𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, May 30, 2022
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Generated Tue 31 May 02:43:27 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2022/05/30/


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

⦿ [Meme] Abolishing Rule of Law | Techrights

⦿ [Meme] Administrative Council of the European Patent Organisation Can Oust António Campinos Next Month (But Will It?) | Techrights

⦿ Scenes From Vilnius: EPO and Friends Converge for Lobbying and Self-Congratulatory Talks | Techrights

⦿ Inside the EPO: It’s Not a Pretty Picture and the Administrative Council Lacks the Incentive to ’Clean House’ | Techrights

⦿ IRC Proceedings: Sunday, May 29, 2022 | Techrights

⦿ [Meme] The Mass Litigation Clique | Techrights

⦿ [Meme] It Was Just an Accident | Techrights

⦿ Sites That Keep Abreast of Free/Libre Software and GNU/Linux News | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/05/30/abolishing-rule-of-law/#comments
		http://techrights.org/2022/05/30/campinos-and-the-portuguese-government/#comments
		http://techrights.org/2022/05/30/epo-in-vilnius/#comments
		http://techrights.org/2022/05/30/epu-must-clean-house/#comments
		http://techrights.org/2022/05/30/irc-log-290522/#comments
		http://techrights.org/2022/05/30/meme-the-mass-litigation-clique/#comments
		http://techrights.org/2022/05/30/monopoly-tony-accident/#comments
		http://techrights.org/2022/05/30/tux-machines-turning-18/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/05/30/memorial-day/#comments
		http://techrights.org/2022/05/30/wordpress-turns-19/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/abolishing-rule-of-law/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/abolishing-rule-of-law/

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Gemini_version_available_♊︎


✐ [Meme]_Abolishing_Rule_of_Law⠀✐


Posted in Europe, Patents at 6:42 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_strong_and_stable:_2012_______2017_________2022⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disgusted_Examiner:_The_ILOAT_did_indeed_‘consider’_the
legality_of_the_registration_fee_the_EPO_charges_its_employees_when_they_file
an_internal_appeal._In_Judgment_4422,_consideration_18,_in_fine,_it_
(laconically)_stated:_“Moreover,_there_is_no_legal_basis_on_which_to_hold_that
the_registration_fee_which_an_internal_appellant_is_required_to_pay_upon_filing
an_internal_appeal_is_unlawful_or_provides_a_ground_to_vitiate_the_final
decision.”_Of_course,_the_judgment_does_not_recount_which_grounds_the
complainants_invoked_in_support_of_their_objection_against_the_registration
fee,_nor_was_the_Tribunal_bothered_about_the_obvious_implications_of_the_(level
of_the)_fee_on_(equal)_access_to_justice,_or_the_fact_that_the_opinion_of_the
Internal_Appeals_Committee,_a_consultative_body,_primarily_serves_to_enlighten
the_President_(in_most_cases)_on_which_final_decision_to_take_on_an_internal
appeal;_an_opinion_for_which_the_appealing_EPO_employees_are_being_made_to_pay
for,_but_which_they_receive_–_icing_on_the_cake_–_only_AFTER_the_President_has
seen_it_and_taken_his_decision_thereon_(Article_14(1)_Impl._Reg._Art._106-113
EPO_Service_Regulations,_giving_hence_the_President_all_liberty_to_send_the
opinion_back_to_the_Internal_Appeals_Committee_for_‘reconsideration’_if
needed…)._Neither_did_the_Tribunal_bother_to_put_into_perspective_its_own_case
law,_which_emphasised_that_an_“Organisation_has_an_obligation_to_maintain_a
properly_functioning_appeal_system”_(Judgment_4384,_consideration_7;_as_well_as
Judgment_3027,_consideration_6_and_Judgment_1968,_consideration_5)_as_part_of
its_duty_of_care_towards_its_employees,_with_the_obvious_implication_that_it_is
for_the_Organisation_to_ensure_the_maintenance,_that_is,_the_financing_of_the
registration_of_internal_appeals,_such_registration_quite_certainly_forming
part_of_the_proper_functioning_of_an_appeal_system.⦈_


Summary: The Rule of Law is nowadays entirely ignored by an institution which
claims to protect (patent) law


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣚⣛⣣⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡼⢶⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣖⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠄⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠊⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡃⢔⣵⣴⣿⣷⣿⠛⠁⠀⠀⠀⠠⠂⠀⠀⠙⠃⣿⣤⣿⢿⣧⣿
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⣿⠀⠸⠶⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
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⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣠⣴⣾⣿⣿⠁⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣆⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⣷⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠉⠉⢹⣿⣿⣿⣷⣄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⢀⡿⠀⠀⠀⠀⡿⠀⠀⢀⣿⣿⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣄⠀⠀⠀⢀⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⡂⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⢀⣿⠙⣿⣿⣿⣿⠄⣴⢿⠃⠀⠀⠀⠀⠃⠀⠀⣸⣿⣿⣿⡄⠀⠀⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠿⢇⠀⠀⠐⣿⡷⠄⣴⡎⣿⢀⣈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⠃⠀⣸⠿⢿⡿⠿⠿⢿⣿⣾⣾⣿⣄⣿⣿⣿⣿⣾⡿⣋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⠄⠀⠀⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡳⣫⢹⠘⡞⡍⡇⠐⢺⡇⣇⣏⡍⡎⡗⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡰⣩⢱⠁⡏⠙⡆⠐⢻⢸⣮⡭⢹⢡⣿⣿⠇⠉⣠⣿⣿⣿⣿⣿⡍⠩⠀⠀⠸⠉⣳⠀⡏⠙⡞⣾⡭⡧⣳⣫⢹⢸⠟⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣣⢊⡆⣇⠇⡇⣾⣼⡇⠉⢏⢞⣜⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡱⠃⡀⡇⠄⡇⣽⢸⢸⣿⢣⠇⣾⠿⠿⠀⠘⠛⣿⣿⡟⠛⠛⠃⠀⠀⠀⠀⡴⢃⡆⡇⠃⣇⢟⡵⣵⡿⣫⠋⢊⣄⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣓⣒⣢⣼⡒⠑⠛⠛⡣⢠⣟⣒⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣜⣓⣒⠀⠙⢚⣴⣿⣘⣸⣇⣚⡐⣲⣶⠒⠂⢸⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⣑⢺⣼⣞⣒⣲⣼⣓⣒⠊⠯⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣽⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣬⣤⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢛⠻⠻⢿⠿⢿⠿⠿⢻⠿⡿⢻⡟⣻⠿⠿⡿⠿⠟⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣬⣴⣤⣼⣀⣮⣤⣼⣴⣤⣮⣼⣧⣭⣬⣥⣤⣼⣤⣧⣼⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⢿⣿⡿⢿⡿⣿⡿⢿⣿⢿⣿⢿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣴⣴⣧⣼⣼⣤⣼⣼⣤⣤⣼⣤⣤⣤⣦⣦⣼⣧⣷⣵⣴⣥⣬⣦⣾⣾⣦⣴⣿⣾⣨⣤⣤⣮⣧⣦⣿⣶⣤⣾⣦⣆⣢⣾⣶⣤⣤⣴⣴⣷⣷⣷⣷⣶⣤⣾⣼⣴⣼⣼⣼⣦⣬⣆⣢⣶⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣋⣉⡉⣉⣉⣉⣙⣙⣹⣝⣋⣝⣙⣽⣹⣝⣹⢻⣭⣟⣽⣋⣉⣏⣉⣙⣹⣭⣋⣻⣏⢫⢫⣋⣏⣹⣏⣉⣿⣿⣯⣏⣯⣝⣹⣝⣽⣉⣋⣏⣟⣿⣫⣉⣉⣝⣫⣉⣯⣙⣉⣫⣫⣿⣹⣟⣟⣫⣯⣽⣽⣹⣿⣿⣿⣿⣿
⣿⠛⡟⢻⠿⣿⢿⠿⣿⠟⠻⠟⡿⣿⡿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣷⣶⣶⣷⣿⣾⣾⣶⣾⣷⣷⣷⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⠻⢻⠿⠿⠿⠿⠿⢿⡟⢻⠿⢿⢿⣿⢿⠿⠿⡟⠿⠿⠿⣿⡿⢿⠿⢿⣿⢿⣿⠿⣿⡿⡟⣿⢻⡿⣿⢿⠟⡟⡟⠻⡿⢻⢻⡿⢿⣿⠿⢿⡿⢻⡿⠟⠻⠿⢿⠻⠿⢿⠿⠟⠟⢿⠻⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⡿⣷⣿⣷⣷⣿⣷⣶⣷⡾⢷⣿⡾⡿⣾⣶⣷⣷⣷⢶⣾⣿⣾⣾⣶⣾⣷⣿⣿⣶⣿⣿⣶⢿⣿⣾⣿⣷⣿⡶⣷⣶⣶⣾⣿⡿⣾⣿⣾⣶⣷⣿⢷⣷⣶⣶⢿⣿⣾⢾⣿⣷⣷⣾⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣤⣼⣧⣽⣯⣤⣤⣵⣤⣬⣤⣤⣧⣬⣷⣤⣤⣤⣤⣤⣤⣷⣯⣾⣵⣽⣽⣮⣬⣮⣿⣽⣿⣿⣿⣹⣥⣼⣧⣴⣾⣴⣧⣬⣤⣯⣯⣯⣦⣧⣿⣥⣽⣥⣦⣬⣯⣽⣯⣼⣯⣤⣧⣤⣮⣮⣦⣴⣴⣽⣿⣿⣿⣿⣿
⣿⣉⡏⢭⣉⣉⣩⣩⣏⣯⣹⣫⣯⣨⣯⣩⣏⣈⣩⣏⣈⣝⣁⣏⣈⣍⣿⣁⣉⣩⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣱⣁⣏⣏⣉⣉⣝⣩⣻⣁⣉⣽⢈⣉⡈⢉⣉⣩⣉⣹⣿⣯⣫⣏⣏⣍⣩⣿⣍⣍⣿⣿⣩⣉⣏⣭⣈⣈⣯⣹⢻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠈⠙⢻⣿⣿⣿⣿⣿⣿
⣿⡻⡿⡻⠛⠛⢛⣻⡻⣹⠋⠻⡛⢻⢟⢛⡿⡻⡛⡻⡻⣻⡟⡟⠟⠛⣛⠛⡟⢛⢟⡿⣛⡟⣿⠛⢛⢻⡛⡻⠛⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣾⢿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⡿⡿⢿⣿⡿⢿⣷⣿⡿⣿⡿⡿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣤⣴⣴⣤⣾⣯⣧⣴⣯⣦⣶⣶⣵⣵⣼⣷⣿⣬⣿⣮⣤⣤⣦⣴⣶⣯⣦⣷⣾⣦⣷⣶⣴⣶⣤⣯⣦⣷⣿⣦⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿
⣿⣘⣉⣃⣯⣿⣙⣟⣇⣈⣉⣏⣉⣁⣩⣈⣉⣽⣙⣿⣟⣈⣉⣯⣍⣈⣉⣿⣏⣽⣡⣛⣝⣉⣝⣯⣻⣐⣟⣿⣏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡻⣻⡛⡛⣛⣟⣟⢻⢛⡻⣿⢻⣻⡛⡛⢻⠋⠛⣻⢩⢛⣻⠋⠋⢛⠛⢻⡻⢛⡟⢛⢟⡟⢻⢟⠛⡻⣻⠋⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⡿⠿⢿⢿⣿⠿⠿⢿⢿⠾⢿⢿⢿⡿⡿⠿⠿⠿⠿⢿⢿⢿⢿⣿⠿⣿⠿⢿⢿⢿⢿⡿⡿⡿⡿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣶⣾⣾⣷⣾⣿⣦⣧⣷⣷⣶⣽⣶⣶⣷⣦⣶⣷⣶⣶⣾⣶⣷⣿⣶⣿⣷⣷⣾⣾⣿⣿⣷⣼⣿⣾⣷⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣋⣩⣷⣉⣙⣇⣉⣡⣿⣍⣸⣭⣃⣹⣠⣯⣹⣹⣩⣩⣫⣁⣭⣩⣯⣿⣙⣯⣿⣹⣝⣽⣿⣣⣉⣹⣹⣩⣭⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⣿⣿⣿⣿⣿⣿
⣿⠉⡿⠛⠛⢹⠻⠋⠛⠛⢻⠙⠙⢿⠟⢛⠟⡻⠙⠛⢻⠉⡛⠛⡟⡿⣻⢻⣍⠛⡿⠙⣿⢻⡏⣯⣯⢹⢹⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠿⠿⠿⠻⠿⠿⠿⠿⢿⡿⢿⣿⡿⡿⡿⢿⠿⢿⠿⢿⠿⢿⢿⣟⠿⠿⢿⡿⡿⠿⡿⡿⣿⡟⠛⠿⠿⠿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣾⣤⣶⣶⣶⣶⣷⣿⣾⣧⣽⣾⣿⣧⣷⣷⣷⣷⣷⣿⣾⣿⣿⣿⣿⣾⣿⣾⣿⣾⣿⣿⣿⣷⣶⣶⣷⣿⣼⡇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣅⣵⣮⣼⣿⣬⣩⣨⣭⣨⣤⣧⣻⣮⣮⣵⣭⣤⣬⣨⣸⣬⣪⣾⣷⣬⣾⣪⣮⣨⣵⣅⣽⣼⣮⣮⣭⣿⠇⠹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣬⣤⣿⣦⣤⣤⣯⣮⣥⣧⣷⣵⣿⣤⣮⣮⣿⣮⣼⣧⣮⣮⣦⣤⣥⣧⣵⣿⣮⣯⣾⣤⣤⣵⣇⣮⣮⣦⣰⣥⠀⠐⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⠛⠋⡻⠛⣿⢛⠛⢹⢩⣿⢻⢿⢻⣿⣯⠹⣙⠛⠟⡛⠛⡟⣿⡿⣻⢻⡟⢻⢻⠟⠛⡟⠋⠏⠙⠛⠋⠙⢰⣰⢦⡖⡄⡄⣤⢠⠀⣤⣄⢠⣄⢀⣀⠀⣀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠿⡿⢿⠿⠿⡿⠿⠿⢟⡿⡟⡿⠟⠿⠿⠿⠿⠟⡿⢻⢻⢻⢿⣿⡿⣿⣿⡟⠟⠿⢿⠿⣿⣿⣿⣟⡃⠸⠹⠸⣷⠇⣷⢻⡟⠀⣿⣿⣸⣽⢸⢺⢱⡇⠀⢸⠏⣿⣽⢸⢸⢻⡇⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣾⣾⣶⡶⣶⣶⣾⢷⣶⣶⡶⣴⣶⣶⣶⣶⣿⣾⣾⣾⣿⡿⡶⡾⣿⣶⣶⣶⣶⣶⢿⣾⣿⣷⣷⣶⣶⢶⣶⣤⣤⣤⣤⣤⣤⣤⢍⣈⣈⣈⣈⣉⣀⣘⠀⠙⠋⠘⠚⠘⠀⠃⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣴⣦⣤⣾⣵⣷⣷⣬⣦⣤⣤⣧⣼⣤⣤⣤⣿⣿⣷⣇⣷⣮⣾⣮⣼⣿⣦⣵⣵⣿⣵⣤⣤⣦⣴⣤⣶⣤⣤⣴⣵⣿⣾⣯⣴⣼⣤⣤⣦⣯⣾⣾⣷⣾⣵⣿⣧⣰⣷⣤⣧⣶⣷⣴⣧⣤⣤⣤⣤⣤⣦⣿⣿⣿⣿⣿⣿
⣿⣉⣟⣏⣫⣛⢙⣩⡛⣏⣏⣏⢿⣋⣛⢉⣹⣩⣝⣹⣫⣫⣛⣟⣝⣿⣹⣉⣋⢉⣉⣹⣹⣝⣝⣙⣏⣩⣏⣹⣏⣿⣏⣏⣫⣫⣯⣉⣛⣏⢏⡙⢙⣋⣉⣹⣉⣝⣝⣝⡏⣋⣟⣉⣙⣻⣋⣋⣏⣩⡋⣿⣿⣿⣿⣿⣿⣿
⣿⠿⢿⠿⠿⠻⠿⢿⠿⠿⡿⢿⣿⠻⡿⢻⠻⣿⣿⠻⠿⡟⠿⢿⠿⠿⣿⡿⣿⢿⣟⡟⠻⠿⡿⠿⠿⠻⡟⢿⠟⡿⡿⡿⣿⠟⡿⠿⠻⠿⣿⡿⢿⡿⠿⢿⠿⡿⠻⣿⢿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⡶⣷⣾⣶⣷⣶⣶⣶⣶⣷⣶⣶⣾⣶⣿⢷⡷⣾⢷⣶⢶⣾⣶⣿⣷⣾⣷⣿⣷⣶⣶⡷⣷⣶⣶⣷⣶⣾⣿⣾⣿⣷⣿⣷⣷⣶⣶⣿⣷⣾⣶⣶⡶⣷⣶⣶⣿⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣆⣠⣮⣤⣥⣴⣿⣿⣿⣧⣵⣧⣴⣧⣧⣷⣬⣤⣤⣄⣾⣦⣤⣿⣿⣴⣆⣧⣭⣤⣯⣧⣤⣧⣿⣷⣿⣿⣦⣄⣤⣤⣧⣿⣿⣽⣿⣬⣴⣤⣦⣰⣧⣤⣧⣤⣼⣭⣤⣤⣴⣽⣿⣵⣶⣯⣴⣤⣬⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 191

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/campinos-and-the-portuguese-government/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/campinos-and-the-portuguese-government/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Administrative_Council_of_the_European_Patent_Organisation_Can_Oust
António_Campinos_Next_Month_(But_Will_It?)⠀✐


Posted in Europe, Patents at 11:33 am by Dr. Roy Schestowitz


He is, after all (in_his_very_own_words), the “f***ing president” (vulgarity
used repeatedly in violation of the EPO‘s Code of Conduct)


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


Summary: António_Campinos has an uncertain_future_at_the_EPO; unlike Ronaldo,
Campinos is a disgrace to Portugal and the Portuguese government should decline
calls for endorsement (Campinos is hardly even Portuguese; he calls himself a
“nomad” and admits he spent a lot of his life in France)


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

                    ䷩ 𝚕𝚒𝚗𝚎 1281

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/epo-in-vilnius/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/epo-in-vilnius/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Scenes_From_Vilnius:_EPO_and_Friends_Converge_for_Lobbying_and_Self-
Congratulatory_Talks⠀✐


Posted in Europe, Patents at 6:29 am by Dr. Roy Schestowitz


Sourced from the official footage [1, 2]


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gurry_and_Ernst:_Gurry_crushing_his_own_staff;_Ernst
protecting_two_presidents_who_crush_EPO_staff⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gurry_and_Ernst:_Tap-tap_on_nose:_Just_slap_them_like_this⦈_


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gurry_speech⦈_


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_saboteur⦈_


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇INPI_import⦈_


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Topic's_mistress;_Mihaly⦈_


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Paymaster⦈_


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


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Welcome⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Lecture⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Handshake⦈_


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Battistelli⦈_


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


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


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


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Say_yes⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇UPC_plotters⦈_


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Chief_of_EPO⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Coming_soon:_UPC!_-Battistelli_a_decade_ago⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇'Cooperation'_(coercion)_money⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Private_signing:_Nothing_to_see_here,_move_along...⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Where's_all_the_wine_gone?⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇One_second_later:_Oh,_there_it_is!_Battistelli_fuel⦈_


Summary: Old footage (almost a decade old) shows the proximity between many of
today’s culprits, who gradually ruined the EPO with a wide web of nepotism,
corruption, and unconstitutional actions


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

                    ䷩ 𝚕𝚒𝚗𝚎 2471

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/epu-must-clean-house/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/epu-must-clean-house/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Inside_the_EPO:_It’s_Not_a_Pretty_Picture_and_the_Administrative_Council
Lacks_the_Incentive_to_‘Clean_House’⠀✐


Posted in Europe, Patents at 11:25 am by Dr. Roy Schestowitz


Video_download_link | md5sum b23dc64fca8e5f6e5a707ca8bedbbcc8
EPO Blunders in Pictures
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-in-memes-and-photos.webm


Summary: The Administrative Council of the European Patent Organisation (AC or
Council for short) has an opportunity to tentatively give António_Campinos the
boot next_month; this might not be enough, however, because we already saw how
Benoît_Battistelli was replaced by his friend and many of Battistelli’s other
friends remain in positions of power to this date


THIS morning’s EPO posts [1, 2, 3, 4] were mostly memes and photos (or video
frames). The video above adds words and necessary context to these.


In order to better understand the significance of some of our memes, which are
frequent, be sure to click on the link that says “context” (or links that say
the same). The memes are typically based on something which is true; they add a
humourous slant, that’s all…


“A huge political effort and coordination will be needed in order to restore
order (stability through lawfulness) at the Office.”For instance, this morning
we mentioned misuse of the EUIPO’s diplomatic immunity status; it was abused
(or there was attempt to abuse it) by the Campinos family; we already explained
how alcohol was involved and why it’s doubly tragic considering the death of
the driver’s grandfather, Jorge. So what the meme says is not really a joke; it
is factual and it stresses the irony. It’s worth noting that it’s common
knowledge in EPO circles (the story about the son getting drunk and trying to
‘borrow’ immunity after crashing the car). Additionally, from what I am hearing
these days, Mr. Campinos is already down for the count because he’s not
supported by EPO “users” (or “clients” or “customers” as Team Campinos
habitually calls them). Campinos no longer enjoys broad support from the
Council, never mind ‘his’ staff. When he started they thought he was some guru
in diplomacy; how wrong were they… and the media too for that matter (wishful
thinking from patent maximalists and profiteers)…


A huge political effort and coordination will be needed in order to restore
order (stability through lawfulness) at the Office. For that to happen the
unqualified kakistocracy needs to be removed entirely, and preferably punished
in the process (consequences such as being unable to find employment
elsewhere).


The video above basically expands upon the EPO posts that are mostly photos and
memes. But expect us to have lots of material soon; we are working hard to
explain to a less patent-savvy audience what happens at the EPO and why it
matters.


“The last thing the Council wants right now is true accountability because so
many present and past delegates are complicit at several levels.”The Council
will have a meeting_in_4_weeks (warning: epo.org link) and the future of
Campinos hangs in the balance; they are likely to decide whether to replace
him.


“I hope he is replaced,” an associate told us today, “but the nepotism and
corruption must be also fixed at the same time or the series of clowns will
continue…”


Just like back in 2017, they will try exceptionally hard to cover up what
actually happened during the past 12 years. A lot of illegal activity was
enabled by the Council and the Council is well aware of it. The last thing the
Council wants right now is true accountability because so many present and past
delegates are complicit at several levels. Any accountability can end their
career. █



                    ䷩ 𝚕𝚒𝚗𝚎 2567

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/irc-log-290522/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/irc-log-290522/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Sunday,_May_29,_2022⠀✐


Posted in IRC_Logs at 2:15 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-290522.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-290522.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-290522.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-290522.gmi
Over HTTP:


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                          Enter_the_IRC_channels_now


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                    ䷩ 𝚕𝚒𝚗𝚎 2694

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/meme-the-mass-litigation-clique/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/meme-the-mass-litigation-clique/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Mass_Litigation_Clique⠀✐


Posted in Europe, Patents at 8:27 am by Dr. Roy Schestowitz


Where are those European SMEs they love boasting about? Or ambitious
scientists/inventors?


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇No,_we_used_to_work_together;_qualifications_don't_matter⦈_


Summary: Today’s EPO is little but a litigation_corporation or a front group of
frequently-litigating_corporations, run by unsuitably qualified (or with fake
diplomas) people who defraud_the_public


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡱⣹⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⢦⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢨⡊⣾⣿⣿⣿⢿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣿⠅⠘⠛⠛⢻⣿⣿⣿⠟⠟⠛⣿⣿⣿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⡿⠿⢿⣿⣿⣿⠿⢿⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⣠⡄⢸⣿⣿⣿⣇⠸⠀⣿⣿⡿⡦⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡏⢹⣿⣿⣿⡀⢸⣿⣿⣿⣿⡆⠀⣿⣿⣇⡂⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢹⣿⢹⡆⣻⣧⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠤⠀⣼⣁⣼⣥⣼⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡈⣅⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠈⠙⠀⠀⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣲⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⢤⡌⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢰⣧⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣶⣤⣴⣭⣝⣛⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠘⣛⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢀⣄⣠⣤⣤⣤⣤⣴⣦⣤⣤⣤⡆⡹⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⣸⡆⢭⣤⣬⣽⣿⠾⣿⣫⣻⣿⡾⣿⣿⣿⣿⣿⢶⣮⣉⡛⢿⣿⣿⣿⡷⢿⣿⢿⣿⣿⣿⣿⣿⠺⠳⠛⠟⠟⠿⠛⠇⠟⠿⠛⠻⠏⣱⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢹⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠶⣿⡇⠀⠀⠘⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠳⢰⣿⡄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠝⠀⠈⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠀⠈⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠈⠛⢿⣿⣿⣿⣿⡿⠗⠖⠀⠲⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠘⣿⣿⡟⠀⠸
⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⣿⡄⠀⠀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢽⣿⣿⣿⡿⠿⠿⠿⠈⠞⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠇⠀⠹⠿⢿⣿⣿⣿⣿⣿⣏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣆⠨⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣧⣀⢀
⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣉⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣭⣥⣍⣉⣛⣛⡻⠿⠿⠿⢿⠀⠹⢿⣿⣿⣿⣿⡛⠁⠀⠀⠀⢺⠟⡉⠛⢢
⣟⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣟⣿⣿⣿⣿⣿⣿⡿⣟⢿⣻⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣬⣍⣛⣛⠛⠀⠀⠀⠀⠐⠀⠈⠀⠀⠸
⡿⣿⣽⣾⣺⡿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣳⣦⣌⣙⠛⠿⢿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣯⣿⣿⣿⢻⢿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀
⣳⣯⡾⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⠉⣙⣻⣿⣷⣿⣾⣾⣷⣯⣧⣧⣿⣾⣿⣏⣿⣿⣯⣿⣽⣻⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀
⠀⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⡟⠛⠉⠀⠐⠒⢛⣛⠛⠛⠛⠛⠉⠉⠉⠉⠉⢩⣝⣛⣛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀
⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⣻⢿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣬⣭⣭⣭⣭⣭⣍⣭⣍⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣉⣩⣭⠍⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠛⠋⠉⠉⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⡟⣛⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣯⠉⠁⠹⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⢶⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡓⠈⠙⠻⣿⣯⡀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠘⣿⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⡟⠻⢦⣄⠙⡆⠀⠀⠀⠀⠀⣠
⠁⠈⠠⢀⠀⠀⢻⠀⠀⣇⠀⢠⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣭⣿⡏⠃⠀⠀⠀⠀⠀⣿⣿⣿⣯⠛⠋⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⡘⣭⣿⣿⣷⣶⣮⠐⠼⢀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠂⠼⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣃⠀⠀⠠⣤⣴⡐⠻⢿⣛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠃⢦⣴⣾⣿⣿⣿⣷⠀⣇⢊⠔⠠⢀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠐⣻⠇⠀⠀⠀⠀⠀⢀⣯⣿⢹⣿⣿⣿⣿⣿⡄⠀⢠⡯⣿⠀⠈⠉⠀⠀⠐⠀⠤⢀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠉⠿⠿⠟⠿⠿⠿⠟⠛⠛⠉⠁⠲⠶⠆⠀⠀⠋⣙⡿⠿⣿⣿⣷⠰⠈⡟⠂⠀⣾
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠃⠁⠂⢄⠀⠀⢸⣇⣿⠂⢻⣿⣿⣿⡏⣇⠀⢸⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣷⣭⣻⡆⠐⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⠀⠀⠀⠈⠐⡸⣿⣿⢠⠀⢻⣿⣿⡷⣿⠀⣾⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣭⣇⡠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣦⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⣶⣦⣤⣄⣀⣿⣷⡏⠺⢭⣽⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠀⠒⠠⠀⠀⠀⠀⠀⠀⢠⣤⣴⢤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⡿⣬⣙⠿⣿⣿⣿⣿⠹⢇⣿⡀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡧⢹⣿⠿⠶⠝⠿⣿⣧⣼⣿⣇⡀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣚⣷⣤⣤⣤⡄⣤⣤⣿⣿⣿⣶⣮⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⣹⣄⣠⣠⡆⣿⣿⣿⠿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2772

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/monopoly-tony-accident/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/monopoly-tony-accident/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_It_Was_Just_an_Accident⠀✐


Posted in Europe, Patents at 7:55 am by Dr. Roy Schestowitz


Context: Immunity_of_the_Intellectual_Property_Office_of_the_European_Union
Causes_Outrage_in_Spanish_Media (what the meme below says is factual, not just
a joke)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Well,_my_dad_died_in_a_car_accident;__My_son_drove_drunk_and
crashed_the_car;_EUIPO_diplomatic_immunity;_Tony's_victims;_EPO;_Tony's_son;
EPO_pensioners;_Tony's_son⦈_


Summary: The EPO is (and has been over the past decade or more) run by a bunch
of drunkards; Worst of all, António_Campinos has absolutely no oversight at the
EPO; the tail_wags_the_dog…


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_tandemocracy⦈_


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠘⣛⣛⣛⣛⢛⣻⢟⣛⡻⣟⣛⢟⣛⡻⠀⣁⣀⢛⡀⣀⡀⣛⣛⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⣿⣹⢸⣿⣿⣿⣿⢸⣿⣿⠀⣿⣿⢸⡇⣿⠄⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣤⣛⣿⣜⣛⣛⣛⣛⣚⣛⣫⠀⠛⠛⠘⠃⠛⠂⣛⣛⣼⣿⣿⣿
⣿⣿⣿⣛⡉⠉⠉⠉⣩⣿⣿⣿⢟⣸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⣶⣶⣎⣾⡿⣷⣾⢿⣽⢶⡍⣷⣎⣷⣶⡝⢯⡶⣦⣶⢶⡄⣶⡆⣷⢾⢽⡏⣿⢹
⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⣿⣿⣿⣿⠁⣿⣿⢸⣿⣨⣥⣿⣿⣿⣿⡏⣸⣇⣭⣿⢻⣷⣯⣷⣽⣻⣾⡟⣿⢸
⠉⣻⣿⣿⣿⣿⠏⠉⠁⢠⡄⠉⢹⣿⣿⣿⡟⣿⣿⡿⢿⣿⣿⠿⣿⣿⡿⢿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣀⣀⠀⠀⠀⠉⠉⢡⣭⣮⣭⣭⣿⣮⣭⣾⣵⣯⣭⣭⣽⣇⠉⠁⠉⢈⣉⣁⡩⠮⢽⠾⣷⣭⣾
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠁⠰⣾⣿⣿⢿⡇⣿⣿⡇⢸⣿⣿⠀⣿⣟⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⠉⣖⡆⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⠟⠙⢩⣿⠟⠋⠉⢨⣄⣀⣼⣿⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡆⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⡿⢿⡇⢸⣿⣿⠀⣿⣿⣇⠌⠀⠀⠙⠻⠶⢦⣴⢾⣿⣿⡻⣿⠇⠀⠀⠀⠀⠈⠙⠓⠂⠄⢸⣿⣿⣿⡟⣴⣾⣿⣿⡿⣿⣿⣿⣿⣉⠀⠀⠀⢸⣿⡇⠀⠀⢉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡆⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙⣍⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣄⣀⡀⠾⠿⡇⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢸⡇⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠐⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⢿⠒⣽⠿⣯⠛⠓⠛⢳⡳⠟⠅⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⣿⣿⣿⣛⣿⣟⣛⡉⠭⣉⠉⢿⣿⣟⠉⠁⠠⠍⢛⠛⠻⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⣦⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣤⣬⢿⣶⣿⣷⣤⣿⣷⣤⣦⣄⣿⣿⣦⡀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣇⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡼⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⣿⢿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢘⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⣴⣸⠟⠀⠀⠀⠀⠠⠷⣟⡾⠈⡟⠿⠁⠀⡸⣿⣿⣿⣏⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣲⣶⠶⠶⠦⠯⠯⣤⣄⠀⢀⡀⠆⠤⠜⣭⣼⠟⠀⣐⣸⠣⣿⣿⣿⣯⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣻⡞⠃⡀⠀⠀⠀⠀⢠⣤⣤⣄⠈⠁⠀⢤⡌⠈⠁⠈⠉⠋⣸⣀⠙⠋⣿⠿⡿⠿⢿⣿⣿⣿⡷⣿⣋⣍⣙⣿⣿⣿⠁⠀⠀⠀⠀
⡟⣭⣭⣭⣭⠍⣥⣄⣤⣄⣭⣽⢿⣽⡟⣭⡟⡯⡭⡄⣭⣭⠝⣭⣭⣥⣤⣤⣤⣭⣡⢩⣠⢰⣶⣿⣿⣿⣿⣿⣿⡯⠙⣻⠆⠀⠀⠀⠶⠤⠤⠴⡶⡶⠾⠿⠿⠿⢄⠀⠻⡿⠿⠿⣽⠛⠊⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⡇⡿⣿⡏⣿⣶⣽⣷⣿⡿⣿⣿⢸⣿⡇⡟⡇⣇⡇⣿⡇⣟⡀⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⢸⣿⣽⣿⣿⣿⣿⣿⣿⣶⣯⡀⠀⠀⢀⢠⡀⠀⠠⠰⡇⠶⠖⠄⠐⠛⠃⠂⠺⣶⡶⠉⣛⣇⠀⢉⡉⠿⢿⠟⠀⠀⠀⠀⠀
⣿⣲⢲⣚⣒⣛⡒⢀⣄⢀⣀⢀⣀⣠⣄⣀⣀⢀⡘⣒⣺⢶⣒⣀⢀⢒⣐⢀⣤⡒⣒⢒⣒⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠸⢇⢀⡄⠀⠀⣀⣀⣀⣴⣿⣶⣤⣤⣵⣼⣾⡅⠀⢸⡎⠀⠀⠀⠀⠀
⢸⣿⣼⢿⣿⣿⡇⣿⣩⢸⣿⣸⣿⣹⣿⣿⣿⢸⡂⣿⣿⡇⣿⢸⢿⢸⣗⢸⣯⣵⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡶⣶⣤⣤⡄⠀⠁⠀⠉⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡄⠀⢹⡇⠀⣠⠀⠀⢠
⣾⣾⣿⣾⣿⣿⣾⣾⣿⣾⣾⣿⣾⣾⣽⣿⣿⣾⣷⣿⣷⣿⣿⣾⣾⣾⣿⣷⣿⣮⡉⣽⡽⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠓⢀⣙⣛⣛⣶⠶⣶⣶⣤⣦⣤⣾⡟⢻⢿⣿⣿⣿⣿⣯⣭⠁⠀⠀⠸⠃⢠⡟⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣮⣬⣡⣤⣤⣬⣤⣷⣦⣤⣤⣴⣶⣾⣷⣾⣶⣿⡿⢿⣿⣿⣿⣷⣆⠘⠃⠶⠿⣿⡗⢾⣿⡇⢠⣼⣇⣾⠃⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢛⣿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣍⣐⣛⠀⠰⣧⡀⠘⢻⣤⠭⠀⣿⣿⡻⢿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣧⣤⣤⣬⣭⣶⣦⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠃⢄⡀⣿⣷⣄⠈⢻⣧⠈⠻⠻⣿⣿
⠀⠈⠉⣿⣿⠉⠉⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⢉⣹⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⠟⠛⠛⠛⢻⣿⡛⠛⠛⠛⠛⣛⣛⡛⣻⡿⠿⠁⠀⠀⠀⠀⠈⠻⠾⠛⠛⠀⠀⠁⣤⣤⡄⠙⠛
⠂⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠴⠿⣿⣿⣿⣿⢧⡤⠀⠀⡿⣯⠀⠀⠀⠀⠀⢸⣿⡇⠀⠉⠀⠀⣗⣿⣿⣿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀
⢠⢀⣴⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠂⠀⠀⠀⠀⠀⠐⠚⣿⣾⡧⣦⠀⠀⠀⠃⠀⣦⡄⠀⠀⠀⣸⣿⡇⣶⣴⢤⣤⡄⣤⣤⣄⡄⣋⣀⣀⡀⣀⠀⢀⡀⠂⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀
⢸⣸⣿⣿⣿⡇⢸⣿⡆⣀⣼⣷⣶⣦⠀⠀⠀⠀⠸⢦⡤⢄⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⠛⠁⠀⠀⠀⠀⡀⣿⠃⠀⠀⠀⣿⣿⣇⡛⠻⠸⠁⠧⠿⠿⠿⣷⢿⢸⢹⣿⣽⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀
⣸⣿⣿⣿⣿⣷⠈⠉⠹⣿⡕⣶⢻⣿⣄⣄⣤⣤⣼⡄⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⠻⠛⠻⠀⠀⣿⣿⣿⢣⣷⣶⣦⣶⣶⣶⣶⣤⣭⣤⢤⡤⣦⣀⡶⠒⠶⠖⠀⠀⠀⢸⡛⠃⠠⠀⠀
⣿⣿⣿⣿⣿⣿⢀⣠⣴⠀⢻⡇⢾⣹⢿⣿⡇⣻⠃⢝⣷⡅⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠇⢰⣶⣶⡆⣶⡆⣶⡆⢠⠀⠀⣿⣿⣿⣮⣙⣽⣟⠛⠋⢛⣻⣻⠟⠿⡸⣣⣿⠛⠛⠀⠐⠲⠀⠀⢀⣾⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣄⢈⣈⡁⠉⠀⠈⠛⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣧⡄⣿⡇⣿⡇⠰⠄⠀⣿⣿⣿⣿⣿⡏⠉⠁⠀⠘⠿⠿⠀⠀⣿⠿⠿⠀⣀⠀⡀⣀⡀⣀⡀⣘⡃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣙⣮⢹⣿⣧⣿⡿⢀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣏⡀⣿⡇⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⡄⠀⠀⠀⠀⠀⠀⠈⠉⣿⢹⣿⣿⣷⣿⢿⡏⠛⣷⣅⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠋⠘⠛⠙⠻⠇⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣘⣛⣛⠃⠙⠛⠛⠁⠀⠀⠀⣿⣿⡿⠿⠿⠺⢲⡇⣤⠐⠀⠀⠀⠀⠀⠀⠿⠘⠿⠃⠋⠛⠘⠃⠀⢓⠋⠀⠀⠀⢠
⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⣠⣤⣤⣤⠤⠼⠇⠀⢿⢿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣴⣿⣿⣗⡀⠀⠠⠀⠀⠉⠀⠻⠷⣴⣄⢶⣰⣶⣦⡖⣦⢲⡖⣶⢶⣶⣿⢾⣿⠀⠀⠘
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠐⢺⣿⣿⣦⠩⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⢀⠀⠈⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⢹⡟⣧⡶⢸⡇⣿⢸⠻⠿⠰⠽⠃⠀⠀
⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⣄⣬⣿⣿⣿⡆⢠⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠢⠐⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣆⣐⣉⣡⣧⣿⣿⣿⣿⡇⡀⢾⣿⣿⣿⡟⣛⣛⡿⣟⣛⣛⣿⢟⣫⣅⡂⢠⡀⠠⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⢠⣀⠀⠀⠀⢰⣶⠒⠀⠀⠀⠀
⠠⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⢟⠛⠛⠛⢿⣿⣿⣿⡟⠁⠀⠈⢿⣶⣿⡇⣿⡏⡧⣿⣿⣿⡇⣿⡏⣿⣧⣿⣷⣴⣢⠀⡠⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣟⠀⠀⠀⠀⡴⠀⢻⣿⣷⡤⠀⠉⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠻⢀⠀⢀⠀⠰⠟⠛⠁⠃⠀⠀⠲⢙⣾⣿⡇⣿⡟⣇⣿⣿⣛⡇⣿⡇⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠘⢿⡿⠿⠛⡛⠀⠀⠀⠈⠁⣰⣿⢹⣭⣥⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣤⣆⠀⠠⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣻⣿⡇⠿⠷⠆⠿⢿⣿⣷⡻⣷⡿⢇⡿⣿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⢀⣁⣘⡻⠁⠚⠚⠙⠿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⡇⠿⠿⣿⣿⣿⣿⠀⠘⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣏⣁⣾⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣗⣿⢻⣧⣷⣷⣶⣶⣲⡦⣶⠄⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠙⠋⠛⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
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⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 2954

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/05/30/tux-machines-turning-18/#comments
    Gemini version at gemini://gemini.techrights.org/2022/05/30/tux-machines-turning-18/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Sites_That_Keep_Abreast_of_Free/Libre_Software_and_GNU/Linux_News⠀✐


Posted in Free/Libre_Software, GNU/Linux, Site_News at 4:33 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 42ce70e9e091fc4c34182c3377af1b5b
Tux Machines Turning 18
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/tuxmachines-18.webm


Summary: There is an impending anniversary — one that few Web sites can claim
to have reached


THE SITE Tux Machines turns 18 very soon. It’s 1.5 years older than Techrights
and both overlap in the sense that Tux Machines stories get folded into Daily
Links, notably the Free/Libre software and GNU/Linux sections (not limited to
that).


Some time next month or maybe in July we have an announcement to make. And
later this year Techrights turns 16. The video above explains how we got here.
█


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇TuxMachines_at_18⦈_


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⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3035

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_30/05/2022:_Memorial_Day,_Slow_News_Day⠀✐


Posted in News_Roundup at 4:38 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o BSD
          o Fedora_Family_/_IBM
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o SaaS/Back_End/Databases
          o Content_Management_Systems_(CMS)
          o FSFE
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o AstroTurf/Lobbying/Politics
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
    * § GNU/Linux⠀➾


          o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_May_29th,_2022⠀⇛


                 This week we got some great news, starting with the
                 arrival of AlmaLinux 9 as a pure replacement for CentOS
                 Linux, and continuing with a major Clonezilla Live
                 release for all your disk cloning/imaging needs, as well
                 as a new major Alpine Linux release for fans of minimal,
                 security-oriented distros.


                 PulseAudio fans also got a new major release of this
                 open-source sound server that brought various
                 enhancements and bug fixes, Arch Linux newcomers got an
                 updated menu-based installer with lots of goodies, and
                 Ubuntu users received a new important Linux kernel
                 security update.


          o ⚓ Unix Men ☛ 9_Reasons_to_use_Linux_on_FireStick⠀⇛


                 A few years back, Linux was predominantly used for
                 servers and was not deemed acceptable for FireStick and
                 desktops. However, its user interface and convenience
                 have progressively improved over time. Linux has evolved
                 to the point that it can now replace other software. Many
                 people use it every day all across the world.


                 There are multiple explanations for choosing Linux over
                 other software applications. Yet to provide you with a
                 clear image we have compiled a list of ten reasons why
                 you should use Linux on your FireStick.


          o § Desktop/Laptop⠀➾


                # ⚓ Daniel Lange ☛ Daniel_Lange:_Work-around_for_randomly
                  dropping_WiFi_connections_on_ChromeOS⠀⇛


                       These things are meant to be very consumer-style
                       end-user devices. You log in with your Google
                       account and everything works. Until it doesn’t.


                       Just setting it up caused the first issue:


                       I was always thrown back to a black screen and then
                       another login-screen despite having successfully
                       logged in initially to create the “owner” user of
                       the Chromebook. No error message, not useful UI
                       feedback. Just logging in again and again and
                       again.


                       The issue is … not having a GMail account
                       associated with my Google account. Duh! So add a
                       GMail.com address as the primary to your Google
                       account and the initial setup completes. Of course
                       you cannot delete that GMail.com association again
                       because the owner user is linked to the email and
                       not the account. Well, you can delete it but then
                       you cannot configure “owner” items of your
                       Chromebook any more. Great job, Google. Not.
                       Identity management 101 fail.


                       Kudos to Anurag Chawake for blogging about the
                       issue. The Google support forum thead claims this
                       is solved now. But it didn’t work for me, so this
                       may be needing to trickle down through ChromeOS
                       releases or be deployed on more Google infra. Or
                       whatever. We can’t tell from outside the Googleplex
                       as – of course – “Rebecca” sheds no light on what
                       the identified “root cause” was:


                # ⚓ Hacker Noon ☛ The_Linux_Writing_Contest_by_Linode_and
                  HackerNoon⠀⇛


                       This one is for all the Linux lovers – Linode &
                       HackerNoon are excited to host a Linux Writing
                       Contest! Here’s your chance to win money from a
                       whopping $3,000 monthly prize pool! It could be any
                       story on #linux operating system. It could be your
                       opinion piece, an expert interview, or a tutorial –
                       anything that’s related to Linux.


                       Entering the contest is quite easy. Just submit
                       your article to HackerNoon with the #linux tag, and
                       you’ll be qualified as a participant in the
                       contest, from June 1st to August 30th.


          o § Server⠀➾


                # ⚓ May_2022_Web_Server_Survey [Ed: Microsoft is all minuses
                  and unlisted]⠀⇛


                       In the May 2022 survey we received responses from
                       1,155,729,496 sites across 273,593,762 unique
                       domains and 12,069,814 web-facing computers. This
                       reflects a loss of 5.23 million sites but a gain of
                       1.63 million domains and 95,200 computers.


                       nginx gained the largest number of domains (+1.24
                       million) and also a hefty amount of web-facing
                       computers (+21,500), further securing its lead in
                       both metrics. The total number of domains powered
                       by nginx is now 75.0 million (+1.68%) and its
                       market share has increased to 27.4% (+0.29). In
                       terms of web-facing computers, nginx now has a
                       total of 4.60 million; and although its leading
                       market share fell slightly to 38.1%, Apache’s fell
                       slightly further, extending the gap between the two
                       to 9.54 percentage points.


                       nginx also continues to lead with a 30.7% share of
                       all sites, despite losing the largest amount this
                       month (-6.57 million). Apache follows with a share
                       of 23.0%, but also lost a large number of sites (-
                       2.32 million). The largest gain in this metric was
                       seen by Google, which added 2.96 million sites to
                       its total and increased its market share to 4.14%.
                       LiteSpeed made the second largest gain of 1.26
                       million sites, and stays slightly ahead of Google
                       with a share of 4.35%.


                       Google and LiteSpeed also made the only significant
                       gains in the active sites metric, with Google
                       gaining 977,000 and LiteSpeed gaining 151,000.
                       Google has a greater lead in this metric, with a
                       market share of 9.49% versus LiteSpeed’s 4.60%.


                       Cloudflare is continuing to edge its way up towards
                       the leaders in the top million websites. This month
                       it gained an additional 1,822 sites and now
                       accounts for more than 20% of the top million sites
                       for the first time. Meanwhile, both Apache and
                       nginx lost more than a thousand sites each in the
                       top million, making it look ever more likely that
                       Cloudflare could gain places by the end of the
                       year. Apache, nginx and Cloudflare currently have
                       top-million site shares of 22.8%, 21.7% and 20.0%
                       respectively.


                       One surprise this month was that the largest
                       computer growth was seen not by nginx, but by the
                       awselb (Amazon Web Services Elastic Load Balancing)
                       web server, which gained 26,200 computers to reach
                       a total of 378,000. These computers are likely to
                       form only a small fraction of the AWS
                       infrastructure used by the 1.86 million sites that
                       are served from these computers, as AWS ELB
                       achieves fault tolerance and scalability by
                       automatically distributing incoming application
                       traffic across multiple targets, and can also
                       spread traffic across multiple AWS Availability
                       Zones.


          o § Audiocasts/Shows⠀➾


                # ⚓ KDE_Goals_Retrospective:_Wayland⠀⇛


                       Continuing the series from last week, here’s
                       another interview with one of our Goal Champions.


                # ⚓ KDE_Goals_interview:_Wayland_with_Méven_Car_–_Kockatoo
                  Tube⠀⇛


                # ⚓ Video ☛ Sony’s_PC_friendliness_means_Spider-man_on_the_Deck
                  is_possible._Plus_more_Steam_Deck_news!_–_Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Linux_5.18.1⠀⇛


                       I'm announcing the release of the 5.18.1 kernel.

                       All users of the 5.18 kernel series must upgrade.

                       The updated 5.18.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.18.y
                       and can be browsed at the normal kernel.org git web
                       browser:

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

                       thanks,

                       greg k-h
                # ⚓ LWN ☛ Linux_5.17.12⠀⇛


                # ⚓ LWN ☛ Linux_5.15.44⠀⇛


                # ⚓ LWN ☛ Linux_5.10.119⠀⇛


                # ⚓ Linux_5.18_released,_Bootlin_contributions_inside⠀⇛


                       Linux 5.18 has been released a bit over a week ago.
                       As usual, we recommend the resources provided by
                       LWN.net (part 1 and part 2) and KernelNewbies.org
                       to get an overall view of the major features and
                       improvements of this Linux kernel release.


                       Bootlin engineers have collectively contributed 80
                       patches to this Linux kernel release, making us the
                       28th contributing company according to these
                       statistics.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Excellent_Utilities:_Whoogle_Search_–_self-
                  hosted_metasearch_engine⠀⇛


                       This is a series highlighting best-of-breed
                       utilities. We cover a wide range of utilities
                       including tools that boost your productivity, help
                       you manage your workflow, and lots more besides.
                       There’s a table listing the tools in this series at
                       the bottom of this page.


                       Google has a firm grip on the desktop. Their
                       products and services are ubiquitous. Don’t get us
                       wrong, we’re long-standing admirers of many of
                       Google’s products and services. They are often high
                       quality, easy to use, and ‘free’, but there can be
                       downsides of over-reliance on a specific company.
                       For example, there are concerns about their privacy
                       policies, business practices, and an almost
                       insatiable desire to control all of our data, all
                       of the time.


                       What if you are looking to move away from Google
                       and embark on a new world of online freedom, where
                       you are not constantly tracked, monetised and
                       attached to Google’s ecosystem.


                # ⚓ Slashdot ☛ Lotus_1-2-3_Ported_To_Linux_–_Slashdot⠀⇛


                       Lotus-1-2-3, an ancient spreadsheet program from
                       Lotus Software (and later IBM), has been ported to
                       a new operating system.


                # ⚓ PC Perspective ☛ AmiKit,_Emulate_Amiga_On_Windows,_macOS,
                  And_Linux_–_PC_Perspective⠀⇛


                       Once you’ve decided what hardware you want to
                       install AmiKit on you, which includes original 68K
                       Amigas expanded with the Vampire upgrade card, you
                       will have access to over 300 games and programs.
                       That is not a bad deal for around $10, assuming you
                       are an Amiga fan of course. If you need to access
                       more modern file, the Rabbit Hole feature allows
                       you to launch Windows/Mac programs from within the
                       AmiKit environment.


                # ⚓ Its FOSS ☛ Surfshark_VPN_Now_Offers_a_Full-fledged_GUI_App
                  for_Linux⠀⇛


                       With VPN providers, it is often important to look
                       for Linux support.


                       Some VPN services only provide you with OpenVPN
                       configuration, and others offer a CLI app.


                       ProtonVPN, Mullvad, and a handful of other
                       providers provide a full-fledged GUI app for Linux.


          o § Instructionals/Technical⠀➾


                # ⚓ LinuxOpSys ☛ 13_Modern_Alternatives_to_Linux_Commands⠀⇛


                       When you get started out with learning Linux, you
                       are introduced to the command-line interface and a
                       set of standard Linux commands that have been there
                       since the Linux kernel was written.


                       While the good old Linux commands work as intended,
                       developers have come up with modern alternative CLI
                       tools that extend the functionality of these
                       standard Linux commands. They are more effective
                       and ship with added functionalities.


                       In this guide, we learn some of the modern
                       alternatives to Linux commands that you might
                       consider trying out.


                # ⚓ Red Hat Official ☛ 2_tools_that_make_RHEL_my_dream_Linux⠀⇛


                       Learn how Flatpak and Toolbx make Red Hat
                       Enterprise Linux (RHEL) 8 and 9 both fun to use and
                       capable of handling the serious stuff.


                       I run Red Hat Enterprise Linux (RHEL) 9 on my
                       laptop, and I have a lot of fun with it. Because I
                       run Slackware on my desktop, I’m used to stability,
                       and that’s what I appreciate in RHEL.


                # ⚓ Install_LibreNMS_on_Debian_11/Debian_10⠀⇛


                       Follow through this tutorial to learn how to
                       install LibreNMS on Debian 11/Debian 10. LibreNMS
                       is a fully featured MySQL/PHP and SNMP based
                       network monitoring system.


                # ⚓ Linuxiac ☛ How_to_Convert_Images_to_ASCII_Art_in_Linux
                  Terminal_with_Artem⠀⇛


                       This article shows how to create ASCII art by
                       converting images in the Linux command line with
                       the Artem app.


                       Every Linux enthusiast spends a significant amount
                       of time on the command line. This time, however,
                       we’ll look at one of the most fun parts of the
                       Linux terminal: creating ASCII art from images.


                       These can be used for various purposes, for
                       example, in SSH warning banners and welcome
                       messages.


                # ⚓ ID Root ☛ How_To_Install_phpMyAdmin_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       phpMyAdmin on Ubuntu 22.04 LTS, as well as some
                       extra required by phpMyAdmin


                # ⚓ Ubuntu Handbook ☛ How_to_Enable_&_Improve_On_Screen
                  Keyboard_in_Ubuntu_22.04_|_UbuntuHandbook⠀⇛


                       Need on-screen virtual keyboard? Here’s how to
                       enable and use the function in Ubuntu 22.04 LTS.


                       The default GNOME desktop environment has built-in
                       on-screen keyboard for use in case you don’t have a
                       physical keyboard. It’s easy to enable this feature
                       by doing following steps one by one:


                # ⚓ Linux Cloud VPS ☛ How_to_Install_Vue_CLI_on_Ubuntu_20.04_|
                  LinuxCloudVPS_Blog⠀⇛


                       VueJS is a popular JavaScript framework for
                       building interactive web application user
                       interfaces. It builds on top of standard HTML, CSS,
                       and JavaScript, and is very easy to integrate with
                       other projects and libraries. Vue CLI is a complete
                       Vue development package.


                       In this tutorial, we will show you how to install
                       Vue CLI and create a VueJS project on your Ubuntu
                       20.04 server.


                # ⚓ Video ☛ How_to_install_Ubuntu_Cinnamon_Remix_22.04_LTS_–
                  Invidious⠀⇛


                       In this video, I am going to show how to Ubuntu
                       Cinnamon Remix 22.04 LTS.


                # ⚓ MySQL_vs_SQLite_vs_PostgreSQL:_Comparing_the_Relational
                  Database_Management_Systems⠀⇛


                       In this tutorial, we are going to explain the
                       differences between relational database management
                       systems such as MySQL, SQLite, and PostgreSQL.


                       This type of relational database management system
                       is used worldwide, based on relational models,
                       where the information is stored in tables linked
                       between with relations, making the data to be
                       easily referenced. We will explain the advantages
                       and disadvantages of every type in a couple of
                       sentences so you can better understand which one
                       you should use in different scenarios. Let’s get
                       started!


                # ⚓ Mass_Effect_2_with_Mods_on_Linux⠀⇛


                       This guide will explain the full process of
                       installing and modding Mass Effect 2 (Origin
                       version, original game, not Legendary Edition) on a
                       Linux computer. First I will explain the setup, but
                       you can skip to the “Installing Lutris” section to
                       get right into it.


                       Windows applications can be made to run on Linux
                       using Wine, which is a kind of translation layer
                       that makes programs think they are running on
                       Windows while translating all the low-level stuff
                       for your Linux computer to understand. It is
                       different from a virtual machine in that it doesn’t
                       actually run a copy of Windows, but just provides
                       the features necessary for Windows applications to
                       run on Linux. In this article I will mention the
                       term “Wine Prefix”. This basically means the
                       directory, in which the Windows things get
                       installed, for example “~/Games/mass-effect-2/”.


                # ⚓ Linux Shell Tips ☛ How_to_Remove_Line_of_Text_from_Multiple
                  Files_in_Linux⠀⇛


                       The Linux operating system never disappoints when
                       it comes to file management tweaks. Think of any
                       hurdle associated with file management and Linux
                       will solve it. Consider this scenario.


                       Supposing you are a web/system admin or user that
                       is handling various web-based projects
                       simultaneously. Scanning through these project
                       files, you might notice inconsistencies dues to
                       unwanted line entries.


                # ⚓ How_To_Set_Up_MariaDB_On_Rocky_Linux_8_|_LinuxTeck⠀⇛


                       There are several ways that we can install and
                       maintain the databases, including commercial
                       products like Microsoft SQL Server or Oracle. But
                       with open-source software, there are often many,
                       many choices for various platforms and operating
                       systems.


                       In this tutorial, I will show you how easily we can
                       install and configure MariaDB on Rocky Linux in
                       just a few steps. We will install the packages
                       directly from the repository of Rocky Linux. This
                       means that your database software is being kept up-
                       to-date by package maintainers who are experts in
                       maintaining their particular flavor of software.
                       These maintainers also test updates thoroughly
                       before making them available to users, so you don’t
                       have to worry about whether or not a new version of
                       your software is going to work correctly on your
                       system.


                       The MariaDB relational database management system
                       is an open-source, multi-threaded system licensed
                       under the GNU Public License (GPL), well-suited to
                       replace MySQL databases. It is fast, scalable, and
                       robust. In terms of performance, MariaDB is
                       superior to MySQL. MariaDB (often called MySQL)
                       because it has very similar features and
                       functionality to MySQL. A typical implementation
                       would be to replace the MySQL module in the widely
                       used LAMP (Linux, Apache, MySQL, PHP) stack. Since
                       the company was acquired by Oracle Corporation in
                       2009, the developers of the original project
                       created MariaDB as a fork of MySQL.


                # ⚓ Linux Handbook ☛ How_to_Change_Ownership_of_Files_and
                  Folders_Recursively⠀⇛


                       You can use the chown command in Linux to change
                       the ownership of the file(s) and directories. It’s
                       quite simple to use.


                       chown owner_name file_or_folder
                       The problem arrives when you change the ownership
                       of a directory, its content remains unchanged. The
                       solution is not too complicated as well.


                # ⚓ Dedoimedo ☛ How_to_install_and_use_IrfanView_in_Linux_–
                  Tutorial⠀⇛


                       My Windows to Linux migration saga continues. We’re
                       still a long way off from finishing it, but it has
                       begun, and I’ve also outlined a basic list of
                       different programs I will need to try and test in
                       Linux, to make sure when the final switch cometh
                       that I have the required functionality. You can
                       find a fresh bouquet of detailed tutorials on how
                       to get SketchUp, Kerkythea, KompoZer, as well as
                       Notepad++ running in Linux, all of them using WINE
                       and successfully too, in my Linux category.


                       Today, my focus will be on IrfanView, a small,
                       elegant image viewer for Windows, which I’ve been
                       using with delight for decades now. It’s got
                       everything one needs, and often more than the
                       competitors, hence this bold foray of using it in
                       Linux despite the fact there are tons of native
                       programs available. But let’s proceed slowly and
                       not get too far ahead of ourselves. After me.


                # ⚓ Cloudbooklet ☛ How_to_Install_MongoDB_on_Ubuntu_22.04⠀⇛


                       How to install MongoDB on Ubuntu 22.04. MongoDb or
                       Mongo is a most popular open source NoSQL database.
                       It does not rely upon a traditional table based
                       relational database structure. It uses JSON based
                       dynamic schemas which are editable anytime.


                       In this guide you are going to learn how to install
                       and setup MongoDB on your Ubuntu 22.04 server. You
                       will also learn to configure remote connection to
                       your Mongo database.


                # ⚓ ID Root ☛ How_To_Install_MariaDB_on_AlmaLinux_9_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       MariaDB on AlmaLinux 9. For those of you who didn’t
                       know, MariaDB is a popular, free, and open-source
                       database management system that is a compatible
                       drop-in replacement for the hugely popular MySQL
                       database management system. MariaDB is compatible
                       with a wide range of operating systems including
                       Linux, FreeBSD, Mac, and Windows.


                       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 MariaDB database on AlmaLinux
                       9. You can follow the same instructions for CentOS
                       and Rocky Linux.


                # ⚓ ID Root ☛ How_To_Install_Syncthing_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Syncthing on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, Syncthing is an open-source continuous
                       file synchronization used to sync files between two
                       or more computers in a network. Syncthing does not
                       upload your data to the cloud but exchanges your
                       data across your machines as soon as they are
                       online at the same time. It supports cross-platform
                       and is available on Windows, macOS, Linux, Android,
                       and much more it is possible to sync multiple
                       devices.


                       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 Syncthing on Ubuntu 22.04
                       (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ TecAdmin ☛ How_To_Install_XRDP_on_Ubuntu_22.04_–_TecAdmin⠀⇛


                       XRDP is a remote desktop service for the Linux X
                       servers. That allows us to connect remote Linux
                       desktop systems over Microsoft RDP (​Remote Desktop
                       Protocol). XRDP also supports two-way clipboard
                       transfer (text, bitmap, file), audio redirection,
                       and drive redirection (mount local client drives on
                       the remote machines).


                       XRDP is an easy-to-install and configurable service
                       for Ubuntu systems. But you can also use a VNC
                       server to access the remote desktop of the Ubuntu
                       systems. Find a tutorial to install a VNC server on
                       Ubuntu systems.


                       This tutorial will provide you with the
                       instructions to install the XRDP service on Ubuntu
                       22.04 Desktop systems.


                # ⚓ Explaining_Ansible_Facts_With_Examples_–_OSTechNix⠀⇛


                       This tutorial explains what Ansible facts are, and
                       how to gather system information i.e facts in
                       Ansible playbooks.


                       A Brief Introduction To Ansible Facts


                       Facts are the information about the managed hosts.


                       When you run the playbook, ansible will try to
                       collect system-related information about the
                       managed host and store it in the memory until the
                       playbook is completed.


                       The information can be an IP address, operating
                       system, filesystem and more. This information
                       gathering is taken care of by the “setup” module.


          o § Games⠀➾


                # ⚓ Ubuntu Pit ☛ 5_Best_Chess_Games_for_Linux_You_can_Try_in
                  Your_Leisure⠀⇛


                       
                       The chess game is the most popular and classic
                       among all the popular gaming genres. People love to
                       enjoy playing Chess in their leisure as it is good
                       to relieve their stress. While working on our PC,
                       having a short break can improve our work speed and
                       help us to be more concerned. And enjoying a round
                       of chess games can be the best way to spend the
                       break time. Well, if you are not familiar with any
                       chess games for Linux, we can probably help.


          o § Desktop Environments/WMs⠀➾


                # ⚓ A_Journey_Begins_(GSoC_–_2022)⠀⇛


                       I am overjoyed to announce that my proposal to XFCE
                       for GSoC – 2022 got selected !


                       Oh ! I forgot to introduce myself. My name is Amrit
                       Borah and I am a somophore undergraduate student at
                       the Indian Institute of Information Technology
                       Guwahati (IIITG), India, pursuing Computer Science
                       Engineering (CSE). I have only recently completed
                       my 4th semester at college.


                # ⚓ GSoC’22:_The_Journey_Begins⠀⇛


                       I am pleased to inform you that my proposal for
                       GSoC with Xfce, under the mentorship of André
                       Miranda, has been accepted. So this summer, I will
                       be contributing to Xfce. Allow me to introduce
                       myself and the work that I will be doing.


                       I am Yogesh Kaushik, a sophomore at IIIT Delhi in
                       the Computer Science Engineering branch. As per the
                       suggestions of a few intelligent souls in my
                       college, I dual-booted my system and began using
                       Linux for regular use in my first semester of
                       college. My first Linux distribution was Kali, and
                       that’s how I was introduced to Xfce. Over time, I
                       also tried quite a few other desktop environments
                       like KDE and GNOME. But for me, the simplicity of
                       Xfce is simply unmatched. So when I got the
                       opportunity to contribute to it, I can’t refuse it.
                       Luckily the opportunity didn’t turn me down. Enough
                       of my introduction; let me now tell you about my
                       objectives for GSoC this year.


                # ⚓ Its FOSS ☛ 11_Themes_to_Make_Xfce_Look_Modern_and
                  Beautiful⠀⇛


                       Xfce is known for being one of the most lightweight
                       desktop environments yet flexible enough to carry
                       out heavy loads easily.


                       One major issue with Xfce is that its default
                       interface may look old and outdated to many users.
                       This could be offputting for some new users who
                       prefer beautiful-looking Linux distributions.


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


                      # ⚓ KDE ☛ Energy_Consumption_Lab_Is_Ready_For_FOSS
                        Community!_Dispatch_From_The_Sprint⠀⇛


                             On Saturday 21 May 2022 KDE Eco held the
                             first of several in-person Sprints for the
                             community lab to measure the energy
                             consumption of Free Software. The Sprint had
                             been postponed twice due to Corona, but the
                             third time was a charm.


                             KDAB Berlin was gracious in hosting us. They
                             offered us not only a space to construct the
                             lab, but also donated hardware and a brand-
                             new power meter (!), and they even invited
                             everybody to a delicious lunch. In total
                             there were 11 of us at the Sprint, with two
                             participants travelling across Germany to be
                             there. KDE and KDAB Berlin were well-
                             represented (Björn, Volker, Nico, Cornelius,
                             Tobias, Joseph), but the event had broad
                             appeal: several Qt company employees (André,
                             Fabian, Sami) as well as the Green Coding
                             Berlin project (Arne) and a Hasso-Plattner-
                             Institut/Universität Potsdam researcher
                             (Sven) joined us.


                      # ⚓ KDE_Eco_Sprint_2022⠀⇛


                             Last weekend, on May 21st, some people
                             (including me) met in Berlin for what I
                             believe is the first in-person KDE sprint
                             since you-know-what happened (there was LAS,
                             but that’s not technically a KDE sprint). We
                             met in KDAB’s office, which was incidentally
                             also the location of the last in-person
                             sprint before unamed things happened.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Daniel_García_Moreno:_GNOME_Outreachy_2022⠀⇛


                             It’s time to move to Gtk4. That could be an
                             easy task for new project or for small
                             projects without a lot of custom widgets, but
                             gtranslator is old and the migration will
                             require some time.


                             Some time ago I did the Gtk2 to Gtk3
                             migration. It was fun and during the journey
                             we redesigned a bit the interface, but the
                             internals didn’t change a lot. Now we can do
                             the same, migrate to Gtk4 and also update the
                             User Interface.


                             Thankfully, I’m not alone this time, the
                             GNOME community is there to help. A couple of
                             months ago, Maximiliano started a series of
                             commits to prepare the project to the Gtk4
                             migration, and today starts the Outreachy
                             program and we’ve a great intern to work in
                             this. Afshan Ahmed Khan will be working
                             during this summer in the GNOME Translation
                             Editor migration to Gtk4.


    * § Distributions and Operating Systems⠀➾


          o ⚓ DebugPoint ☛ Top_10_Linux_Distributions_for_Windows_Users_in
            2022⠀⇛


                 We compiled an inventory of the 10 best Linux
                 distributions for Windows users in 2022 based on how easy
                 they are to adopt and successfully migrate from Windows.


          o § BSD⠀➾


                # ⚓ Trying_FreeBSD,_and_a_rant_about_system⠀⇛


                       Being a bit bored, I figured I’d try to install
                       FreeBSD on both my Raspberry Pi and amd64 machine,
                       with Wifi.


                       My first attempt at getting Wifi working caused my
                       Pi to hang on reboot. I went on the hunt on the
                       interwebs to see what the problem might be. It took
                       me down a series of rabbit-holes. It was a
                       frustrating experience. Like many things in
                       computing, the solution turned out to be relatively
                       simple /once/ you’ve actually figured out the
                       solution.


                       What follows is likely to be an incomplete list of
                       things to do.


          o § Fedora Family / IBM⠀➾


                # ⚓ Automation_of_FAS_verification_in_Packit_Service [Ed: Why
                  is Fedora still outsourcing to Microsoft proprietary
                  prison?]⠀⇛


                # ⚓ Fedora Magazaine ☛ 4_cool_new_projects_to_try_in_Copr_for
                  May_2022_–_Fedora_Magazine⠀⇛


                       Copr is a build system for anyone in the Fedora
                       community. It hosts thousands of projects for
                       various purposes and audiences. Some of them should
                       never be installed by anyone, some are already
                       being transitioned to the official Fedora Linux
                       repositories, and the rest are somewhere in
                       between. Copr gives you the opportunity to install
                       third-party software that is not available in
                       Fedora Linux repositories, try nightly versions of
                       your dependencies, use patched builds of your
                       favorite tools to support some non-standard use
                       cases, and just experiment freely.


                       If you don’t know how to enable a repository or if
                       you are concerned about whether it is safe to use
                       Copr, please consult the project documentation.


                       This article takes a closer look at interesting
                       projects that recently landed in Copr.


                # ⚓ Red Hat ☛ Red_Hat_Developer_roundup:_Best_of_May_2022 [Ed:
                  It's all just Red Hat 'hooks' to get you hooked on IBM
                  support contracts]⠀⇛


                # ⚓ Enterprisers Project ☛ 5_ways_to_create_an_empathetic
                  organization [Ed: This is the company that recently blasted
                  an employee for using a GMail account in his own spare time,
                  telling him he was "IBM employee 100% of the time"]⠀⇛


                       In Part 1 of this two-part series I discussed the
                       importance of empathy as a strategic tool for
                       today’s leadership. I explained how all of my
                       experience and the push towards hybrid work have
                       led me to understand the value of being a Chief
                       Empathy Officer in an agile, fast-moving technology
                       organization.


                       To go a step further, empathy is something that the
                       entire organization can be built around. The
                       leaders in the organization can start the fire and
                       feed it, but the culture, as a whole, needs to also
                       grow and evolve.


                # ⚓ PHP_version_8.0.20RC1_and_8.1.7RC1_–_Remi’s_RPM_repository
                  –_Blog⠀⇛


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


          o § Debian Family⠀➾


                # ⚓ Bits_from_Debian:_Debian_welcomes_its_new_Outreachy_interns
                  [Ed: Corporate influence (decision-making) in diversity
                  clothing]⠀⇛


                       Debian continues participating in Outreachy, and
                       we’re excited to announce that Debian has selected
                       two interns for the Outreachy May 2022 – August
                       2022 round.


                       Israel Galadima and Michael Ikwuegbu will work on
                       Improve yarn package manager integration with
                       Debian, mentored by Akshay S Dinesh and Pirate
                       Praveen.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ OMG Ubuntu ☛ Ubuntu_22.10_Replaces_Gedit_with_New_Text
                  Editor_–_OMG!_Ubuntu!⠀⇛


                       Ubuntu 22.10 is trying out a brand new text editor.


                       Daily builds of the ‘Kinetic Kudu’ come with the
                       new GNOME ‘Text Editor’ app in place of seasoned
                       software stalwart ‘Gedit‘.


                       Since Gedit is labelled as ‘text editor’ in Ubuntu
                       you may need to re-read that sentence to understand
                       the subtle difference.


                       Ubuntu 22.10’s new text editor is Text Editor, a
                       GTK4 app shipping as part of GNOME’s core apps
                       collection since the GNOME 42 release back in
                       March. The new app has the package name gnome-text-
                       editor and replaces the text editor whose package
                       name is gedit.


                       Let’s look at what the change is happening.


                # ⚓ Ubuntu ☛ Canonical_at_Embedded_World_2022_|_Ubuntu⠀⇛


                       Embedded World 2022 is almost here! From 21-23 June
                       2022, the 20th edition of the embedded world
                       Conference will bring together experts from all
                       areas of research for embedded systems, IoT & Edge
                       devices.


                       It’s a very special event: We’ll be celebrating the
                       launch of Ubuntu Core 22. Ubuntu Core is an
                       optimised version of Ubuntu engineered for IoT and
                       embedded systems. Ubuntu Core helps manufacturers
                       meet these challenges with an ultra-secure, small-
                       footprint and low-touch operating system, backed by
                       a growing ecosystem of silicon & ODM partners.


                       Indeed, Ubuntu is supported across a wide-variety
                       of SoCs (Systems on a chip) from industry-leading
                       vendors including Intel, NVIDIA, Xilinx, NXP and
                       Qualcomm. With the optimised Ubuntu on these
                       platforms, you will get a first-class pre-validated
                       operating system to develop your solution on and
                       accelerate your project deliveries.


                # ⚓ Ubuntu ☛ Embedded_Linux_development_on_Ubuntu_–_Part_III_|
                  Ubuntu⠀⇛


                       Welcome to the concluding chapter of this journey
                       on embedded Linux development with Ubuntu. We
                       covered a lot of ground, so let us quickly recap
                       what we learned so far.


                       In Part I we introduced Snaps, software packages
                       designed for the world of IoT. Snap packages
                       isolate and encapsulate an entire application,
                       increasing the security and stability of embedded
                       devices.


                       Snapcraft is the command-line tool to build snaps.
                       It simplifies embedded development by allowing the
                       packaging of any app for any Linux device.
                       Snapcraft keeps your software up-to-date by
                       automatically checking for updates four times a
                       day. Head over to Part II to read more on Snapcraft
                       and how it secures, eases and strengthens embedded
                       Linux development.


                       In this concluding blog post, we’ll pull the
                       different threads together and introduce Ubuntu
                       Core, a version of the Ubuntu operating system
                       designed and engineered for IoT systems. Built on
                       snaps packages, Ubuntu Core automatically updates
                       itself and its applications to create a confined
                       and transaction-based system ideal for embedded
                       devices.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Raspberry_Pi_RP2040_board_comes_with_0.42-
                  inch_display,_Qwicc_I2C_connector⠀⇛


                       
                       We’ve recently written about ESP32-C3-0.42LCD board
                       with ESP32-C3 wireless microcontroller, a 0.42-inch
                       display, and a Qwicc connector for expansion. But
                       it turns out the developer, 01Space, has also
                       launched an almost identical board, RP2040-0.42LCD,
                       with Raspberry Pi RP2040 MCU replacing the ESP32-C3
                       WiFi and Bluetooth MCU.


                       The RP2040 board loses WiFi 4 and Bluetooth LE
                       connectivity compared to the ESP32-C3 board but
                       does gain one extra I2C and SPI interface. The rest
                       of the specifications are exactly the same as far
                       as I can tell. 01Space provides instructions and
                       Arduino samples for the board on Github with the
                       former relying on the Arduino Core mbed release, as
                       well as Adafruit NeoPixel and u8g2 libraries. The
                       latter needs some modifications that are explained
                       in the Github repo.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ A_whole_new_user_experience_for_Arduino_Cloud_is
                  rising_|_Arduino_Blog⠀⇛


                       Arduino Cloud has a new container for all the cloud
                       services. You can take a look by clicking the
                       Arduino Cloud button in the main header on any of
                       the website’s pages. Once you’re in there, you’ll
                       be greeted with three new varieties of Arduino
                       Cloud


                # ⚓ Arduino ☛ Arduino_User_Groups_are_back_in_your_maker-hood_|
                  Arduino_Blog⠀⇛


                       You might recall that we mentioned the triumphant
                       return of Arduino User Groups (AUG) during Arduino
                       Week? Well, the in-person maker meetups are now
                       back!


                       We’ve got some very ambitious plans for Arduino
                       User Groups, so let’s take a look at what’s
                       happening right now, and what’s coming soon to your
                       maker-hood.


                       [...]


                       Most importantly, AUGs are there to represent and
                       spread the open source philosophy upon which
                       Arduino was founded. It’s all about sharing,
                       learning and community.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ PR Newswire ☛ Is_Android_Studio_an_Easy_IDE_Platform_to
                  Launch_Applications?_GoodFirms_Review⠀⇛


                # ⚓ Android Headlines ☛ How_To_Set_Up_A_Guest_Mode_On_Android⠀⇛


                # ⚓ Make Use Of ☛ How_to_Create_a_New_Google_Account_on
                  Android⠀⇛


                # ⚓ HowTo Geek ☛ How_to_Crop_Videos_on_Android⠀⇛


                # ⚓ 9to5Google ☛ Google_starts_removing_‘Movies_&_TV’_tab_from
                  Play_Store_–_9to5Google⠀⇛


                # ⚓ Gizmo China ☛ Oppo_to_Reveal_ColorOS_Android_13_Rollout
                  Roadmap_on_June_8th_at_its_Developer_Forum⠀⇛


                # ⚓ Gizmo China ☛ Android_12_update_available_for_Oneplus_5,_5T
                  via_LineageOS_19⠀⇛


                # ⚓ Gizmo China ☛ Android_12_update_goes_live_for_the_Xiaomi
                  12X⠀⇛


                # ⚓ Android Central ☛ How_to_replace_the_Android_12_lock_screen
                  clock_on_a_Google_Pixel_|_Android_Central⠀⇛


                # ⚓ Giz China ☛ Samsung_Exynos_2300_–_Android’s_first_3nm
                  flagship_SoC_exposed⠀⇛


                # ⚓ TechRadar ☛ Serious_security_bugs_put_millions_of_Android
                  devices_at_risk_|_TechRadar⠀⇛


                # ⚓ 7_Best_Ways_to_Fix_Android_TV_Remote_Not_Working_–_Guiding
                  Tech⠀⇛


                # ⚓ TechRadar ☛ Nothing_Phone_(1)_could_be_the_most_exciting
                  Android_phone_of_the_year_|_TechRadar⠀⇛


                # ⚓ Android Headlines ☛ Create_Lists_In_Style_With_‘Listy’
                  Android_App⠀⇛


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


          o ⚓ Medevel ☛ Wallabag_an_open_source_self-hosted_app_for_saving_web
            pages⠀⇛


                 Wallabag is an open source app for saving web pages to
                 read them later. It allows writers to save and classify
                 articles. It’s written with PHP.


                 Wallabag extracts the articles content and display it in
                 a comfortable view. Wallabag is supported by many feed
                 aggregators, and RSS readers.


          o ⚓ Apache Blog ☛ The_Apache_News_Round-up:_week_ending_27_May_2022⠀⇛


                 Farewell, May –we’re wrapping up the month with another
                 great week. Here are the latest updates on the Apache
                 community’s activities…


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ 9to5Linux ☛ Mozilla_Firefox_101_Is_Now_Available_for
                        Download,_This_Is_What’s_New⠀⇛


                             
                             Firefox 101 is quite a minor update, so don’t
                             expect any important changes. Probably the
                             most interesting change in Firefox 101 is the
                             fact that Mozilla re-implemented the dialog
                             prompt for saving or opening files, which was
                             removed in Firefox 98 when Mozilla
                             implemented an optimized download flow.


                      # ⚓ Mozilla ☛ Support.Mozilla.Org:_What’s_up_with_SUMO_–
                        May⠀⇛


                             Q2 is a busy quarter with so many exciting
                             projects on the line. The onboarding project
                             implementation is ongoing, mobile support
                             project also goes smoothly so far (we even
                             start to scale to support Apple AppStore),
                             but we also managed to audit our localization
                             process (with the help of our amazing
                             contributors!). Let’s dive more into it
                             without further ado.


                      # ⚓ Mozilla ☛ New_(…and_less_new)_Council_members_–_H2
                        2021_–_H1_2022_–_Mozilla_Reps⠀⇛


                             As you know, we all elected three new members
                             to our Reps Council. As usual, we are writing
                             a post about them and the wonderful things
                             they did for Mozilla.


                             However, this time, I have to admit
                             something:


                             A few months ago, you elected two other new
                             members to the Reps Council. They finished
                             their onboarding and started actively
                             contributing to the program. But….we did not
                             post about them!


                             So in this post, and terribly late, we want
                             to talk about all these five new (and…less
                             new) council members.


                             Let’s get to know them!


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PostgreSQL:_PostgreSQL_JDBC_42.3.6_Released⠀⇛


                       The JDBC team has released version 42.3.6 to fix a
                       regression introduced in 42.3.2


                # ⚓ PostgreSQL ☛ PostgreSQL:_Registration_for_Postgres_Vision
                  2022_is_Open!⠀⇛


                       Postgres Vision 2022 is coming soon! Registration
                       is now open. Join us for this free online event on
                       June 14 and 15 – and engage with Postgres experts
                       from around the world. Check out the agenda and
                       register at postgresvision.com


          o § Content Management Systems (CMS)⠀➾


                # ⚓ WP_Briefing:_Episode_32:_An_Open_Source_Reading_List⠀⇛


                       In the thirty-second episode of the WordPress
                       Briefing, WordPress Executive Director Josepha
                       Haden Chomphosy shares her open source reading list
                       for that post-WordCamp Europe downtime.


          o § FSFE⠀➾


                # ⚓ Paul Schaub ☛ Europe_Trip_Journal_–_Entry_27:_Oh_Champs-
                  Élysées⠀⇛


                       Yesterday I had some breakfast in my hostel and
                       after that I took the metro to the Châtelet station
                       which is close to the Seine. When I was in Paris
                       near the start of my trip (which is almost 4 weeks
                       ago at this point) I had walked down the riverside
                       path of the Seine and therefore had missed some
                       points of interest that lay behind the quay wall.


                       One of these things is the famous Louvre. I did not
                       plan on visiting the inside, as I’m not really into
                       looking at paintings, so I settled on sightseeing
                       the building from the outside. The campus (I’m not
                       actually sure if it all belonged to the Louvre) is
                       huge. You are encircled by large facades and are
                       stared down from statues of famous people on the
                       balconies above. Then, walking though an archway,
                       you enter a large yard with the glass pyramids in
                       the middle.


          o § Programming/Development⠀➾


                # ⚓ Vlang_(or_another_new_project)⠀⇛


                       The language of my choice for this weekend was V/
                       Vlang. I already took a look at V maybe one month
                       before, but have never programmed anything using
                       it. So I decided to just try it out.


                       After a few hours of using, I must say I really
                       enjoy the programming language. It is very simple
                       to program in, the code is very readable and with
                       many features by default.


                # ⚓ Drew DeVault ☛ bleh_(Drew_DeVault’s_blog_on_SourceHut_and
                  More)⠀⇛


                       A few weeks ago, the maintainer of a project on
                       SourceHut stepped down from their work, citing
                       harassment over using SourceHut as their platform
                       of choice. It was a difficult day when I heard
                       about that.


                       Over the past few weeks, I have been enduring a bit
                       of a depressive episode. It’s a complex issue
                       rooted in several different problems, but I think a
                       major source of it is the seemingly constant deluge
                       of hate I find myself at the receiving end of
                       online. I had to grow a thick skin a long time ago,
                       but lately it has not been thick enough. I am
                       finding it increasingly difficult to keep up with
                       my work.


                       Perhaps it this has something to do with the
                       backlash, not just against me and my work, but
                       against others who use and participate in that
                       work. It’s not enough to dislike my programming
                       language, but the skeptics must publicly denounce
                       it and discourage others from using it. It’s
                       irresponsible, if not immoral, to design a language
                       without a borrow checker in 2022. SourceHut’s
                       email-oriented approach might not be for everyone,
                       and instead of simply not using it, skeptics must
                       harass any projects that do. This kind of
                       harassment is something I hear about often from
                       many maintainers of projects on SourceHut. It
                       breaks my heart and I feel helpless to do anything
                       about it.


                # ⚓ Qt ☛ New_Community_Manager,_QtCS2022,_and_Upcoming_Plans⠀⇛


                       I’m Pedro Bessa, and I am Qt’s new Community
                       Relations Manager. Nice to meet you!


                       Maybe you have seen me around already, but if not,
                       let me briefly introduce myself.
                       It’s been almost three months since I joined Qt,
                       and throughout this time, I have been getting to
                       know people and learning how things work around
                       here.


                # ⚓ Understanding_Interface_Analog-to-Digital_Converters_(ADCs)
                  with_DataStorm_DAQ_FPGA⠀⇛


                       Analog-to-Digital Converter (ADC) is used for the
                       conversion of analog signals such as voltage to
                       digital form so that they can be read and processed
                       by a microcontroller or microprocessor. The user
                       program must start the ADC conversion process, and
                       it takes several microseconds for the conversion to
                       complete.


                       ADC converters are very useful for controlling and
                       monitoring applications such as temperature
                       sensors, pressure sensors, and force sensors to
                       monitor analog output voltages.


                # ⚓ OpenSource.com ☛ Dynamically_linking_libraries_while
                  compiling_code_|_Opensource.com⠀⇛


                       Compiling software is something that developers do
                       a lot, and in open source some users even choose to
                       do it themselves. Linux podcaster Dann Washko calls
                       source code the “universal package format” because
                       it contains all the components necessary to make an
                       application run on any platform. Of course, not all
                       source code is written for all systems, so it’s
                       only “universal” within the subset of targeted
                       systems, but the point is that source code is
                       extremely flexible. With open source, you can
                       decide how code is compiled and run.


                       When you’re compiling code, you’re usually dealing
                       with multiple source files. Developers tend to keep
                       different classes or modules in separate files so
                       that they can be maintained separately, and
                       possibly even used by different projects. But when
                       you’re compiling these files, many of them get
                       compiled into a single executable.


                       This is usually done by creating shared libraries,
                       and then dynamically linking back to them from the
                       executable. This keeps the executable small by
                       keeping modular functions external, and ensures
                       that libraries can be updated independently of the
                       applications that use them.


                       Programming and development


                # ⚓ Medevel ☛ 7_Top_UI_Components_for_React.js_in_2022⠀⇛


                       Even with so many other frameworks coming into the
                       market, the good old React platform has still
                       managed to keep its position cemented. One of the
                       big reasons for Reacts’ longevity is the fact that
                       this platform is instantly upgraded with the latest
                       updates as they happen, and third-party developers
                       are also quick to release frameworks that give
                       users the latest functionality.


                       While this is great in terms of the usability of
                       the software, it does make it a little challenging
                       to differentiate the quality frameworks from those
                       that aren’t up to the mark. In this article, we are
                       looking at some of the best component libraries
                       that you can use with your next React project.


                # § Perl / Raku⠀➾


                      # ⚓ LWN ☛ Perl_5.36.0_released_[LWN.net]⠀⇛


                             Version 5.36.0 of the Perl language is out.
                             “Perl 5.36.0 represents approximately a year
                             of development since Perl 5.34.0 and contains
                             approximately 250,000 lines of changes across
                             2,000 files from 82 authors.” Changes include
                             the enabling of function signatures, Unicode
                             14.0 support, experimental iteration over
                             multiple values, and a lot more; see the
                             release notes for the full list.


                      # ⚓ Rakulang ☛ 2022.22_Complete_Timeline_–_Rakudo_Weekly
                        News⠀⇛


                             Oleksandr Kyriukhin announced a new version
                             of the Comma Complete IDE for subscribers,
                             with a new impressive real-time overview of
                             every open file, socket, process, thread
                             plotted on a timeline. And other assorted
                             fixes and updates, of course!


    * § Leftovers⠀➾


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Some_Backstory_and_Observations_about_Living_with_Heart
                  Disease⠀⇛


                       In November of 2021, I went to the emergency room
                       after my girlfriend insisted on it. I had a pulse
                       of 220 and a blood pressure of 55/37. For the
                       medical nerds out there, my heart condition was
                       ventricular tachycardia. I remember hospital staff
                       telling me that I had been very close to death.
                       Once they brought me back from death’s door, they
                       admitted me for a hospital stay that lasted a week.


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Monday⠀⇛


                       Security updates have been issued by Debian
                       (modsecurity-apache, pngcheck, rsyslog, and
                       smarty3), Fedora (firefox, golang-github-
                       opencontainers-runc, gron, kernel, kernel-headers,
                       kernel-tools, logrotate, mingw-pcre2, and rubygem-
                       git), Mageia (admesh, chromium-browser-stable,
                       golang, kernel, kernel-linus, and pidgin), Red Hat
                       (firefox, openvswitch2.13, openvswitch2.15,
                       openvswitch2.16, rsyslog, and thunderbird), SUSE
                       (bind, curl, opera, pcp, postgresql12, and
                       postgresql14), and Ubuntu (gnupg2 and ntfs-3g).


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Record ☛ Cybersecurity_lessons_for_after_Roe_from
                        the_frontlines_of_bodily_autonomy⠀⇛


                             The leak of a Supreme Court opinion draft
                             overturning Roe v. Wade earlier this month
                             and a wave of state-level laws in the U.S.
                             radically limiting abortion are forcing many
                             Americans to re-examine the relationship
                             between their digital privacy and the ability
                             to make their own health decisions.


                             But marginalized groups have already been
                             navigating those challenges and learning hard
                             fought lessons about cybersecurity —
                             including sex workers whose labor is often
                             criminalized; queer people also targeted by
                             state-level laws pushed by conservative U.S.
                             legislators; and reproductive rights
                             activists overseas.


                             “The decisions around one’s body should
                             always be private, but when the right to
                             reproductive health is blocked by civil and
                             state initiatives, when people can even get
                             chased, privacy becomes key not only to
                             reproductive rights but to the integrity of
                             that person,” said Angela Alarcón, a
                             campaigner at international digital rights
                             nonprofit Access Now.


                             The right for people to control what happens
                             to their own body, or bodily autonomy, is a
                             key framework for understanding access to
                             reproductive healthcare as a human right, as
                             well as modern organizing movements for sex
                             worker and queer rights. But bodily autonomy
                             is now also intimately linked with
                             information that is collected about people by
                             the devices they carry around in their
                             pockets as well as expanding networks of
                             private-party and state surveillance.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Wired ☛ Elon_Musk’s_Twitter_Plans_Would_Mean_Less_Free
                  Speech_for_Many_|_WIRED⠀⇛


                       IN MARCH 2021, a Turkish court ordered the news
                       site Diken to remove a critical story about an ally
                       of the country’s president, Recep Tayip Erdogan.
                       Yaman Akdeniz, a Turkish lawyer and digital rights
                       activist, posted a tweet urging his followers to
                       read the story before the decision went into
                       effect. Then the court ruled that his tweet also
                       needed to be removed. But for more than a year
                       Twitter has defied the order, allowing the tweet to
                       remain up.


                # ⚓ Time ☛ An_AI_Company_Scraped_Billions_of_Photos_For_Facial
                  Recognition._Regulators_Can’t_Stop_It⠀⇛


                       More and more privacy watchdogs around the world
                       are standing up to Clearview AI, a U.S. company
                       that has collected billions of photos from the
                       internet without people’s permission.


                       The company, which uses those photos for its facial
                       recognition software, was fined £7.5 million ($9.4
                       million) by a U.K. regulator on May 26. The U.K.
                       Information Commissioner’s Office (ICO) said the
                       firm, Clearview AI, had broken data protection law.
                       The company denies breaking the law.


          o § Civil Rights/Policing⠀➾


                # ⚓ AccessNow ☛ Saudi_Google_Cloud_center:_shareholder_vote_can
                  prevent_storm_of_human_rights_abuses⠀⇛


                       Access Now and human rights organizations from
                       across the globe are urging Alphabet shareholders
                       to use their vote at the Annual General Meeting on
                       June 1 to ensure that the company upholds basic
                       human rights principles and commitments before it
                       proceeds with its cloud region plan in Saudi Arabia
                       — a country with a woeful record of surveillance,
                       repression, and egregious human rights abuses.


                       “Alphabet shareholders will be jeopardizing the
                       safety and security of millions of people if they
                       don’t vote for human rights at the AGM,” said Marwa
                       Fatafta, MENA Policy Manager at Access Now.
                       “Building a Google Cloud data center in a country
                       like Saudi Arabia — where surveillance,
                       persecution, and repression rule — is dangerous,
                       but it can be stopped today before real-life harm
                       is done.”


                # ⚓ AccessNow ☛ Letter_to_Alphabet_Shareholders:_Vote_YES_to
                  Uphold_Google’s_Human_Rights_Commitments⠀⇛


                       Alphabet’s plans to expand its data center
                       operations to countries with significant human
                       rights concerns should raise a big red flag for
                       responsible shareholders. The company’s choice to
                       establish a Google Cloud data center in Saudi
                       Arabia in particular raises serious concerns about
                       Alphabet’s compliance with its own policies and
                       public commitments on human rights. The undersigned
                       human rights organizations, therefore, urge
                       Alphabet shareholders to use their vote at the
                       upcoming Annual General Meeting on June 1, 2022, to
                       ensure that Alphabet upholds basic human rights
                       principles before it proceeds with its cloud region
                       plan in Saudi Arabia.


                       The U.S. State Department Country Report on Saudi
                       Arabia details a grim human rights record,
                       including executions for nonviolent offenses;
                       forced disappearances; torture and cases of cruel,
                       inhuman, or degrading treatment of prisoners and
                       detainees by government agents; harsh and life-
                       threatening prison conditions; arbitrary arrest and
                       detention; political prisoners or detainees;
                       harassment and intimidation against Saudi
                       dissidents living abroad; arbitrary or unlawful
                       interference with privacy; espionage and
                       infiltration of technology platforms; use of cyber
                       surveillance technologies to spy on dissidents and
                       human rights defenders; serious restrictions on
                       free expression, including media censorship; and a
                       notorious justice system that flagrantly violates
                       due process rights.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ New_Gemini_Post,_Gemlog_Style!⠀⇛


                       Setting up and figuring out this Gemini Space!


                # ⚓ On_the_shortcomings_of_gemini_protocol⠀⇛


                       FWIW, images are supported. They are not rendered
                       by default, you have to click on them and then it
                       does render them (if the browser can, that is;
                       there are terminal-based ones; though even
                       terminals can display images nowadays! even xterm,
                       which I use!).


                # ⚓ Exiting_the_chaotic_information_superhighway⠀⇛


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Medevel ☛ Arkcase_an_open_source_agnostic_case_management
                  solution_for_business.⠀⇛


                       Arkcase is an open source case management platform
                       that enables users to customize, automate end to
                       end case management activities. It also helps users
                       reduce the complexity and unpredictability of your
                       organization.


                       [...]


                       Arkcase licensed under the LGPL-3.0 license.


                # ⚓ Medevel ☛ Primo_is_a_low-code_website_generator_and
                  designer⠀⇛


                       Primo is a free easy-to-use low-code website
                       editor, creator, and publisher.


                       Unlike its competitors, It does not require
                       extensive setup or configuration.


                       Primo uses Svelte under the hood, which proven to
                       be reliable as for real-world and enterprise
                       projects.



                    ䷩ 𝚕𝚒𝚗𝚎 4876

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_30/05/2022:_WordPress_Turns_19⠀✐


Posted in News_Roundup at 1:30 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o Reviews
          o BSD
          o PCLinuxOS/OpenMandriva_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o GNU_Projects
          o Licensing_/_Legal
          o Programming/Development
                # Perl_/_Raku
          o Standards/Consortia
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Monopolies
                # Copyrights
    * § GNU/Linux⠀➾


          o ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#184⠀⇛


                 Welcome to this week’s Linux Weekly Roundup.


                 We had another wonderful week in the world of Linux
                 releases with Bluestar Linux 5.17.9, Pearl Linux OS 11,
                 and LXLE Focal.


          o § Audiocasts/Shows⠀➾


                # ⚓ Jupiter Broadcasting ☛ CPU_as_a_Service_|_LINUX_Unplugged
                  460⠀⇛


                       A new Linux update allows Intel to control features
                       in your CPU using hardware-level DRM.


                # ⚓ GNU_World_Order_462⠀⇛


                       Can you rename a file that’s set to read-only? If
                       you said “no” then you don’t know UNIX file
                       permissions as well as you think you do. Hear all
                       about the details in this episode.


                # ⚓ Episode_325_–_Is_one_open_source_maintainer_enough?_–_Open
                  Source_Security⠀⇛


                       Josh and Kurt talk about a recent OpenSSF issue
                       that asks the question how many open source
                       maintainers should a project have that’s “healthy”?
                       Josh did some research that shows the overwhelming
                       majority of packages have one maintainer. What does
                       that mean?


                # ⚓ Video ☛ These_Pacman_Scripts_Should_Ship_With_Arch_Linux_–
                  Invidious⠀⇛


                       At one point in time the pacman contrib scripts
                       shipped with pacman and shipped with Arch Linux but
                       due to maintenance issues it was split out.


          o § Applications⠀➾


                # ⚓ Ubuntu Pit ☛ Top_15_Best_Google_Drive_Clients_for_Linux
                  System_in_2022_|_UbuntuPIT⠀⇛


                       Google Drive is one of the best Cloud Storage
                       options in the market. It offers sufficient storage
                       for free to fulfill our primary requirements,
                       including storing photos, Gmail, or various
                       documents. The popularity of Google drive
                       increasing day by day, and we can assume that cloud
                       storage will take the throne from physical storage
                       shortly. So it’s always better to adapt ourselves
                       to changing technology. But Google doesn’t offer
                       any official Google Drive client for Linux.


                       You must be aware of the importance of a Google
                       Drive client if you are a Linux user. And so, you
                       must be looking for one to use. If so, I am sure
                       you are on the right track because this content
                       will lead you to the best 15 Google Drive clients
                       for Linux users.


                # ⚓ Adriaan de Groot ☛ Calamares_Handoff_|_[bobulate]⠀⇛


                       I’ve wrapped up the Calamares 3.2 branch today. It
                       is now in bug-fix-only mode, or LTS. The main
                       development branch, calamares, is now for a future
                       3.3 release. The new release will drop a bunch of
                       legacy support, dating back to Debian 8. This
                       cleans up a bunch of #ifdefs and means we can
                       target just one Qt version. The release wraps up my
                       paid involvement with Calamares – call 3.1 and 3.2
                       the “era of [ade]” if you will – and for now, hands
                       the project over to the community.


                       I’m sure there will be another maintainer at some
                       point. The project itself is Free Software, it
                       isn’t going to go away, be co-opted, or destroyed.


                # ⚓ Barry Kauler ☛ Containers_now_have_top-level_zram⠀⇛


                       Early on, I was thinking that to support top-level
                       zram for containers, each container would need its
                       own zram device. However, yesterday I realised the
                       obvious; the main layered filesystem and the
                       layered filesystems of the containers, could all
                       use the same zram. It is simply a matter of having
                       a sub-folder in the zram for each aufs layer.


                # ⚓ Beta News ☛ Surfshark_VPN_for_Linux_gets_proper_GUI⠀⇛


                       What makes Surfshark one of the best paid VPN
                       services on the market? Well, besides being
                       extremely affordable, it has no device limit and is
                       very easy to use on many platforms, including
                       Windows, macOS, Android, iOS, and iPadOS. Not to
                       mention, the developers are constantly adding new
                       features — they don’t rest on their laurels. I
                       highly recommend the service.


                       A desktop Linux version of Surfshark has been
                       available for a while now, but sadly, it did not
                       have a graphical user interface (GUI) — you had to
                       configure and run it from the terminal. While this
                       technically worked, it was clunky and annoying,
                       making Surfshark on Linux inferior to versions for
                       other operating systems.


          o § Instructionals/Technical⠀➾


                # ⚓ A_decade_of_dotfiles⠀⇛


                       My first commit to my dotfiles repository was ten
                       years ago. Here are a few things I’ve learned about
                       maintaining a system configuration in that time.


                # ⚓ John Goerzen ☛ John_Goerzen:_Fast,_Ordered_Unixy_Queues
                  over_NNCP_and_Syncthing_with_Filespooler⠀⇛


                       It seems that lately I’ve written several shell
                       implementations of a simple queue that enforces
                       ordered execution of jobs that may arrive out of
                       order. After writing this for the nth time in bash,
                       I decided it was time to do it properly. But first,
                       a word on the why of it all.


                # ⚓ Linux Capable ☛ How_to_Install_PHP_8.1_on_AlmaLinux_9⠀⇛


                # ⚓ Linux Shell Tips ☛ How_to_Delete_All_Files_in_a_Directory
                  Except_Few⠀⇛


                       File deletion is an important yet sensitive aspect
                       of Linux administration. The Linux commands behind
                       file deletion operations help us get rid of files
                       we do not need.


                       There is usually a high chance that the files we
                       wish to delete reside in a single folder or
                       directory. If we did not need all these files; once
                       we navigate to that directory, it would be easier
                       to get rid of them with a simple rm command
                       implementation.


                # ⚓ How_to_Install_Psensor_Temperature_Monitoring_Application
                  on_Ubuntu_20.04⠀⇛


                       Having control of your system also means knowing
                       what the temperature of your computer is at any
                       given moment. Although this may sound difficult,
                       the reality is that it is not and it helps to
                       prevent errors and hardware damage. Therefore, we
                       have prepared the following post for you to learn
                       how to Install Psensor Temperature Monitoring
                       Application on Ubuntu 20.04.


                # ⚓ UNIX Cop ☛ Installing_Nginx_on_OpenBSD_7.1⠀⇛


                       Nginx is a web server created with a focus on
                       performance, high concurrency and low resource
                       usage. It serves the majority of the top websites.
                       Whilst this is mostly due to its performance, it’s
                       also relatively easy to get started with.


                       By default, Nginx deals with web requests
                       asynchronously i.e. a single nginx process can
                       serve multiple requests concurrently. However,
                       because of this design Nginx, as compared to web
                       servers like Apache, can’t embed server side
                       programming languages like PHP into its own
                       process. This means those tasks are to be handled
                       by completely separate processes and then reverse
                       proxied back to the clients via Nginx. Therefore,
                       at its core, Nginx is actually just a reverse
                       proxy.


                       In this article, we’re going to go through the
                       process of compiling and installing Nginx through
                       source. While installation through the package
                       manager is fairly easy, we do not get as much
                       control over the Nginx binary as we get by
                       compiling from source. I have chosen OpenBSD for it
                       serves very well as a secure server operating
                       system.


                # ⚓ UNIX Cop ☛ How_To_Install_RPM_Fusion_on_Fedora_34/35/36⠀⇛


                       RPM Fusion is a software repository, providing add-
                       on packages for Fedora Linux. It was born as a
                       merge of the older repositories Livna, Dribble and
                       Freshrpms. They distributed software that Fedora
                       will not, either because it does not meet Fedora’s
                       definition of free software, or because
                       distribution of that software may violate US law.


                       The RPM Fusion repository comes in two variants,
                       Free and Non-Free. The free repository contains a
                       free version of the software that is open source
                       and non-free, which have mostly almost all free
                       software but are closed source and mainly
                       proprietary.


                # ⚓ UNIX Cop ☛ How_To_Install_Bareos_Backup_Solution_on_Fedora
                  36⠀⇛


                       In this article, we will show you how to install
                       Bareos backup solution on Fedora 36


                       Bareos (Backup Archiving Recovery Open Sourced) is
                       a backup software, originally forked from the
                       Bacula project. It is network-based, multi-client
                       and very flexible with an architecture oriented
                       towards scalability. Thus the learning curve might
                       be considered somewhat steep. The project is backed
                       by the commercial company Bareos GmbH & Co. KG,
                       based in Germany.


                # ⚓ UNIX Cop ☛ How_to_speed_Up_dnf_Package_Manager_In_Fedora,
                  RHEL_and_CentOS⠀⇛


                       DNF or Dandified YUM is the next-generation version
                       of the Yellowdog Updater, Modified (yum), a package
                       manager for .rpm-based Linux distributions. DNF was
                       introduced in Fedora 18 in 2013, it has been the
                       default package manager since Fedora 22 in 2015,
                       Red Hat Enterprise Linux 8 , and OpenMandriva; and
                       also an alternative package manager for Mageia.


                       Perceived deficiencies of yum (which DNF is
                       intended to address) include poor performance, high
                       memory usage, and the slowness of its iterative
                       dependency resolution. DNF uses libsolv, an
                       external dependency resolver.


                # ⚓ H2S Media ☛ How_to_install_Signal_Messenger_on_Ubuntu_22.04
                  LTS_Jammy⠀⇛


                       Learn the steps to install the Signal Private
                       Messenger app on Ubuntu 22.04 LTS Jammy JellyFish
                       using the command terminal.


                       Signal is one of the popular open-source messaging
                       apps that has been known for several years for its
                       end-to-end encryption and its independent structure
                       as a non-profit organization operated by a
                       foundation — not a large tech company. It is a
                       handy tool for communication among activists and
                       other people who are particularly concerned about
                       their privacy.


                       End-to-End communication in Signal is encrypted.
                       This means that only those people who are involved
                       in the conversation can read the content of
                       messages any other user who is not the part of the
                       chat, not even the company itself – are unable to
                       do so. Signal is particularly serious about
                       privacy, even sticker packages have their own
                       encryption. In addition, Signal has developed the
                       encryption protocol that other services such as
                       Skype and Whatsapp use.


                # ⚓ Install_LibreNMS_on_Ubuntu_22.04/Ubuntu_20.04_–
                  kifarunix.com⠀⇛


                       Follow through this tutorial to learn how to
                       install LibreNMS on Ubuntu 22.04/Ubuntu 20.04.
                       LibreNMS is a fully featured MySQL/PHP and SNMP
                       based network monitoring system.


                # ⚓ Video ☛ How_to_install_ONLYOFFICE_on_Debian_11_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       ONLYOFFICE on Debian 11. Enjoy!


                # ⚓ Linux Made Simple ☛ How_to_install_Mine-imator_1.2.9_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Mine-imator
                       1.2.9 on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                # ⚓ How_to_Show_Hidden_Files_in_Ubuntu_22.04_LTS_(and_hide
                  them)⠀⇛


                       Hiding a file or folder is a feature that helps you
                       increase your device’s privacy and security. You
                       wouldn’t want a 5-year-old child to mess up your
                       most essential documents. And how would you feel if
                       someone deleted your hours of work just as a prank?


                       The easiest way to tackle such ‘accidents’ is to
                       keep your files hidden and later unhide them when
                       needed. If you don’t know how to hide and unhide
                       files on Ubuntu, then good news for you. Because
                       that’s exactly what we will cover here.


                # ⚓ How_To_Change_Linux_Hostname_(Ubuntu,_CentOS_&_more)⠀⇛


                       A Linux hostname is a unique name that identifies a
                       computer on a network. When working on multiple
                       computers on the same network, you may get confused
                       because of duplicate hostnames. So the need to
                       change your hostname arises.


                       In this article, we cover the best methods
                       (including terminal and GUI) on how to change Linux
                       hostname in some of the major Linux distributions.
                       Let’s get started.


                # ⚓ Download_A_Collection_of_Passwords_&_Wordlists_for_Kali
                  Linux_(2022)⠀⇛


                       Today you’ll be able to download a collection of
                       passwords and wordlist dictionaries for cracking in
                       Kali Linux.


                       A wordlist or a password dictionary is a collection
                       of passwords stored in plain text. It’s basically a
                       text file with a bunch of random passwords in it.


                # ⚓ Best_WiFi_Adapters_For_Kali_Linux_in_2022_(That_Supports
                  Packet_Injection)⠀⇛


                       Today you will learn which are the best wifi
                       adapters that are most commonly used for hacking in
                       Kali Linux.


                       If you’re new to Kali Linux or wifi hacking, the
                       most important hardware you need besides a computer
                       with Kali Linux installed, is a USB wireless
                       network adapter with a wifi card (chipset) that
                       supports packet injection and monitor mode.


                # ⚓ Linux_Tech_Tips_to_Become_a_Better_College_Student⠀⇛


                       Are you a college student struggling to make your
                       way up to progress? Are you seeking a competitive
                       advantage? If yes, then first, you need to remember
                       that being a good student is not merely only about
                       good grades. It is your study time and dedication
                       to education that will help you become a better
                       student. Hence, for that, you should switch to
                       Linux.


                       Linux is the greatest operating system, perfect for
                       students because it comes with a variety of
                       features and unique tools that can assist you very
                       well in your study.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ Distro Watch ☛ Review:_Tails_5.0⠀⇛


                       In the past I’ve felt as though Tails was one of
                       the better distributions available for people who
                       wanted to communicate anonymously or visit websites
                       without giving away their location. It was a solid
                       tool, if somewhat held back by two issues. One was
                       that some of the included software was either
                       geared more toward technically experienced users or
                       hadn’t yet matured. Early versions of OnionShare
                       come to mind as software which still had some
                       problems when it was first introduced in Tails. The
                       other issue was performance. GNOME is one of the
                       heaviest open source desktop environments and early
                       versions of GNOME 3 were particularly cumbersome,
                       especially when run on lower-end hardware.


                       What I have appreciated about Tails 5 is it feels
                       like a polished, evolutionary step forward without
                       (as far as I can tell) any regressions from the 4.x
                       series. GNOME 38 still isn’t as responsive and
                       smooth as later versions of GNOME (40 and newer)
                       have been for me, but it feels a little better than
                       past releases.


                       I really like the new Kleopatra tool which acts as
                       a one-stop application for all our encryption key
                       management, file signing, and encryption needs.
                       Kleopatra is another tool I feel has become more
                       polished in recent years and I enjoyed having it in
                       Tails 5.


                       Both Tor Browser and OnionShare worked beautifully
                       for me. I think Tor Browser has always been a solid
                       experience and it continues to be good. OnionShare
                       was a good idea in the past, but I sometimes
                       encountered stability issues with it. The current
                       version feels easier to use and entirely stable.


                       I like the initial configuration screen Tails
                       displays when the distribution starts. The default
                       settings lock down the system (using MAC
                       randomization, locking the Unsafe Browser option,
                       and locking admin functions). However, we can
                       toggle these features if we wish to give more
                       flexibility. This walks a careful line between
                       being secure by default while allowing users
                       latitude to perform more actions.


                       Last, but not least, I appreciate the detail and
                       honesty of the Tails documentation. There are a lot
                       of tips and guidelines on the project’s website. I
                       especially appreciate the project is transparent
                       about both the features Tails offers and the
                       limitations. Some projects boast they will prevent
                       all viruses or will keep people safe on-line, or
                       will keep you anonymous. Tails doesn’t make wild
                       marketing claims. The developers explain how their
                       tools work and how they help, but also warn there
                       are limits and nothing is guaranteed. I appreciate
                       this balanced approach to keeping users informed.


                       In short, if you need to browse the web or want to
                       share files without giving away your location, then
                       Tails is probably one of the most secure and
                       easiest to use distribution to do this.


          o § BSD⠀➾


                # ⚓ Matthias Schmidt ☛ Time_Machine_like_Backups_on_OpenBSD⠀⇛


                       Time Machine is a backup software by Apple, part of
                       macOS allowing easy and foolproof backups. In a
                       nutshell, it creates incremental backups on a
                       storage medium of your choice and you can access
                       the data either with a graphical client or directly
                       via file system tools. I especially like that you
                       only have to plug in an external USB drive which is
                       immediately recognized, the backup starts and the
                       drive is unmounted as soon as the backup is done.
                       Since Time Machine is Apple only and I use OpenBSD
                       on all my personal machines, I decided to write my
                       own Time Machine like solution.


          o § PCLinuxOS/OpenMandriva Family⠀➾


                # ⚓ PCLOS Official ☛ Subtitler_1.5.5⠀⇛


                       Subtitler is a free Desktop application to search
                       and download right subtitle blazingly fast. Now
                       available in the software repository.


                # ⚓ PCLOS Official ☛ Catalyst_Web_Browser_3.1.0⠀⇛


                       Catalyst browser is an amazing and elegant
                       Electron/Chromium based web browser. Now available
                       in the software repository.


                # ⚓ PCLOS Official ☛ Fifo_Web_Browser_1.1.0⠀⇛


                       Fifo browser is a privacy orientated browser based
                       on modern frameworks. Experience a modern browser
                       based on new frameworks. Easily integrate your day
                       with Fifo. Since Fifo is so modern, you don’t need
                       to worry about change, you can just enjoy the
                       experience.


                # ⚓ OpenMandriva_New_LXQt_ISOs_for_Rock_&_Rolling⠀⇛


                       For Rock and Rolling users OpenMandriva Community
                       has made ISOs using the LXQt desktop.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ elementary_OS_7_“Horus”:_Expected_New_Features⠀⇛


                       A highlight of the expected new features of
                       elementary OS 7 “Horus” which caters to changes
                       across look-and-feel, features and performance.


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ Avnet_introduces_RZBoard_V2L_which_packs
                  Renesas_RZ/V2L_SoC_and_comes_in_Raspberry_Pi_4_form-factor⠀⇛


                       The RZBoard V2L from Avnet, is a Single Board
                       Computer (SBC) that shares a similar design to the
                       Raspberry Pi 4 model B. One of the main differences
                       between these SBCs is that the RZBoard V2L is
                       powered  by the powerful RZ/V2L System on Chip
                       (SoC) from Renesas Electronics. Avnet also has
                       these SBCs in stock and they are available for
                       $147.


                       The RZ/V2L processor combines a dual core Arm
                       Cortex-A55 CPU (up to 1.2GHz), an ARM Cortex-M33, a
                       Mali GT31 3D-GPU and an AI accelerator (DRP-AI). In
                       addition, there is a H.264 video (1920/1080)
                       encode/decode function implemented in silicon. 


                # ⚓ Raspberry_Pi_Power⠀⇛


                       In the referenced entry, OP (me) makes a curious
                       statement about the Raspberry Pi power usage: “Uses
                       too much power”…


                       [...]


                       It took me too long to figure it out – I had a USB
                       power supply that worked just well enough most of
                       the time that it was always a mystery.


                       Actually, the micro-USB connector and the USB
                       standard call for power supplies that do not
                       provide adequate power. The cable is rated for
                       500mA, not 2A, so even if you have an overpowered
                       supply, a cheap cable can cause a voltage drop
                       rendering the Pi useless.


                # ⚓ CNX Software ☛ NanoPi_R5S_Rockchip_RK3568_mini_router
                  launched_for_$59_and_up⠀⇛


                       
                       The Rockchip RK3568-powered NanoPi R5S SBC with two
                       2.5GbE ports, one Gigabit Ethernet port, and M.2
                       NVMe storage is now available for $59, or $75 with
                       a metal enclosure.


                       As previously mentioned, the mini router board is
                       equipped with 2GB RAM, 8GB eMMC flash, two USB 3.0
                       ports, as well as an HDMI output for people wanting
                       to make use of the Rockchip RK3568 processor’s
                       multimedia capabilities, or simply have a user
                       interface on a monitor.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Notebook Check ☛ Nothing_phone_(1):_a_launch_date_and
                  European_pricing_for_the_first-gen_Android_device_allegedly
                  leaks_out_–_NotebookCheck.net_News⠀⇛


                # ⚓ Chrome Uboxed ☛ Gmail_is_rolling_out_search_filter_chips_in
                  labels_on_Android⠀⇛


                # ⚓ Android Police ☛ You_can_now_download_the_(second)_earliest
                  known_build_of_Android_ever⠀⇛


                # ⚓ 9_Android_Features_You_Should_Be_Using_Every_Day⠀⇛


                # ⚓ Dignited ☛ How_To_Enable_Developer_Options_on_Google_TV_or
                  Android_TV⠀⇛


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


          o ⚓ Medevel ☛ Lodestone_is_an_open-source_free_document_search
            engine⠀⇛


                 Lodestone is designed to be the modern and digital
                 equivalent of a home filing cabinet. If you’ve gone
                 searching for something similar in the past, you might be
                 familiar with terms like Electronic Document Management
                 System (EDMS), Document Management System (DMS) or
                 Personal Archival.


                 [...]


                 Lodestone is released under the GPL-3.0 license.


          o § Content Management Systems (CMS)⠀➾


                # ⚓ WordPress ☛ WordPress_Turns_19_–_WP_Tavern⠀⇛


                       Today marks 19 years since 19-year old Matt
                       Mullenweg partnered with Mike Little to release the
                       first version of WordPress based on the b2/cafelog
                       software. The blog where he shared his thoughts on
                       life and tech was starting to get more traffic and
                       he wanted to ensure its future after the b2/
                       cafelog’s main developer disappeared.


                       Mullenweg had the vision for what WordPress should
                       be, even before it had a name.


          o § GNU Projects⠀➾


                # ⚓ GNU ☛ hello-2.12.1_released_[stable]⠀⇛


                       This release has no code changes since 2.12, but
                       just a minor documentation fix and updated
                       translations.


          o § Licensing / Legal⠀➾


                # ⚓ WordPress ☛ Software_Freedom_Conservancy_Receives_Court
                  Ruling_Affirming_GPL_as_Both_Copyright_License_and
                  Contractual_Agreement⠀⇛


                       The Software Freedom Conservancy (SFC), a non-
                       profit that provides infrastructure support for
                       free and open source software projects, has
                       received a favorable ruling in its right-to-repair
                       lawsuit against Vizio, an American TV manufacturer.
                       The SFC alleges that Vizio has demonstrated
                       “repeated failures to fulfill even the basic
                       requirements of the General Public License (GPL),”
                       after the company refused to provide the source
                       code for software with copyleft licenses that it
                       bundles with its products.


                       Vizio had filed a request to “remove” the case from
                       California State Court into U.S. Federal Court.
                       After hearing oral arguments from both sides, the
                       court has granted SFC’s motion to remand the case
                       back to California State Court.


          o § Programming/Development⠀➾


                # ⚓ Weekend_lack_of_focus⠀⇛


                       I feel like doing an experiment with HTTP Basic
                       Authentication. What if instead of just sending the
                       user:password encoded I provide a session token
                       during the login (using regular post via HTTPS) and
                       from this point on use user:token? And why not
                       encrypt with SHA instead of just encoding?


                       I was reading about OAuth2 because of my job and
                       was thinking about using it in my personal project
                       but wow… what an over-complicated solution for
                       something simple as my project!


                # ⚓ The New Stack ☛ What_Made_GoLang_So_Popular?_The_Language’s
                  Creators_Look_Back_–_The_New_Stack⠀⇛


                       Since the day it was open sourced in 2009, the Go
                       programming language has consistently grown in
                       popularity. Now the five Google software engineers
                       behind its original creation are taking a look back
                       at what fueled that growth.


                       Writing in Communications of the ACM, Go’s five
                       original creators stress that even their earliest
                       work “benefited greatly from advice and help from
                       many colleagues at Google.” And the paper’s second
                       sentence emphasizes that it’s now a public project
                       “with contributions from thousands of individuals
                       and dozens of companies.”


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ Perl_Weekly_Challenge_166:_Hexadecimal_Words
                        and_K-Directory_Diff⠀⇛


          o § Standards/Consortia⠀➾


                # ⚓ [Old] What’s_in_a_Name?⠀⇛


                       Any solution in this area needs to recognize that
                       one size does not fit all. For some applications a
                       single “name=[string]” will be sufficient and it
                       would be seriously counter-productive to force
                       those folks to engage in detailed encoding. Another
                       barrier to detailed encoding is that few people
                       have knowledge to encode the universe of name forms
                       at a detailed level. Requiring metadata creators to
                       make distinctions outside of their understanding
                       would only result in error-ridden metadata. Better
                       a blind single string than mis-coded details. Yet
                       there will be applications and their metadata
                       communities that can or must make use of the
                       subtleties of name details that are not of interest
                       to others.


                       Because of both the great variety of name forms and
                       the variability of applications that make use of
                       names, I recommend a metadata vocabulary that
                       follows the principle of minimum semantic
                       commitment. This means a vocabulary that includes
                       broad classes and properties that can be used as is
                       where detailed coding is not needed or desired, but
                       which can be extended to accommodate many different
                       contexts.


                       The trick then is to define broad classes that aid
                       in defining semantics but do little restriction.
                       Classes for things like “Agent”, with subclasses
                       for “Person”, “Groups of Persons”, and perhaps
                       “Non-persons”. Properties could begin with “name”
                       which could be subdivided into any definable part
                       of a name that people find useful. Further
                       specificity can be provided by application profiles
                       that define such requirements as cardinality or
                       value types for the various properties.
                       Applications themselves could contain rules for the
                       displays that are needed for their use cases.


                       The challenge now is to find a standards group that
                       is interested to take this on.


    * § Leftovers⠀➾


          o ⚓ Counter Punch ☛ Animal_Factory⠀⇛


                 Even then farming for them was a hobby, an avocation, a
                 link to a way of life that was slipping away. My
                 grandfather, who was born on that farm in 1906, graduated
                 from Purdue University and became a master electrician,
                 who helped design RCA’s first color TV. My grandmother,
                 the only child of an unwed mother, came to the US at the
                 age of 13 from the industrial city of Sheffield, England.
                 When she married my grandfather she’d never seen a cow, a
                 few days after the honeymoon she was milking one. She ran
                 the local drugstore for nearly 50 years. In their so-
                 called spare time, they farmed.


                 My parent’s house was in a sterile and treeless
                 subdivision about five miles away, but I largely grew up
                 on that farm: feeding the cattle and horses, baling hay,
                 bushhogging pastures, weeding the garden, gleaning corn
                 from the harvested field, fishing for catfish in the
                 creek that divided the fields and pastures from the small
                 copse of woods, learning to identify the songs of birds,
                 a lifelong obsession.


          o ⚓ The_apps_I_use_to_read_and_write_for_this_blog⠀⇛


                 Because I’ve been asked a couple times recently:


                 I keep up with 345 websites and newsletters using an app
                 called NetNewsWire. It’s free and I have it on my Mac,
                 iPhone, and iPad. It’s a type of app called a newsreader.


          o ⚓ critique_of_everyday_life_by_henri_lefebvre_(3)⠀⇛


                 more broadly, lefebvre is trying to develop a ‘theory of
                 needs’ (299) that illuminates the relationship between
                 nature and culture in everyday life. he does so by
                 suggesting that we think dialectically about need and
                 desire: ‘there is a transfer from need to desire which
                 crosses the social and society in its entirety’ (305).
                 this quote should make it clear that he’s not arguing for
                 a naive account of nature or essence, since ‘the circuit
                 from need to desire and from desire to need is constantly
                 being interrupted or distorted’ (305).


          o ⚓ Historical_or_Cultural_Bindings⠀⇛


                 Drone Day proceeds glowingly. I place my headphones over
                 my ears to hear and the combination of Purpll + Draume
                 delights. Is anyone else listening? That relates to a
                 topic I’ll address later in this meandering essay (I
                 laughingly call it an *essay*). The short answer is that
                 Flavigula’s Drone Day broadcast has had at this moment of
                 writing a peak of 29 simultaneous listeners. How does
                 that make me feel? It doesn’t, really. More on this later
                 in the *essay*. For now – back to Purpll + Draume! A
                 lovely combination! Perhaps one to win universal acclaim!
                 I guffaw. Soon Draume will be in other hands. I sold it
                 to attain a more gentle yet more controllable reverb –
                 Red Panda Context. Honestly, though, it may house hidden
                 madness like its cousins 2.7182818 times removed, Tensor
                 and Raster. Draume has one timbrel quality I will miss.
                 At least I have the unique *overdriven reverb* that spews
                 from its innards encased in stone, never to be struck
                 from the earth. Not that the earth will be around for
                 much longer – or so I hear. Fuck um.


          o ⚓ My_Fourth_Basket⠀⇛


                 I recently took up basketry as a hobby. Each basket has
                 been a bit better, as one would expect, but this one — my
                 fourth — is the first one I’m truly happy with. It’s the
                 first one that I’ve stained and sealed with a wood oil
                 and I think it really completes what otherwise looks like
                 a half-finished product.


          o ⚓ Little_Problems⠀⇛


                 But it sure does feel like the last few years have been a
                 string of problems strung together.


                 Some of them are big (family members dying, lockdowns,
                 depression, lockdown depression), but most of them are
                 small (see aforementioned noisy neighbour).


          o ⚓ Hackaday ☛ Autonomous_Inflatable_Canoe⠀⇛


                 With the summer months nearly upon us, many are dreaming
                 of warm afternoons spent floating on a quiet lake. Unless
                 you’re [Kolins] anyway. Apparently his idea of a good
                 time is controlling a full-sized inflatable canoe not
                 from onboard with a pair of oars, but from the shore with
                 a RC transmitter.


          o § Education⠀➾


                # ⚓ My_students_cheated…_A_lot⠀⇛


                       I’m debating right now whether or not to write my
                       account of what happened. Leaning toward writing
                       this. And, then I’ll debate myself later on whether
                       or not to share it…Debated…going to share. No
                       names, or any other identifying information.
                       Overall my students are really great. This could be
                       a fiction. There was a lot of cheating, so the
                       story is long. I mean this could be a podcast. It
                       ends well too, for the most part.


                       One more side note. Why tell this story? Since this
                       whole thing happened I’ve told the story a bunch of
                       times, and sometimes I get requests to tell it.
                       This is also a story for my future students about
                       what not to do. So, here is a long form version.
                       I’m not interested in outing my students, or
                       casting shade on them. There were many fantastic
                       students in my course while the cheating completely
                       overwhelmed everything like a metastasizing slime
                       mold. People cheat in college for lots of reasons.
                       I don’t condone the behavior. I teach my courses
                       because I’m interested in engaging students in the
                       material. When cheating happens, it can reflect on
                       me as an instructor and whether or not the course
                       merits engagement. So, this is a story about
                       cheating, but also about how I tried to turn things
                       around and get students to engage in my course.
                       Anyway, without further ado:


                       [...]


                       I had nothing better to do so I wrote an R program
                       to help me fill out the forms. Who knew I could
                       automate pdf text entry from R. You learn something
                       new everyday.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Rackmount_Hardware_Placement_Issues?_IKEA_LACK
                  To_The_Rescue!⠀⇛


                       [hackbyte] reminds us about a classic hack that,
                       even though we’ve seen floating around for over a
                       decade, has somehow never quite graced our pages
                       before. Many of us keep small home labs and even,
                       at times, collections of servers that we’d be
                       comfortable be calling mini-datacenters. However,
                       if you use the ever-abundant 19″ switches, servers
                       and other hardware, keeping these mounted and out
                       of the way can be a thorny experience. Which leads
                       us to, undoubtedly, unintentional – but
                       exceptionally handy – compatibility between IKEA
                       LACK table series and 19″ rackmount hardware.


                # ⚓ Hackaday ☛ Adjustable_Workholding_For_Honeycomb_Tables,
                  With_A_Bit_Of_DIY⠀⇛


                       Honeycomb tables are often found on laser cutters,
                       where they provide a way for work material to be
                       laid flat while not interfering with things like
                       airflow. This leads to a cleaner laser cut and a
                       nicer finish, but if one’s work depends on precise
                       positioning and placement, they leave something to
                       be desired because there’s no good way to attach
                       rails, jigs, or anything of the sort in an easy and
                       stable fashion.


                # ⚓ Hackaday ☛ Laser_Driver_Design_Keeps_Safety_First⠀⇛


                       [Les] from [Les’ Lab] has designed a driver for
                       laser diodes up to 10 watts, and decided to show us
                       how it operates, tells us what we should keep in
                       mind when designing such a driver, and talks about
                       laser safety in general. This design is an
                       adjustable current regulator based on the LM350A,
                       able to provide up to 10 watts of power at about 2
                       volts – which is what his diode needs. Such obscure
                       requirements aren’t easily fulfilled by commonly
                       available PSUs, which is why a custom design was
                       called for.


                # ⚓ Hackaday ☛ Better_Robots_Through_Gallium⠀⇛


                       In the movie Terminator 2, the T-1000 robot was
                       made of some kind of liquid metal that could change
                       shape among other interesting things. According to
                       a chemical engineer at North Carolina State
                       University, there may be something to the idea.
                       [Michael Dickey] has been experimenting with
                       gallium, a liquid metal, that scientists think may
                       unlock a new generation of flexible devices.


                # ⚓ Hackaday ☛ Relax_And_Enjoy_This_Simple_Drone_Synthesizer⠀⇛


                       You’d think that a synthesizer that makes as much
                       noise and sports as many knobs as this one would
                       have more than a dozen transistors on board. Surely
                       the circuit behind the panel is complex, and there
                       must be at least a couple of 555 timers back there,
                       right?


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Nobel_Laureate_Calls_for_Ending_Intellectual
                  Property_Rules_for_COVID_Vaccines⠀⇛


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ [Old] Lowering_the_cost_of_anonymization⠀⇛


                             The objective of this thesis is to make it
                             easier to understand, use, and deploy strong
                             anonymization practices. We make progress
                             towards this goal in three ways.


                             First, we make it easier to understand what
                             anonymization means, and lower the cost of
                             entry for new practitioners. After a
                             historical tour of a number of possible
                             definitions, we introduce differential
                             privacy, a central concept studied throughout
                             this thesis. We then systematize and organize
                             the existing literature on variants and
                             extensions of differential privacy: we
                             categorize them in seven dimensions, compare
                             them with each other, and list some of their
                             main properties.


                             Second, we consider a natural class of weaker
                             variants of differential privacy: definitions
                             that assume that the attacker only has
                             partial knowledge over the original data. We
                             raise some fundamental issues with existing
                             definitions, and we establish strong
                             theoretical foundations to solve these issues
                             and clearly delineate between distinct attack
                             models. We use these foundations to improve
                             existing results on the privacy of common
                             aggregations and draw links between our
                             notions and older syntactic definitions of
                             privacy. Then, we provide strong negative
                             results for cardinality estimators, a class
                             of algorithms that cannot be made private
                             even under very weak assumptions.


                             Third, we focus on practical applications. We
                             present novel algorithms to detect
                             reidentifiability and joinability risks of
                             large datasets, and we describe the design of
                             a differentially private query engine
                             designed to be usable to non-experts. We
                             propose multiple possible improvements to
                             this query engine, and discuss a number of
                             trade-offs between privacy, utility,
                             usability, and extensibility; we then discuss
                             operational challenges arising when rolling
                             out anonymization at scale, from choosing
                             parameters to providing appropriate education
                             and guidance to engineers working on
                             anonymization pipelines.


                      # ⚓ Site36 ☛ Prüm_II:_EU_Committee_criticises_planned
                        obligation_for_facial_recognition⠀⇛


                             All EU member states are to network their
                             police facial images and investigation files
                             across Europe. This puts pressure on some
                             governments without such systems.


                      # ⚓ Joint_letter_to_the_National_Commission_for_Safai
                        Karamcharis_against_the_increasing_surveillance_of
                        Safai_Karamcharis_in_the_country⠀⇛


                             In the past two years, we have come across
                             multiple news reports related to Safai
                             Karamcharis across the country being made to
                             wear tracking devices in order to enable
                             their surveillance by the authorities.
                             Concerned by the human rights violations that
                             such actions will trigger, IFF is releasing a
                             joint letter initiated by the All India
                             Lawyers Association For Justice (AILAJ) to
                             express our concerns over these ongoing
                             violations to the National Commission for
                             Safai Karamcharis.


          o § Defence/Aggression⠀➾


                # ⚓ Counter Punch ☛ Modern_America’s_Murderous_Apotheosis_at
                  Uvalde⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_The_Key_Role_Firearms_Makers_Play
                  in_America’s_Gun_Culture_Revealed_in_Six_Charts⠀⇛


                       Americans have blamed many culprits, from mental
                       illness to inadequate security, for the tragic mass
                       shootings that are occurring with increasing
                       frequency in schools, offices and theaters across
                       the U.S.


                # ⚓ Modern Diplomacy ☛ Israel_admits_involvement_in_the_killing
                  of_an_Iranian_army_officer_–_Modern_Diplomacy⠀⇛


                       Col. Sayad Khodayee, 50, was fatally shot outside
                       his home in Tehran on Sunday when two gunmen on
                       motorcycles approached his car and fired five
                       bullets into it, according to state media. Iran has
                       blamed Israel for the killing, which bore the
                       hallmarks of other Israeli targeted killings of
                       Iranians in a shadow war that has been playing out
                       for years on land, sea, air, and cyberspace.


                       Although a spokeswoman for the Israeli prime
                       minister declined to comment on the killing. But
                       according to an intelligence official briefed on
                       the communications, Israel has informed American
                       officials that it was behind the killing.


                # ⚓ Modern Diplomacy ☛ Playing_games_in_NATO,_Turkey_eyes_its
                  role_in_a_new_world_order⠀⇛


                       NATO’s spat over Turkish opposition to Swedish and
                       Finnish membership is about more than expanding the
                       North Atlantic military alliance. It’s as much
                       about Turkish President Recep Tayyip Erdogan’s
                       immediate political goals as Turkey’s positioning
                       itself in a new 21st-century world order.


                       On its surface, the spat is about Turkish efforts
                       to hinder support for Kurdish ethnic, cultural, and
                       national aspirations in Turkey, Syria, and Iraq and
                       a crackdown on alleged supporters of a preacher who
                       lives in exile in the United States. Turkey accuses
                       the preacher, Fethullah Gulen, of instigating a
                       failed military coup in 2016.


                # ⚓ MEMRI ☛ Jordanian_Islamic_Scholar_Bilal_Al-Qasrawi:_A
                  Nuclear_Attack_By_The_Infidels_Against_The_Future_Islamic
                  State_Is_Not_A_Concern;_We_Can_Afford_To_Lose_Two_Million
                  People,_They_Cannot⠀⇛


                       Jordanian Islamic scholar Bilal Al-Qasrawi said in
                       a May 20, 2022 show on the Hizb-ut-Tahrir-
                       affiliated Al-Waqiyah TV (Lebanon) that when an
                       Islamic caliphate is reestablished, the infidels
                       might use nuclear weapons against Muslim countries,
                       but that the Muslims nonetheless will not
                       surrender. He said that if the infidels kill a
                       million or two million Muslims, the Muslims will
                       kill as many infidels, adding: “We can afford to
                       lose a million [lives], but can they? No. That’s
                       it.” For more information about Bilal Al-Qasrawi,
                       see MEMRITV clip no 4559.


                # ⚓ TruthOut ☛ Gun_Lobby_Intervened_Against_a_Republican’s_Gun
                  Law._Then_He_Lost_His_Seat.⠀⇛


          o § Environment⠀➾


                # § Wildlife/Nature⠀➾


                      # ⚓ Common Dreams ☛ Opinion_|_Six_Decades_on_From_Rachel
                        Carson’s_Silent_Spring,_Birds_Facing_‘Inexorable
                        Decline’⠀⇛


                             In her landmark 1962 book, Silent Spring,
                             biologist Rachel Carson chronicled the damage
                             — and looming consequences — of human
                             “contamination of air, earth, rivers, and sea
                             with dangerous and even lethal materials,”
                             which she called “elixirs of death.” In the
                             book’s spellbinding opening parable, which
                             profiles a fictional town of the future, she
                             wrote:


                      # ⚓ Edinburgh_Zoo_urges_visitors_to_stop_‘tampering_with
                        signs’_after_disrespectful_behaviour_from_guests_|
                        Edinburgh_News⠀⇛


                             On Facebook, the zoo posted a picture of two
                             of its gentoo penguins, and asked visitors to
                             “Be GENTOO with our things”.


                             The post read: “We’re delighted to see so
                             many enthusiastic faces but please remember
                             that alongside respecting our team and other
                             visitors, our wonderful exhibits and signage
                             deserve the same treatment.”


          o § Finance⠀➾


                # ⚓ The Conversation ☛ Who_really_owns_the_oil_industry’s
                  future_stranded_assets?_If_you_own_investment_funds_or_expect
                  a_pension,_it_might_be_you⠀⇛


                       When an oil company invests in an expensive new
                       drilling project today, it’s taking a gamble. Even
                       if the new well is a success, future government
                       policies designed to slow climate change could make
                       the project unprofitable or force it to shut down
                       years earlier than planned.


                       When that happens, the well and the oil become
                       what’s known as stranded assets. That might sound
                       like the oil company’s problem, but the company
                       isn’t the only one taking that risk.


                       In a study published May 26, 2022, in the journal
                       Nature Climate Change, we traced the ownership of
                       over 43,000 oil and gas assets to reveal who
                       ultimately loses from misguided investments that
                       become stranded.


                       It turns out, private individuals own over half the
                       assets at risk, and ordinary people with pensions
                       and savings that are invested in managed funds
                       shoulder a surprisingly large part, which could
                       exceed a quarter of all losses.


                # ⚓ Nature ☛ Stranded_fossil-fuel_assets_translate_to_major
                  losses_for_investors_in_advanced_economies⠀⇛


                       The distribution of ownership of transition risk
                       associated with stranded fossil-fuel assets remains
                       poorly understood. We calculate that global
                       stranded assets as present value of future lost
                       profits in the upstream oil and gas sector exceed
                       US$1 trillion under plausible changes in
                       expectations about the effects of climate policy.
                       We trace the equity risk ownership from 43,439 oil
                       and gas production assets through a global equity
                       network of 1.8 million companies to their ultimate
                       owners. Most of the market risk falls on private
                       investors, overwhelmingly in OECD countries,
                       including substantial exposure through pension
                       funds and financial markets. The ownership
                       distribution reveals an international net transfer
                       of more than 15% of global stranded asset risk to
                       OECD-based investors. Rich country stakeholders
                       therefore have a major stake in how the transition
                       in oil and gas production is managed, as ongoing
                       supporters of the fossil-fuel economy and
                       potentially exposed owners of stranded assets.


                       [...]


                       The code of the network model, for imputing missing
                       financial information and for generating figures,
                       are available at ref. 45. The code that generates
                       the network inputs from the E3ME-FTT-GENIE
                       scenarios and from the company database is
                       available from the authors on reasonable request.
                       The code used by E3ME-FTT-GENIE to generate the
                       underlying scenarios is available from the authors
                       on reasonable request. The model is described in
                       detail in ref. 13.


                # ⚓ SBP_expands_scope_of_data_collection_to_curtail_digital
                  banking_frauds [Ed: They always find some 'compelling'
                  excuses for more surveillance]⠀⇛


                       May 27, 2022: The State Bank of Pakistan (SBP) on
                       Friday directed all scheduled banks as well as
                       microfinance banks to submit data of all digital
                       frauds and scams on a monthly basis while the
                       purview of reporting is also expanded from fake
                       calls by Fraudsters to other digital channels
                       including the mobile app, E-Commerce Transactions,
                       ATMs and POS.


                # ⚓ Web3_in_Japan⠀⇛


                       As it is custom, whatever trend appears in America
                       becomes mainstream in Japan after it has completely
                       lost its cool. This time the government and a
                       billionaire think what the Japanese people really
                       should care about is some jpgs.


                # ⚓ Common Dreams ☛ Opinion_|_Are_We_Headed_for_Mass_Revolts_to
                  Upturn_the_Global_Economic_Model?⠀⇛


                       While it has long been blatantly obvious that the
                       global economic model is not working for all, the
                       rate of accumulation of wealth by a small minority
                       is now breathtaking – if not totally obscene.


                # ⚓ Common Dreams ☛ Opinion_|_As_World’s_Mega_Rich_Geared_Up
                  for_Davos,_Central_Bankers_Went_Rogue_—_and_Rational⠀⇛


                       We had quite a show up in the Alps last week, the
                       first in-person gathering of the world’s mega rich
                       since Covid hit. The occasion? The annual World
                       Economic Forum at the Swiss resort of Davos, an
                       ever-so-sober gathering that has an assortment of
                       global deep thinkers sharing their wisdom with deep
                       pockets ever eager for policy ideas that don’t
                       involve sharing their wealth.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Scheerpost ☛ Happy_Memorial_Day⠀⇛


                       “Happy Memorial Day,” a new original cartoon by the
                       inimitable Mr. Fish, considers the service of our
                       past soldiers and the reprehensibility of
                       ventriloquizing their ultimate sacrifice.


                # ⚓ Frontpage Magazine ☛ Islamophobia_and_Islamoignorance⠀⇛


                       In short, it’s perfectly legitimate to criticize
                       and even reject an ideology if that ideology poses
                       a serious threat to one’s society. It would be
                       irrational to pretend that Nazism was a force for
                       peace and justice.


                # ⚓ RFERL ☛ Iranian_Religious_Song_Seen_As_Attempt_To
                  Indoctrinate_Children⠀⇛


                       In the song, the children pledge allegiance to
                       Supreme Leader Ayatollah Ali Khamenei — the
                       “commander.” Khamenei’s followers have tried to
                       elevate his status by bestowing him the title of
                       imam, the highest title in Shi’ite Islam.


                # ⚓ Why_Everyone_Should_Use_Adguard⠀⇛


                       I hate ads. I think anyone who knows me can attest
                       to the fact that I hate ads. For most of my ad-
                       blocking needs, I use uBlock Origin on my desktop
                       browser, and that seems to work fine most of the
                       time.


                       But there are situations where uBlock Origin does
                       not cut it. For instance, I couldn’t find a way to
                       block ads in mobile apps on my iOS device. (I know
                       you’re saying “just buy the ad-free version and
                       support the developer!” but there’s no way in hell
                       I’m going to pay a weather app $12/mo just to get
                       ad-free access)


                # ⚓ TruthOut ☛ Some_Republicans_Fume_at_Michigan_GOP_for
                  Defending_Candidates_Busted_for_Fraud⠀⇛


                # § Misinformation/Disinformation⠀➾


                      # ⚓ [Old] Fact_Checking_the_1619_Project_and_Its
                        Critics⠀⇛


                             The New York Times’ 1619 Project entered a
                             new phase of historical assessment when the
                             paper published a scathing criticism by five
                             well-known historians of the American
                             Revolution and Civil War eras. The group
                             included previous critics James McPherson,
                             Gordon Wood, Victoria Bynum, and James Oakes,
                             along with a new signature from Sean Wilentz.
                             The newspaper’s editor-in-chief Jake
                             Silverstein then responded with a point-by-
                             point rebuttal of the historians, defending
                             the project.


                             Each deserve to be taken seriously, as they
                             form part of a larger debate on the merits of
                             the 1619 Project as a work of history and its
                             intended use in the K-12 classroom
                             curriculum. While the project itself spans
                             some four centuries, devoting substantial
                             attention to racial discrimination against
                             African-Americans in the present day, the
                             historians’ criticism focuses almost entirely
                             on the two articles that are most directly
                             pertinent to their own areas of expertise.
                             The first is the lengthy introductory essay
                             by Nikole Hannah-Jones, the Times journalist
                             who edited the project. The second is a
                             contentious essay on the relationship between
                             slavery and American capitalism by Princeton
                             University sociologist Matthew Desmond.


                             How should readers assess the competing
                             claims of each group, seeing as they appear
                             to be at bitter odds? That question is
                             subject to a multitude of interpretive issues
                             raised by the project’s stated political
                             aims, as well as the historians’ own
                             objectives as eminent figures – some might
                             say gatekeepers – in the academic end of the
                             profession.


                             But the debate may also be scored on its many
                             disputed factual claims. To advance that
                             discussion, I accordingly offer an assessment
                             for each of the main points of contention as
                             raised by the historians’ letter and
                             Silverstein’s response.


          o § Censorship/Free Speech⠀➾


                # ⚓ Catholic World Report ☛ Large_US_companies_rated_on_respect
                  for_free_speech,_religious_freedom⠀⇛


                       With some American companies able to have a
                       profound impact on the exercise of free speech and
                       religious freedom, Alliance Defending Freedom and
                       Inspire Investing have launched a Business Index to
                       rate their commitment to these values.


                       “CEOs and business leaders have positions of
                       considerable power. They shouldn’t weaponize their
                       influence or the companies they run to divide
                       Americans or engage in speech censorship or anti-
                       religious bigotry,” ADF Senior Vice President for
                       Corporate Engagement Jeremy Tedesco said in a May
                       26 statement.


                # ⚓ Nasdaq ☛ How_The_Federal_Government_Showed_Me_The
                  Importance_Of_Bitcoin⠀⇛


                       The feds seized my website JeromeBaker.com during
                       Operation Pipe Dreams, which was a federal effort
                       to bring those of us selling bongs and pipes across
                       state lines to justice. It was 2003. There were not
                       a lot of website seizures going on. The internet
                       didn’t really start in earnest until 1996. There
                       wasn’t a lot of regulation out there at first. Porn
                       was big on the internet. And then, buying and
                       selling drug paraphernalia caught on.


          o § Civil Rights/Policing⠀➾


                # ⚓ Medforth ☛ Sharia_in_Italy:_Burned_with_an_iron_because_she
                  did_not_wear_a_veil⠀⇛


                       The girl, who was harassed by her Islamic
                       relatives, reportedly ran away from home several
                       times until she reported the incidents. She was
                       later placed in a sheltered community and even
                       attempted to take her own life in the family home.
                       According to the public prosecutor’s office,
                       represented by prosecutor Donato Greco, the abuse
                       continued for months. However, this was always
                       denied by the family members, although the judges
                       eventually acknowledged they were guilty.


                # ⚓ The Guardian UK ☛ French_prosecutor_suspects_antisemitism
                  in_murder_of_elderly_man⠀⇛


                       “It’s no longer a question of telling us it’s the
                       act of a mentally disturbed person. The truth of
                       antisemitism must no longer be hidden,” Goldnadel
                       wrote.


                       France has experienced a sharp rise in violence
                       targeting its roughly 500,000 Jews, the largest
                       community in Europe, in addition to jihadist
                       attacks in recent years.


                # ⚓ Free Press Journal ☛ Lucknow:_Maulana_chains_2_boys_at
                  madrasa_to_prevent_them_from_running_away⠀⇛


                       The case came to light after a local made a video
                       and sent it to the police, who reached the site and
                       freed the children before detaining the accused.


                # ⚓ NDTV ☛ Hindu_Man_Killed_Over_Relationship_With_Muslim_Woman
                  In_Karnataka:_Cops⠀⇛


                       The victim’s mother accused the girl’s father and
                       brother of stabbing her son in the First
                       Information Report (FIR).


                # ⚓ TruthOut ☛ Want_to_Win_a_Union_at_Work?_Here’s_What_the
                  Amazon_Labor_Union_Can_Teach_Us.⠀⇛


                # ⚓ TruthOut ☛ Starbucks_Workers_United_Wins_in_US’s_Most_Anti-
                  Union_City⠀⇛


                # ⚓ Common Dreams ☛ Organizers_Herald_100th_Win_as_Starbucks
                  Unionization_Wave_Continues⠀⇛


                       The tally of unionized Starbucks locations is
                       continuing to swell, with the latest additions
                       coming after pro-unionization votes late last week
                       in Seattle and Birmingham, Alabama.


                       The coffee giant’s CEO “Howard Schultz and
                       Starbucks are getting creamed in union vote after
                       union vote,” labor journalist Steven Greenhouse
                       tweeted Saturday.


                # ⚓ Common Dreams ☛ Opinion_|_Corporate_Criminal_Law_Heading
                  for_Extinction?⠀⇛


                       Crimes without criminals was not a subject for
                       study when I was in law school. The two were seen
                       as part of the same illegal package. That was
                       before notorious corporate lawyers and a cash
                       register Congress combined to separate economic,
                       health and safety crimes from corporate
                       accountability, incarceration and deterrence.


          o § Monopolies⠀➾


                # ⚓ TruthOut ☛ Infant_Formula_Crisis_Highlights_Breastfeeding
                  Barriers_in_Southern_States⠀⇛


                # § Copyrights⠀➾


                      # ⚓ Digitization_Wars,_Redux⠀⇛


                             We now have another question about book
                             digitization: can books be digitized for the
                             purpose of substituting remote lending in the
                             place of the lending of a physical copy? This
                             has been referred to as “Controlled Digital
                             Lending (CDL),” a term developed by the
                             Internet Archive for its online book lending
                             services. The Archive has considerable
                             experience with both digitization and
                             providing online access to materials in
                             various formats, and its Open Library site
                             has been providing digital downloads of out
                             of copyright books for more than a decade.
                             Controlled digital lending applies solely to
                             works that are presumed to be in copyright.


                      # ⚓ [Old] Review_of:_Free_Culture:_How_Big_Media_Uses
                        Technology_and_the_Law_to_Lock_Down_Culture_and_Control
                        Creativity.⠀⇛


                             This is the third book by Stanford law
                             professor Larry Lessig, and the third now in
                             which he furthers his basic theme: that the
                             ancien regime of intellectual property owners
                             is locked in a battle with the capabilities
                             of new technology. Lessig used his first
                             book, Code and Other Laws of Cyberspace
                             (Basic Books, 1999), to explain that the
                             notion of cyberspace as free, open, and
                             anarchic is simply a myth, and a dangerous
                             one at that: the very architecture of our
                             computers and how they communicate determine
                             what one can and cannot do within that
                             environment. If you can get control of that
                             architecture, say by mandating filters on
                             content, you can get substantial control over
                             the culture of that communication space. In
                             his second book, The Future of Ideas: the
                             Fate of the Commons in a Connected World
                             (Random House, 2001), Lessig describes how
                             the change from real property to virtual
                             property actually means more opportunity for
                             control, not less. The theme that he takes up
                             in Free Culture is his concern that certain
                             powerful interests in our society (read:
                             Hollywood) are using copyright law to lock
                             down the very stuff of creativity: mainly,
                             past creativity.


                             Lessig himself admits in his Preface that his
                             is not a new or unique argument. He cites
                             Richard Stallman’s writings in the mid-1980′s
                             that became the basis for the Free Software
                             movement as containing many of the same
                             concepts that Lessig argues in his book. In
                             this case, it serves as a kind of proof of
                             concept (that new ideas build on past ideas)
                             rather than a criticism of lack of
                             originality. Stallman’s work is not, however,
                             a substitute for Lessig’s; not only does
                             Lessig address popular culture where Stallman
                             addresses only computer code, but Lessig has
                             one key thing in his favor: he is a master
                             story-teller and a darned good writer, not
                             something one usually expects in an academic
                             and an expert in constitutional law. His book
                             opens with the first flight of the Wright
                             brothers and the death of a farmer’s
                             chickens, followed by Buster Keaton’s film
                             Steamboat Bill and Disney’s famous mouse. The
                             next chapter has the history of photography
                             and how the law once considered that snapping
                             a picture could require prior permission from
                             the owners of any property caught in the
                             viewfinder. Later he tells how an improvement
                             to a search engine led one college student to
                             “owe” the RIAA $15,000,000. Throughout the
                             book Lessig illustrates copyright through the
                             lives of real people and uses history,
                             science and the arts to make this law come to
                             life for the reader.


                      # ⚓ Torrent Freak ☛ 6,500_IPTV_Pirates_Identified_After
                        Accessing_Police-Controlled_Service⠀⇛


                             Police in Italy have revealed details of an
                             operation against pirate IPTV services and
                             subscribers. In addition to targeting around
                             500 ‘pirate’ sites, servers, and Telegram
                             channels, police say IT specialists were able
                             to identify 6,500 people who accessed a
                             pirate IPTV platform under police control.


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