summer of Code work by Leah South in 2017,
                             and by Ilya Zarubin in 2021.


                      # ⚓ How_do_you_append_to_a_Vector_in_C++?⠀⇛


                             Appending to a vector means adding one or
                             more elements at the back of the vector. The
                             C++ vector has member functions. The member
                             functions that can be used for appending are:
                             push_back(), insert() and emplace(). The
                             official function to be used to append is
                             push_back(). The use of these three member
                             functions to append to a C++ vector is
                             explained in this article.


                      # ⚓ How_Do_You_Find_Something_in_a_Vector_in_C++?⠀⇛


                             C++ vector does not have a find member
                             function. However, the algorithm library has
                             a find() function of different types that can
                             be used to find something in a C++ vector.
                             The algorithm library has four groups of find
                             () functions that can be classified as Find,
                             Find End, Find First, and Adjacent Find.


    * § Leftovers⠀➾


          o ⚓ Heading_Into_the_Fall⠀⇛


          o ⚓ Opinion_|_An_Unwillingness_To_Abide_Lost_Cause_Idolatry_Any
            Longer:_Robert_E._Lee_Comes_Down_At_Last⠀⇛


          o ⚓ So_Long_to_a_Sense_of_Community⠀⇛


                 As the echoes of 1960s’ solidarity lose even their place
                 in the rearview mirror of life, and slogans from
                 political campaigns that purport to hold community in awe
                 (“Not me. Us.”), perhaps a reckoning demands attention?


                 The left, or at least those who could fit into a defunct
                 phone booth of old, is now siloed into identity movements
                 of either one kind or another. What prospects are there
                 for any kind of community? The sad, if not disastrous
                 answer, is nearly none.


          o § Education⠀➾


                # ⚓ Why_won’t_Donald_Trump_go_away?_Because_Americans_can’t
                  tell_appearance_from_reality⠀⇛


                       There are those who argue we’ve long been unable to
                       tell the difference between appearance and reality,
                       while others believe it is a recent phenomenon
                       caused by misinformation. But rather than arguing
                       which came first, we need to focus on those who
                       don’t recognize the problem at all.


          o § Health/Nutrition⠀➾


                # ⚓ Conservationists_and_Locals_Praise_Biden_EPA’s_Move_to
                  Protect_Bristol_Bay_From_Pebble_Mine⠀⇛


                       Conservationists, local tribes, and commercial
                       fishers celebrated on Thursday the Biden
                       administration’s move to permanently protect
                       Alaska’s Bristol Bay watershed from the proposed
                       Pebble Mine and similarly destructive projects.


                       “The people of Bristol Bay are counting on the EPA
                       to listen to the science and finish the job of
                       protecting our lands and waters.”—Robert Heyano,
                       United Tribes of Bristol Bay


                # ⚓ Address_the_Global_Public_Health_Crisis:_Ban_Glyphosate
                  Now!⠀⇛


                       (Since this article was written, Jose Tarazona has
                       stepped down from his position and the letter has
                       been forwarded to his successors, Manuela Tiramani
                       and Benedicte Vagenede.)


                       Mason wrote to Tarazona  because the licence for
                       glyphosate is up for renewal in the EU in 2022 and
                       the Rapporteur Member States (France, Hungary, the
                       Netherlands and Sweden), tasked with risk assessing
                       glyphosate and appointed by the European Commission
                       in 2019, said in June 2021 that there was no
                       problem with glyphosate-based herbicides, the
                       world’s most widely used weedkillers in
                       agriculture.


                # ⚓ ‘Time_for_Waiting_Is_Over’:_Biden’s_New_Vaccine
                  Requirements_Target_US_Workforce⠀⇛


                       “The time for waiting is over,” President Joe Biden
                       said in a televised address at the White House on
                       Thursday.


                       In an effort to bring the coronavirus pandemic
                       under control as the ultra-contagious Delta variant
                       kills about 1,500 Americans per day and imperils
                       the nation’s fledgling economic recovery, Biden on
                       Thursday announced new vaccine requirements
                       affecting tens of millions of workers in the United
                       States.


                # ⚓ LA_School_District_Is_Considering_Mandatory_Vaccinations
                  for_Students_12_&_Older⠀⇛


                # ⚓ ‘Appalled’_by_Vaccine_Booster_Plans,_WHO_Chief_Rebukes_Big
                  Pharma,_Rich_Nations⠀⇛


                       With the Biden administration expected to begin
                       offering third doses of Pfizer’s coronavirus
                       vaccine to the U.S. public in less than two weeks
                       despite vocal pushback from many experts, the head
                       of the World Health Organization on Wednesday
                       demanded a moratorium on booster shots until at
                       least the end of the year in order to free up
                       supply for low-income nations.


                       “Low- and lower-middle income countries are not the
                       second or third priority.”—Dr. Tedros Adhanom
                       Ghebreyesus


                # ⚓ Biden_to_Issue_Covid-19_Vaccine_Mandate_for_Federal
                  Workers⠀⇛


                       During a Thursday night speech laying out his
                       administration’s plans to contain the coronavirus
                       pandemic that continues to overwhelm the nation’s
                       hospitals, U.S. President Joe Biden is expected to
                       announce that the vast majority of federal workers
                       must be vaccinated against Covid-19.


                       According to the New York Times, “The mandate will
                       apply to employees of the executive branch,
                       including the White House and all federal agencies
                       and members of the armed services—a workforce that
                       numbers more than four million—but not to those who
                       work for Congress or the federal court system.”


                # ⚓ Opinion_|_Vaccine_Mandates_and_Patent_Waivers_for_the
                  Common_Good⠀⇛


                       The upsurge of COVID-19 cases, hospitalizations,
                       and deaths in the United States serves as a bitter
                       reminder that the pandemic is not over. The global
                       economy will not return to normal until the disease
                       is under control everywhere.


                # ⚓ Health_Advocates_Say_Biden’s_Global_Covid-19_Summit_Must_Be
                  ‘More_Than_Just_PR’⠀⇛


                       With the White House expected to propose a late-
                       September international summit on the coronavirus
                       pandemic response, health justice advocates on
                       Thursday told the Biden administration that for the
                       meeting to be “more than just PR,” rich governments
                       must commit to ramping up vaccine production and
                       rectifying the grossly unequal distribution of
                       lifesaving jabs.


                       “Biden has an opportunity to help launch an urgent
                       global vaccine manufacturing, delivery, and
                       knowledge sharing program that can fight variants
                       and end the pandemic.”—Peter Maybarduk, Public
                       Citizen


                # ⚓ Florida_Judge_Shoots_Down_Ron_DeSantis’s_Mask_Ban_for
                  Second_Time_in_2_Weeks⠀⇛


                # ⚓ Biden_Set_to_Mandate_Vaccinations_for_Federal_Workers_With
                  No_“Opt-Out”_Options⠀⇛


                # ⚓ 88,000_tons_of_radioactive_waste_–_and_nowhere_to_put_it⠀⇛


                # ⚓ Nearly_18_Million_US_Adults_Couldn’t_Afford_a_Prescription
                  Medication_This_Year:_Study⠀⇛


                       Around 15.5 million U.S. adults under the age of 65
                       and 2.3 million seniors were unable to afford at
                       least one doctor-prescribed medication this year,
                       according to a study released Thursday as the Biden
                       administration unveiled its plan to reduce the
                       nation’s sky-high drug prices.


                       The new study (pdf) was based on four nationally
                       representative surveys conducted in recent months
                       by the polling outfit Gallup in partnership with
                       West Health, a nonprofit organization focused on
                       lowering healthcare costs.


                # ⚓ Years_after_9/11,_first_responders_are_still_dying_from
                  exposure._This_is_their_story⠀⇛


                       The problem with this mainstream narrative is that
                       it frames those attacks as something singular and
                       isolated: they happened, and people died tragically
                       on that horrific day. But that is not the reality
                       lived by hundreds of thousands of 9/11 World Trade
                       Center first responders and survivors. For them,
                       it’s not over: the death toll continues to mount
                       every week since. It will continue to do so late
                       into this century. For them, 9/11 is a 20-year (and
                       counting) ordeal of mass death.


                       This is the untold 9/11 narrative, in which the
                       United States was attacked; and then, in the days
                       and months after, first responders and the people
                       that lived, worked and studied in lower Manhattan
                       and western Brooklyn were betrayed both by
                       municipal officials and the Bush administration’s
                       Environmental Protection Agency. The reason, of
                       course, relates to money: Officials in both
                       agencies were more concerned amount preserving the
                       pulse of Wall Street than the lungs of close to a
                       half million people, including roughly 90,000
                       rescue and recovery workers.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Manjaro_Cinnamon_Switches_Default_Browser_To
                        Vivaldi⠀⇛


                             Manjaro and Vivaldi announced a change to the
                             default browser for the popular community
                             edition Manjaro Cinnamon from the open-source
                             Firefox to Chromium-based Vivaldi. The
                             Manjaro team is hoping that this move gives
                             Vivaldi the attention it deserves according
                             to Bernhard Landauer of Manjaro.


                             Vivaldi offers many features such as tab
                             grouping, split screen support, built-in mail
                             client, and gestures. Vivaldi also offers
                             many privacy controls such as anti-tracking
                             and ad blocking by default. The company
                             Vivaldi Technologies was founded by Tatsuki
                             Tomita and Jon Stephenson von Tetzchner, who
                             was the co-founder and CEO of Opera Software.


                      # ⚓ Manjaro_Cinnamon_changes_to_Firefox_from_Vivaldi_as
                        default_web_browser⠀⇛


                             There are few Linux distributions that give
                             these kinds of surprises and Manjaro is one
                             of them. We are talking about changing the
                             usual defaults , usually free software
                             totems, for more debatable and even
                             proprietary alternatives, as is the case at
                             hand: Manjaro Cinnamon puts Vivaldi as the
                             default web browser and although it is still
                             an anecdote for the no importance of this
                             particular flavor …


                             Indeed, it is a controversial decision for
                             what it means: replacing free software with
                             proprietary software, when it is not
                             essential . As you know, it is very common
                             for Linux distributions to include
                             proprietary add-ons to offer the basic or
                             desired functionality, that is, both so that
                             certain hardware components work, and so that
                             they do so with the best guarantees. This is
                             usually done through drivers.


                             But it is also common for large Linux distros
                             to facilitate the installation of popular
                             proprietary applications, such as Steam,
                             Spotify, VSCode or many others. What is quite
                             unusual is to find a distribution that pre-
                             installs some of these applications, much
                             less one that replaces a free software
                             application with a proprietary one, when the
                             free one meets contracted quality
                             requirements.


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Damned_If_You_Do;_Damned_If_You_Don’t:
                                    ProPublica’s_Bizarre_Reporting_On_WhatsApp
                                    Abuse_Reports⠀⇛


                                         I’ve been struck over the years
                                         by how much reporting on
                                         technology involves attacking
                                         companies for what they do — even
                                         if for totally contradictory
                                         reasons. Everything is viewed
                                         through the lens of assuming the
                                         worst possible intentions. And,
                                         yes, sometimes perhaps that’s
                                         deserved. Companies act badly and
                                         no one should give them the
                                         benefit of the doubt if they
                                         can’t show reasons it ought not
                                         to be. But sometimes, it just
                                         gets ridiculous, as is clear in a
                                         recent ProPublica piece that
                                         attacked WhatsApp for its
                                         “report” feature. Now, I like
                                         ProPublica a lot and feel that
                                         they do some of the best
                                         investigative reporting around.
                                         But this was not that.


                                  # ⚓ EFF_Activists_To_Lead_Protest_Demanding
                                    Apple_Cancel_iPhone_Scanning_Program_and
                                    Keep_Its_Privacy_Promises_To_Customers⠀⇛


                                         For more about Apple’s program:
                                         https://www.eff.org/deeplinks/
                                         2021/08/apples-plan-think-
                                         different-about-encryption-opens-
                                         backdoor-your-private-life


                                  # ⚓ Don’t_Stop_Now:_Join_EFF,_Fight_for_the
                                    Future_at_Apple_Protests_Nationwide⠀⇛


                                         Activists from EFF, Fight for the
                                         Future, and other digital civil
                                         liberties organizations have
                                         planned protests around the
                                         country for Monday, September 13,
                                         at 6PM PT to demand that Apple
                                         completely drop its planned
                                         surveillance software program.
                                         You can find a list of the
                                         protests here. Protests are
                                         already planned in Boston,
                                         Atlanta, Washington D.C., New
                                         York City, and Portland (OR).


                                         EFF will host a protest at San
                                         Francisco Union Square, with
                                         signs, stickers, and speakers,
                                         but you can protest no matter
                                         where you are:


                                  # ⚓ The_Catalog_of_Carceral_Surveillance:
                                    Prison_Gaming_and_AR/VR_Services⠀⇛


                                         In one of their newest patents,
                                         granted February of 2021, Securus
                                         describes their latest
                                         revolutionary technology. A
                                         tablet, which would be issued to
                                         individual inmates to allow them
                                         to make video calls, access
                                         information about their case, and
                                         give them the opportunity to pay
                                         money for temporary access to
                                         video games. WIth this new
                                         invention Securus re-asserts
                                         their determination to extract
                                         every last penny from
                                         incarcerated people. Just because
                                         you are in prison doesn’t mean
                                         you get a pardon from the
                                         insatiable maw of capitalism. 


                                         Not only is this tablet useful
                                         for extracting money from
                                         prisoners. Securus also proposes
                                         that it can also be used as a
                                         biometric surveillance device.
                                         According to the patent: “the
                                         monitoring system may be
                                         configured to collect sensor
                                         information from the resident
                                         communications device in order to
                                         detect unsafe conditions during a
                                         gaming session. For instance, the
                                         monitoring system may collect
                                         sensor information from the
                                         resident communications device
                                         indicating a level of stress or
                                         agitation by the resident during
                                         game play. One or more gyroscope
                                         sensors included within the
                                         resident communications device
                                         may be used to detect unsafe
                                         handling of the resident
                                         communications device. Heart rate
                                         and blood pressure information
                                         detected by sensors worn by the
                                         resident may be transmitted via
                                         RFID (Radio Frequency
                                         Identification) to the resident
                                         communications device.”


                                         Taking this to its logical
                                         conclusion, the sensors and
                                         biometrics in such a handheld
                                         device could be used as an
                                         indicator of a prisoners mood, if
                                         the prisoner gets excited or
                                         angry at the game the system
                                         could determine that the prisoner
                                         is uncooperative or a recidivism
                                         risk, this data could potentially
                                         be used in parole hearings or
                                         when deciding to give
                                         punishments/rewards to prisoners.
                                         If Securus has its way, your
                                         “gamer moment” could land you in
                                         trouble and even then you will
                                         have no escape from micro
                                         transactions. 


                                  # ⚓ Australian_Surveillance_Has_Reached_New
                                    Heights_–_Invidious⠀⇛


                                         The world is watching Australia
                                         right now and is looking on in
                                         confusion because we keep making
                                         mistake after mistake after
                                         mistake and some how we’ve now
                                         reached an insane level of
                                         surveillance that has been tried
                                         in the past and wasn’t a good
                                         idea then and still isn’t a good
                                         idea now.


                                  # ⚓ Twitter_takes_on_Facebook_Groups_with
                                    invite-only_Communities⠀⇛


                                         Similar to how groups on Facebook
                                         and Reddit’s subreddits work,
                                         each Twitter Community will have
                                         its own moderators who are able
                                         to set rules and invite or remove
                                         people. Twitter invited a handful
                                         of users to create the first
                                         Communities and will let anyone
                                         apply to create their own on its
                                         website. “Communities are just
                                         invite-only for now, but we’re
                                         working on ways for people to
                                         discover and join Communities
                                         they want to be a part of,” the
                                         company said in a statement. That
                                         makes Communities harder to join
                                         than subreddits or public groups
                                         on Facebook. Twitter is also
                                         approving moderators to start.


                                  # ⚓ Facebook_developing_machine_learning
                                    chip:_Report⠀⇛


                                         Facebook Inc is developing a
                                         machine learning chip to handle
                                         tasks such as content
                                         recommendation to users, The
                                         Information reported on Thursday,
                                         citing two people familiar with
                                         the project.


                                         The company has developed another
                                         chip for video transcoding to
                                         improve the experience of
                                         watching recorded and live-
                                         streamed videos on its apps,
                                         according to the report.


                                  # ⚓ Twitter_is_beginning_to_test_labels_for
                                    bot_accounts⠀⇛


                                         Initially, in what Twitter is
                                         calling a test, a small number of
                                         developers will be invited to be
                                         able to apply the labels to their
                                         accounts. For accounts in the
                                         test that have activated the
                                         labels, an “Automated” label will
                                         appear on profile pages and on
                                         tweets themselves for accounts.
                                         Twitter says all developers will
                                         be able to use the labels by the
                                         end of the year.


          o § Defence/Aggression⠀➾


                # ⚓ Opinion_|_How_Can_America_Wake_Up_From_Its_Post-9/11
                  Nightmare?⠀⇛


                # ⚓ Why_America_Goes_to_War⠀⇛


                       Innumerable wars originate, wrote Alexander
                       Hamilton in Federalist No. 6, “entirely in private
                       passions; in the attachments, enmities, interests,
                       hopes, and fears of leading individuals in the
                       communities of which they are members.” As an
                       illustration of this truth, he cited the case of
                       Pericles, lauded as one of the greatest statesmen
                       of classical Athens, who “in compliance with the
                       resentment of a prostitute, at the expense of much
                       of the blood and treasure of his countrymen,
                       attacked, vanquished, and destroyed the city of the
                       Samnians” before igniting the disastrous
                       Peloponnesian War in order to extricate himself
                       from political problems back home. Adapted from The
                       Spoils of War by Andrew Cockburn (Verso Books,
                       September 2021).


                # ⚓ New_Opportunities_For_Progressives_in_an_Evolving_Middle
                  East?⠀⇛


                       First, NATO partners still retain their concern
                       over terror threats emanating from the less stable
                       areas of the region. The American reliance on Qatar
                       to broker a deal with the Taliban and assist in
                       permitting a (relatively) orderly withdrawal from
                       Afghanistan is a case in point.


                       Second, and related to the first, is persistent
                       concern over Iran. In American (and Israeli) eyes
                       at least, Iran still aspires to be a nuclear power,
                       as well as a conventional military power able to
                       counter the influence of the “pro-Western” states.
                       Through its Shi’ite proxies and other allies, Iran
                       continues to expand its presence in the region,
                       whether in Iraq, Syria, Lebanon (though Hizbollah)
                       and Gaza in one direction, into Yemen in another.
                       While there are signs of pragmatic relations
                       developing among such former adversaries as Iran,
                       Saudi Arabia, and the Taliban, Iran remains a major
                       source of American apprehension.


                # ⚓ Twenty_Years_After_9/11:_a_Health_Worker’s_Perspective⠀⇛


                       On the following day, the University of Hawaiʻi
                       Department of Family Practice (before the name was
                       changed to Family Medicine) held a debriefing
                       session with all staff, residents, and faculty in
                       attendance. We came to some conclusions that we
                       wrote about in the medical school newsletter:


                       One participant, a Muslim and Arab woman, was
                       silent through most of the session, but at the end,
                       she related that she first wanted to hear what
                       others had to say. She told us that she had grown
                       up with, and constantly lived with anti-Muslim,
                       anti-Arab sentiments being expressed around her –
                       such that she often found it most prudent to hide
                       her ethnicity.


                # ⚓ Opinion_|_20_Years_of_Wasted_Money_and_Missed_Opportunities
                  Since_9/11⠀⇛


                       Twenty years have now passed since 9/11.


                # ⚓ Many_FBI_Files_on_9/11_Remain_Classified._Victims’_Families
                  Want_Them_Released.⠀⇛


                # ⚓ The_Fierce,_Enduring_Legacy_of_America’s_Anti–Afghanistan
                  War_Protests⠀⇛


                       After 20 years of US imperial intervention,
                       Afghanistan is a deeply war-wounded country, its
                       cities in ruins and hundreds of thousands of its
                       people in graves. It didn’t have to end this way.


                # ⚓ The_$8_Trillion_Cost_of_Failure⠀⇛


                       They weren’t kidding when they called Afghanistan
                       the “graveyard of empires.” Indeed, that cemetery
                       has just taken another imperial body. And it wasn’t
                       pretty, was it? Not that anyone should be
                       surprised. Even after 20 years of preparation, a
                       burial never is.


                # ⚓ Opinion_|_The_Moral_Idiocy_and_Suicidal_Tendency_of_Endless
                  War⠀⇛


                       We pretend to have enemies, but mostly what we
                       “have” are people whose lives simply don’t matter.
                       And then we kill them, either directly—via
                       airstrikes or other war games, turning them into
                       collateral damage—or indirectly. . .by simply
                       failing to notice that they exist.


                # ⚓ How_the_War_on_Terror_Created_the_“Muslim_American”⠀⇛


                       On September 12, 2001, the day after horrific
                       terrorist attacks shook the country, The New York
                       Times published an editorial titled “The National
                       Defense.” In it, the paper focused on “the urgent
                       work of determining how an open and democratic
                       society can better defend itself” against
                       terrorism. Sandwiched between several security-
                       related policy suggestions, the Times sounded this
                       note of caution:


                # ⚓ “Humane”:_Yale_Historian_Samuel_Moyn_on_“How_the_United
                  States_Abandoned_Peace_and_Reinvented_War”⠀⇛


                       In his new book, Yale historian Samuel Moyn
                       explores whether the push to make U.S. wars more
                       “humane” by banning torture and limiting civilian
                       casualties has helped fuel more military
                       interventions around the world. He looks in detail
                       at the role of President Obama in expanding the use
                       of drones even as he received the Nobel Peace
                       Prize. “What happened after 2001 is that, in the
                       midst of an extremely brutal war on terror, a new
                       kind of war emerged. … It was important to
                       Americans to see their wars fought more humanely,”
                       says Moyn. “Even though this represents a kind of
                       progress, it also helped Americans sustain war and
                       helped make the war on terror endless.” Moyn’s new
                       book is “Humane: How the United States Abandoned
                       Peace and Reinvented War.”


                # ⚓ Legacy_of_the_US_Response_to_9/11_Is_Terror,_Domestic
                  Surveillance_and_Drones⠀⇛


                # ⚓ Sept._11_–_Day_of_Warning⠀⇛


                       Nineteen young male fanatics, armed only with
                       boxcutters, hijacked four airliners and flew them
                       like projectiles into the World Trade Center and
                       the Pentagon.


                       This date should be marked to warn of the terrible
                       harm that can be inflicted by just a few religious
                       zealots.


                # ⚓ Civilian_Deaths_Aren’t_News_for_Fox_News⠀⇛


                       CNN, for example, ordered reporters to frame
                       reports of civilian deaths with reminders that “the
                       Pentagon has repeatedly stressed that it is trying
                       to minimize” such casualties, and that “the Taliban
                       regime continues to harbor terrorists who are
                       connected to the September 11 attacks that claimed
                       thousands of innocent lives in the US” (Washington
                       Post, 10/31/01).


                # ⚓ Declassifying_the_9/11_Investigation⠀⇛


                       With families of 9/11 victims threatening to
                       protest his appearance at events commemorating the
                       20th anniversary of the attacks, President Joe
                       Biden took the notable step last week of ordering
                       the Justice Department and other agencies to
                       disclose new portions of their long-secret files on
                       the Qaida plot.


                       The executive order on Sept. 3 appears to stave off
                       the prospect that the president might be picketed
                       on the eve of 9/11 memorial services, just days
                       after the final, chaotic withdrawal of U.S. forces
                       from Afghanistan.


                # ⚓ “Turning_Point”:_Legacy_of_the_U.S._Response_to_9/11_Is
                  Terror,_Domestic_Surveillance_&_Drones⠀⇛


                       As this week marks the 20th anniversary of the 9/11
                       attacks on the World Trade Center in New York City
                       and the Pentagon in Washington, D.C., we look at a
                       new five-part documentary series on Netflix about
                       the attacks and the response from the United
                       States, both at home and abroad. “Turning Point: 9/
                       11 and the War on Terror” features a wide range of
                       interviews with survivors of the attacks, U.S.
                       officials, former CIA members and veterans, as well
                       as soldiers in the Afghanistan National Army,
                       Taliban commanders, and Afghan officials, warlords
                       and civilians. “What we really wanted to do was
                       tell the story not just of what happened that day,
                       but how we got there and where our response to
                       those attacks took us as a country,” says director
                       Brian Knappenberger. We also speak with co-
                       executive producer Mohammed Ali Naqvi, an award-
                       winning Pakistani filmmaker, who says the film was
                       an attempt to go “beyond the binary narrative of
                       good versus evil.”


                # ⚓ Caving_to_NRA_and_Pro-Gun_Democrats,_Biden_Withdraws_ATF
                  Nominee⠀⇛


                       “It is hugely disappointing and unconscionable that
                       50 members of the U.S. Senate as well as at least
                       one senator who caucuses with the president’s party
                       would deny President Biden his choice to lead the
                       ATF.”—Kris Brown, Brady


          o § Environment⠀➾


                # ⚓ Climate_change:_Fossil_fuels_must_stay_underground,
                  scientists_say⠀⇛


                       And this “bleak picture”, the scientists say, “is
                       very probably an underestimate of what is
                       required”.


                       The carbon budget determined by the modelling would
                       give the world a 50% chance of limiting warming to
                       1.5C.


                       But the study says: “That does not consider
                       uncertainties around, for example, climate-system
                       feedbacks


                       “So to ensure more certainty of stabilising at this
                       temperature, [even] more carbon needs to stay in
                       the ground.”


                # ⚓ Failing_Key_Climate_Test,_Biden_Nominates_Fossil_Fuel
                  ‘Crony’_to_Federal_Energy_Post⠀⇛


                       Climate campaigners and critics of corporate
                       influence in politics responded with alarm Thursday
                       to President Joe Biden’s selection of Willie L.
                       Phillips Jr. for a key federal energy post, given
                       the raging climate emergency and the nominee’s
                       record both in government and as a private
                       attorney.


                       “We’re deeply concerned about whether the new
                       commissioner will be too closely tied to the energy
                       utilities that have put profit above people.”—Jean
                       Su, Center for Biological Diversity


                # ⚓ Ro_Khanna_Vows_to_Put_Big_Oil,_PR_Firms_in_Hot_Seat_‘Like
                  the_Big_Tobacco_Hearings’⠀⇛


                       Rep. Ro Khanna on Thursday fired a broadside at an
                       often-overlooked enabler and profiteer of the
                       worsening climate emergency—the public relations
                       and advertising firms that continue to serve the
                       fossil fuel industry—by announcing that their
                       deceptive practices would be scrutinized during
                       forthcoming congressional hearings on Big Oil
                       climate misinformation.


                       “You can’t address the climate crisis without
                       addressing climate misinformation.”—Rep. Ro Khanna


                # ⚓ Opinion_|_The_Dixie_Fire_and_the_Day_I_Became_a_Climate
                  Refugee⠀⇛


                       At 10 a.m. on July 22nd, I interviewed a New York
                       University professor about using autonomous robots,
                       drones, and other unmanned devices to suppress
                       structural and wildland fires. I sent the interview
                       to an online transcription service, walked down the
                       steps of my second-floor office and a block to the
                       Greenville post office, where I mailed a check to
                       California Fair Plan for homeowners’ fire
                       insurance. I then drove 25 miles to a dental
                       appointment. I was lucky to make it home before
                       burning debris closed the roads.


                # ⚓ Climate_Campaigners_Demand_‘Action,_Not_Words’_After
                  Biden’s_‘Code_Red’_Comments⠀⇛


                       Responding to U.S. President Joe Biden’s recent
                       comments calling the climate emergency a “code red”
                       situation, environmental and Indigenous leaders
                       representing a coalition of advocacy groups on
                       Thursday implored the administration to act
                       accordingly by declaring a climate emergency and
                       stopping all fossil fuel projects.


                       “In the face of the climate crisis, we should not
                       be expanding the fossil fuel industry and allowing
                       the government to subsidize and hand off funds to
                       the fossil fuel industry.”—Tara Houska, Giniw
                       Collective


                # § Energy⠀➾


                      # ⚓ Line_3_Resisters_Light_the_Way_in_a_Battle_for_Life
                        on_Earth⠀⇛


                      # ⚓ Big_Oil’s_Delay_Tactics_Are_the_New_Climate_Science
                        Denialism⠀⇛


                             This story originally appeared in The
                             Guardian and is published here as part of
                             Covering Climate Now, a global collaboration
                             of news outlets strengthening coverage of the
                             climate story.


                      # ⚓ As_World_Burns,_Morrison_Says_Australia’s_Sticking
                        With_Coal⠀⇛


                             Defying a “code red” warning about the
                             climate crisis and sustained pressure to take
                             urgent action on the planetary emergency, the
                             conservative government of Australian Prime
                             Minister Scott Morrison on Thursday vowed to
                             continue coal mining.


                             Asked at a press conference whether his
                             government would put a time limit on the coal
                             industry, Morrison responded that the mining
                             sector is “absolutely critical to Australia’s
                             future. And we’ll keep on mining. Of course
                             we’ll keep on mining.”


                      # ⚓ Coastal_Tribes_in_Louisiana_Are_in_Desperate_Need
                        After_Ida_Wallops_Their_Communities⠀⇛


                             “I am in desperate need of a camper
                             trailer,” Traditional Chief Shirell Parfait-
                             Dardar of the Grand Caillou/Dulac Band of
                             Biloxi-Chitimacha-Choctaw Tribe, told me
                             outside of her totaled home in Chauvin,
                             Louisiana, about 70 miles southwest of New
                             Orleans. Hurricane Ida, which made landfall
                             in Louisiana with 150 mile per hour wind on
                             August 31, took the roof off of her home and
                             smashed to bits her sewing workshop, located
                             next door. 


                             Parfait-Dardar and her family embody the word
                             “resilience.” When I visited the family on
                             September 7, her husband was working to
                             create a shelter for the family amid the
                             Category 4 storm’s destruction. 


                      # ⚓ ‘Majority_of_Fossil_Fuels_Must_Stay_in_Ground_to_Meet
                        1.5C_Goal’⠀⇛


                             By Daniel Welsby, James Price, and Steve Pye,
                             The Conversation. Reposted from The
                             Conversation under a Creative
                             Commons license.Global mean surface
                             temperatures reached 1.2C above the pre-
                             industrial average in 2020, and the
                             Intergovernmental Panel on Climate Change
                             warned in its recent report that Earth could
                             hit 1.5C in as little as a decade. The 0.3C
                             separating these two temperatures make a
                             world of difference. Scientists believe that
                             stabilising our warming world’s temperature
                             at 1.5C could help avoid the most serious
                             effects of climate change.


                             Fossil fuels such as coal, oil and natural
                             gas are the source of just over 80% of the
                             world’s energy. Burning them accounts for 89%
                             of human-derived CO₂ emissions. To avert
                             catastrophic warming, the global community
                             must rapidly reduce how much of these fuels
                             it extracts and burns. Our new paper,
                             published in Nature, revealed just how tight
                             the world’s remaining carbon budget is likely
                             to be.


                      # ⚓ Tory_Peer_Nicky_Morgan_Joins_‘Fossil_Bank’_Santander
                        After_Calling_for_Greener_Financial_System⠀⇛


                             A Tory peer and ex-minister who called on the
                             UK’s financial sector to cut its carbon
                             emissions has joined a bank that has invested
                             nearly £25 billion in fossil fuels since the
                             Paris Agreement.


                             Nicky Morgan, a former MP who now sits in the
                             House of Lords, joined Santander UK – part of
                             the Spanish banking giant – as an Independent
                             Non-Executive Director last month. 


                # § Wildlife/Nature⠀➾


                      # ⚓ How_Wildlife_Rescuers_Can_Protect_Public_Health⠀⇛


                      # ⚓ Amazon_fires_are_rising_threat_to_Brazil’s_great
                        rainforest⠀⇛


                             Brazil’s great rainforest is a reservoir of
                             global richness. Its government has reduced
                             that wealth and burned a resource.


          o § Finance⠀➾


                # ⚓ Scam_the_Rich:_A_Conversation_With_Novelist_Marlowe
                  Granados⠀⇛


                       Scammers like Anna Delvey and Billy McFarland get
                       all the credit. Their schemes—pilfering millions
                       from wealthy people for fake businesses and
                       fraudulent music festivals—scream for attention.
                       It’s harder to get credit for lower-stakes grifts:
                       like convincing a man you’ve just met to pay for
                       your cab fare back to Brooklyn, or getting an
                       invite to a Hamptons house based on charm alone.
                       You must possess both smarts and joie de vivre to
                       pull off that kind of con—if you even want to call
                       it that. In Happy Hour, the debut novel by the
                       Toronto-based writer Marlowe Granados, two 21-year
                       old-women named Isa and Gala are con artists of
                       this more intimate sort.


                # ⚓ Rashida_Tlaib_Corrects_Jim_Clyburn:_‘$3.5_Trillion_Is_the
                  Floor’⠀⇛


                       Congresswoman Rashida Tlaib of Michigan pushed back
                       late Wednesday after fellow Rep. Jim Clyburn—the
                       third-ranking Democrat in the House—said that $3.5
                       trillion was not the “floor” but rather the
                       “ceiling” for the emerging budget reconciliation
                       package, a position that puts him firmly at odds
                       with many members of his own party.


                       In an appearance on CNN, Clyburn (D-S.C.) falsely
                       claimed that “no one has ever said” the popular
                       $3.5 trillion figure represents the floor for
                       reconciliation negotiations. In recent days, as
                       Common Dreams has reported, Sen. Bernie Sanders (I-
                       Vt.), Rep. Pramila Jayapal (D-Wash.), and other
                       prominent progressives have publicly made clear
                       that $3.5 trillion is already a compromise and that
                       they will not approve of anything less.


                # ⚓ Battle_of_the_Plutocrats_in_Virginia⠀⇛


                       Youngkin refers only fleetingly to his history in
                       the top echelons of the financial sector (with that
                       platinum entry pass, an MBA from Harvard Business
                       School). But flaunting his previous position as the
                       co-CEO of The Carlyle Group can be a double-edged
                       sword, given the Group’s long track record of
                       asset-stripping and job destruction.


                       Dirt-throwing opponents can take advantage of
                       someone offering himself to voters as a” job
                       creator” who has a 25-year-long background as a
                       vulture capitalist in a multinational firm lacking
                       a real record of job creation.


                # ⚓ Cheap_Fun:_Job_Growth_Under_Trump_and_Biden⠀⇛


                       Anyhow, it’s time to see how the economy’s job
                       performance under Biden stacks up against its
                       performance under Trump. As I always say, this is
                       silly since there are so many things that are
                       beyond the president’s control, so the comparison
                       really is not telling us much. But, you know if the
                       situation were reversed, Donald Trump would be
                       touting this graph to the sky. He probably would
                       even have a huge neon version on top of Trump
                       Tower.


                       So, here’s where we stand now. Including the August
                       number, and the 135,000 upward revision to growth
                       for the prior two months, Biden has now created 4.5
                       million jobs in the first seven months of his
                       presidency.  Trump lost 2.9 million jobs over his
                       four years in office.


                # ⚓ ‘Tax_These_Moochers’:_Top_1%_Dodge_$163_Billion_in_Taxes
                  Each_Year⠀⇛


                       A Treasury Department report released Wednesday
                       estimates that the richest 1% of Americans are
                       responsible for more than $160 billion in unpaid
                       taxes per year, a finding that comes as Democratic
                       lawmakers are working to bolster IRS enforcement
                       capacity in their emerging reconciliation package.


                       Authored by Natasha Sarin, the deputy assistant
                       secretary for economic policy at the Treasury
                       Department, the new report argues that “today’s tax
                       code contains two sets of rules: one for regular
                       wage and salary workers who report virtually all
                       the income they earn; and another for wealthy
                       taxpayers, who are often able to avoid a large
                       share of the taxes they owe.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ ‘Step_Up_and_Do_the_Right_Thing’:_Groups_Urge_Congress_to
                  Pass_Build_Back_Better_Bill⠀⇛


                       In the face of a massive corporate lobbying blitz
                       and continuing opposition from Republican and
                       right-wing Democratic U.S. lawmakers to President
                       Joe Biden’s Build Back Better plan, 93 advocacy
                       groups on Thursday sent a letter to Congress urging
                       members to “stand up to this pressure” and pass the
                       ambitious $3.5 trillion budget reconciliation
                       package.


                       “One of the biggest indications that President
                       Biden’s Build Back Better plan would provide
                       transformative change to working families is that
                       corporations are spending millions to try to defeat
                       it.”—Heidi Shierholz, EPI


                # ⚓ In_Buffalo,_Progressive_India_Walton_Fights_Off_‘Sore
                  Loser’_Democratic_Mayor_and_GOP_Allies⠀⇛


                       “I return to the mantra of Senator Bernie Sanders:
                       the way to win against organized money is with
                       organized people. So we continue to
                       organize.”—India Walton


                # ⚓ Kathy_Hochul’s_Future_Ambitions_Create_an_Opening_for_the
                  Left⠀⇛


                       In her first major move as governor since replacing
                       the disgraced Andrew Cuomo in August, Kathy Hochul
                       signed into a law a sweeping extension of a
                       statewide eviction moratorium that had been set to
                       expire. Hochul, returning to Albany for a special
                       session, brokered a deal with Democratic
                       legislative leaders to safeguard hundreds of
                       thousands of tenants until January 15.


                # ⚓ Democrats_May_Tie_Disaster_Relief_to_Raising_Debt_Ceiling,
                  Putting_GOP_in_a_Bind⠀⇛


                # ⚓ ‘The_Last_Thing_We_Need’:_Ocasio-Cortez_Urges_Californians
                  to_Vote_No_on_Newsom_Recall⠀⇛


                # ⚓ The_impact_of_Open_Source_Software_and_Hardware_on
                  technological_independence,_competitiveness_and_innovation_in
                  the_EU_economy:_Final_Study_Report⠀⇛


                       Based on the results of our empirical analyses, the
                       following recommendations are derived. [...]


                # ⚓ Texas_Gov._Greg_Abbott_signs_social_media_‘censorship’_bill
                  into_law⠀⇛


                       The law targets companies with at least 50 million
                       monthly users in the US, including Facebook,
                       Twitter and Google’s YouTube. The legislation,
                       billed by the governor’s office as protecting
                       Texans “from wrongful censorship on social media
                       platforms,” would allow residents of the state to
                       sue companies for reinstatement of accounts.


          o § Misinformation/Disinformation⠀➾


                # ⚓ Warren_urges_Amazon_to_fix_algorithm_‘feeding
                  misinformation_loops’⠀⇛


                       Sen. Elizabeth Warren (D-Mass.) is urging Amazon to
                       create a plan to modify its algorithm after her
                       staff found books spreading misinformation about
                       the COVID-19 pandemic prominently displayed in
                       searches about the virus and vaccines.


                       “As cases of COVID-19 continue to rise, Amazon is
                       feeding misinformation loops through its search and
                       ‘Best Seller’ algorithms, potentially leading
                       countless Americans to risk their health and the
                       health of their neighbors based on misleading and
                       inaccurate information that they discover on
                       Amazon’s website,” Warren wrote in a letter sent to
                       Amazon CEO Andy Jassy.


                # ⚓ This_image_from_an_episode_of_The_Simpsons_has_been
                  digitally_altered_to_add_a_reference_to_vaccines⠀⇛


                       The Simpsons did NOT predict the Covid-19 pandemic.


                       An image has been shared multiple times in Facebook
                       posts that claim it shows a character from The
                       Simpsons holding a piece of paper supposedly
                       containing a phrase that predicted the vaccine
                       rollout in 2021. The image, however, has been
                       digitally altered: in the original Simpsons
                       episode, the paper has a different phrase unrelated
                       to vaccines written on it.


          o § Censorship/Free Speech⠀➾


                # ⚓ Impossibility_Of_Content_Moderation:_Scientist_Debunking
                  Vaccine_Myths_Gets_A_YouTube_Strike_For_Medical_Misinfo⠀⇛


                       Here’s another one in our never ending series on
                       the impossibility of doing content moderation at
                       scale, and how (all too frequently) people trying
                       to expose bad behavior are punished as if they’re
                       promoting bad behavior.


                # ⚓ Connecticut_Court_Orders_Blogger_To_Turn_Over_Electronic
                  Devices_To_Cop_Suing_Over_Alleged_Defamation_By_Blog’s
                  Commenters⠀⇛


                       Things are getting dumber and way less
                       constitutional in a defamation lawsuit filed by a
                       Connecticut law enforcement officer. Lt. Vincent
                       Benvenuto — despite being the beneficiary of all
                       the official and codified protection and
                       forgiveness government workers only seem willing to
                       give to other government employees — sued a
                       blogger, demanding the blogger hand over
                       identifying information on commenters who offended
                       the Lieutenant.


                # ⚓ Texas_Gov._Greg_Abbott_Announces_On_Twitter_The
                  Livestreaming_On_Facebook_Of_His_Signing_Of_A_Bill_That
                  Removes_1st_Amendment_Rights_For_Both⠀⇛


                       We’ve talked a bunch about just how incredibly
                       unconstitutional Texas’s social media content
                       moderation bill, HB20 is, so I don’t really need to
                       cover any of that again. You can look it up — or
                       just read how a court found Florida’s similar bill
                       unconstitutional.


                # ⚓ High_Court_finds_media_outlets_are_responsible_for_Facebook
                  comments_in_Dylan_Voller_defamation_case⠀⇛


                       The High Court found that, by running the Facebook
                       pages, the media groups participated in
                       communicating any defamatory material posted by
                       third parties and were therefore responsible for
                       the comments.


                # ⚓ The_Good_Death—Cancel_Culture_and_the_Logic_of_Torture⠀⇛


                       Cancellation is a public execution, during which a
                       person is pilloried and destroyed. But while we
                       have become used to the cycle of manufactured
                       outrage that preludes every cancellation, the
                       desperate public apologies, and the devastating
                       consequences for the people whose lives are ruined,
                       we are often at a loss to know what we could do to
                       stop this type of serial assault. Part of the
                       solution is to gain as clear an understanding of
                       the phenomenon as possible by probing its
                       structure. Philosophical and historical scholarship
                       on public executions and torture can help to
                       illuminate the moral logic that drives the cycle of
                       abuse. For both public shaming and cancellation are
                       structured like public acts of torture, and their
                       aims are disturbingly similar means of enforcing
                       political or cultural conformity.


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


                # ⚓ Afghan_journalists_tell_of_Taliban_beatings_after_covering
                  protests⠀⇛


                       Naqdi said he was accosted by a Taliban fighter as
                       soon as he started taking pictures.


                       “They told me ‘You cannot film’,” he said. “They
                       arrested all those who were filming and took their
                       phones,” he told AFP.


                       Naqdi said the Taliban tried to grab his camera,
                       but he managed to hand it to someone in the crowd.


                       Three Taliban fighters caught him, however, and
                       took him to the police station where the beatings
                       started.


                # ⚓ Afghan_Media_Say_Taliban_are_Jailing,_Attacking_News_Crews
                  During_Kabul_Protests⠀⇛


                       The Taliban have detained, beaten and threatened
                       several journalists covering protests in Kabul and
                       other districts in Afghanistan, and told some news
                       crews that they need permission to film.


                       More than 14 reporters and photographers were
                       detained over two days this week while covering
                       demonstrations for women’s rights and protests
                       against Pakistan, according to the Afghan
                       Independent Journalists’ Association (AIJA).


          o § Civil Rights/Policing⠀➾


                # ⚓ The_Board_Meeting⠀⇛


                       N There was a meeting. They had an agenda.N It was
                       time to talk about loving a manN in the
                       supermarket, how that mightN affect sales of
                       imported candyN and levels of light in the
                       produce.N It was the best meeting they’d ever had.N
                       Everyone wanted it to last forever, likeN it had
                       seemed April was going to last yearN or was it the
                       year before that. PeopleN at the meeting had a lot
                       in common.N Not only were they all employed byN the
                       same company, but also most of themN drove to the
                       meeting in a car, sometimesN the same car, so there
                       was barelyN a meter between them. They could all
                       voteN and they could all hold forth on the beauty
                       and dangerN of poisonous berries. It was a perfect
                       meeting.N They each had one blue eye and two green
                       ones.


                # ⚓ Sixth_Circuit_Reaffirms_It’s_A_Fourth_Amendment_Violation
                  To_Chalk_Car_Tires_For_Parking_Enforcement_Purposes⠀⇛


                       Two years ago, the Sixth Circuit Court of Appeals
                       surprised the city of Saginaw, Michigan by finding
                       the process of marking car tires with chalk for
                       parking enforcement violated the Fourth Amendment.
                       The city certainly didn’t expect multiple
                       ticketholder Alison Taylor’s lawsuit to make it
                       this far. And it certainly didn’t expect the
                       Appeals Court to reverse the district court’s
                       decision that no Fourth Amendment violation had
                       taken place.


                # ⚓ Republican_FreeDumb_is_Killing_Us⠀⇛


                # ⚓ The_End_of_White_Hegemony?⠀⇛


                       William Frey, of the Brookings Institute, reports,
                       “Yet most notable is the small decline in white
                       population — the first in any census since 1790.
                       During much of the nation’s history, white
                       population growth mirrored the national growth
                       rate, including a substantial slowdown during the
                       Great Depression.”  He adds, “Yet, since the 1970s,
                       white population growth has shown continued
                       declines — plummeting to just 1.2% in 2000 to 2010
                       and now to a -2.6% loss (or over 5 million people)
                       for the 2010s.”  And he notes, “Fewer births and
                       more deaths resulted in a natural decrease (more
                       deaths than births) for the 2010s decade, even
                       before the COVID-19 pandemic.”


                       Frey goes further noting two parallel develops that
                       compound the overall demographic shift.  “All of
                       the nation’s 2010-to-2020 growth is attributable to
                       people of color—those identifying as Latino or
                       Hispanic, Black, Asian American, Native Hawaiian or
                       Pacific Islander, Native American, and as two or
                       more races,” he finds. Adding, “Together, these
                       groups now comprise more than 40% of the U.S.
                       population.”  In addition, “Between 2010 and 2020,
                       the nation’s under-age-18 population registered an
                       absolute decline of more than 1 million.  …. As a
                       result, white Americans now comprise less than half
                       of the nation’s under-age-18 population.”


                # ⚓ Body_Cam_Video_Shows_Cop_Killing_A_Harmless_Dog_Within_15
                  Seconds_Of_Arriving_At_The_Scene⠀⇛


                       I don’t often write about cops killing dogs. It’s
                       not that it’s a rarity. It actually happens all the
                       time.


                # ⚓ Texas_Providers_May_Face_Jail_Time_for_Prescribing_Abortion
                  Pills⠀⇛


                # ⚓ How_Chevron_Used_the_Law_and_the_FBI_to_Target_Whistle-
                  Blowing_Lawyer_Steven_Donziger⠀⇛


                # ⚓ ‘Game-Changer’:_Biden_DOJ_Applauded_for_Suing_Texas_Over
                  New_Abortion_Ban⠀⇛


                       Reproductive rights advocates on Thursday praised
                       the Biden administration for legally challenging
                       Texas’ new anti-choice measure banning the
                       termination of pregnancy after six weeks and
                       empowering “vigilantes” to sue anyone who “aids and
                       abets” such an abortion.


                       “It’s a game-changer that the Department of Justice
                       has joined the legal battle to restore
                       constitutionally protected abortion access in Texas
                       and disarm vigilantes looking to collect their
                       bounties.”—Nancy Northup, Center for Reproductive
                       Rights


                # ⚓ DOJ_Sues_the_State_of_Texas_Over_Its_Restrictive_Anti-
                  Abortion_Law⠀⇛


                # ⚓ AOC_Pans_Greg_Abbott’s_Pledge_to_End_Rape_in_Texas:_“GOP
                  Laws_HELP_Abusers”⠀⇛


                # ⚓ Opinion_|_On_Deregulation_and_Covid_Masks,_Libertarians_Are
                  Loud._On_Female_Liberty,_Deafening_Silence⠀⇛


                       It was a bad week for freedom in America. With
                       Texas banning most abortions and empowering self-
                       appointed vigilantes to stop women from exercising
                       their right to reproductive healthcare, and the
                       Supreme Court letting it stand, you’d think
                       freedom-loving libertarians would be out in full
                       force protesting.


                # ⚓ Parliament_unanimously_approves_“Water_is_ours”_citizens’
                  initiative⠀⇛


                       A citizens’ initiative entitled ‘Water is ours’
                       (Finnish: Vesi on meidän) has been unanimously
                       approved by Parliament.


                       The initiative had sought to prevent the
                       privatisation of Finland’s water supply, and to
                       date is the first such citizens’ initiative to
                       receive unanimous backing by MPs. Parliament has
                       previously approved only two other citizens’
                       initiatives.


                # ⚓ Unconstitutional_Texas_social_media_bill_attacks_human
                  rights⠀⇛


                       Yesterday, September 2, the U.S. state of Texas’
                       legislature passed a bill that aims to stop social
                       media companies from “censoring conservative
                       views.” This bill and others like it across the
                       United States have been drafted in direct response
                       to platforms’ removal of misinformation, incitement
                       to violence, and other content that platforms have
                       deemed in violation of their community guidelines.
                       The legislation includes vague, sweeping language
                       prohibiting platforms from banning or blocking a
                       person based on viewpoint or geographic location,
                       attempting to give judges broad powers to overturn
                       social media platforms’ decisions about their own
                       content moderation policies.


                # ⚓ California_bill_seeks_to_halt_prison-to-ICE_deportation
                  pipeline⠀⇛


                       Leonel Sanchez thought he was about to go home to
                       his family after serving three-and-a-half years for
                       assault and other crimes in California, saying he
                       felt redeemed after he started reading the Bible,
                       attending Alcoholics Anonymous and even fighting
                       wildfires as a prisoner.


                       Instead of walking free, he became one of the 1,500
                       foreign-born California prisoners who earn their
                       release each year, only to be transferred to
                       federal detention and told they may be kicked out
                       of the country. He is in U.S. Immigration and
                       Customs Enforcement (ICE) custody, likely to be
                       deported to Mexico, a country he left at age 10 and
                       where he has no friends or known relatives.


                       In an atmosphere still charged by Trump-era
                       rhetoric linking immigration and violent crime,
                       some Californians may have little sympathy for the
                       foreign-born who can be deported because of felony
                       convictions. But advocates for people like Sanchez
                       question whether it serves justice to punish them a
                       second time or send them away regardless of their
                       individual circumstances, the rehabilitation they
                       sought on the inside, or the conditions in their
                       homelands.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ AT&T_Whines_About_Spectrum_Hoarding_Now_That_T-Mobile_Is
                  Doing_It⠀⇛


                       Economists predicted the T-Mobile merger would
                       result in a lot of layoffs, something that’s been
                       proven true so far. Those same economists also
                       predicted that the merger will also inevitably
                       result in higher prices for consumers, though
                       that’s expected to take a few years as investors
                       pressure the three remaining companies to take
                       advantage of reduced competition.


          o § Monopolies⠀➾


                # ⚓ ARIPO_Member_States_adopt_the_Kampala_Protocol_on_Voluntary
                  Registration_of_Copyright_and_Related_Rights [Ed: Colonialism
                  by WIPO with misuse of the word “right” (like they used to
                  say slave ownership was a “right”)]⠀⇛


                       Late last month (August), the Kampala Protocol on
                       voluntary registration of copyright and related
                       rights within the framework of the African Regional
                       Intellectual Property Organization (ARIPO) was
                       adopted at a Diplomatic Conference held in Kampala,
                       Uganda. The Protocol establishes a regional
                       voluntary registration of copyright and related
                       rights. It creates and maintains a regional
                       database for copyright and related rights for ARIPO
                       and the ARIPO Member States.


                # ⚓ U.S._Antitrust_Cops_Unveil_Data_Backing_Facebook_Monopoly
                  Case⠀⇛


                       The Federal Trade Commission on Wednesday revealed
                       figures that it said shows Facebook is far and away
                       the most dominant company in the market. The
                       numbers had been redacted in an earlier complaint.


                # § Patents⠀➾


                      # ⚓ Gofore_Plc:_Gofore_Plc’s_Business_Review_1_–_31
                        August_2021:_Growth_continued_in_August_–_Through
                        competitive_tendering,_Gofore_included_in_two_framework
                        agreements_in_Europe [Ed: Gofore just got a contract
                        from EPO but no details given; sometimes it’s hidden
                        [1, 2]]⠀⇛


                      # ⚓ Gofore_Plc:_Gofore_Plc’s_Business_Review_1_–_31
                        August_2021:_Growth_continued_in_August_–_Through
                        competitive_tendering,_Gofore_included_in_two_framework
                        agreements_in_Europe
                        ⠀⇛


                             Gofore has been successful in digitalising
                             the Finnish society. Our expertise in public
                             sector projects is strong and we have also
                             identified the opportunity to export this
                             expertise in other parts of Europe. In
                             August, a major step was taken on this path
                             when we reached framework agreements with the
                             OECD (Organisation for Economic Co-operation
                             and Development, Paris) and the European
                             Patent Office (EPO, Munich) through
                             competitive tendering. In the case of the
                             OECD, the framework agreement covers
                             procurement related to digital services and
                             capabilities


                      # ⚓ Did_the_Pandemic_Affect_2020_Australian_PCT
                        Filings?⠀⇛


                             As I reported back in January, there were
                             some indications of weakening patent filings
                             by Australian applicants in 2020. Domestic
                             applicants filed 10% fewer Australian
                             standard applications than in 2019. And while
                             provisional filings overall fell by only 2%,
                             those prepared with professional assistance –
                             which involve greater expense, but are also
                             far more likely to provide a sound basis for
                             valuable future patent rights – fell by
                             nearly 5%. While perhaps not the sole factor,
                             it is logical to assume that the business
                             impact of the COVID-19 pandemic was somewhat
                             influential in this decline. Of course,
                             Australian application numbers are not the
                             only indicator of filing activity. Each year,
                             Australian residents file over 1,500
                             international applications under the Patent
                             Cooperation Treaty (PCT), representing
                             potential future filings not only in
                             Australia, but also in any of the other 152
                             (as at the time of writing) contracting
                             states. So it is also interesting to know
                             whether there was a corresponding decline in
                             PCT filings by Australian residents in 2020.


                      # ⚓ [Old]_Assignor_Estoppel:_When_Can_A_Party_Challenge_A
                        Patent_They_Sold?⠀⇛


                             In patent law, the doctrine of “assignor
                             estoppel” refers to barring a party who
                             assigned a patent from later challenging the
                             validity of the patent. Assignor estoppel is
                             an equitable doctrine that has been relied
                             upon in order to prevent someone who has
                             assigned the rights to a patent (or patent
                             application) from later contending that what
                             was assigned was, in fact, worthless. The
                             doctrine has been applied to not just
                             inventors, but also parties in privity with
                             the original inventor, such as a corporation
                             founded by the inventor. Essentially, the
                             doctrine of assignor estoppel is grounded in
                             fair dealing when selling patents.


                      # ⚓ The_EPO_Conducts_A_Survey_On_Users’_Experience_With
                        ViCo_Proceedings_In_Opposition [Ed: EPO did something
                        illegal (as usual), then_rigged_the_courts, and after
                        ‘legalising’ this offence by abusing courts it kindly
                        asks for our view on it?]⠀⇛


                             The European Patent Office (EPO) is
                             conducting a survey (https://www.epo.org/
                             news-events/news/2021/20210901.html)
                             concerning the experience of users in
                             opposition oral proceedings by
                             videoconference (ViCo). At aera we think it
                             is important that as many as possible provide
                             their input to the EPO since the feedback
                             from users, apparently, will inform the
                             decision of the EPO on whether to continue
                             with ViCo proceedings in the future.


                             Our own experience is that it works well from
                             a technical perspective, Zoom being the EPO’s
                             preferred connection software. We also agree
                             with the position, often stated as a major
                             advantage of ViCo proceedings, that ViCo can
                             save parties to oral proceedings time and
                             money that would otherwise be spent
                             travelling to Munich or The Hague. Hence,
                             from a convenience perspective, it could be
                             argued that ViCo should be allowed to
                             continue, even as a mandatory measure (as is
                             currently the case in view of the pandemic).


                             However, convenience is only part of the
                             picture. Most opponents do not oppose
                             European patents as a matter of convenience.
                             Often, technology important for the parties’
                             businesses is at stake. Indeed, when the EPO
                             flags convenience and cost saving as
                             attractive features of ViCo, they often
                             implicitly give the impression that it is
                             convenience for the EPO that is meant.


                      # § Software Patents⠀➾


                            # ⚓ China_surge_in_business_method_patents
                              continues,_while_Japan_and_South_Korea_also_see
                              growth [Ed: By Western standards many of these
                              are fake patents for faked 'growth' (only the
                              litigation firms stand to benefit)]⠀⇛


                                   Statistics prepared by Japan Patent
                                   Office show wide regional variations –
                                   business method filings in Japan itself
                                   continue to grow as grant rate tops 70%


                            # ⚓ $2,000_for_Vitek_IP_prior_art⠀⇛


                                   On September 9, 2021, Unified Patents
                                   added a new PATROLL contest, with a
                                   $2,000 cash prize, seeking prior art on
                                   at least claim 1 of U.S. Patent
                                   9,245,295, owned by Vitek IP, LLC, an
                                   NPE. The ’295 patent generally relates
                                   to a call-to-action lockout on a mobile
                                   device coupled to a data network. The
                                   invention has been developed primarily
                                   for controlling responses while
                                   experiencing media content on mobile
                                   electronic devices.


                # § Copyrights⠀➾


                      # ⚓ Meet_the_CC_Summit_Presenter:_Juan_Miguel_Palma
                        Peña⠀⇛


                             Based in: Mexico City, Mexico 


                      # ⚓ Digital_Death_Penalty?_Legal_Battle_over_Piracy
                        Disconnections_Heats_Up_in_Appeals_Court⠀⇛


                             ISP Cox Communications is squaring off
                             against several major record labels at the
                             Court of Appeals for the Fourth Circuit. The
                             ISP warns of devastating consequences when it
                             has to disconnect alleged pirates, equating
                             it to a digital death penalty. The music
                             companies doubt this, pointing out that Cox
                             terminated the accounts of 600,000
                             subscribers who failed to pay their bills.


                      # ⚓ Funimation_DMCA_Notices_Shut_Down_Pirate_Anime_Apps,
                        Force_Others_to_Consider_Future⠀⇛


                             A wave of DMCA/cease-and-desist notices sent
                             on behalf of anime company Funimation has
                             caused several piracy-focused apps and
                             services to run for cover. Due to threats of
                             law enforcement referrals for non-compliance,
                             three apps have already shut down while
                             others are taking evasive action to avoid the
                             same fate.


                      # ⚓ Another_Mod_War:_Jagex_Demands_Shutdown_Of_HD
                        RuneScape_Mod,_Retracts_After_Public_Backlash⠀⇛


                             The gaming industry modding wars continue. We
                             had recently discussed Nintendo’s continued
                             war on anyone who mods its games, including
                             shutting down tournaments for incredibly
                             minor uses of mods that make those
                             tournaments possible. We’ve also been
                             discussing Take-Two’s attack on its modding
                             community for the Grand Theft Auto franchise.
                             On the flip side, companies like CD Projekt
                             Red and Bethesda have so embraced their own
                             modding communities as to have hired some of
                             them onto their teams as salaried employees.


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