𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, October 27, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Thu 28 Oct 02:40:03 BST 2021 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2021/10/27/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmScBUgZwyXW8e6VTQ7hn4TPr2dPrqRq4mBq4A6SJD33QU QmNq798z2Jmsd7aRXgNnfjRvXzECKPp7piDVUnWvgsGMmw QmRVquEDfjUxjZohz6NpGuYae1hJY5sYhcGTzygC15t1qe QmS8QHtXh2RotXbWpZsvGPyWGq3WgJPQrsFc5JaTmqKcxD QmYzF6VmHg31fxPQwnB9o6yJM36EqoqsYXvNMqVE941LM6 QmXCdRHxnSMKmGrnRzrnSPCDWQmdjzEejArfYqZsaBy35Z Qmf9EcBFemckbJcR5iWC3PVGJxQ5xe3ZqCGKzz681rKMmD QmdjD3F5X1T9xbTPMY2Wrk5YUS8tfKUD5inGbqQ8rnJrpo QmSJxiMQEysAS6b1cT6LbxyB2gmL92RHnKe2bugqURX7jK QmZ9XrCCvCG4m4kD1sxmesDGxEpk9EjEVk5vNUFHZ87Ryw QmZQbFL87wWvs9kFDSndgbof4kDmQTqYdyokNAjNg8H7Ca QmSfTwYRE2mM7875hHQK9fmXEAAZS4i3r9frAmfJcCFGks QmWq5A18omXMGWTTDzH6NZwrkQWd1pUiLRptBpgDHHhvXq QmVR1Se3jKzW513QvSLv9utzGvBbi5C3cdSBwWspCid4vi Qme5Me7St6kgikNpzT1KeDRhhmCJJtsLSFQyP8TDyvd8MW QmagsjCozdhV3doZKjmRs6GYXQb7U425VW5GsX4YUfg2Fu QmXdXQ45MDdfyLhvFXMoFQarrFy2cSYrkTKdKtneXpHrYF QmNooKJgn2ZLXZJyZNJCACY5R84RsQy1y85ycxgS8JMkdA QmcbJ2ejJ9JqECW5WmJC4LeEqkjC7w6kcJ6wjwLthVmoEU QmR26bCkmAgeJHsLEpDDduxsZtvTiPxLdppYuH4w8mzfdo Qmex86DPLV4yK5WC34kReVXbdEtRT7fvt7mBVzMTGbSCct ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ The EPO’s Overseer/Overseen Collusion — Part XXV: The Balkan League - Fresh Blood or Same Old, Same Old? | Techrights ⦿ Beatriz Busaniche Speaks Up in Defense of Richard Stallman | Techrights ⦿ ’Shaping the New Normal’ Survey at the EPO Got 5,554 EPO Staff to Participate, But It Was Controlled by Liars With an Agenda | Techrights ⦿ IRC Proceedings: Tuesday, October 26, 2021 | Techrights ⦿ Many of the National Delegations (or Delegates) in the EPO’s Administrative Council Have No Understanding of What They Vote on | Techrights ⦿ [Meme] EPO Presidential Surveys | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/10/27/balkan-league-summary/#comments http://techrights.org/2021/10/27/beatriz-busaniche-on-rms/#comments http://techrights.org/2021/10/27/better-epo-survey/#comments http://techrights.org/2021/10/27/irc-log-261021/#comments http://techrights.org/2021/10/27/political-patent-offices/#comments http://techrights.org/2021/10/27/presidential-surveys/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/10/27/murena-for-eos/#comments http://techrights.org/2021/10/27/xorg-server-21-1/#comments ䷩ 𝚕𝚒𝚗𝚎 63 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/balkan-league-summary/#comments Gemini version at gemini://gemini.techrights.org/2021/10/27/balkan-league-summary/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_–_Fresh Blood_or_Same_Old,_Same_Old?⠀✐ Posted in Europe, Patents at 5:06 am by Dr. Roy Schestowitz Series parts: 1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In! 2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous” Endorsement? 3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes 4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States 5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja” 6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch Courage 7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity 8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and Pusillanimous_Hibernia 9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss Cheese 10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the Controversial_Christian_Bock 11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_– Battistelli’s_Swiss_Apprentice? 12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection 13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian Facilitators_–_Spain 14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian Facilitators_–_Portugal 15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria… 16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the Austrian_Double-Dipper 17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic Nordic_Bloc 18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord 19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States 20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group 21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The Doyen_and_His_“Protégée” 22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_– North_Macedonia_and_Albania 23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_– Bulgaria 24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_– Romania 25. YOU ARE HERE ☞ The Balkan League – Fresh Blood or Same Old, Same Old? 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_Balkan_gallery⦈_ Some new faces on the EPO’s Administrative Council representing the Balkan states that voted in favour of Battistelli’s “Strike Regulations” in June 2013. Clockwise from top left: Goran Gerasimovski (MK), Marian Cătălin Burcescu (RO), Ledina Beqiraj (AL), and Vladya Borisova (BG). Summary: We take stock of “captured states” that voted in favour of unlawful “Strike Regulations” In this part we conclude our whistle-stop tour of the “Balkan League” states that helped to rubber-stamp Benoît_Battistelli‘s “Strike Regulations”. As we have seen, there have been a lot of changes in those delegations since 2013. “Insofar as they are prepared to swallow the sugar-coated “Kool-Aid” narrative being spoon-fed to them by the spin-doctors of Team Campinos, they might not even realise that there is a problem.”By a strange coincidence, the only delegation which remains unchanged is the one representing Croatia, which is still headed by Željko Topić’s “protégée” Ljiljana Kuterovac. As far as the other delegations are concerned, it’s not clear to what extent the new generation of representatives are aware of the damage caused by the actions of their predecessors in supporting Battistelli’s “reign of terror” at the EPO. “It’s very clear that, in many of these countries, the appointment of the head of the national “IP” office – who also acts as the head of delegation on the EPO’s Administrative Council – is treated as a sinecure which is typically handed out as a “reward” to some local party political opportunist.”Insofar as they are prepared to swallow the sugar-coated “Kool-Aid” narrative being spoon- fed to them by the spin-doctors of Team Campinos, they might not even realise that there is a problem. It’s very clear that, in many of these countries, the appointment of the head of the national “IP” office – who also acts as the head of delegation on the EPO’s Administrative Council – is treated as a sinecure which is typically handed out as a “reward” to some local party political opportunist. In the case of two of the new delegates pictured above, it can be said without fear of contradiction that their appointments were overtly political in nature: • the North Macedonian delegate Goran Gerasimovski who is a member of the Macedonian SDSM; and • the Romanian delegate Marian Cătălin Burcescu who is a member of the Romanian PNL. In the case of the two other delegates – Ledina Beqiraj from Albania and Vladya Borisova from Bulgaria – there isn’t enough information available to indicate whether or not their appointments might have been influenced by ulterior political considerations. “…it deserves to be pointed out that not all member states from the Balkan region were prepared to kowtow before Battistelli.”In any event, it remains to be seen whether the new representatives from the “Balkan League” states will continue to play the role of “captured delegates”, meekly subservient to Battistelli’s successor Campinos, or whether they will manage to take a principled stand for justice and the rule of law at the EPO. The voting record of these delegations during the Battistelli era, and afterwards under Campinos, gives little cause for optimism in this regard. The actions of these countries on the EPO’s Administrative Council tend to confirm their reputation as "captured_states". However, it deserves to be pointed out that not all member states from the Balkan region were prepared to kowtow before Battistelli. “In the next part we will stay in the general vicinity of the Balkan Peninsula as we turn our attention to Greece and its neighbours, Cyprus and Turkey.”Two of the successor states of the former Yugoslavia – namely, Slovenia and Serbia – frequently took a critical stance towards the Corsican despot and his nefarious machinations at the EPO. Both of these delegations withheld their support during the vote on the “Strike Regulations” in June 2013. However, before we take a closer look at the “abstentionists”, we will continue and complete our examination of the remaining delegations that supported Battistelli on that occasion. In the next part we will stay in the general vicinity of the Balkan Peninsula as we turn our attention to Greece and its neighbours, Cyprus and Turkey. █ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠙⠛⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣴⣶⣤⣤⣤⣄⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⣀⣀⣀⣀⣀⡀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠐⠀⢤⣾⣧⣠⣽⣟⣉⢉⣇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⣿⣿⣿⣻⢛⣿⣿⠇⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠉⠉⢻⡿⠋⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠶⠶⡟⣿⣾⣽⣭⣿⢫⠶⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡶⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠋⠁⠀⠀⠀⢿⣾⡙⠛⢛⡵⣸⠀⠀⠀⠩⣇⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡞⠿⡟⠓⠀⠁⠛⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠁⠀⠀⡀⠂⠁⠀⠀⠀⠀⠈⠿⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⡀⠀⢾⣅⣼⠃⣐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠉⠈⠸⣷⡄⡀⠀⣤⡆⢹⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣛⣛⣛⣛⣛⣛⣿⣿⠉⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣄⠀⠀⣴⡁⢸⣿⣿⣿⣿⢿⢿⡋⠀⠀⠀⢀⣀⣸⣿⣿⣿⠋⠀⠀ ⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣯⡛⠛⠛⣿⣿⣿⡔⣠⣀⠈⢿⠂⠀⢿⠃⢸⣿⣿⣿⡽⠘⢨⣿⡟⠛⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣟⡂⠀⠘⠛⠉⠹⠹⢿⡳⠈⠀⠀⠸⢸⡈⣿⡏⠀⠀⠀⢘⣿⣿⣿⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣾⣯⡄⠀⠀⠀⠀⠀⢾⣆⡆⠀⠀⠀⣾⡇⠫⡅⠀⠀⠀⠈⠻⢿⢏⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣷⣿⣷⢿⡟⠀⠀⠀⠀⠀⠈⠷⡃⠀⠀⢠⣿⡇⢘⠃⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⠀⢀⠠⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⣛⣛⣏⣁⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢸⣿⠃⠀⠀⠀⣸⡦⠀⠀⠀⢰⠀⣿⣿⣿⡿⣿⠀⢀⣀⣀ ⣿⣿⣥⣄⠀⠀⢠⣦⣼⣿⣿⣿⣾⣿⣀⣀⣀⣀⣀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⠁⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣷⣿⣷⣶⣶⣼⣿⡀⠀⠀⠀⢟⣼⣷⣄⣀⣨⡄⣿⣶⣿⣽⣿⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣶⣬⣁⡻⣿⣿⣿⠿⣃⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⡿⣫⣶⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⠆⠉⠈⠀⠀⠀⠁⠙⠚⠛⣿⣜⢿⣿⣿⣿⣿⣿⣿⣦⡤⣠⣿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣦⣤⣤⡤⠤⠶⠶⡖⣀⣀⢸⡟⠀⢈⣉⣙⣛⣿⠟⣫⣾⣿⣿⣿⣿⣿⡿⠇⠀⣦⡻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡇⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣤⣶⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⠿⢿⡿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⢀⣄⠀⠤⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣶⣾⣷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣃⣤⣼⣿⣾⣶⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣯⣹⣯⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣟⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠙⠛⠁⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⣭⣾⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⢀⠙⠻⠿⠿⠿⠋⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⣤⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣾⠟⠀⠀⡃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⠇⢹⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣯⡄⠀⣈⠃⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢿⠃⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⡾⢿⠟⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠴⠃⠀⠙⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⠜⣿⣿⣿⣿ ⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣄⠻⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣐⣻⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⢀⣴⡶⢲⣦⡀⠀⠀⠸⣿⣿⣿⠏⣱⣿⣚⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣀⡆⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣿⠁⣾⢛⣿⣆⡀⠀⢿⣿⣿⣾⣿⣯⠀⠀⠈⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⡟⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣯⣭⣭⣽⡟⡛⠋⠁⠚⣸⠻⠛⠛⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠐⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⢠⢏⠁⠀⣓⠒⠢⠤⠌⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣩⣽⣿⣿⡻⣿⡏⠀⠀⠀⢸⣿⠟⠛⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢡⣺⣺⣆⠤⠄⣐⠚⠉⠀⠅⢻⣿⠿⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣷⣿⣿⡟⠁⢿⠇⠈⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠺⠃⠀⠉⠙⠛⠓⠲⠶⢭⣤⣝⣾⣶⠆⠛⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⣿⣿⣭⣤⣤⣶⣶⣶⡶⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠍⠀⣰⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 263 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/beatriz-busaniche-on-rms/#comments Gemini version at gemini://gemini.techrights.org/2021/10/27/beatriz-busaniche-on-rms/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Beatriz_Busaniche_Speaks_Up_in_Defense_of_Richard_Stallman⠀✐ Posted in Free/Libre_Software, FSF, GNU/Linux at 1:13 am by Guest Editorial Team Published two days ago in this_site =============================================================================== Beatriz Busaniche sent us this comment in July 2021. She wrote it originally in Spanish. Here are both the original text and our translation to English. =============================================================================== ⚓ Spanish (Original)⠀⇛ Soy Beatriz Busaniche, activista de Software Libre y Derechos Humanos de Argentina desde hace 20 años. Escribo estas palabras porque me considero desde hace mucho tiempo amiga de Richard Stallman, un hecho del que siempre me sentí y me siento orgullosa. Richard se ha hospedado en mi casa muchas veces, hemos compartido eventos, reuniones sociales, actividades políticas y públicas, organicé muchísimas de sus conferencias en mi país. En todos estos años siempre se ha comportado de forma totalmente respetuosa, cálida y generosa conmigo, mi familia y mis amigos. Richard hizo aportes inmensos al mundo de las tecnologías, sentó las bases de la cultura del Software libre, un movimiento indispensable en los tiempos que corren, nos ayudó a pensar críticamente lo que hacemos y cómo lo hacemos. Como movimiento, le debemos mucho y debemos hacernos cargo de que nos hemos ocupado poco de Richard como ser humano. Quienes tenemos la suerte de conocerlo bastante, sabemos que es una persona sensible, amorosa, con flaquezas y debilidades como cualquiera de nosotros, una persona que igual que cualquiera de nosotros comete errores pero que es capaz de cambiar de opinión frente a argumentos claros y razonables. Sabemos también que es una persona con una lógica imbatible que no siempre aplica a las cuestiones de la vida social. Como feminista que soy, siempre he luchado por romper los estereotipos y los procesos de normalización hegemónica. Siempre pensé que debíamos aprender a integrar las minorías y las diferencias y sobre todo, luchar por la justicia y los derechos para todas las personas. No hemos sido justos con RMS en los últimos meses y me siento profundamente avergonzada por no haber levantado mi voz en su defensa con más firmeza en ocasiones anteriores. Como bien dice Richard en su declaración del 12 de abril pasado[*], y como bien sabemos todos los que hemos convivido con él en alguna instancia, su forma de razonar y analizar es muy peculiar pero es algo que está más allá de lo que él puede decidir. ¿De qué nos sirve llamarnos progresistas, feministas, antifascistas si no somos capaces nosotros mismos de lidiar con la neurodiversidad? No voy a juzgar a quienes no quieren a RMS, cada quién construye las afinidades y opiniones que quiere, pero arrojar piedras sobre RMS por su dificultad para escapar de la literalidad es un acto de crueldad indigno de quienes creemos en un mundo más justo y diverso. No cuenten conmigo para eso. * RMS_addresses_the_free_software_community (Archived) ↑ ⚓ English Translation⠀⇛ I am Beatriz Busaniche from Argentina, and I have been a free software and human rights activist for 20 years. I’m writing because I am very proud to consider myself a longtime friend of Richard Stallman. He has stayed in my home many times. I have organized many of his conferences here in Argentina, and we have shared events, social gatherings, and political and public activities. In all these years Richard has always behaved in a totally respectful, warm, and generous way to me, my family, and my friends. Richard has made huge contributions to the world of technology. He laid the foundation for the culture of free software, which has grown into a movement that is crucial to our world today. He has helped us to think critically about what we do and how we do it. Our movement is forever in his debt, and we must acknowledge that we have not met our responsibility to appreciate Richard as a human being. Those of us who are lucky enough to be well acquainted with him know that he is a sensitive, loving person, with weaknesses and imperfections like anyone. He can make mistakes, just like any of us. Yet, he has an extraordinary capacity for logical thinking, and is able to change his position when presented with clear and reasonable arguments. Sometimes, however, he expresses his ideas in an unusually direct way that may seem strange to some. As a feminist, I have always worked to challenge stereotypes and over- generalizations about people. I believe that we should be inclusive of those with differences and, above all, fight for justice and the rights of all people. I feel that Richard has been treated unfairly in recent months, and I am deeply ashamed for not having raised my voice in his defense more firmly before this. In his statement of April 12, 2021[**], Richard admits—and those of us who know him well will concur—that his way of reasoning and analyzing situations is very idiosyncratic, an aspect of his personality beyond his control—an example of what might be called neurodiversity. What is the point of calling ourselves progressives, feminists, or anti-fascists, if we ourselves cannot deal with someone who thinks and expresses himself differently? I am not going to judge those who do not want to associate with Richard Stallman, everyone is entitled to form their own opinion. But I think that throwing stones at him for his tendency to speak logically and literally is an act of cruelty unworthy of those of us who believe in a more just and diverse world. In that, count me out. ** RMS_addresses_the_free_software_community (Archived) ↑ ䷩ 𝚕𝚒𝚗𝚎 405 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/better-epo-survey/#comments Gemini version at gemini://gemini.techrights.org/2021/10/27/better-epo-survey/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ ‘Shaping_the_New_Normal’_Survey_at_the_EPO_Got_5,554_EPO_Staff_to Participate,_But_It_Was_Controlled_by_Liars_With_an_Agenda⠀✐ Posted in Europe, Patents at 9:13 am by Dr. Roy Schestowitz The dictatorship hates independent surveys whose outcome it cannot control or take out of context. Previously, staff representatives who ran a survey (not controlled or ‘authorised’ by the king) got in serious trouble. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Another_survey?_Oh,_independent_survey..._Oy_vey⦈_ Summary: Last year’s EPO ‘study’ (hogwash about “quality” and other unscientific_junk) was likely biased by virtue of autocrats controlling it and exploiting it for nefarious agenda and brainwashing_of_national_delegates*. The Staff Union of the EPO (SUEPO) has a new survey in the making. OVER the years we saw many EPO surveys and SUEPO (union) surveys; with dictators like Benoît_Battistelli and António_Campinos spying on all the staff and flagrantly violating privacy laws (without any legal consequences) folks can imagine what sort of answers staff gives to each; set aside the effect of push_polling or loaded questions… In any case, SUEPO is running a survey right now; we don’t want to disclose URLs (that would interfere with the process), but someone has sent us a copy of a paper from last week, which we’re reproducing below. 22 October 2021 su21030cp – 0.2.1 Teleworking Survey 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇SUEPO survey⦈ Reassessing the Telework preferences a year later Back in mid-2020, the Shaping the New Normal survey was conducted and with a participation rate of 86% it allowed for a quite large amount of 5554 staff members to be heard. Among the topics addressed by the survey there was future teleworking (e.g. different schemes, locations and durations, the relationship between long-term teleworking and expatriation benefits and the impact of extended teleworking and flexibility on the performance of daily tasks), working at the Office’s different sites and the future use of its buildings and premises. The different schemes were covered by 5 different scenarios or personas. Now, over a year after Shaping the New Normal survey, it is important once again to launch a survey among staff to assess how the intended use of teleworking may have evolved after this one year pandemic period. This survey aims at assessing whether and how the proposed mid-term policy by the President would actually fit the wishes of staff. The survey contains solely 10 survey questions, chosen to mimic the questions asked in the Shaping the New Normal survey. The survey will be open for answers during 4 weeks. After the closure of this survey the results will be published to staff and the information used to argue and support the proposals within the working group. Take the SURVEY now! Thank you for considering your participation! SUEPO Central Staff Union of the European Patent Office (SUEPO) As always, SUEPO surveys are very interesting as they reveal what staff really thinks. Not what managers (politicians) want to show. The dictatorship of the EPO just uses surveys for self-serving propaganda purposes, looking to justify decisions already made regardless (before the surveys). █ _____ * They said the “Council expressed its keen interest in the presentation of the analysis following the recent survey on “Shaping the new normal”.” But Office management controlled it all. Under normal circumstances it might seem OK. But they’re lying to the Council routinely. ⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣶⣾⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡃⠀⣶⡙⢿⡿⡿⠿⣿⡿⣿⣿⠟⠋⠉⠀⠀⢀⣀⣤⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣟⣷⢹⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⢨⠻⡌⠃⠀⠀⣼⣷⡏⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣭⣿⣵⣿⣿⣼⣫⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠰⠘⠃⠀⠀⢠⡆⠛⣿⣧⠀⠀⠨⣻⣿⣿⣿⣿⣿⣿⡿⣿⣦⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣾⣿⣞⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⣀⢸⠇⠁⠀⠸⣿⠀⠀⠀⠉⠉⠉⠉⠀⣀⣀⣤⣍⠛⠣⢤⣤⣈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⡆⠙⠀⡀⠄⠸⣇⢿⣆⠀⠀⢤⡤⠶⡾⠟⣛⣻⣿⠟⣦⠀⠀⠀⠉⠙⠒⠤⣀⡈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠘⠁⢀⢠⡆⠃⠀⣤⣿⣾⣿⠀⠠⠐⠒⣚⡃⣨⣭⣿⣆⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⠋⢠⢿⠻⣿⠙⠩⡍⠛⣿⣿⡟⣿⡿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⣶⠸⠈⢀⣰⣾⣿⣿⣿⣿⡶⠶⠾⠛⠻⡏⣩⠭⢿⣶⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠮⣿⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠿⠷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⢁⣠⣼⣿⣿⣿⣿⡿⠙⣿⡇⠀⢀⠂⡏⡧⠤⠔⠾⣤⣼⣿⣿⣿⣿⣿⣿⣷⡆⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣇⠲⠾⣤⣿⡇⠀⣠⣤⣿⣛⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢫⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡈⢻⣿⡟⠁⠀⢠⡄⢰⣿⣿⣄⠹⠋⡋⡿⠀⣀⣨⣟⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⢸⣿⣶⡿⠰⣠⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠘⠻⠟⠀⠸⢻⣿⣶⣲⣾⡁⣾⣿⣿⣿⣆⠘⠿⡟⠚⣛⣉⡽⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⣿⠟⡞⠂⠃⠀⠀⠀⠀⠰⠿⢿⣏⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠉⠀⠈⠹⢿⣿⣯⠻⣾⣿⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⣿⣷⠏⠇⠀⠀⠀⠀⠀⠀⠀⠠⣴⣽⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠛⠓⠀⠀⠀⠀⠙⠛⠃⠙⠛⠛⠛⢛⣗⠛⠛⠛⣻⣟⡛⠛⢛⡟⠛⠛⠋⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⢛⣿⣟⣿⠀⠀⠛⠃⣤⠀⠀⠪⣤⣶⡄⠚⠃⠀⠀⠉⠀⠈⠀⠀⢠⣤⢠⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣿⣿⣀⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠸⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢸⢸⠐⠶⠶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢸⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⣿⠁⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⠀⠀⠀⠀⣿⠀⠀⢨⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠂⠀⠀⠀⢺⡿⠁⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠘⢸⡏⠀⠀⠀⠀⣿⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣾⣏⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⠀⠀⠀⢸⡸⢷⠀⠀⠀⠀⡏⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣤⣾⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠰⣤⣀⠀⣀⣤⠔⠀⢱⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠈⣿⣿⡏⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣀⣿⣿⢫⣥⣭⡛⣭⣝⢫⣭⢛⣭⣭⣍⢠⣤⣤⣬⢩⣤⢠⣤⢠⣤⣤⡌⣭⣭⣭⡛⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⡇⣿⣿⣼⣿⢸⣿⢸⣿⠈⢹⣿⠉⢸⣿⣼⣿⢸⣿⣏⡁⣿⣏⣿⡇⣸⢹⡿⠋⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣼⣿⣿⣧⣿⡿⣿⣿⢸⣿⢸⣿⠀⢸⣿⠀⢸⣿⢻⣿⢸⣿⡟⠃⣿⡏⣿⡆⠁⠀⠁⠀⠠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠿⠟⠹⠿⠿⠇⠻⠿⡘⠿⠾⢟⣤⡸⠿⣀⠸⠿⠸⠿⠸⠿⠿⠇⠿⠇⠿⠇⠀⠀⠀⠀⢀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢋⣬⣭⡙⢩⣤⢩⣤⢀⣤⣭⣛⢻⣿⡟⣯⣄⣤⣤⣄⣤⡍⣩⡝⢋⣤⣄⡘⠃⠀⠀⠠⢻⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠁⡇⠘⠂⠀⠀ ⠀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⣀⣀⣀⣾⣿⣿⡟⠀⢾⣿⡹⠟⢸⣿⢸⣿⢸⣿⣏⣿⡟⣿⡇⣿⡇⣿⣏⡉⢹⣧⣿⠃⠿⠇⣿⣧⠸⠿⠀⠠⢊⡞⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⣉⣩⣧⡔⢨⣝⢿⣷⢸⣿⢸⣿⢸⣿⡟⣿⡄⣿⣷⣿⠇⣿⡟⠃⡈⣿⡟⠀⣿⡷⣿⠏⠘⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⡇⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠸⠿⠾⠟⠘⠿⠾⠟⠸⠿⠇⠿⢇⠸⠿⠿⠀⠿⠿⠿⡀⠿⠇⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⠀ ⠀⠉⠛⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠏⠋⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣾⣶⣿⣿⣰⣿⣶⣾⣶⣶⣿⣷⡖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠿⠇⠀⡀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣾⣷⢸⣿⣷⠀⠀⣼⣿⣿⡇⢰⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣽⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⠀⠀⣿⣿⣿⡇⠀⢿⣿⣸⣿⣿⣿⠇⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣧⠛⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢈⠻ ⠀⠀⠀⠀⠀⠼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⣼⣿⣿⣧⠀⢙⣿⣿⡇⠀⣸⣿⢻⣿⣿⣿⠀⠃⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣆⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠠⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠘⢿⣿⡗⠀⢹⣿⠧⣿⣿⣿⠀⠀⡙⢿⠀⠀⠀⢠⣶⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⡟⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢸⣿⡇⠀⠙⠿⠀⣿⡿⢻⠀⠀⣿⣍⠀⠀⢠⠿⠿⢿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⡄⣿⣷⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠓⠀⣿⣿⢰⠀⠀⣿⣿⣇⠀⠀⠀⠀⢠⣿⣀⣀⣀⣤⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⢯⠀⠐⢿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠛⠘⠀⠈⢿⣿⣿⡆⢸⣿⣿⡿⠿⠿⢿⣿⣿⣿⠀⠀⠀⢁⣾⣿⣿⣿⠰⣿⠋⠁⠀⠀⢸⣾⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⢠⠀⠀⢸⣿⡟⠛⠻⣿⢷⣦⠀⠀⠾⠟⠟⠀⠀⠀⠈⢨⢿⣿⣿⡿⠀⠉⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⡄⣿⣿⠈⠀⠀⠘⣿⠃⠀⠀⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡇⠀⠀⠀⠀⡿⠀⠀⠀⠐⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢶⠖⠀⠀⠀⠀⠀⠀⠀⠐⠟⠚⠋⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⣿⡇⢀⠀⠀⠘⠃⠀⠀⠀⡎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠟⣷⢼⠀⠀⢀⣠⣴⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⢠⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⣤⣾⣿⣿⣿⣿⣿⣿⠆⢤⣀⠀⠀⠀⠀⠀⠀⣀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣶⡄⣶⢰⡆⠀⠀⣶⢰⣆⣶⢰⡶⣦⢰⡶⠆⣶⢶⣴⣶⠆⣶⣴⡆⣶⢶⣆⣶⡶⢰⣆⣶⠶⣶⠾⡋⣶⢶⡆⣶⣶⡖⣶⣶⣦⣶⣰⣶⣶⡶⢲⣦⡶⢹⣿⣿⡿⢱⡶⣦⢰⣦⡶⠀⣶⣰⣶⣶⡶⢲⣦⡶⠀⠀ ⠀⢸⣿⣿⡇⣿⢿⡇⠀⠀⣿⢸⣿⣿⢸⡇⣿⢸⡿⠂⣿⠾⢻⣿⠃⣿⣿⡇⣿⢸⣿⣿⡟⢸⣿⣿⠀⣿⠘⠃⣙⢷⡆⣿⣿⡇⣿⣿⣯⢿⣿⡏⣿⡟⠈⣿⠃⠿⠿⠿⡇⢸⡇⣿⠈⣿⠇⠀⢿⣿⡇⣿⡟⠈⣿⠃⠀⠀ ⠀⠈⠛⠛⠑⠛⠘⠃⠇⠀⠛⠘⠋⠛⠘⠛⠛⠘⠛⠃⠛⠀⠘⠛⠓⠛⠘⠃⣛⣛⣃⠛⢛⣘⡃⣛⣀⣛⣸⣧⣛⠚⣃⣛⠛⠃⠛⠛⠛⠘⠛⢃⠛⠛⣀⣛⣀⠛⢛⣛⣠⣘⠓⢛⣄⠛⠀⡆⠘⠛⠃⠛⠛⠀⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣻⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣜⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣻⡁⡂⣁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⡟⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⡿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢟⠻⠟⡛⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣛⣛⣊⣋⣛⣻⣉⣛⣿⣿⣻⣯⣻⣹⣐⣢⠀⣋⣤⣘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣀⣀⠈⠉⠻⠋⠉⣀⣀⠈⠀⢺⣷⣤⣀⡀⠈⠁⣀⠘⠙⣿⠋⠁⣀⠈⠙⠋⠁⣀⣀⠈⠁⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⠆⠀⢩⣭⠉⠉⠀⡀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠿⠿⠿⠷⠀⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⠿⠆⠀⠀⠙⠛⠛⠋⠀⢀⣷⣝⠤⠙⠐⠃⠿⠄⠀⠛⠀⢀⣿⠀⠀⢠⣤⣤⣤⣤⠀⠀⠈⠛⠛⠛⠛⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⡟⠛⣶⣾⡟⠛⠻⢿⠀⢸⡟⠛⣿⣿⡟⠛⠻⢿⣿⣿⣿⣦⣤⡿⣿⡇⠀⠀⠴⠏⠀⠀⣶⣶⣾⡇⠉⠉⠋⣒⣒⡆⠀⠀⠶⠦⠀⠉⣿⣶⣦⣮⠉⠉⠈⠛⠒⣶⣷⣶⡶⢤⣴⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⢿⡏⠁⠈⠀⡀⠀⡀⠛⢿⠇⠀⠀⠈⠀⠀⠀⡀⠛⢿⡇⠀⠀⠀⠹⠣⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠟⠛⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛⠛⢿⡟⠀⠀⠀⠉⠀⠏⠙⣻⠀⠸⢿⡇⣿⣿⣿ ⣿⣿⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣿⣿⣿ ⣿⣿⡇⣿⠀⢀⡀⡀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⠠⠀⠀⠀⢀⢀⠀⠀⣿⠀⠀⠀⠀⢀⠀⡀⢀⠀⠠⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⢸⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⡷⠃⣠⣿⣿⣿⣿⣿⣿⠿⠄⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⣶⣾⣾⣿⠎⢿⣿⣶⣿⣾⣶⣶⡏⣤⣷⣶⣶⣾⣶⣿⣿⣿⠀⢀⣿⣿⣿⣶⣿⣷⡆⢐⣾⣿⣷⣿⣿⣿⣶⣤⠀⣿⣶⣶⣾⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⡿⠗⠀⠿⣿⣿⣿⣿⣿⡿⠓⠘⢿⣿⣿⣿⣿⣿⣏⢀⢠⣿⣿⣿⣿⣿⣿⠎⠛⢿⣿⣿⣿⣿⣿⣿⣿⢠⢰⣿⣿⣿⣿⣿⣯⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⡧⣾⢻⣿⣿⣿⣿⣿⣷⢘⣸⣿⣿⣿⣿⣿⣿⣗⡀⠀⣾⣿⣿⣿⣿⣿⣿⡾⢼⣿⣿⣿⣿⣿⣷⣶⠀⡀⠿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣿⣾⢼⣿⣿⣿⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿ ⣿⣿⣧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢇⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 591 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/irc-log-261021/#comments Gemini version at gemini://gemini.techrights.org/2021/10/27/irc-log-261021/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Tuesday,_October_26,_2021⠀✐ Posted in IRC_Logs at 2:28 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights- 261021.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-261021.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-social-261021.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes- 261021.txt Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmaRadmLWmqAjP95ePsruoWEmr4qu54CojFhQM2SD6HgvA #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmaBuPGF1NMxjYQP2eVehET6NReLxKCvRWWpCKhJA9Wgzb (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as 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═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/political-patent-offices/#comments Gemini version at gemini://gemini.techrights.org/2021/10/27/political-patent-offices/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Many_of_the_National_Delegations_(or_Delegates)_in_the_EPO’s_Administrative Council_Have_No_Understanding_of_What_They_Vote_on⠀✐ Posted in Europe, Patents at 8:14 am by Dr. Roy Schestowitz Video_download_link | md5sum f5d3b011ab2bcec45277ecbd8a2083bc http://techrights.org/videos/misleading-delegates.webm Summary: One must consider the possibility that ignorance or gullibility (which lack of qualifications may entail) possibly became a contributing factor — malice and bribery aside — in systemic failure of the EPO’s governance THE 25th part of the series was published this morning (index below). We may take a short recess and then continue; in the meantime we have this discussion about what António_Campinos tells people in the EPO‘s Administrative Council as well as the EC; based on the EPO’s site (the “news” section), he openly_tells them_lies_about_the_UPC, which Benoît_Battistelli might still be planning to preside over. They’ve long used this unconstitutional piece of trash (an illegal coup) as an excuse for their staff-crushing ‘reforms’. The whole thing is just insane. Earlier this week the EPO’s “news” section told a bunch of lies about “quality” (more keyword-stuffing than actual information) and we’ve already seen that many delegates lack background (educational and/or experience) when it comes to matters of patents; many don’t understand the sciences, either, as they’re basically political animals who compensate for a lack of skills with a breadth of connections. The sooner the public understands this, the better. The media sure is trying to keep the public in the dark on these matters. Such media apathy is complicity in the coup — a takeover whose end goal is to crush scientists for the financial benefit of law firms and their largest clients (multinational monopolistic corporations). █ Series parts: 1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In! 2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous” Endorsement? 3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes 4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States 5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja” 6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch Courage 7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity 8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and Pusillanimous_Hibernia 9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss Cheese 10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the Controversial_Christian_Bock 11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_– Battistelli’s_Swiss_Apprentice? 12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection 13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian Facilitators_–_Spain 14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian Facilitators_–_Portugal 15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria… 16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the Austrian_Double-Dipper 17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic Nordic_Bloc 18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord 19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States 20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group 21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The Doyen_and_His_“Protégée” 22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_– North_Macedonia_and_Albania 23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_– Bulgaria 24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_– Romania 25. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_– Fresh_Blood_or_Same_Old,_Same_Old? ䷩ 𝚕𝚒𝚗𝚎 814 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/27/presidential-surveys/#comments Gemini version at gemini://gemini.techrights.org/2021/10/27/presidential-surveys/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_EPO_Presidential_Surveys⠀✐ Posted in Deception, Europe, Patents at 9:33 am by Dr. Roy Schestowitz Who would have thought a survey organised by the regime would serve the regime? 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Obama_confusion:_See?_The_staff_whom_I_spied_on_while_they participated_in_the_survey_are_happy⦈_ Summary: The 'social_democracy' of Benoît_Battistelli and António_Campinos as demonstrated by a controlled survey (controlled by the subject of the survey, EPO governance) ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⢻⡏⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢿⣣⠀⠀⠃⠀⣙⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣹⣿⣿⣿⣿⣿⡟⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⢤⣾⣿⣿⣿⣿⣯⠉⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⣕⣿⣿⣿⠏⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢀⡿⠛⠛⠛⠛⢿⣿⣿⡿⠛⠛⠻⠿⢿⣿⣿⣿⣿⡿⣿⣿⣽⠛⠏⠁⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⠛⠀⠀⠀⢀⡃⢻⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠈⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣹⣼⠄⠀⡀⣠⣴⣾⣿⣿⣿⣧⣌⣉⣟⡲⣽⣿⣿⣿⢵⣿⣡⣿⣿⣿⣦⣄⣀⠘⠋⠀⢠⣺⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⢹⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⠙⠁⠈⠁⠀⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⢰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⠀⠚⠱⠀⠀⠈⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⢸⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣿⠃⠀⠀⠀⣴⣶⡀⢀⣭⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡷⣾⣷⡀⠀⢸⣿⣧⢘⣿⣿⠋⠻⣿⣿⣿⣿ ⣿⣿⣿⡿⣿⣷⠀⢠⣤⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣧⣤⣴⣶⣷⣶⣶⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢻⣿⣷⣄⠀⣿⣿⣷⣿⣿⣷⡆⢡⣼⣿⣿ ⣿⢻⡏⣿⣻⣿⠀⣾⣿⠇⢞⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢣⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠹⣿⣿⣦⣾⣿⣿⣾⠟⣿⣇⠀⣿⣿⣿ ⣿⠸⣿⣿⣿⣿⣴⣿⣿⠀⣼⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢻⣿⣿⣿⣿⣿⣿⣿⠿⠟⢣⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣦⡈⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⠛⢦⡀⠀⠻⠋⣿⣿⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣉⠉⠉⠉⣉⣡⣤⢶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⣽⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡶⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢻⣿⣿⣿⣶⣿⣿⣿⣿⠇⠀⠀⠀⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠐⠂⢼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⢀⠤⡆⢀⣤⣤⣴⣦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣀⣀⣀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⣼⠀⠿⢲⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠀⠀⠀⠀⣿⣄⣀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⣿⣿⣿⣿⢛⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣽⣻⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣀⠀⠉⠻⣟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠁⠐⣙⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠸⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⡿⠟⣩⣿⣿⣿⣿⣿⠏⠁⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣏⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣇⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢺⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡙⣿⣿⣿⠏⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠃⢠⡿⠛⠛⠛⠛⢿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⠟⠀⠀⠀⠀⠁⢻⣿⡟⠀⠀⠀⣿⣿ ⠈⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣌⣹⣼⠀⠀⣀⣠⣴⣾⣿⣿⣿⣧⣄⣉⣟⡲⣽⣿⣿⣿⣹⣿⣡⣿⣶⣿⣶⣄⣀⠘⠋⠀⠀⢘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠜⠋⠁⠀⠀⠁⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⢀⣷⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢙⡙⠖⠀⠀⠀⢨⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢃⠀⠀⢠⣶⡄⠀⣠⣭⢽⣟⣸⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣷⡄⠀⠘⣿⣿⡀⣿⣿⡏⠹⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⢿⣿⡆⢠⣤⣄⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⡧⣤⣴⣶⣷⣶⣶⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⠻⣿⣿⣦⠀⢻⣿⣷⣿⣿⣿⣿⡆⠁⣼⣿⣿ ⣾⢫⣿⣿⣘⣿⡇⢸⣿⡏⡬⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢣⣝⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡈⣿⣿⣷⣬⣿⣿⣷⣿⢻⣿⣧⠈⣿⣿⣿ ⣿⠧⣿⣿⣿⣿⣧⣿⣿⠇⢠⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⢣⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⠛⣧⡀⠀⠹⠏⣿⣿⣿⣦⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣉⠉⠉⠉⣉⣡⣤⢶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⢹⣿⣿⣿⣿ ⠀⠉⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡾⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⣾⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣠⣤⣴⣶⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠻⠋⣁⣀⣀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⣸⠀⠿⢓⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⣿⣄⣀⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⣿⣿⣿⢻⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣛⣻⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⢻⡿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠁⠐⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠸⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⡿⠟⣹⣿⣿⣿⣿⣿⠟⠀⣻⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣯⠉⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⣭⣿⣿⣿⠏⠀⠀⣿⣿ ⡀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠃⢀⠿⠛⠛⠛⠛⢿⣿⣿⡿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠋⠁⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⠀⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿ ⠘⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣹⣼⠄⠀⠀⣠⣴⣾⣿⣿⣿⣧⣄⣉⣗⠲⣽⣿⣿⣿⣹⣿⣡⣿⣿⣿⣶⣄⣀⠘⠋⠀⠠⢺⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠸⠋⠁⠈⠉⠉⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢿⠉⡟⠉⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣸⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠨⠀⠀⠁⠀⠀⠀⢰⢿⣿⣿⢁⠀⠀⣤⣶⡀⠀⣤⣭⢿⡿⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⡀⠀⢸⣿⣧⠀⣿⣿⡄⠙⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡆⠀⣤⣔⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡧⣤⣴⣶⣷⣶⣦⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⢻⣿⣷⣄⠀⢿⣿⣷⣿⣿⣿⣿⡆⢡⣼⣿⣿ ⣷⠏⣿⣿⣞⣿⡇⢰⣿⡿⢹⣻⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢳⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠙⣿⣿⣦⣸⣿⣿⣿⡿⢻⣿⣇⠉⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣧⣾⣿⡇⢀⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣧⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⣧⡀⠉⠹⠟⣽⣿⣿⣦⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣉⠉⠉⠉⡉⣡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⣹⣿⣿⣿⣿ ⠀⠉⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⡾⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⣽⣿⣿⣷⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠈⠂⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⣠⣤⣤⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠟⠋⣀⣄⣀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⣸⠀⠿⢷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⣿⣄⣀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣿⣿⣿⣿⣻⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣛⣻⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣀⠀⠉⢻⡿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠃⠀⣹⢿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢨⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣴⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣻⣿⣿⣿⣿⣿⠏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣀⣾⣿⣿⣿⣿⣟⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢽⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⣶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡭⣿⣿⣿⡏⠀⠀⣿⣿ ⡀⢰⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡛⠙⠁⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡿⠀⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿ ⠘⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣌⣹⣼⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣀⢐⣖⠲⣽⣿⣿⣿⣽⣿⣡⣿⣾⣿⣦⣄⣀⠘⠃⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠜⠛⠁⠀⠀⠁⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⠀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢋⠞⢿⠋⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠀⠀⠀⠀⠀⠀⢘⢿⣿⡿⠁⠀⢀⣴⣦⠀⢀⣤⡌⠿⣿⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣆⠀⠀⢿⣿⣆⠘⣿⣿⡀⠋⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡆⠀⣤⣄⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣧⣤⣤⣶⣿⣶⣦⣬⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⣿⣧⡀⠘⣿⣿⣶⣿⣿⣿⣿⡆⢡⣼⣿⣿ ⣷⡟⣿⣿⣇⣻⡇⢀⣿⣿⠉⣟⣻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢣⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡄⢿⣿⣿⣦⣹⣿⣿⣿⡿⣿⣿⣇⠈⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣧⣾⣿⡇⢀⣾⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⢧⡀⠉⠹⠿⢹⣿⣿⣧⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠉⠀⣽⣿⣿⣿⣿ ⠀⠉⠉⠀⠀⠀⠀⢙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣽⣿⣿⣯⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠒⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠈⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣤⣤⣴⣦⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⣀⣀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⢰⠁⠿⢣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⣿⣄⣀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢿⣿⣿⣿⣿⣻⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣻⣿⣿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣀⠀⠈⢻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠃⠀⣹⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⠿⠟⣻⣿⣿⣿⣿⣿⠟⠀⢿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⣢⣾⣿⣿⣿⣿⣟⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣭⠈⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡌⣿⣿⣿⡏⠀⠀⣿⣿ ⡀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣽⢿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠿⠀⠀⠀⠀⠃⢻⣿⡿⠀⠀⠀⣿⣿ ⠘⣶⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣌⣹⣼⠀⠀⠀⣠⣴⣾⣿⣿⣿⣆⣀⢐⣖⠲⣽⣿⣿⣿⢽⣿⣡⣿⣷⣿⣶⣄⣀⠘⠋⠀⠀⣬⣿⣿⣿⡯⠃⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠴⠟⠉⠀⠁⠉⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣟⣀⢀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢹⡻⠏⠂⠀⠀⠀⢽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⢼⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠀⠀⠀⠀⠀⠀⡠⣿⣿⢿⣃⠀⢠⣶⡆⠀⢠⣤⡍⠿⣿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣄⠀⠘⣿⣿⡄⢸⣿⣧⢀⠹⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⠀⣤⣄⢺⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣧⣄⣤⣶⣿⣶⣦⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠞⢿⣿⣦⡀⠸⣿⣿⣶⣿⣿⣿⣿⡆⢡⣼⣿⣿ ⣿⡟⣽⣿⣇⣻⡇⢀⣿⣿⢹⣿⣛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢣⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣐⢿⣿⣿⣄⣿⣿⣿⣾⠿⣿⣿⣇⠉⣿⣿⣿ ⣿⡇⢼⣿⣿⣿⣧⣼⣿⡏⢀⣿⣿⡟⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⣷⡄⠉⠹⠿⢹⣿⣿⣧⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⢡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣿⣿⣷⣿⣿⣿⣿⣿⣿⠇⠉⠁⣹⣿⣿⣿⣿ ⠀⠘⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⡼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣾⣯⣿⣿⣿⡏⠀⠀⠀⠈⠉⢉⣿⣿ ⠀⠀⠀⠀⠀⠀⠂⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣤⣤⣠⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⣀⣄⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⢰⠁⠿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⣿⣄⣀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢿⣿⣿⣿⣿⣻⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣻⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠁⢻⣟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠃⠐⣹⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠹⠿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠐⣠⣾⣿⣿⣿⣿⣯⡁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⣶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡼⣿⣿⣿⡏⠀⠈⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠃⢠⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⠙⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣿⡿⠀⠀⠀⠀⡃⢻⣿⡟⠀⠀⠈⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣌⣽⣼⠄⠀⠀⣠⣴⣾⣿⣿⣿⣆⡀⢐⣒⠲⣽⣿⣿⣿⣹⣿⣩⣿⣿⣿⣷⣄⣀⠘⠃⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠸⠟⠉⠀⠀⠉⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣹⡹⡿⠓⠀⠀⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠌⠀⠀⠀⠀⠀⠀⢠⣻⣿⡿⢣⣶⣆⠀⢀⣴⣦⠀⠘⠿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣾⣏⠋⠘⣿⣿⣆⠈⣿⣿⡄⣀⠀⠟⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⢸⣿⡇⢀⣾⣟⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⣧⣤⣤⣶⣿⣶⣤⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣿⣷⣄⠹⣿⣿⣧⣾⣿⣿⣿⣿⣾⡆⢡⣼⣿⣿ ⣿⣿⣿⢻⣿⣷⣜⣿⡇⢸⣿⣿⣿⢟⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢃⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠹⣿⣿⣷⣼⣿⣿⣿⣽⠟⣿⣿⣿⣇⠁⣿⣿⣿ ⣿⣿⣿⠰⣿⣿⣿⣿⣣⣿⣿⡏⣹⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿ ⠛⢿⣿⠄⠈⠉⠻⠏⣿⣿⣿⣄⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠁⣹⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣯⣭⣿⣿⣿⡿⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠲⢀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠯⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣶⣬⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⣄⣠⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠻⠋⢀⣀⣀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⡞⠸⠷⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡎⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⢸⣷⣀⡰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⡟⣷⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣀⠀⠉⢻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠃⠐⣹⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⠿⠟⣹⣿⣿⣿⣿⣿⠏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⣢⣾⣿⣿⣿⣿⣏⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠆⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢺⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⣶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠗⠛⠀⠀⡭⣿⣿⣿⠏⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠃⢀⠿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠟⠀⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣌⣽⣼⠄⠀⠀⣠⣴⣾⣿⣿⣿⣆⡀⢐⣒⠢⣽⣿⣿⣿⣽⣿⣡⣿⣿⣿⣶⣄⣀⠘⠃⠀⢀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⡰⠋⠁⠀⠀⠉⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⠀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢫⡚⡯⠁⠀⠀⠀⢘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣧⡄⠀⣴⣶⠀⠀⠀⠘⠿⡿⣞⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡼⢿⣿⣿⣿⡄⢿⣿⣧⠀⠀⠀⠀⡛⠋⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣧⣤⣤⣶⣿⣶⣤⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⢻⣿⣿⣶⣿⣿⣷⠀⣾⣿⣶⡆⢁⣼⣿⣿ ⣿⣿⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢣⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣇⠈⣿⣿⣿ ⣿⣿⣿⣷⠱⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⡿⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠾⠄⠀⠈⠛⠋⣿⣿⣿⣁⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠉⠁⣽⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠀⠀⣀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣯⣭⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⡀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠠⣴⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⣔⡀⣤⣤⣤⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠟⠋⢀⣀⣀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⣿⣿⣿⣿⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣙⣿⣿⣿⣽⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣀⠀⠈⢹⡏⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠁⠀⡝⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠸⠿⠟⣩⣿⣿⣿⣿⣿⠋⠁⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣇⠀⠀⣿⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⢼⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⡿⠷⠛⠀⠀⠁⣼⣿⣿⠏⠀⠀⣿⣿ ⡀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠙⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠗⠀⠀⠀⠀⡀⢻⣿⡟⠀⠀⠀⣿⣿ ⠈⣾⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣌⣽⣼⠀⠀⠀⣠⣴⣾⣿⣿⣿⣆⡀⢐⣖⠢⣽⣿⣿⣿⣹⣿⣡⣽⣿⣿⣧⣄⣀⠘⠂⠀⢀⠨⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⠋⠁⠀⠀⠁⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣾⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⠀⣷⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢏⠨⠿⠉⠀⠀⠀⢈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠈⠟⠟⣘⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⣠⣤⣤⣻⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠟⠋⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⡧⣤⣴⣶⣿⣶⣤⣬⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⡀⠀⠀⣿⣿⣷⡀⠃⣴⣿⣿ ⣿⣿⣿⡿⣿⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢃⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⡷⣣⠀⠘⠻⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⣾⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠾⣿⣿⣿⣷⣿⣿⣿ ⠛⣿⣿⠾⠕⠀⠀⠀⠀⣿⠛⣿⣿⣿⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⣡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⣽⣿⣿⣿⣿ ⠀⠉⠁⠀⠀⠀⠀⠀⢈⣿⣷⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⣴⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣠⣤⣤⣤⣤⣄⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠻⠋⠁⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣿⣿⣿⣿⢿⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣻⣿⣿⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠀⢛⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⣣⠀⠀⠁⠐⣹⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠸⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢸⡿⠛⣹⣿⣿⣿⣿⣿⡟⠀⣺⡏⢹⠙⡏⣿⡉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠈⣂⣼⣿⣿⣿⣿⣏⡁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣇⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⣿⡷⠛⠀⠀⡀⣿⣿⣿⠏⠀⠈⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⡿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⡿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣽⣴⠄⠀⠀⣠⣴⣼⣿⣿⣿⣆⡀⢐⣒⠢⣽⣿⣿⣿⢱⣟⣡⣽⣶⣿⣶⣄⣀⠘⠃⠀⠀⠘⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠜⠉⠁⠈⠀⠙⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡷⠋⠀⠀⢰⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢙⠈⠃⠁⠀⠀⠀⡼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣉⣻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠘⠟⡿⣺⣿⣾⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠟⠋⠀⠀⠀⠀⢀⣠⣤⣤⣠⣀⣨⣿⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠠⣼⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣤⣤⡀⠀⠀⢻⢿⡧⣄⣤⣶⣷⣶⣤⣬⣽⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡆⠀⠀⠀⠀⠀⠀⣾⣿⣾⡆⢁⣼⣿⣿ ⣿⣿⣿⡿⣟⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠘⣌⢣⣙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⠈⣿⣿⣿ ⣷⣿⣿⢦⡟⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣶⣶⡄⠀⠀⠀⠈⡀⠿⢻⣿⣿⣿⣿⣿⣿⠿⠟⢁⣾⢷⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣿⣿⣿ ⠛⣿⡿⠓⠄⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⢹⣦⣄⡉⠉⠉⠉⠉⢡⣤⢾⣻⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿ ⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣴⠛⠯⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⠈⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⣴⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣶⣦⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣧⣤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠋⠁⠈⢀⣤⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣾⣿⣿⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣙⣿⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠀⠙⡋⠻⣿⣿⣿⠾⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢧⣢⠀⠀⠁⠀⡘⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⢶⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠘⠿⠛⢉⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣌⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⠸⣿⣿⣿⡇⠀⠀⣽⣿ ⠀⠀⠀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣴⣿⣿⠇⠀⠀⣿⣿ ⠀⠠⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠿⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣸⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⢿⣿ ⠀⣴⣿⣿⣿⠀⠀⠀⠀⣫⣷⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⣱⣴⠀⠀⠀⣠⣠⣼⣿⣿⣷⣆⡀⢒⡒⠬⣿⣿⣿⣿⠱⣝⣡⣼⣤⣶⣦⣄⡀⠐⠀⠀⠀⢈⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢻⣿ ⠀⢸⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣏⣿⣿⣷⠋⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⠀⠀⠀⣵⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠁⠀⠁⠀⠀⠀⠀⠀⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⢐⡦⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣉⣻⢟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡕⢀⣷⣝⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⢻⣿⣿⣿⣿⡟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠅⢼⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣤⣬⣿⣶⣤⣭⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠢⠄⠀⠀⠀⠀⠀⠀⣰⣷⣶⡀⠁⢴⣿⣿ ⣿⣿⣿⠟⡛⠀⠀⠀⠀⠀⠀⢽⣟⢻⢿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠀⠀⠀⠀⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢾⣿⣿ ⣷⣿⣿⠄⠃⠀⠀⠀⠀⠀⠀⠼⠙⠀⠐⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⣾⣷⣄⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿ ⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠿⠟⠉⠉⣁⣤⢴⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣛⣉⣿⣿⣿⣶⣤⣚⠺⢯⣷⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣋⠀⠀⠀⠈⠻⣿⣿⣿⣴⠿⠟⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⣤⣼⣿⣿⠁⠐⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠀⠛⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠈⢧⣣⠀⠀⠁⠀⠘⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠐⣶⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠘⠿⠛⣋⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠐⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⠸⣿⣿⣿⡇⠀⠀⣻⣿ ⠀⠀⢀⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣥⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠷⠛⠀⠀⠀⢹⣿⣿⠏⠀⠀⣿⣿ ⠀⠰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⢀⡿⠛⠛⠛⠻⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣻⣿⠇⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄⣹⣼⠀⠀⠀⣠⣠⣼⣿⣿⣷⣆⡀⢒⡒⠬⣿⣿⣿⣿⢱⣟⣡⣽⣤⣶⣦⣄⡀⠐⠂⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠁⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣏⢿⣿⢿⠊⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⠀⠀⣷⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠩⠀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣦⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣉⣻⢿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⢀⣷⣜⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⢻⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡤⢼⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣡⣤⣤⣬⣷⣶⣤⣭⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢋⠂⠀⠀⠀⠀⠀⠀⢸⣷⣶⡆⠁⣴⣿⣿ ⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⢀⣿⣿⢻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢸⠅⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢿⣿⣿ ⣿⣿⣿⠀⠑⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢁⣾⣷⣄⣿⣿⣿⣷⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠂⠄⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿ ⠛⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣭⣽⣿⣿⣅⣤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠈⠻⣿⡏⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⠏⠀⠀⢠⣤⣿⣷⠀⠁⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⢀⣙⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠛⠉⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣀⠀⠀⠙⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⣢⠀⠀⠃⠐⡩⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣴⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⡿⠛⣹⣿⣿⣿⣿⣿⠏⠀⢻⡏⢹⠙⡏⣿⣉⢉⡏⢹⠹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⢠⣼⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡿⢸⡇⢠⠘⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣇⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢼⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣲⣾⣾⣶⡶⠟⠒⠓⠓⠚⠲⢶⣿⣷⣾⣿⠗⠛⠀⠀⡀⣿⣿⣿⠏⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢠⠿⠛⠛⠛⠻⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿ ⠀⣴⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡈⣽⣼⠀⠀⠀⣤⣠⣼⣿⣿⣷⣆⡀⢒⡒⠬⣿⣿⣿⣿⣹⣟⣡⣽⣵⣿⣦⣄⣀⠘⠃⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⠋⠁⠀⠀⠁⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣿⣿⣷⠋⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⠀⠀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢉⠨⠍⠀⠀⠀⠈⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⢘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣉⡻⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠟⣟⢐⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣁⣀⣤⣬⣷⣶⣬⣭⣹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⢯⡇⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠁⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⡪⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡹⢽⡏⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⠈⢿⣿⣿ ⣷⣿⣿⢆⢛⠀⠀⠀⠀⠀⠉⢿⠋⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⣶⠆⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣷⣿⣿⣿ ⠛⢿⣿⠚⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⢠⠀⢀⣽⣜⣅⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⣹⣿⣿⣿⣿ ⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠁⠙⠻⠫⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡄⠀⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠁⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⣦⣴⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠋⠙⢿⣿⣿⣿⣿⣿⣿⣷⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠈⠻⡿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣢⠀⠀⠋⠀⣭⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠚⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⡿⠟⣹⣿⣿⣿⣿⣿⡟⠀⢿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣏⠉⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡇⠀⠀⣿⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⠾⣾⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣗⢲⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⠏⠀⠀⣿⣿ ⠀⢠⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⢠⠿⠛⠛⠛⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⢟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿ ⠈⣾⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⡀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣄⣽⣼⠀⠀⠀⣤⣰⣾⣿⣿⣷⣂⠐⢒⠲⢭⣿⣿⣿⣿⣩⣿⣉⣽⣾⣿⣶⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠐⠛⠉⠁⠀⠈⠸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⡀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢩⠋⠯⠩⠀⠀⠀⡸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣙⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡄⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠨⠻⡿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⠉⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⣻⣿⣿⣿⣿⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣀⣠⣴⣿⣷⣤⣭⣙⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⣾⣿⣷⡆⢁⣴⣿⣿ ⣿⣿⣿⡿⣯⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⡂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⡇⣯⠀⠀⠀⠀⠀⠈⢟⢛⠏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡸⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣠⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣎⣯⣼⡅⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠿⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣈⠉⠉⠉⠛⢉⣡⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡀⢂⣿⣯⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣴⣻⠿⣿⣷⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣋⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠙⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠈⠉⠉⠉⠻⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣽⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣄⠁⠙⢻⣿⢿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣿⣣⠀⠈⠛⢹⣿⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠺⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⣻⡿⢿⣻⣿⣿⣿⣿⣿⡿⠇⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠈⣶⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠠⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠇⢰⢸⠅⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣏⠀⢀⣿⣿ ⠀⠀⣄⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⠾⣾⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⢲⣾⣾⣷⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⣿⣿⣿⣿⡏⠀⠀⣿⣿ ⣀⢰⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣃⢰⠿⠛⠛⠛⠿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠐⠃⢿⣿⡿⠀⠀⠈⣿⣿ ⢸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⢀⣀⣀⣤⣤⣤⣽⣾⠄⠘⠓⣲⣷⣿⣿⣿⣷⣒⠲⢶⣦⣽⣿⣿⣿⣿⣹⣿⣋⣿⣿⣿⣷⣤⣀⠘⠛⠀⢄⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿ ⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⠺⠻⠙⠛⠉⠋⠛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣠⣀⣀⢴⣿⣿ ⣰⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢻⣿⣿⠿⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣻⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡽⠉⠹⠧⠀⠀⠀⡽⣿⣿⣿⣯⣇⠂⠀⠀⠀⠀⠀⡻⢿⣿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣀⡿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣤⣤⣶⣿⣷⣬⣭⣟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⣽⣿⣿⣷⠉⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢹⣿⢻⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢛⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣉⠉⠉⠛⠛⣉⣡⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠁⠉⠁⣿⣿⣿⣿⣿ ⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣴⣿⠿⢿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣋⠀⠀⠀⢈⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣄⠁⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠿⠿⣿⣿ ⠘⢿⣣⠀⠀⠛⢑⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠻⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢻⡿⠟⣻⣿⣿⣿⣿⣿⡿⠃⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠋⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠘⣶⣾⣿⣿⣿⣿⣯⡉⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠈⠓⠚⠾⢶⣿⣷⣾⣷⡾⢾⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⠶⢾⣾⣷⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡿⣿⣿⣿⡏⠀⠈⣿⣿ ⣄⢰⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⡇⠉⢉⠉⠉⢻⣿⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣝⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠃⠀⠀⠀⠇⢻⣿⡿⠀⠀⠈⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠊⠀⠀⠀⣀⣀⣤⣤⣤⣤⣼⢀⣀⣰⣿⣿⣿⣿⣿⣏⣘⣛⡶⢮⣽⣿⣿⣿⣿⢻⣿⠿⢃⣾⣿⣷⣤⣀⠘⠛⠀⢤⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⢹⣿⡇⠀⠀⠀⣿⣿ ⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣐⠺⠯⠛⠉⠋⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣱⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣸⣿⣀⣀⣀⢰⣿⣿ ⣠⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣼⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⠃⠙⠇⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠺⢿⡿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⠟⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⡿⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣶⣿⣿⣿⣶⣦⣭⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⢨⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠈⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢹⣿⢿⡿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣁⣴⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢹⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⢿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⠈⠉⣉⣡⣤⣬⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⣿⣶⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠙⠁⣽⣿⣿⣿⣿ ⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⢈⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣽⣟⣛⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⢠⣔⠲⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠉⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢾⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣄⠁⠩⢿⣿⣿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣿⣣⠀⠀⠛⢙⣿⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠿⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢻⡿⢿⣻⣿⣿⣿⣿⣿⡿⠇⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠺⣷⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⡄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣇⠀⠀⣿⣿ ⠀⠀⣄⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⢺⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⡶⠾⣾⣷⡶⠟⠖⠓⠓⠚⢶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡿⣿⣿⣿⡏⠀⠀⣿⣿ ⣄⢰⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣿⠀⠠⡀⢈⣙⣿⣿⣟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠀⣯⡉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⡏⢿⣿⡿⠀⠀⠨⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠚⠀⠀⢀⣀⣠⣤⣤⣤⣤⣴⣀⣤⣴⣿⣷⣿⣿⣿⣯⣍⣙⡷⠦⣽⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⣷⣤⣀⠘⠋⠀⢚⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⣿⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣰⢻⠿⠛⠉⠉⠋⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣶⣾⣿⣿⣿⣿⣿⡏⠀⠀⢱⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣠⣀⡀⢰⣿⣿ ⣠⣿⣿⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣾⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠏⠉⠋⠀⠀⠀⠿⣿⣿⣿⣿⡗⠁⠀⠀⠀⠀⠀⢻⢿⡿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠐⢽⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⠿⠋⠀⠇⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣈⡿⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣾⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢉⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢾⣿⢿⡿⠻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣡⣴⣿⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡆⢿⣿⣿⣿⣿⣋⠄⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⠀⣉⣡⣤⣤⣬⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿ ⠀⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠈⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣛⠿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⡲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠈⣿⠀⠀⠉⠙⠋⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣄⠁⠈⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣿⣣⠀⠀⠛⢐⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠺⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⡀⠀⠀⢻⡿⠟⣻⣿⣿⣿⣿⣿⡿⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠈⣶⣾⣿⣿⣿⣿⣿⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⡅⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣄⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⢺⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⡶⠾⣾⣶⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⢟⣿⣿⣿⡏⠀⠀⣿⣿ ⣀⢰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠻⠀⠠⡀⢈⣙⣿⣿⣟⡛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡯⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠃⠀⠀⠀⠂⢻⣿⡿⠀⠀⠈⣿⣿ ⠈⣾⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣁⣤⣴⣿⣷⣿⣿⣿⣯⣍⣙⡷⠶⣽⣿⣿⣿⣿⢿⣿⣿⠟⢰⣿⣷⣄⣀⠘⠛⠀⠄⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠁⢺⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣐⠚⠟⠉⠉⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣶⣿⣿⣿⣿⣿⡏⠀⠀⢑⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀⢠⣿⣿ ⣠⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣋⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠃⠐⠇⠀⠀⠀⠻⣿⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⢺⠿⡿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠛⠛⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⡿⠛⠀⠇⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⣘⠀⡿⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣾⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢩⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣹⣿⣿⣇⠈⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠘⣿⠻⠟⠸⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡿⠿⢟⣁⣴⣿⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢘⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⢿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⠀⢉⣡⣤⣤⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣳⣴⣳⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿ ⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠈⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣛⠿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⡲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠋⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣲⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣄⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣿⣣⠀⠀⠛⢙⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠻⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⡀⠀⠀⢽⡿⢿⣻⣿⣿⣿⣿⣿⡿⠂⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣙⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠈⣶⣾⣿⣿⣿⣿⣯⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⢞⣶⣶⣿⣷⣾⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠺⢾⣶⡶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⠿⣿⣿⣿⡏⠀⠀⣿⣿ ⣄⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠀⠀⠄⢀⣙⣿⣿⣿⡛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠈⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠇⢿⣿⡿⠀⠀⠈⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣤⣤⣿⣷⣿⣿⣿⣿⣍⣉⣟⠶⣽⣿⣿⣿⣿⣿⣿⣿⠿⢀⣿⣷⣄⣀⠘⠛⠀⢄⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⢾⣿⡇⠀⠀⠀⣿⣿ ⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⣐⠚⠛⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣾⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣀⣀⣀⢠⣿⣿ ⣠⣿⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⠀⠀⠀⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣷⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠉⠨⠀⠀⠀⣯⢿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⢙⢿⡿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⣻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⠟⠁⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣨⠀⡿⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣶⣿⣿⣿⣿⣷⣶⣮⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢫⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⠉⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢸⣿⢻⠟⠽⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⡿⠿⢟⣡⣼⣿⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢺⣽⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⢿⡯⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⡀⣈⣡⣤⣤⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣶⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⣿ ⠀⠹⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣋⡀⠀⠀⠀⣙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣟⣛⡻⢿⣿⣿⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢀⣲⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢾⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣄⠁⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣿⣣⠀⠀⠛⢑⣽⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢸⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠻⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⡀⠀⠀⢻⡿⠟⣻⣿⣿⣿⣿⣿⡿⠂⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠘⣶⣿⣿⣿⣿⣿⣯⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡆⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⡀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⢀⣿⣿ ⠀⠀⣀⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⠞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⢾⣷⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⢿⣿⣿⣿⡏⠀⠀⣿⣿ ⡄⢰⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠟⠿⠃⠀⠄⢀⣙⣿⣿⣿⡛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠘⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⠃⠀⠀⠀⠃⢻⣿⡿⠀⠀⠈⣿⣿ ⠘⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠃⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣂⣤⣤⣿⣷⣿⣿⣿⣿⣍⣉⣟⠶⣽⣿⣿⣿⣿⡟⣿⣿⡿⢀⣿⣷⣄⣀⠘⠛⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⣿⣿ ⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⡐⠘⠛⠋⠙⠈⠋⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡏⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⣀⣰⣿⣿ ⣠⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠏⠋⠏⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⢿⡿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⣻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⠟⠁⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⢀⡯⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢩⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⠉⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⢻⠿⠻⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⡿⠿⣟⣡⣼⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢻⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⣈⣡⣤⣤⣼⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣜⣷⣦⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠉⠙⠁⣿⣿⣿⣿⣿ ⠀⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣋⡀⠀⠀⠀⣙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣟⣛⡻⢿⣿⣿⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢠⣒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⠉⠉⠉⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣄⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣄⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⣿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠛⢘⣽⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠻⣿⣿⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣬⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢿⡿⠿⣻⣿⣿⣿⣿⣿⡿⠇⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⠉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠘⣶⣿⣿⣿⣿⣿⣿⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣾⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣄⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⠉⠁⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⠞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢾⣶⣶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⡻⣿⣿⣿⡏⠀⠀⣿⣿ ⣄⢰⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠟⠿⠃⠀⠄⢀⣉⣿⣿⣿⣋⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡆⠈⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠇⢻⣿⡿⠀⠀⠘⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣆⣤⣴⣿⣿⣿⣿⣿⣿⣬⣉⣟⡲⣽⣿⣿⣿⣿⡟⣿⣿⠿⠀⣿⣷⣤⣀⠘⠛⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⣺⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠐⡸⠟⠉⠉⠉⠋⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⡀⢰⣿⣿ ⣰⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠉⠂⠀⠀⠀⠿⣿⣿⣿⡟⡗⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⢉⣛⣿⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡀⡿⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣻⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢫⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣸⣿⣿⣾⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠉⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢹⣿⣛⠿⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢟⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠻⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⢿⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣷⣤⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣽⣿⣿⣿⣿ ⠀⠙⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣿⣣⠀⠀⠃⢐⣽⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠺⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⡀⠀⠀⢹⡿⠟⣹⣿⣿⣿⣿⣿⠟⠀⢿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⢴⣾⣿⣿⣿⣿⣯⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣇⠀⠀⣿⣿ ⠀⠀⣀⣿⣷⠀⠀⠀⢺⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⡞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢺⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⣿⣿⣿⣿⡏⠀⠀⣿⣿ ⡀⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠻⠁⠀⠄⢀⣉⣿⣿⣿⡋⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠈⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠃⠀⠀⠀⠃⢻⣿⡟⠀⠀⠈⣿⣿ ⠘⣾⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣤⣴⣿⣷⣿⣿⣿⣿⣤⣉⣟⡲⣽⣿⣿⣿⣿⡿⣿⣿⡿⠀⣿⣶⣄⣀⠘⠋⠀⠀⢾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⠋⠁⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠏⠀⠀⢈⣾⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡯⣿⡟⠀⠀⠀⢾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠀⠀⠀⠀⠝⣿⣿⣿⠓⡄⠀⠀⠀⠀⠀⠀⠘⠿⡿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢉⣻⣿⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⠻⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢻⡿⠀⠀⠀⠀⠀⠀⣽⣿⣿⡆⢉⣼⣿⣿ ⣿⣿⣿⡟⣿⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢠⢼⣿⣖⣾⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣟⠈⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⢸⣿⠫⠯⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢼⣿⣿⣿⠇⠀⠀⠀⢀⡀⠈⣨⡿⣾⡟⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠿⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠀⠀⢀⠀⠀⣱⣤⢸⣿⣹⣻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣹⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠙⠿⠾⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣄⠀⠈⢻⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢿⣢⠀⠀⠁⠀⣘⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠐⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢹⠿⠟⣩⣿⣿⣿⣿⣿⠇⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣍⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣯⠈⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢚⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⠁⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠠⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⢀⣈⣻⣿⣿⣉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣹⣿⠟⠀⠀⠀⠀⠂⢹⣿⡿⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⢛⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⠠⣤⣤⣄⣤⣄⣤⣴⣾⣿⣿⣿⣿⣿⣤⣉⣝⡲⢾⣿⣿⣿⣿⡟⣿⣿⡿⠃⣴⣦⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠋⠀⠀⠀⠀⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣶⣶⣿⣿⣿⣾⠏⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⢀⡀⡀⠀⣷⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡇⠁⠉⠀⠀⠀⠘⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢹⣽⣿⡿⣦⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠈⠿⡿⣸⣷⣟⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡽⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠋⢉⣛⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡡⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠛⢻⡅⠀⠀⠀⠀⠀⠀⣺⣿⣷⡆⢉⣴⣿⣿ ⣿⣿⣿⡟⣯⠀⠀⠀⠀⠈⠩⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣴⡆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣦⣀⠈⠹⣿⣿⣷⡄⠀⠀⠀⣈⣼⣷⣀⡜⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⣣⣫⠀⠀⠀⠀⠀⠈⣟⠉⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡟⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢻⣅⣴⣿⣗⣆⣻⣿⣿⣿⣷⣄⢹⣿⣿⣿⡀⠀⣼⣿⣿⣿⢛⡁⠀⠀⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⢼⣯⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣤⣼⣿⣿⣿⠀⣜⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿ ⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⠀⠀⢵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠟⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠀⣴⣾⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⡇⠀⠀⠀⣶⣶⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⡟⠉⢉⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠘⣿⣿⣿⡏⠉⣄⢀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠁⢆⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣧⣤⣠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠐⢷⣡⣽⣿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠈⠹⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⣣⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠒⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢸⠿⠟⣻⣿⣿⣿⣿⣿⠏⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣷⠀⠀⠀⢨⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡾⠶⠶⠿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⠚⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠰⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠻⠇⠀⠀⠀⢀⢹⣿⣿⣋⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣻⣿⠟⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿ ⠘⣶⣿⣿⣿⠀⠀⠀⠀⣉⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣠⣴⣴⣾⣿⣿⣿⣿⣿⣦⣌⣭⣓⢾⣿⣿⣿⣿⡿⣿⣿⡿⠃⣰⣦⣄⣀⠘⠃⠀⠀⠨⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠒⠛⠁⠁⠀⠉⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⡀⢀⣿⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⠇⠂⠀⠀⠀⠠⢿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢘⣽⣿⣿⣯⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣥⣽⡟⠝⠀⠀⠀⠀⠀⠀⠀⠘⠽⣿⣹⣿⣾⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢉⣙⣟⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣋⡀⠀⠀⠀⢀⣀⣄⡀⠠⣿⡁⢐⠄⠀⠀⠀⠀⠀⠀⢀⠀⠑⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢯⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢻⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠈⢿⣿⣿⣦⡀⠀⠸⣿⣿⣷⠀⠿⠳⢢⡄⠀⠀⠀⠀⠀⠀⣸⣿⣷⡆⠉⣴⣿⣿ ⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠈⣿⣟⣿⣿⣿⣓⠀⠀⢰⣶⣿⠷⣶⣶⡆⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣵⡆⠀⠀⠀⣀⣀⡹⣿⣿⣷⣄⠀⠘⣿⣿⣧⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⠁⣿⣿⣿ ⣿⣿⣿⣇⣽⠀⠀⢠⣴⣶⣦⡛⠻⠻⠿⣿⣿⠃⠀⣸⣿⡋⢠⣿⠏⠀⣤⣤⠀⠀⠙⠛⠛⠿⣿⡿⠿⠟⠛⢛⣤⣴⣿⣟⣄⠀⠀⠀⢿⣿⣿⣽⣿⣿⣿⣧⠀⣿⣿⣿⡇⠀⣴⣾⣿⣿⠇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠇⡍⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⣹⡆⠀⣸⣿⣿⣿⣿⣿⠃⣼⣿⠟⠀⠀⠀⣶⣤⣀⢀⣀⣤⣤⣤⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣵⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠙⠁⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⠉⢹⣶⣿⣿⢿⣿⣿⣯⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢷⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠀⠈⣿⣿⣄⣤⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⠛⢛⠁⠘⡂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⣀⣀⡄⠐⠂⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣥⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣄⠀⠀⢠⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣯⡾⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣄⠀⠈⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⣣⠀⠀⠃⠀⡜⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠲⣷⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⢾⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡾⠶⠶⠿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡾⠚⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠌⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠇⠀⠀⢀⣠⢽⣿⣿⣍⡉⣉⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⠟⠂⠀⠀⠀⠂⢹⣿⡟⠀⠀⠐⣿⣿ ⠰⣾⣿⣿⣿⠀⠀⠀⠠⢻⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⡤⣤⣤⣄⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣤⣭⣙⣺⣿⣿⣿⣿⡿⣿⣿⡿⠃⣰⣶⣄⣀⠘⠓⠀⠀⢹⣿⣿⣿⣯⠂⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠴⠙⠉⠈⠈⠁⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⡏⠢⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢺⣽⣿⣿⣯⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡀⣬⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⡿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢀⣬⣻⣟⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠟⠋⣀⣀⡀⠀⠀⠀⠀⠈⠉⣿⠗⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⢸⣿⣿⣧⢙⢻⣀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡆⢉⣴⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⡓⢀⣠⣤⢀⣤⣤⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣵⡆⠀⠀⠀⠀⠀⣀⣀⠹⣿⣿⣦⡀⠀⠙⣿⣿⡄⠨⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⣧⣏⠀⣀⣀⡀⠀⢮⣽⣿⣿⣿⠉⠁⢸⣿⠋⢸⣿⡟⠀⣠⣄⠀⠀⠀⠀⠉⠛⠛⠿⣿⡿⠿⠛⠛⢻⣦⣴⣿⣟⣤⠀⠀⠀⠀⠘⢿⣿⣷⣽⣿⣿⣿⡄⠀⣿⣿⣿⡄⢄⣠⣶⣶⣶⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⢻⡏⠘⢿⣿⣿⣦⡉⠁⠈⠛⡇⠀⢠⣿⣶⢤⣾⣿⠁⣼⣿⡏⠀⠀⠀⠀⠀⣷⣦⣀⣀⣠⣤⣤⣴⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢶⣾⣿⣿⠛⠁⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠙⠃⠀⠁⠀⠀⠉⠻⣿⣿⣦⡄⠰⢷⣠⣿⣿⡿⣿⣿⡏⣰⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠀⠀⠋⠉⡏⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣼⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⢶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡧⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣯⣭⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡚⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠉⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡜⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣆⠀⠀⠐⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣻⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠼⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⢾⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⢲⣾⣿⣿⣿⣿⣍⡉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⠀⣿⣷⠀⠀⠀⢺⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⣾⠶⠶⠿⠷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡞⠞⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡈⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠋⠀⠐⢀⣤⣼⣿⣿⣧⡄⢈⣉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠂⠀⠀⠀⠂⢹⣿⡟⠀⠀⠈⣿⣿ ⠘⣶⣿⣿⣿⠀⠀⠀⠀⡻⣻⣿⣿⣿⣧⠀⠀⠒⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣴⣭⣳⣿⣿⣿⣿⡿⣿⣿⡿⠃⢰⣦⣄⣀⠘⠃⠀⠀⢼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠒⠙⠁⠁⠀⠈⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⡝⠎⠀⠀⠀⠀⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⡿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢨⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣤⣿⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡟⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠑⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡀⠀⠀⠀⣠⣤⡚⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⢉⣰⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣟⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠑⣿⣿⣿ ⣿⣿⣿⣦⡏⠀⠀⠀⠀⠀⠨⣿⣿⠿⠿⠙⢱⣿⠷⢰⣿⡷⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠟⠛⠛⢫⣦⣴⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⣾⣷⣆⠹⣿⣿⣧⡀⠸⣿⣿⣇⠀⠀⢀⣠⣤⣄⠺⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⡿⠯⡷⣿⣿⣦⡀⠀⠈⠙⠿⣧⠀⢀⣞⣫⠀⣼⣿⠃⣰⣿⡇⠀⠀⠀⠀⠀⠈⣿⣦⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣽⣿⣿⣷⢠⣿⣿⣿⠀⣴⣿⣿⠟⠋⠀⠈⠁⣹⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠈⠙⢿⣿⣶⣤⡀⢀⣷⠀⣼⣿⡿⣼⣿⡏⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠃⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡇⠀⠉⠷⠘⠿⠃⣿⣿⡱⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠈⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⢸⣿⣸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⢶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣽⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠿⠿⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣕⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⣿⣿⣟⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡈⢽⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⡡⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠬⢿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⠹⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠲⢯⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣻⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢭⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⣤⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠀⣄⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⣾⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡾⠞⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⠝⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⢀⣤⢼⣿⣿⣧⡄⢈⣉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⣿⠟⠀⠀⠀⠀⠂⢻⣿⡟⠀⠀⠀⣿⣿ ⠰⣾⣿⣿⣿⠀⠀⠀⠠⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣴⣭⣳⣿⣿⣿⣿⣿⣻⣿⡿⠇⢰⣶⣄⣀⠘⠃⠀⠀⢚⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⡄⠀⢀⠒⠋⠁⠈⠉⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣻⠏⠀⠀⢠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣟⡙⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⠋⠀⠀⠀⠀⠀⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢼⣽⣿⣻⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠶⣿⣿⢃⠂⠀⠀⠀⠀⠀⠀⠰⠊⣿⣹⣿⣼⣿⣿ ⣿⣿⣿⣿⣟⠀⠀⠀⠀⢈⣟⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣬⣿⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡩⢿⢋⠤⠅⠀⠀⠀⠀⠀⠀⠀⢀⠋⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⢛⣻⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⡀⠀⠀⠀⣢⣤⡛⠢⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠉⣴⣿⣿ ⣿⣿⣿⡟⣿⠀⠀⠀⠀⠈⢰⣿⡿⣿⣿⣿⡗⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠐⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠁⣿⣿⣿ ⣿⣿⣿⣦⣿⠀⡀⠀⠀⠀⢾⣟⣟⣻⠻⠛⠃⣿⡿⠂⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⢈⠉⠙⠻⠿⠿⠟⠛⠛⢻⣦⣴⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⢻⣿⣿⣦⡀⢹⣿⣿⣆⠀⠀⢀⣤⣤⡄⡾⢿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⠫⡗⠺⣿⣷⣆⠀⠈⠁⠻⣿⠆⠀⣼⣭⡄⣴⣿⡇⢠⣿⡿⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⣷⢠⣿⣿⡿⢀⣼⣿⣿⠟⠁⠀⠉⠁⣽⣿⣿⣿⣿ ⠀⠙⠃⠀⠁⠀⠈⠻⣿⣿⣦⡄⠀⣹⡀⣸⣿⣿⢵⣿⡿⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠃⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠈⠸⠈⠻⠃⢸⢿⡧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣿⣶⣵⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣽⣿⣿⣿⣿⣿⡟⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠛⠻⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡘⣿⣿⣭⣽⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣈⠻⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣯⣡⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠈⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡌⣿⣿⣄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠒⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠹⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⡠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣄⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⣾⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⡞⠞⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠌⣿⣿⣿⡇⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠋⠀⠐⢀⣤⣼⣿⣿⣧⠄⢈⣉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣟⣻⣿⠟⠃⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿ ⠘⣾⣿⣿⣿⠀⠀⠀⠀⢻⣻⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣴⣭⣳⣿⣿⣿⣿⣿⣿⣿⡿⠇⢰⣦⣄⣀⠘⠃⠀⠠⢘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⢀⠂⠛⠉⠁⠈⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣶⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⡅⠀⠀⠀⠀⠀⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣥⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠺⣿⣸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣤⣿⣭⣍⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢇⢔⡀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠋⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣫⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⣠⣌⠙⡂⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠋⣴⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⢽⣿⣟⢿⣿⣿⡳⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠸⣿⣿⣧⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⡀⠀⠀⠀⢶⣟⣿⣛⠻⠋⠓⣿⡟⠃⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠛⠻⠿⠿⠟⠛⠛⢻⣦⣴⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⢻⣿⣿⣆⡀⢻⣿⣿⡆⠀⠀⣀⣤⣤⡀⣺⣿⣿⣿⣿⣾⣿⣿ ⠛⣿⣿⢣⠛⠺⣿⣷⣦⡀⠈⠁⠻⣿⠂⠀⣼⣭⡆⣴⣿⡇⢠⣿⡿⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣻⣿⣿⣷⢰⣿⣿⣿⢀⣾⣿⣿⠟⠁⠀⠈⠁⣹⣿⣿⣿⣿ ⠀⠛⠃⠀⠀⠀⠈⠻⣿⣿⣦⡄⠀⣹⡀⣸⣿⣿⢵⣿⡿⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠀⠼⠘⠛⠃⢸⢿⡇⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⣿⣤⣧⣮⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣽⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣭⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡜⣿⣿⣯⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣈⠹⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣯⣣⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠼⣿⣿⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣐⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠈⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣣⠀⠀⠋⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠂⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢰⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠘⣤⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢪⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⣾⠶⠶⠿⠷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⠞⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⠈⣽⣿⣿⡇⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠇⠀⠐⢀⣤⣼⣿⣿⣧⠄⢈⣉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠂⢻⣿⡟⠀⠀⠀⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣴⣭⣳⣿⣿⣿⣿⣿⣿⣿⡿⠇⢰⣦⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⢀⠢⠛⠉⠀⠀⠁⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⢀⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡷⠕⠠⠀⠀⠀⠀⣽⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠅⠀⠀⠀⠀⠀⠀⠘⠫⣿⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⢿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣤⣿⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢇⠝⠄⠀⠀⠀⠀⠀⠀⢀⠀⠙⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣷⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⢀⣤⣅⠑⣀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡆⠉⣴⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⢙⣾⣿⣻⣿⣿⡃⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⢾⣿⣿⡆⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⣷⣿⢀⣀⠀⠀⠀⠽⣿⣯⣟⠿⠛⢻⣿⠛⢰⣿⡿⠀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠙⠻⠿⠿⠟⠛⠛⢻⣶⣼⣿⣟⣤⠀⠀⠀⠀⠀⠀⢀⣶⣤⡘⢿⣿⣷⣄⠈⣻⣿⣿⡄⠀⠀⣠⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠻⠓⠻⣿⣷⣆⠀⠈⠁⠟⣿⠀⢠⣯⣽⢀⣾⣿⠁⣼⣿⡇⠀⠀⠀⠀⠀⠈⣿⣶⣤⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣮⣿⣿⣿⣶⢾⣿⣿⡇⣠⣾⣿⡿⠋⠀⠀⠈⠁⣿⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠈⠻⣿⣷⣦⡄⠀⣿⠀⣾⣿⡿⣾⣿⡏⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⢿⣿⣿⣿⣿⣶⣷⣿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⠀⠀⠟⠙⠟⠁⣿⣿⣴⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣀⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣀⣨⣿⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣥⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⣿⣿⣭⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣔⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣈⠻⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⡡⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⣿⣿⢟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠈⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡜⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⡿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠸⡿⠟⣛⣿⣿⣿⣿⣿⡗⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡾⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠞⠞⣶⡶⠟⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⡷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢇⠀⠐⢀⣤⣼⣿⣿⣧⠄⢈⣉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⠟⠂⠀⠀⠀⠂⢹⣿⡟⠀⠀⠀⣿⣿ ⠰⣾⣿⣿⣿⠀⠀⠀⠐⢙⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣤⣶⣭⣳⣿⣿⣿⣿⣿⣻⣿⡿⠃⢰⣦⣄⣀⠈⠂⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠐⠛⠁⠁⠀⠁⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠏⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⡙⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡗⠕⠐⠀⠀⠀⠀⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⣬⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢸⣷⣽⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣬⣽⣭⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⢀⣤⡄⠉⡠⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠋⣴⣿⣿ ⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣻⣿⣿⢇⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣵⡎⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⡷⢟⢀⣀⠀⠀⠀⠰⣿⣽⡟⠿⠙⣻⣿⠛⢸⣿⡟⠀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠙⠻⠿⠿⠟⠛⠛⢹⣶⣶⣿⣟⣄⠀⠀⠀⠀⠀⠀⢠⣶⣤⡘⣿⣿⣷⣀⠈⣿⣿⣿⠄⠀⢀⣠⣤⣤⠀⢾⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠋⠇⠻⣿⣷⣆⠀⠀⠈⠛⡿⠀⢠⣯⣽⢠⣾⣿⠁⣼⣿⠇⠀⠀⠀⠀⠀⠈⣿⣶⣤⣠⣤⣴⣴⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⣿⣿⣿⡾⣿⣿⣿⡇⣠⣿⣿⠟⠋⠀⠀⠈⠁⣽⣿⣿⣿⣿ ⠀⠛⠃⠀⠀⠀⠈⠻⣿⣿⣦⡄⠈⣿⠀⣿⣿⡏⣾⣿⡇⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⠀⠀⠗⠙⠟⠀⣿⣿⢼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡀⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⣸⣧⣮⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⣿⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠛⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣥⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⣿⣿⣭⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣔⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣈⠻⣿⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⡱⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢩⣾⣿⢟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⢻⡿⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⣂⠀⠀⠃⢀⣬⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠚⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⠻⡿⠟⣻⣿⣿⣿⣿⣿⡟⠀⣼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠠⢢⣾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⠼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⡞⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢺⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿ ⢀⢰⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠃⠀⠀⣠⣴⣿⣿⣿⣥⠄⣉⣙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⣿⡟⠂⠀⠀⠀⠁⢻⣿⡿⠀⠀⠀⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⠐⠿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣮⣭⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⣼⣶⣄⣀⠘⠃⠀⠀⢺⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠐⣴⣿⣿⣿⣿⣿⣷⡄⠀⢀⠖⠛⠉⠁⠀⠀⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⠿⠋⠀⠀⢨⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣀⢀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⡟⠷⠀⠀⠀⠀⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠉⠘⠀⠀⠀⠀⢦⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠸⠻⠿⣸⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⢀⣬⣿⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠍⡍⠄⠀⠀⠀⠀⠀⠀⢠⠀⡙⠯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣲⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⣀⣁⠉⠀⣂⠀⠀⠀⠀⠀⠀⣽⣿⣿⡎⠋⣼⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⢪⣿⣿⢿⣿⣿⡟⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣵⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠨⣿⣿⣧⠂⠄⠀⠀⠀⠀⠀⠀⣹⣿⣿⣏⠀⣿⣿⣿ ⣿⣿⣿⣗⣏⠀⣀⡀⠀⠀⠣⣿⣻⣟⠿⠛⢻⣿⡿⢀⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠛⢻⣶⣼⣿⣟⡄⠀⠀⠀⠀⠀⠀⢠⣤⡀⢻⣿⣿⣆⡀⢻⣿⣿⣆⠀⠀⣀⣤⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠣⡇⠘⢿⣿⣦⡀⠉⠉⠻⣻⠀⢀⣾⣭⡆⣬⣿⠃⣰⣿⡇⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣻⣿⣿⣷⣉⣿⣿⣿⢄⣼⣿⡿⠋⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿ ⠀⠊⠁⠀⠁⠀⠀⠹⣿⣿⣦⡄⡀⣽⡀⣾⣿⡿⣼⣿⡟⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠯⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡹⣿⣿⣯⣿⣿⣿⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠈⠟⠙⠟⠃⡿⢿⡡⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣿⣬⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣴⣮⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⠿⠿⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⢣⡈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣘⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡉⢽⣿⣿⣿⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢽⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣭⣡⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣠⣿⣿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⢻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⣌⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠺⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢹⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠘⢠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢹⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠈⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠀⡀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⡞⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢺⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠈⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠇⠀⠀⣠⣴⣿⣿⣿⣥⠄⣉⣙⡛⢿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠐⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⣿⠟⠃⠀⠀⠀⠂⢻⣿⡟⠀⠀⠀⣿⣿ ⠸⣾⣿⣿⣿⠀⠀⠀⢐⠿⢿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣮⣭⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⣼⣦⣄⣀⠘⠃⠀⠀⢪⣿⣿⣿⣟⠁⠀⠀⠀⠈⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣷⡄⠀⢄⠆⠛⠉⠁⠈⠈⠙⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⢿⠏⠀⠀⢀⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡏⡏⠾⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠐⠈⠀⠀⠀⡠⣧⣽⣿⠛⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣻⢿⣿⣿⣿⣿⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⢀⣬⣿⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢏⠌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣾⣾⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⣀⣀⠉⠛⣆⠀⠀⠀⠀⠀⠀⣹⣿⣿⡆⢉⣴⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡟⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣵⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣇⠁⣿⣿⣿ ⣿⣿⣿⣗⣟⠀⣀⡀⠀⠀⢨⣿⣻⣟⠿⠟⢻⣿⡿⢀⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠟⠛⠛⢻⣶⣾⣿⣟⡄⠀⠀⠀⠀⠀⠀⢠⣤⡀⢻⣿⣿⣆⠀⢹⣿⣿⣆⠀⠀⣀⣤⣤⡀⠀⢽⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⡿⢣⡇⠘⢿⣿⣦⡀⠉⠉⠻⣻⠀⢀⣾⣭⡆⣬⣿⠃⣰⣿⡇⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣻⣿⣿⣷⣈⣿⣿⣿⢄⣼⣿⡿⠋⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠀⠹⢿⣿⣦⡄⡀⣽⡀⣾⣿⡿⣼⣿⡟⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠯⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡹⣿⣿⣯⣿⣿⣿⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠀⠟⠘⠟⠃⡿⢿⡡⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⣀⣀⣿⣾⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣶⣮⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⠿⠿⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⢧⡈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣅⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣘⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡁⢿⣿⣿⣾⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣭⣩⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⣡⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣸⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⠻⣿⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣯⢂⠀⠀⠃⢀⡌⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠒⣷⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⠸⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣾⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⡋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠈⣤⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⣏⠀⠀⣿⣿ ⠀⠀⣀⣿⣇⠀⠀⠀⢽⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⡞⠶⠶⠿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠺⢺⣶⡶⠛⠒⠓⠓⠚⠶⣶⣿⣷⣾⣿⠷⠛⠀⠀⠠⣾⣿⣿⡏⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠇⠀⠀⣠⣴⣿⣿⣿⣥⠄⣉⣙⡛⢿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠈⠁⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⠿⠂⠀⠀⠀⠃⢻⣿⡟⠀⠀⠀⣿⣿ ⠐⣾⣿⣿⣿⠀⠀⠀⠀⢛⢿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣮⣭⣿⣿⣿⣿⣿⣟⣿⣿⡿⠁⣼⣦⣄⣀⠘⠃⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠂⠫⠉⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⠏⠀⠀⢘⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠯⢟⠓⠀⠀⠀⠀⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿ ⣼⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠀⠀⠀⠈⢢⣿⣟⠂⠃⠀⠀⠀⠀⠀⠀⠘⠻⡿⣹⣿⣟⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⢀⣬⣿⣭⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠋⢴⠄⠀⠀⠀⠀⠀⠀⢀⠀⠁⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣢⡂⠈⠉⠤⠀⠀⠀⠀⠀⠀⣸⣿⣷⡆⠉⣴⣿⣿ ⣿⣿⣿⡿⣿⠀⠀⠀⠀⠈⠷⣿⣿⣿⣿⣿⡗⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣵⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⢸⣿⣿⡆⠀⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⣿⣿⣿ ⣿⣿⣿⣧⣿⠀⣀⡀⠀⠀⠻⣿⣛⣛⠿⠏⢹⣿⡿⠇⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠛⢹⣷⣼⣿⣟⡄⠀⠀⠀⠀⠀⠀⣠⣤⡈⢿⣿⣷⣄⠀⣻⣿⣿⡄⠀⠀⣠⣤⣤⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⠻⡟⠈⢿⣿⣷⡄⠁⠉⠻⢿⠇⠀⣼⣭⡇⣼⣿⡏⢠⣿⡟⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣮⣻⣿⣿⣧⢹⣿⣿⣿⢠⣾⣿⡿⠋⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿ ⠀⠛⠃⠀⠁⠀⠀⠙⢿⣿⣶⡄⡀⣽⡀⣸⣿⣿⣱⣿⡿⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠯⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣹⣿⣿⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠈⠼⠘⠿⠃⡿⠿⡃⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣻⣿⣷⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣀⣀⣿⣲⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣴⣮⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣻⣿⣿⣿⣿⣿⡿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠈⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡘⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡈⢿⣿⣿⣿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣽⣩⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⣨⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣿⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣯⢆⠀⠀⠃⠀⡝⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣿⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢸⣿⠟⣋⣿⣿⣿⣿⣿⡟⠀⣽⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⢹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠀⣠⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠀⣀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⣾⡞⠶⠶⠿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠺⢺⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⡷⠛⠀⠀⡀⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠇⠀⠂⣠⣤⣿⣿⣿⣥⢈⣉⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣟⣻⣿⠛⠁⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿ ⠠⣾⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣦⣤⣮⣝⣺⣿⣿⣿⣿⡟⣿⣿⡿⠀⣴⣦⣄⣀⠐⠒⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠛⠉⠀⠀⠁⠉⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⣀⠀⠀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠟⢻⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⣘⣿⣿ ⣼⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣱⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣃⢀⣬⣿⣭⣙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠑⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢭⣻⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⢀⣀⡠⠂⠀⡠⠀⠀⠀⠀⠀⠀⣺⣾⣷⡖⠋⣸⣿⣿ ⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢩⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⣵⠏⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⣿⣿⣿⡂⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠑⣿⣿⣿ ⣿⣿⣿⣧⣿⠀⣀⣀⠀⠀⢸⣽⣟⣚⡟⠍⠓⣿⣿⠇⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠛⢹⣶⣶⣿⣟⡄⠀⠀⠀⠀⠀⠀⣠⣀⠙⣿⣿⣧⡀⠸⣿⣿⣷⠀⠀⢀⣤⣶⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠛⣿⣿⢏⡛⠀⠻⣿⣷⣄⠈⠉⠹⢿⡇⠀⣼⣭⡅⣠⣿⡟⢀⣿⡿⠀⠀⠀⠀⠀⠘⣷⣦⣄⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣷⣌⢿⣿⣿⣦⣿⣿⣿⡷⣰⣿⣿⠟⠁⠀⠀⠀⠉⠀⣹⣿⣿⣿⣿ ⠀⠉⠁⠀⠀⠀⠀⠈⢿⣿⣷⣤⣀⣹⡇⣰⣿⣿⣱⣿⣿⢁⣾⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠈⠽⠙⠻⠋⠺⢿⡇⢾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢰⢀⢀⣶⣴⣇⣝⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠠⣤⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⡿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠻⠿⠿⠊⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠈⡅⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣕⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠸⣿⣿⣗⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣺⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡉⢿⣿⣿⣿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣝⣫⠎⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣼⣿⣿⢻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠠⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣀⠀⠉⠻⣿⡿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⣯⢆⠀⠀⠓⢐⡝⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠋⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⢿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢽⡿⠟⣻⣿⣿⣿⣿⣿⡏⠀⣿⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠈⣤⣾⣿⣿⣿⣿⣏⠉⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠈⢸⠀⢼⡇⢸⣿⠃⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣯⠉⠁⠀⠀⠈⠓⠚⠚⢶⣿⣷⣾⣷⣾⡞⣶⣶⡿⢷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠚⢾⣶⡶⠟⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡘⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⢠⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⡁⠀⠀⣄⣀⣬⣿⣿⣿⣍⣉⣉⡛⠿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠁⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡟⠀⠀⠀⠀⠁⢻⣿⡟⠀⠀⠐⣿⣿ ⢸⣾⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠂⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣻⣠⣤⣴⣶⣾⣿⣿⣿⣿⣶⣬⣍⣛⣾⣿⣿⣿⣿⣿⣿⡿⠀⣶⣦⣄⣀⠘⠂⠀⠀⢸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⠰⠛⠉⠁⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⡀⢠⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠏⡯⠯⠀⠀⠀⠀⣿⣿⣿⡿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣘⣿⣿ ⣼⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠻⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⢿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠉⣙⣟⣛⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡃⢳⠀⠀⠀⠀⠀⠀⠀⢸⢀⠹⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⣈⣐⢶⠃⠌⡀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡖⠋⣼⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⡖⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⣿⣿⣧⠂⠲⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠉⣿⣿⣿ ⣿⣿⣿⣷⣿⠀⢀⣀⠀⠀⣶⣿⣿⣛⡟⠟⠋⣿⣿⡇⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢈⠙⠛⠛⠿⣿⡿⠿⠟⠻⣷⣶⣿⡿⡄⠀⠀⠀⠀⠀⠀⣀⡀⠻⣿⣿⣦⡀⢸⣿⣿⣧⠂⠀⢀⣤⣦⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⢿⡟⠀⠹⣿⣿⣆⠁⠉⠹⢿⡇⠀⣰⣽⡏⢠⣿⡿⢀⣾⣿⠀⠀⠀⠀⠀⠘⣿⣶⣄⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⣙⣿⣿⣿⡦⣿⣿⣿⡇⣴⣿⣿⠟⠀⠀⠀⠀⠙⠉⣿⣿⣿⣿⣿ ⠀⠙⠋⠀⠁⠀⠀⠈⢻⣿⣷⣤⣀⣸⡇⢰⣿⣿⣣⣿⣿⠃⣼⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠈⢹⠞⠻⠟⢸⢿⣏⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⡁⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⡈⣲⣡⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡗⠀⠀⠠⣤⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣻⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠸⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣕⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⣗⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣺⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠉⣿⣿⣿⣽⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣟⣋⠜⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣬⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠰⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣇⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠉⢻⡟⢿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⡿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⣯⢆⠀⠀⠃⠀⣜⣿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠊⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢸⣿⠟⣫⣿⣿⣿⣿⣿⡗⠀⣺⡏⢹⠙⡏⣿⣉⢉⡏⢹⢙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢺⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠀⣀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⣿⢸⡇⢠⢸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠄⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣿⣿ ⠀⠀⣀⣿⣇⠀⠀⠀⢲⣿⣿⣿⣿⣭⠁⠀⠀⠀⠈⠓⠚⠺⢶⣿⣷⣾⣷⣾⠞⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⠾⣾⣶⠶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⣿⠷⠛⠀⠀⡈⣿⣿⣿⡇⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣻⠀⣿⠋⣠⣤⣤⣈⣽⣿⣿⣿⣉⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⣺⣿⠏⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⣿⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣠⣀⣿⣷⣿⣧⣭⣭⣭⣭⣿⣿⣿⣿⣿⣽⣛⣛⣳⣿⣿⣿⣿⣽⠟⢁⣦⣤⣄⣀⠘⠐⠀⠀⢘⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠐⠛⠉⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⡀⠀⠀⣽⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠋⠇⠀⠀⠀⠀⠀⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⢫⣿⣿⣷⣧⢘⣿⣿ ⣼⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢼⣽⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⣛⣿⣛⡻⠿⢿⣿⣿⣿⣿⣿⣿⠏⠿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠠⠀⠀⠀⠀⠀⠀⠀⢀⢀⠩⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⣀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⡆⠋⣼⣿⣿ ⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡍⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⢸⣿⣿⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠘⣿⣿⣿ ⣿⣿⣿⣯⣿⠀⢀⣀⡀⠀⢪⣽⣿⣒⡟⠻⠋⣾⣿⡇⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣮⡙⠿⠿⠿⣿⣿⣿⠿⠿⣏⣵⡿⡅⠀⠀⠀⠀⠀⠀⣀⡈⢻⣿⣿⣄⡁⢿⣿⣿⣷⠀⠀⣀⣤⣤⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⠟⠛⠀⠙⣿⣿⣆⠈⠉⠙⢿⡇⠀⢰⣿⣿⢠⣿⡿⠁⣼⣿⠀⠀⠀⠀⠀⠸⣿⣿⣶⣄⡀⠀⣀⣤⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⡻⣿⣿⣿⡾⣿⣿⣿⡧⣴⣿⣿⠏⠀⠀⠀⠀⠘⠁⣽⣿⣿⣿⣿ ⠀⠙⠃⠀⠀⠀⠀⠈⠻⣿⣷⣤⣂⣸⡇⢠⣿⣿⣇⣾⣿⠇⣼⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⢹⠞⢿⠟⢸⢿⣟⢼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⡁⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣤⣤⣀⡈⣲⣽⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡗⠀⠀⠠⣤⣬⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣞⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⠿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠸⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣕⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠛⠛⠃⠈⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣗⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣾⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠉⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣟⣋⠜⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢐⣮⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡏⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠉⠻⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⣯⢆⠀⠀⠃⠀⡜⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠈⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣽⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⠰⡿⠛⣋⣿⣿⣿⣿⣿⡇⠀⢼⡏⢹⠙⡏⣿⣉⢉⡏⢹⢹⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣉⠁⠀⠀⢸⡇⢸⢠⠀⣿⡗⢸⡇⢠⠸⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⢼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⣿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣯⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠓⠚⢺⣶⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠷⠋⠀⠀⡈⣾⣿⣿⡇⠀⠀⣿⣿ ⠀⢰⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⠿⣛⣋⡉⣉⣿⣿⣿⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⠳⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿ ⠨⣾⣿⣿⣿⠀⠀⠀⠀⡽⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⡀⣠⣤⣀⣀⣴⣶⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣿⣿⣿⣿⣷⣆⣠⣦⣦⣄⣀⠘⠐⠀⠀⠐⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⣹⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠚⠁⠀⠀⠉⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣳⠇⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⡀⠀⠀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⠱⠂⠀⠀⠀⠀⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣧⣈⣿⣿ ⣼⣿⣿⣿⣿⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⣹⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣟⡿⣿⣿⣿⣿⣿⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢟⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⠀⠀⠀⠀⠐⣒⣽⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣷⣴⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢺⣶⣶⡆⠉⣸⣿⣿ ⣿⣿⣿⡿⣏⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⣿⣿⣦⡀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠘⣿⣿⣿ ⣿⣿⣿⣇⢿⠀⠀⢀⣀⠀⠰⡿⣟⢞⣽⠓⠃⠀⣰⣿⡆⢰⣶⡄⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣍⡛⠻⢿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠈⠻⣿⣿⣄⠀⠘⣿⣿⣧⡀⠀⠀⣠⣤⡄⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿ ⠛⣿⣿⠗⡏⠀⠀⠹⣿⣿⣌⠁⠀⠸⡿⡇⠀⢠⣟⣯⢀⣿⡿⠁⣴⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⣀⡀⠉⠉⠀⠀⠀⠀⠀⢿⣿⣦⡙⣿⣿⣷⣄⢿⣿⣿⣧⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠁⣽⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⣺⡇⢠⣿⣿⢇⣾⣿⠃⣼⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠯⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣎⢿⣿⣿⣸⣿⣾⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠀⠈⣱⠸⠿⠟⢼⣿⠏⣼⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⡁⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣠⠀⠁⣼⢧⡏⠛⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⣤⣦⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⣯⢟⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⢿⣿⣟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢀⢛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⢙⣿⣿⣿⡟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣝⡛⣣⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢊⣹⣿⡿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠈⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠉⠻⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⢂⠀⠀⠃⢐⡜⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠘⣿⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣷⠀⠀⠀⠸⡿⠛⣻⣿⣿⣿⣿⣿⡇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠈⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⣿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠓⠚⠚⢲⣶⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⣶⣿⣷⣾⡿⠷⠛⠀⠀⠀⣽⣿⣿⡇⠀⠀⣿⣿ ⠀⠰⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣻⣿⣿⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⠇⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⣟⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡀⡀⣠⣄⣀⠀⢀⣤⣤⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣋⣹⣿⣿⣿⣷⣀⣤⣤⣄⡀⠘⠀⠀⠀⢘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⣻⣾⣿⣿⣿⣿⣗⡀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠻⠏⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⢀⣀⠀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⠩⠹⠀⠀⠀⠐⢻⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠨⣽⣿⣟⣧⣘⣿⣿ ⣼⣿⣿⣿⣏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠸⠫⢟⢩⣷⣽⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⡿⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⠟⣿⣿⣿⣿ ⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⡉⣩⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣴⣾⣿⣶⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⠉⣼⣿⣿ ⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⣿⣟⣻⣿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⣿⣿⣦⠀⠀⠀⣾⣿⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠘⣿⣿⣿ ⣿⣿⣿⡶⢾⠀⠀⢀⣀⡀⣄⣿⣷⡴⠽⠛⠓⠀⢠⣶⣦⢠⣶⡄⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣷⣄⠀⠙⣿⣿⣆⠀⠀⠀⣠⣤⡄⠀⠀⠀⠸⣿⣿⣿⣷⣿⣿⣿ ⠛⣿⣿⠣⡏⠀⠀⠘⣿⣿⣆⠁⠀⠰⣿⡧⠀⢀⣟⣟⠀⢼⣿⠃⣰⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣅⣀⠀⠈⠉⠉⠉⠀⠀⣿⣿⣦⡹⣿⣿⣷⡄⣻⣿⣿⣧⢠⣾⣿⡿⠁⠀⠀⠀⠀⠈⠁⣽⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠆⢐⡇⢀⣾⣿⡏⣼⣿⠇⣰⣿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣎⢿⣿⣿⢸⣿⣿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠈⠈⢳⠼⢿⠟⢸⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣁⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣟⢿⣿⣾⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⢀⠀⠀⣨⢫⠈⠻⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢤⣦⣽⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣯⢟⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⢷⣿⣾⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣿⣿⣽⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢛⣿⣿⣿⡛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣯⣝⡛⢣⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢊⣙⣿⡿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢧⣀⠀⠉⠹⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡀⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠈⣭⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣷⠀⠀⠀⢠⡿⠛⣫⣿⣿⣿⣿⣿⠇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣹⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢐⣾⣿⣿⣿⣍⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠓⠚⠒⠒⢶⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⣿⠗⠋⠀⠀⠀⢼⣿⣷⠇⠀⠀⣿⣿ ⠀⠠⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣻⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣐⡏⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⣹⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⣠⣬⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⣁⣾⣿⣿⣯⢀⣤⡄⠀⠐⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⢸⣿⣿⣿⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣗⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠁⠀⠀⠀⣺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⠀⡀⠀⢀⣿⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠀⠀⠀⢻⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠈⣽⣿⠚⣦⢈⣿⣿ ⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣙⣿⡅⠀⠀⠀⠀⠀⠀⢘⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢀⣷⣟⣿⣿ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣛⢻⣿⣿⣿⣿⡿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢛⣿⣿⣿⣿ ⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⣰⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣶⣶⣶⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⠆⠉⣼⣿⣿ ⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⢁⣿⣻⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⡀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿ ⣿⣿⣿⠇⣣⠀⠀⠀⣀⡀⠌⡌⣶⡮⠯⠓⠁⠀⠀⣴⣶⠀⣤⣤⠀⠀⠀⠀⠀⠀⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣿⣿⠿⠈⠻⣿⣿⣆⠀⠘⢿⣿⣇⠀⠀⠀⣠⣤⡄⠀⠀⠀⠸⢿⣿⣿⣿⣼⣿⣿ ⠙⣿⣿⠇⠏⠀⠀⠘⢿⣿⣧⠁⠀⠀⣿⣷⠀⠀⣜⢿⡃⡰⣿⡟⢠⣶⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣟⣛⣃⠀⠈⠉⠉⠉⠀⢿⣿⣦⡙⣿⣿⣷⡄⢿⣿⣿⣧⢠⣾⣿⡿⠁⠀⠀⠀⠀⠘⠁⢹⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⣻⠀⣼⣿⡿⣰⣿⡿⢀⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣎⢿⣿⣿⣸⣿⣾⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡌⠈⠻⡄⠿⠿⢣⣿⣿⢡⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣅⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣏⢿⣿⣮⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⡀⠀⢀⢓⡈⠛⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⢰⣶⣼⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣯⢿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠵⢧⣾⣿⠳⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⣿⣿⠭⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠙⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣮⣝⡻⢋⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢊⣙⣿⡿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢷⣀⠀⠉⠹⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣭⣾⣿⣤⣤⣧⣼⣿⣬⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣷⠀⠀⠀⠰⡿⠟⣉⣿⣿⣿⣿⣿⠃⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣅⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⡇⠀⠀⠀⠰⣿⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⠗⠚⠚⠒⠒⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣼⣿⣷⡇⠀⠀⣿⣿ ⠀⠠⣾⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⣼⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠛⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⡀⠀⠀⢀⣴⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⢀⣾⣿⣿⡄⢀⣀⡀⠐⠂⠀⠀⠘⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⢸⣿⣿⣿⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠁⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠷⠉⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⢀⣵⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠐⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣽⣽⢓⣧⠈⣿⣿ ⣼⣿⣿⣿⣏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⡿⠁⠀⠀⠀⠀⠀⠨⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠿⢨⣧⣟⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡾⣻⣿⣿⣿⣿⡿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠬⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠩⢛⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠊⢘⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣶⣶⣶⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡆⠉⣼⣿⣿ ⣿⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣾⢟⢿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠐⣿⣿⣿ ⡾⣿⣿⠴⢟⠀⠀⠀⣀⣀⠠⠈⣶⡾⠫⠓⠁⠀⠀⣴⣶⡄⣤⣤⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⣿⣿⣿⣿⣿⡿⡇⠙⣿⣿⣦⡀⠈⢻⣿⣷⡀⠀⠀⣠⣤⣄⠀⠀⠀⠸⢿⣿⣿⣷⣾⣿⣿ ⠛⣿⣿⠗⠆⠀⠀⠀⢻⣿⣷⡁⠀⠀⢾⣿⠄⠀⣰⠿⡇⠠⣿⡟⢀⣴⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣛⣛⠂⠀⠉⠉⠉⠁⠻⣿⣷⣌⢿⣿⣿⣦⠘⣿⣿⣷⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⡀⠀⣺⠀⣰⣿⡿⢡⣿⣿⢁⣾⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⢹⣿⣿⡇⣿⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠙⡦⠿⡻⠃⣿⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣥⡀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡻⣿⣷⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⢀⡓⣈⡛⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠰⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣷⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠳⢦⣾⣷⡃⢶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⡭⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠙⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣮⣝⡛⢋⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣉⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢷⣀⠀⠉⠹⡟⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠾⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡈⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣷⡆⠀⠀⠀⣽⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⡿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⢠⠿⠟⣋⣿⣿⣿⣿⣿⠏⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⣿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢑⣿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⡗⠚⠒⠒⠒⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠗⠋⠀⠀⠀⢽⣿⣿⡇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣸⣏⢻⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⢿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⡙⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⠀⡀⠀⠀⠀⣤⣶⣯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣗⠀⣴⣿⣿⡄⢀⣄⣀⠐⠂⠀⠀⢐⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠯⠁⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⢀⡀⠀⠀⣽⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁⠀⠀⠀⠀⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢈⣽⣿⠯⣦⢈⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⠁⠀⠀⠀⠀⠀⠐⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠟⢁⣿⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠺⠻⣿⣿⣿⣿⡿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢛⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⢢⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣴⣶⣶⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣶⠆⠉⣸⣿⣿ ⣿⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⣾⣛⢻⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣷⣄⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠐⣾⣿⣿ ⡿⣿⣿⡄⠍⠀⠀⠀⣀⣀⠀⢊⢷⠼⠋⠅⠀⠀⠀⣴⣶⡄⣤⣤⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⣿⣿⣿⣿⣿⣿⣇⠘⢿⣿⣧⡀⠀⢻⣿⣿⡀⠀⠀⣠⣤⣤⠀⠀⠀⠰⢿⣿⣿⣿⣾⣿⣿ ⠛⣿⣿⠇⠅⠀⠀⠀⢻⣿⣷⡀⠀⠀⢾⣿⠄⠀⣰⠿⡇⠠⣿⡟⢀⣴⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣛⣛⠂⠀⠉⠉⠉⠉⠸⣿⣷⣌⢻⣿⣿⣦⠘⣿⣿⣿⢀⣾⣿⡿⠋⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⣀⠀⣺⠀⣰⣿⡿⢡⣿⣿⢁⣾⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡹⣿⣿⣇⣿⣽⣿⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠙⡦⠿⡿⠇⣿⣿⢃⣾⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣥⡀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷⡹⣿⣷⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⢀⡕⣈⠛⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣾⣿⡋⢶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⢛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣭⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠉⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣯⣟⡛⢋⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣍⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢧⣀⠀⠈⠩⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠷⠿⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡘⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣷⡆⠀⠀⠀⣭⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣷⠀⠀⠀⠠⡿⠟⣋⣿⣿⣿⣿⣿⠉⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⠸⣿⣿ ⠀⠀⠘⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⡅⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⣿⡇⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠐⣾⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣼⣿⣷⡇⠀⠀⣿⣿ ⠀⠠⣾⣿⣿⠀⠀⠀⠐⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⡍⢸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠨⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⣠⣶⣶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⡂⢠⣶⣿⣧⠀⣀⡀⠐⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠅⠂⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⢀⣽⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠨⣽⣽⡻⣦⠈⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠏⠀⠀⠀⠀⠀⠘⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠿⢑⣷⣽⣿⣿ ⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠼⢻⣿⣿⣿⣿⡿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⣿⣿⣿⣿ ⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⢡⣬⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡆⠊⣼⣿⣿ ⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠐⣾⢻⢻⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠐⣿⣿⣿ ⡾⣿⣿⠀⠜⠀⠀⠀⣀⣀⠀⠘⣾⠦⠭⠃⠁⠀⠀⣠⣶⡄⣠⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⣇⠙⢿⣿⣧⡀⠀⢛⣿⣿⡄⠀⠀⣠⣤⣤⠀⠀⠀⠨⣿⣿⣿⣿⣼⣿⣿ ⠛⣿⣿⠃⠃⠀⠀⠀⠻⣿⣷⡄⠀⠀⢸⣷⡆⠀⣰⠿⠏⠁⣿⡿⠁⣤⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣛⣛⡛⠒⠀⠉⠛⠛⠋⠻⣿⣷⣌⢻⣿⣿⣦⠈⣿⣿⣿⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣠⠀⢺⠁⢰⣿⣿⢣⣾⣿⠁⣼⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡹⣿⣿⣇⣿⣯⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠁⠙⣤⠞⣿⡏⣿⣿⠇⣼⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣥⡀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡹⣿⣷⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⡀⠀⠉⡙⢂⠛⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣮⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠥⣦⣾⣷⡻⢶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿⣿⠥⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠙⣿⣿⣟⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣯⣝⡻⢇⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣍⣿⡿⣻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢷⣀⠀⠈⠩⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡘⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣷⡆⠀⠀⠀⣥⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣷⠀⠀⠀⠠⡿⠟⣉⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⠀⣿⣿⣿⣾⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⢀⣺⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⡇⠀⠀⠀⢐⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⠻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣽⣿⣿⠇⠀⠀⣿⣿ ⠀⠠⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⣏⢸⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⣿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠘⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⡂⢀⣶⣿⣧⠀⣀⠀⠐⠂⠀⠀⠐⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣽⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠁⠃⠀⠀⠀⣬⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣟⢀⡀⠀⠀⣼⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⣿⣽⠛⣧⠈⣿⣿ ⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠟⠀⠀⠀⠀⠀⠀⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠟⢁⣷⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⡟⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠛⣿⣿⣿⣿ ⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣶⠂⠉⣼⣿⣿ ⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⢿⢛⣻⣿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣇⠐⣿⣿⣿ ⡿⣿⣿⠀⢝⠀⠀⠀⢀⣀⡀⢉⢲⠼⠽⠑⠁⠀⠀⢠⣴⡄⢠⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣦⡀⠈⢻⣿⣧⡀⠀⠀⣠⣤⣄⠀⠀⠀⠸⢿⣿⣿⣷⣼⣿⣿ ⠛⣿⣿⠇⠆⠀⠀⠀⠹⣿⣿⡄⠀⠀⢰⣿⡆⠀⢠⠿⠏⠁⣽⣿⠁⣤⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣛⣛⡛⠒⠀⠉⠛⠛⠛⢿⣿⣦⣜⢿⣿⣿⣄⠈⣿⣿⣷⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⢐⠁⢠⣿⣿⢃⣾⣿⠃⣼⣿⠏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢻⣿⣿⡆⣿⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡇⠀⠙⣧⠻⣿⡏⣾⣿⠏⣼⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣥⡀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⡙⢂⠛⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣮⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠧⣤⣴⣧⡋⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢀⠛⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⣿⣿⠥⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠙⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡛⢟⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣍⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢷⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡌⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣡⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣷⠀⠀⠀⢀⡿⠟⣋⣿⢗⣿⣿⣿⠅⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠇⠸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣏⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⠃⠀⠀⣿⣿ ⠀⠀⡀⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⠻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠀⣬⣿⣷⠇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠐⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣏⢸⣿⠃⠀⠀⠀⠀⠀⢺⣿⡟⠀⠀⠀⢿⣿ ⠠⣾⣿⣿⣿⠀⠀⠀⠀⠹⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⠀⠀⢠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣶⡆⢀⣶⣿⣧⠀⡀⠀⠐⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⢾⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⣸⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⠰⠋⠀⠀⠀⣦⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⢸⣟⡀⠀⠀⠀⢼⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢹⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⡿⣽⡲⣤⢘⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠟⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠸⢠⣷⣙⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠒⣿⣿⣿⣿ ⣷⣽⣿⣿⡗⠀⠀⠀⠀⠀⢆⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠆⠉⣰⣿⣿ ⣯⣿⣿⠟⠅⠀⠀⠀⠀⠀⠀⣾⢹⢹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠐⣿⣿⣿ ⣿⣿⣿⠀⢪⠀⠀⠀⢀⣀⡠⢋⣶⠒⠭⠀⠁⠀⠀⢠⣴⡄⢠⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⡗⠙⣿⣿⣦⡀⠈⢻⣿⣧⡀⠀⠀⣠⣤⣄⠀⠀⠀⠈⣿⣿⣿⣷⣾⣿⣿ ⠙⣿⡿⠞⠈⠀⠀⠀⠙⣿⣿⣄⠀⠀⢰⣿⡆⠀⢠⠿⠏⠁⣿⣿⠁⣤⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣛⣛⡛⠒⠀⠉⠛⠛⠋⢿⣿⣦⣜⢿⣿⣿⣆⠨⣿⣿⣧⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠐⠁⢠⣿⣿⢇⣾⣿⠇⣼⣿⠏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢻⣿⣿⡆⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠙⣧⠚⣿⡏⣾⣿⠏⣼⣿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣥⡀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡙⢂⠻⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⣶⣮⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠧⣤⣴⣧⡋⠴⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢀⢛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⡯⠥⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡛⠓⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿ ⢧⣀⠀⠉⠻⡏⠿⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⢂⠀⠀⠃⠀⡈⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣷⡆⠀⠀⠀⣣⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣷⠀⠀⠀⠰⠿⠟⣫⣿⣽⣿⣿⣿⠇⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⠸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⡉⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⡿⣿⡿⡏⠀⠀⣿⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⢷⡾⡟⠗⠋⠀⠀⠀⢻⣿⣷⠇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⢿⠃⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⢸⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⡂⢀⣶⣿⣧⠀⣀⠀⠐⠂⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⢸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡺⠽⠃⠀⠀⠀⣬⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⠀⢼⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡷⣤⠘⣿⣿ ⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠟⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢡⣧⣝⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠂⠉⣴⣿⣿ ⣿⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⣿⠫⢹⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠐⣿⣿⣿ ⣿⣿⣿⡂⠿⠀⠀⠀⢀⣀⡠⠉⢳⠶⠩⠄⠁⠀⠀⢠⣴⣄⢠⣤⡀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠿⣿⣿⣿⣿⣿⣿⡷⠙⣿⣿⣦⡀⠈⢻⣿⣧⠀⠀⠀⣠⣤⣄⠀⠀⠀⠈⣿⣿⣿⣷⣾⣿⣿ ⠛⣿⡿⠇⠈⠀⠀⠀⠘⣿⣿⣆⠀⠀⢰⣿⡆⠀⢠⡻⢿⠁⣼⣿⠃⣠⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣟⣛⣛⠒⠀⠉⠛⠛⠋⢿⣿⣦⣜⢿⣿⣿⣆⠸⣿⣿⣷⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠰⡇⢠⣿⣿⠇⣾⣾⠇⣰⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢹⣿⣿⡆⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠘⣣⠚⣿⡟⣸⣿⠏⣴⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠂⠛⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠇⣤⣴⣧⡇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡹⣿⣯⠥⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢻⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡻⠓⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠀⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢷⣀⠀⠉⠹⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡈⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣷⡆⠀⠀⠀⣥⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣷⠀⠀⠀⢀⡿⠟⣫⣿⣿⣿⣿⣿⠁⠀⣼⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣷⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⡃⠀⠀⣿⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠠⢿⣿⣿⣿⣏⠉⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠚⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⠟⠗⠋⠀⠀⠁⣽⣿⣷⡇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢴⡋⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠘⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡀⠀⠀⠀⣠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡂⢀⣶⣿⣧⠀⡀⠀⠐⠀⠀⠀⠀⣿⣿⣯⠂⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣾⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠁⠉⠀⠀⠀⣜⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⠀⠀⢼⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⡗⣦⡘⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠟⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠸⠀⣧⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠚⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠂⠉⢴⣿⣿ ⣮⣿⣿⠛⠇⠀⠀⠀⠀⠀⠀⣾⠝⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠐⣿⣿⣿ ⠾⣿⣿⠀⠻⠀⠀⠀⢀⣀⣀⢹⡅⠌⠍⠂⠁⠀⠀⢠⣤⣤⢀⣤⡀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⠿⣿⣿⣿⣿⣿⣿⡷⠙⣿⣿⣦⡀⠀⢻⣿⣧⡀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿ ⠙⣿⡿⠃⠁⠀⠀⠀⠘⢿⣿⣆⠀⠀⠰⣿⣦⠀⢀⡾⢿⠁⣼⣿⠇⣠⣤⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣟⣛⣛⠓⠀⠉⠛⠛⠋⢿⣿⣷⣜⢿⣿⣿⣆⠈⣿⣿⣧⢠⣾⣿⡿⠃⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⠀⠠⡇⢀⣾⣿⡏⣼⣾⠏⣰⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣧⢹⣿⣿⡆⣿⣽⣽⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢘⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠙⢣⠘⣿⡿⣸⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣧⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣻⣿⣷⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⡉⠂⠙⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠿⣫⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣤⣴⣧⡏⠄⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣯⠥⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢿⣿⣟⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣮⣝⡛⠟⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿ ⢷⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⠿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡈⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣭⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⢰⡿⠟⣉⣽⢳⣿⣿⣿⠁⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⠸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⢾⣿⣿⣿⣿⣍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⡃⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠠⣾⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠚⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠈⣸⣿⣷⡏⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠘⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣍⢙⣿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿ ⠠⣾⣿⣿⣿⠀⠀⠀⠀⠸⢿⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⣠⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⡆⢠⣾⣿⣧⠀⣀⠀⠐⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢾⣿ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠈⠀⠀⢰⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡻⠑⠉⠀⠀⠀⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣟⣀⠀⠀⠀⣼⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢹⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⡑⣤⠈⣿⣿ ⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠛⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡘⠀⣷⣟⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠟⠃⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠛⣿⣿⣿⣿ ⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣤⣬⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠆⠁⢴⣿⣿ ⣯⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⣾⠟⢹⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠐⢿⣿⣿ ⣾⣿⣿⠀⢫⠀⠀⠀⢀⣤⣄⠚⡤⠶⠛⠂⠁⠀⠀⢀⣴⣦⢀⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⣦⡀⠀⢹⣿⣧⡀⠀⢀⣠⣶⣆⠀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿ ⠛⢿⡿⠂⡈⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣿⣷⠀⢀⡾⢿⠁⢼⣿⠇⣠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣛⣛⠓⠀⠉⠉⠙⠉⠻⣿⣷⣌⢿⣿⣿⣆⠈⣿⣿⣷⢠⣾⣿⡿⠁⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⡇⢀⣾⣿⡏⣼⣾⠏⣰⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠹⣿⣿⣆⣿⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠙⢣⠘⣽⡿⢸⣿⡟⣰⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⡹⣿⣷⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠂⠛⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢷⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⣤⣴⣧⡏⠤⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⠋⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⠥⢴⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⢻⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣮⣽⡛⠟⡜⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿ ⢧⣀⠀⠈⠙⡛⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡄⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢡⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢻⣿⠀⠀⠀⠠⠿⠟⣉⣿⣯⣽⣿⣿⠇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⡍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⡿⡃⠀⠀⣻⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣅⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡟⠗⠋⠀⠀⠀⣴⣿⣷⠇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢰⡍⡸⢿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠘⢛⣫⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣀⠀⠀⠀⣴⣶⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⡂⢠⣾⣿⣧⠀⣀⡀⠐⠀⠀⠀⠀⣼⣷⣷⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢼⣿ ⠀⢸⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⠨⠁⠀⠀⠀⢠⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⢴⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⠰⣤⠈⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠐⢽⡷⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠛⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣤⣝⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠟⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠟⣿⣿⣿⣿ ⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠁⢘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣴⣬⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⠂⠁⢰⣿⣿ ⣧⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⢞⠉⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡃⠐⣿⣿⣿ ⣿⣿⣿⠀⢫⠀⠀⠀⢀⣤⣄⢊⠤⠔⠜⠀⠀⠀⠀⢀⣴⣦⢀⣤⡄⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣦⡀⠈⢻⣿⣧⡀⠀⢀⣠⣶⣆⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿ ⠛⢿⡿⠃⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣿⣷⠀⢀⡾⢿⠁⢼⣿⠇⣠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣛⣛⠓⠀⠈⠉⠙⠋⠻⣿⣷⣌⢿⣿⣿⣆⠨⣿⣿⣷⢠⣾⣿⡿⠁⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠄⠀⡇⢀⣾⣿⡏⣼⣿⡏⣰⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠹⣿⣿⣇⣿⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠀⠘⢣⠘⢿⡿⢸⣿⡟⣰⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣹⣿⣷⡻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠂⠉⠂⠛⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣷⡻⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠇⣤⣴⣷⡏⠤⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⠥⢴⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⣻⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣮⣽⡛⠟⡜⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣉⣿⡿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡌⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠐⢫⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠠⠿⠛⣩⣿⣿⣿⣿⣿⠇⠀⣼⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠚⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠁⣾⣿⣷⠇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣿⠁⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⣿⣿ ⠈⣾⣿⣿⣿⠀⠀⠀⠀⢼⣽⣿⣿⣿⣦⠀⠀⠃⠀⠀⠀⡀⢀⠠⢄⣀⡀⠀⠀⣴⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣅⣰⣿⣿⣿⡄⢀⣀⠀⠐⠀⠀⠀⢒⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣷⡀⠀⠀⠈⠈⠀⠀⠀⠀⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⠔⠃⠀⠀⠀⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣾⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠀⠀⠀⠀⠀⠺⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡼⣽⢤⣦⢘⣿⣿ ⣼⣿⣿⣿⡯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⢻⡍⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡘⢀⣷⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⡟⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⣿⣿⣿⣿ ⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣄⣤⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⠄⠁⣸⣿⣿ ⣿⣿⣿⠟⡯⠀⠀⠀⠀⠀⠀⣾⢭⢹⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣷⣄⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠐⣽⣿⣿ ⣾⣿⣿⡆⣿⠀⠀⠀⢀⣤⣄⠛⠧⠞⠛⠂⠉⠀⠀⠀⣤⣤⠀⣤⣄⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⣿⣿⣿⣿⣿⣟⣤⣄⠙⣿⣿⣦⡀⠈⣿⣿⣧⠀⠀⣀⣴⣶⡆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⠙⣿⡿⠃⠈⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⣾⣷⠀⠀⡼⠿⠉⢰⣿⡏⢠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣍⣉⠀⠈⠉⠉⠁⠀⠈⠻⣿⣷⣜⢿⣿⣿⣆⢸⣿⢿⡧⣰⣿⣿⠏⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿ ⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠄⠀⡎⠀⣾⣿⡟⣰⣷⡟⢠⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣧⢻⣿⣿⣸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠈⠈⢣⡜⢻⣿⢱⣿⡿⣠⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢻⣿⣿⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢉⠃⠙⠿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣫⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠌⣤⣴⣷⡾⠅⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⣿⣿⠭⣴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠙⢿⣿⣟⠛⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣮⣿⡛⢟⠜⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣠⣽⣿⣻⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢧⣀⠀⠉⠙⡋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⣿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠶⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡀⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢣⣶⣿⣤⣤⣧⣼⣿⣬⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⡦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠸⠿⠛⣉⣿⡿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠃⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣺⣿⣿⣿⣿⡍⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⡿⡃⠀⠀⣿⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣏⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠁⣼⣿⣷⠇⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠛⠛⢛⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⢺⣿⠃⠀⠀⠀⠀⠁⢸⣿⡟⠀⠀⠀⢻⣿ ⠠⣶⣿⣿⣿⠀⠀⠀⠀⢘⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢀⡠⠀⢀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣷⠄⢀⣀⡀⠐⠀⠀⠀⠘⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣼⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢱⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠺⡿⠑⠃⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣴⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠆⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⡾⣦⢘⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⢻⡇⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢘⣧⣝⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⣿⣿⣿⣿ ⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠢⢸⣿⣿⣿⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠄⠀⠀⠰⣿⣿⣷⡄⠀⠀⣤⣶⣆⠀⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⣰⣿⣿ ⣷⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⢸⠻⢹⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣀⡈⢻⣿⣿⣆⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠰⣿⣿⣃⠐⣿⣿⣿ ⡿⣿⣿⠦⡏⠀⢀⣀⣀⠀⣴⠜⠲⠌⠋⠉⠁⠀⣰⣶⡆⣰⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣝⣛⠿⠿⣿⣿⣿⣿⣿⠟⠀⠀⢾⣿⣿⣬⣿⣿⣿⣦⠀⣻⣿⣧⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿ ⠙⢿⡿⠓⠂⠀⠈⢿⣿⣿⡀⠀⠀⠸⣿⡇⠀⣠⡻⡏⢀⣿⡿⢡⣶⣦⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣢⣾⣿⣿⠋⠀⠈⠀⢹⣿⣿⣿⣿ ⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣿⣄⣀⠀⠐⠁⢰⣿⣿⢣⣿⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡟⠁⠙⡶⠻⠿⠟⢿⣿⠫⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈⡁⠉⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠐⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠤⠼⣷⡇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⣒⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣄⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠐⣿⣿⣏⡉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⣿⣿⣿⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣭⣛⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣐⣲⣿⣫⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠀⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿ ⢳⣀⠀⠈⠙⡋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢯⣢⠀⠀⠃⠀⡈⢿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢡⣼⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠨⠿⠟⣉⣿⣻⣿⣿⣿⠇⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣽⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⡌⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡏⠀⠀⣹⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣍⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⡷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⡶⠶⠛⠒⠓⠓⠚⠲⠶⢿⣷⣾⡟⠗⠋⠀⠀⠀⣾⣿⣷⠇⠀⠀⣿⣿ ⠀⢠⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠹⢹⣽⣿⣿⣆⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⢠⣾⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣀⣾⣿⣿⡆⠀⣀⡀⠐⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢹⣿ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠻⠀⠁⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣼⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠀⠀⠀⠀⠻⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⡦⣤⠈⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣙⡯⠁⠀⠀⠀⠀⠀⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢠⣷⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠈⣿⣿⣿⣿ ⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⢘⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠸⣿⣿⡆⠀⢠⣾⣷⠀⠁⢴⣿⣿ ⣿⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣾⠟⢹⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⣶⣿⣷⣌⣿⣿⣿⣆⠀⢹⣿⣧⠀⢸⣿⠿⡃⠐⣿⣿⣿ ⣿⣿⣿⣤⣻⠀⠀⠀⠀⠀⠰⠌⠵⠓⢺⣾⡷⣼⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⡛⠿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡆⣠⣿⣿⣿⣿⣼⣿⣿ ⠙⣿⡿⢿⣿⣿⣦⠀⠀⠘⣿⣷⠀⢀⣾⣃⢀⣾⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⠟⢹⣿⣿⣿⣿ ⠀⠈⠁⠀⠉⠻⣿⣷⣤⣀⠀⠁⠀⣾⣿⣏⣾⣿⣏⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠉⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠈⠹⠶⠛⠿⠝⠿⣿⠺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣶⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠈⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠐⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠒⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⣐⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢲⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⠿⢤⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢠⣿⣧⣄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⣤⣽⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣥⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿ ⢳⣀⠀⠉⠹⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠈⢧⣣⠀⠀⠁⠀⡈⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢳⣾⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠐⠿⠛⣉⣿⣟⣿⣿⣿⠋⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣾⠅⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡍⠁⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣼⣿⣿⡿⡃⠀⠀⣹⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣅⠁⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠚⠒⠲⢿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠋⠀⠀⠁⣼⣿⣷⠇⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠚⠻⣿⣿⣿⣇⠀⠀⠂⠀⠀⠀⠀⢀⢀⣄⣀⣠⠀⠀⢠⣾⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣀⣼⣿⣿⣤⢀⣀⣀⠐⠀⠀⠀⠈⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢻⠰⠃⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣺⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⣽⡳⣦⠘⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡙⡿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢀⣧⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣀⡀⠛⣿⣿⣿⣿ ⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⢻⣿⣧⡀⠀⢸⣿⣿⡆⠀⢴⣿⣿ ⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⢾⢻⢻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠈⢿⣿⣷⡀⢘⣿⣿⣦⡐⣿⡿⣿ ⣾⣿⣿⣔⣗⠀⠀⠀⠀⠀⢰⠌⣒⣘⠛⣩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣛⡛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⣷⡌⣿⣿⣷⢀⣿⣿⣿⣿⣾⣿⣿ ⠙⣿⣿⣿⡻⠀⠀⢀⣀⡀⠀⠀⣿⠟⠀⣿⡿⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿ ⠀⠙⠿⣿⣿⣦⡀⠘⠟⡇⠀⣾⣽⡇⣴⣿⡇⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⣿⣿ ⠀⠀⠀⠀⠙⢿⣿⠀⠨⠶⡆⠿⣿⢳⣿⣿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠉⠀⠉⠛⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⠀⠀⠐⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⣴⣧⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⢿⡀⢀⣲⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⣿⣿⣽⣾⡿⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣞⣭⣤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠼⣶⣿⢟⣿⣶⣤⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣽⣟⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢧⣀⠀⠈⠩⡟⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣣⠀⠀⠁⠀⡀⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣡⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠠⠿⠛⣉⣻⢭⣽⣿⣿⠊⠀⣸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠇⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⡉⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⡿⡃⠀⠀⣽⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣄⠁⠀⠀⠀⠈⠓⠚⠚⠶⣿⣷⣾⣷⠚⠒⠒⠲⢿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⢷⣾⠟⠗⠋⠀⠀⠁⢼⣿⣷⠇⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠐⢾⣿⣯⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠛⠛⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⡋⠸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢻⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠼⠻⣽⣿⣿⣆⠀⠀⠃⠀⠀⠀⠀⣀⣀⡤⢀⠀⠀⠀⢠⣾⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣦⢀⣀⡀⠐⠁⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣺⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢰⣾⣯⣿⣿⣿⣷⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⠙⠃⠀⠀⠀⣼⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣴⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠹⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡶⣤⠈⣿⣿ ⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡙⡯⠁⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣧⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠀⠀⠀⠀⠘⠉⣾⣿⣿⣿ ⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣿⣿⡄⠀⠀⣾⣿⣧⠀⢰⣿⣿ ⣧⣿⣿⠛⡧⠀⠀⠀⠀⠀⠀⣞⠛⢻⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠸⣿⣿⣆⠀⣿⣿⣿⢈⢿⣿⣿ ⡞⣿⣿⣴⣇⠀⠀⠀⠀⠀⠠⡍⠒⣐⠛⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣙⣛⠻⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣆⢹⣿⣿⡆⢻⣿⣿⣿⣽⣿⣿ ⠙⣫⣿⣯⣇⠀⠀⠀⣀⡀⠀⠀⢸⡿⠃⢸⣿⠇⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣿⣿⡏⣿⣿⣧⣿⣿⣋⣿⣿⣿⣿ ⠀⠉⠻⣿⣿⣦⣀⠀⠿⢿⠀⢠⣬⣭⢠⣾⡿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠋⠉⣾⣿ ⠀⠀⠀⠀⠙⢿⣿⡇⠀⠽⣦⠹⣿⡇⣾⣿⠇⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠁⠉⠛⠂⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣾⠄⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⢿⠀⠀⣒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣾⣿⣴⣼⣿⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣸⣍⣁⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣷⣾⡿⣻⣷⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣭⣟⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⢀⢴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿ ⢳⣀⠀⠈⠉⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⠿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⣿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠈⢧⣣⠀⠀⠁⢀⠌⢻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡇⠀⠀⠀⣡⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠀⠿⠟⣉⣿⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⡿⡅⠀⠀⣹⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⠀⣽⣿⣿⣿⣍⠀⠀⠀⠀⠀⠓⠚⠚⠶⢿⣷⣾⢷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⣸⣿⣿⠇⠀⠀⣿⣿ ⠀⠐⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⣸⣟⣸⢿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢿⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⠩⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⣾⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⣿⣿⣧⠀⣀⢀⠈⠂⠀⠀⠀⣺⣿⣿⡍⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⣾⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠐⠁⠀⠀⠀⣤⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣽⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡼⢼⠯⣤⠀⣿⣿ ⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣫⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢀⣯⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⣾⣿⡆⠁⣰⣿⣿ ⣿⣿⣿⠟⡆⠀⠀⠀⠀⠀⠀⣸⢻⢹⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣆⠀⢻⣿⣷⡀⠀⣿⣿⣷⠀⢿⣿⣿ ⡾⢿⣿⣂⢷⠀⠀⠀⠀⠀⢦⡮⠎⠌⢛⡁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣛⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿⣷⡄⢿⣿⣿⡄⣿⣿⣿⣿⣼⣿⣿ ⠈⠿⢿⣷⣶⣄⠀⠀⠀⢀⣀⠀⠀⠠⣿⠟⢀⣿⡿⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⣭⣍⡉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⣿⡼⣿⣿⣇⣿⣿⣋⣿⣿⣿⣿ ⠀⠀⠁⠙⢿⣿⣷⣄⠀⠹⢿⠇⢀⣮⣭⠃⣶⣿⠃⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠉⠙⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⡿⠛⠉⣿⣿ ⠀⠀⠀⠀⠀⠈⠻⣿⣟⠀⢨⢦⠸⣿⡿⢰⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣍⣽⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠁⠈⠛⠃⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⠀⢀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠺⠄⠁⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣼⣷⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣔⣏⣉⣉⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⣿⡿⣻⣷⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣮⣭⡋⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣾⣿⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣿ ⢳⣀⠀⠈⠫⠏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠈⢧⣡⠀⠀⠁⢀⡌⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣇⠀⠀⠈⣥⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠨⠿⠏⣉⣿⣯⣿⣿⣿⠀⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡅⠈⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⣸⣿⣿⡿⡃⠀⠀⣹⣿ ⠀⠀⢀⣿⣇⠀⠀⠀⠠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠒⢿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⡶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠚⠀⠀⠀⢸⣿⣿⠇⠀⠀⣿⣿ ⠀⢐⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢐⣟⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢿⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠄⢀⣀⡀⠀⠀⠀⣴⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣄⣠⣿⣿⣧⠀⣀⢀⠈⠀⠀⠀⠀⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣾⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⠀⠃⠀⠀⠀⢴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⣽⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⡼⢾⢣⣤⢀⣿⣿ ⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⢻⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⢀⣧⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠂⢠⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⣶⣷⡶⠂⠀⢰⣿⣿ ⣿⣿⣿⠽⣇⠀⠀⠀⠀⠀⠀⢸⠻⢻⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣄⠀⢿⣿⣧⠀⠀⣿⣿⣿⡀⠀⣿⣿⣿ ⡿⣿⣿⣶⣿⠀⠀⠀⠀⠀⢶⡪⠄⠶⠛⢁⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣍⣛⠻⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡈⢿⣿⣷⡀⣿⣿⣿⣿⣽⣾⣿⣿ ⠙⢻⡿⣻⣷⣦⡀⠀⠀⠀⣀⣀⠀⠀⢸⣿⠟⢰⣿⡟⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣭⣍⡉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡻⣿⣿⡸⣿⣿⣇⣿⣿⢏⣿⣿⣿⣿⣿ ⠀⠁⠀⠈⠛⢿⣿⣦⣀⠀⠻⢻⠀⢠⣯⣽⢀⣾⣿⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠉⠙⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣿⣿⣷⢿⣿⣿⣿⣿⣿⠟⠉⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠰⣤⡸⣿⡏⣾⣿⠇⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠁⠙⠛⠊⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⢀⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢠⣦⡄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠣⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣦⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⣙⣉⣉⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣽⣯⣿⢟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣭⣛⢋⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣿⣷⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿ ⢳⣀⠀⠈⠹⡍⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠈⢧⡣⠀⠀⠀⠀⠌⠽⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡇⠀⠀⠀⣡⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠈⠿⠛⣉⣿⡿⣿⣿⣿⠀⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⣺⣿⣿⣿⣿⡅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡅⠀⠀⣹⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣅⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⢷⠚⠒⠒⠒⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠓⠛⠀⠀⠀⢸⣿⣿⠇⠀⠀⣻⣿ ⠀⢐⣾⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢰⣟⣸⢿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿ ⠀⣶⣿⣿⣿⠀⠀⠀⠀⠈⠙⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⣾⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣄⣰⣿⣿⣧⠀⣀⣀⠀⠀⠀⠀⠰⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⢾⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⠂⠁⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣴⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼⣴⠠⣦⠀⣿⣿ ⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⣻⠉⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⢠⣧⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⢰⣶⣦⣶⠂⠀⢰⣿⣿ ⣾⣿⣿⡝⡇⠀⠀⠀⠀⠀⠀⢸⠛⢹⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⠀⢹⣿⣷⡄⠀⢸⣿⣿⣏⡀⠀⣿⣿⣿ ⡾⣿⣿⣶⡵⠀⠀⠀⠀⠀⢄⡎⠸⠞⠒⢁⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⡛⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⢻⣿⣿⣄⢸⣿⣿⣿⣿⣶⣿⣿⣿ ⠉⠻⠿⣻⣷⣦⡄⠀⠀⠀⣀⣀⠀⠀⢰⣿⠛⢰⣿⡟⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣭⣍⡉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣟⢿⣿⡇⣿⣿⣿⣸⣿⠟⣹⣿⣿⢿⣿⣿ ⠀⠀⠀⠀⠛⢿⣿⣦⣀⠀⠻⢻⠀⢠⣧⣽⢀⣾⣿⠁⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠉⠙⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⡾⣿⣿⣿⣿⣻⠿⠋⠁⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠸⣤⡸⣿⡏⣼⣿⠏⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠁⠙⠛⠂⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⣦⡄⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⠧⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣧⣆⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⣝⣉⣉⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣿⣽⣿⢻⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣭⣛⠓⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⣿⣿⣵⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿ ⢳⣀⠀⠈⠙⡋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠈⢧⡡⠀⠀⠁⠀⠌⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⣇⠀⠀⠀⢠⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠈⠿⠛⣉⣿⣿⣿⣿⣿⠁⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡟⡅⠀⠀⣹⣿ ⠀⠀⢀⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣅⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⢷⠚⠒⠒⠲⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⢶⣿⣷⣾⡿⠓⠊⠀⠀⠀⣸⣿⣿⠇⠀⠀⣻⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢠⣟⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⠀⢄⣀⡀⠀⠀⢠⣾⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣾⣿⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⣺⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢾⠀⠀⠀⠀⠀⣰⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣺⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⠁⣤⢀⣿⣿ ⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠙⡏⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⢠⣿⣽⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⢠⣶⣦⣴⣶⠀⠀⢰⣿⣿ ⣿⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⣼⡏⠻⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⢹⣿⣷⡄⠀⢸⣿⣿⣟⣟⡅⢀⣿⣿⣿ ⡾⣿⣿⣶⡭⠀⠀⠀⠀⠀⢴⡖⠠⠖⠛⢁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣟⡛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⢻⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿ ⠙⠿⡿⣳⣶⣤⡀⠀⠀⠀⣀⡀⠀⠀⢸⡿⠇⣸⣿⡇⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⡁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⢿⣿⣧⢿⣿⣿⢠⣿⣿⢻⣿⣿⠿⣿⣿⣿ ⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠻⡻⠀⢰⣯⣽⢠⣮⡿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠟⠉⠙⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠟⠁⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⡤⡄⣿⣿⠇⣾⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠀⠙⠛⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣦⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠧⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣤⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢘⣉⣉⣉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⣝⣿⡿⣯⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣽⡛⢋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣭⣿⣯⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿ ⢳⣀⠀⠈⠙⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣣⠀⠀⠀⠀⠈⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣁⣻⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣾⣿⣿⣽⠁⢸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⢾⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡅⠀⠀⣹⣿ ⠀⠀⢀⣿⣇⠀⠀⠀⠀⣼⣿⣿⣿⡁⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⣷⠚⠒⠒⠲⢻⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⢟⢷⣾⡿⠗⠛⠀⠀⠀⣠⣿⣿⠇⠀⠀⣻⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⢿⠃⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⢿⣿ ⠀⣬⣿⣿⣿⠀⠀⠀⠀⠈⠹⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⢀⡠⠀⠀⢠⣾⣿⣗⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣀⣼⣿⣿⣤⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⣺⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠸⠀⠀⠀⠀⠀⣀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣼⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⣄⠀⣿⣿ ⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣧⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⢀⣤⣄⠀⣺⣷⠂⠀⢰⣿⣿ ⣿⣿⣿⠟⡏⠀⠀⠀⠀⠀⠀⢰⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠹⣿⣷⡄⠀⠘⣿⣿⡆⢻⣿⡅⠀⣿⣿⣿ ⠾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠠⡄⠀⠾⠈⣐⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣟⡻⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⢹⣿⣿⣄⠀⣿⣿⣿⢿⣻⣿⣷⣭⣿⣿ ⠙⣻⡟⣻⣷⣦⡀⠀⠀⢀⣀⡀⠀⠀⣼⡿⠃⣸⣿⠇⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⡁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣧⢻⣿⣿⡄⣼⣿⡟⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠟⡟⠀⣰⣭⡕⢰⣿⡏⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣎⣿⣿⣧⣿⣿⣾⡿⠛⠁⠁⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁⠀⡦⡄⣿⣿⠣⣿⣿⢡⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠉⠈⠛⠓⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠐⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠆⠈⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣄⡀⢀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣛⣋⣉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣝⣻⣷⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣮⣝⡛⢋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣛⣿⣋⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣑⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿ ⢳⣀⠀⠈⠙⠋⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣣⠀⠀⠀⢀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣉⣻⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣾⣿⣿⣽⠁⠸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⢾⣿⣿⣿⣿⡀⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡁⠀⠀⣹⣿ ⠀⠀⢀⣿⣇⠀⠀⠀⠀⢾⣿⣿⣿⣅⠀⠀⠀⠀⠀⠓⠚⠚⠲⢿⣷⣾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣿⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⢿⢷⣾⡿⠓⠛⠀⠀⠀⢸⣿⣿⠇⠀⠀⣻⣿ ⠀⠰⣾⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⢿⠃⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⢿⣿ ⠀⣬⣿⣿⣿⠀⠀⠀⠀⠈⢹⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⠠⠀⠀⢠⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻⣯⣀⣼⣿⣿⣤⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠉⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⢺⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢀⣾⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠹⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢨⣏⣀⠀⠀⠀⣰⣿ ⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡘⢹⠁⣤⠀⣿⣿ ⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠙⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣧⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⢀⣤⣄⠀⣼⣶⠂⠀⢰⣿⣿ ⣯⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⢰⠉⢙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣿⣷⡀⠀⠸⣿⣿⣌⣿⣞⡁⠀⢾⣿⣿ ⡾⣿⣿⣶⣢⠀⠀⠀⠀⠀⠠⡅⠚⠸⠚⣃⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⡻⠿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⢻⣿⣿⡄⠀⣿⣿⣷⠽⣻⣽⣷⣬⣿⣿ ⠙⡿⡟⣻⣶⣦⡀⠀⠀⠀⣀⣀⠀⠀⣸⡿⠃⢸⣿⡇⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣦⢻⣿⣿⡀⣼⣿⡿⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠙⢿⣿⣦⡀⠀⠛⠻⠀⢰⣯⡽⢰⣮⡿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣿⣿⣞⣿⣿⣧⣿⣷⣾⡿⠛⠁⠁⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠤⡄⣿⣿⠇⣿⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠉⠀⠙⠛⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠘⢿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⢦⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡀⣠⣴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣋⣈⣙⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣽⣻⣷⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣬⣽⡛⢛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣈⣻⣿⣋⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿ ⢣⣀⠀⠈⠩⡏⠻⢿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣣⠀⠀⠀⢀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣉⣻⣿⣿⣿⣿⠀⠀⢰⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢉⡇⠀⢀⣾⣿⣿⣼⠁⠸⣿⣿ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⢶⣿⣿⣿⣿⡅⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡃⠀⠀⣹⣿ ⠀⠀⢀⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠓⠚⠚⠒⠿⣷⡾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⢿⢷⣾⡟⠗⠛⠀⠀⠀⣠⣿⣿⠇⠀⠀⣻⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⢿⠁⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⢿⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⠹⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢀⠠⠀⠀⢠⣾⣿⣗⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣧⣀⣼⣿⣿⣥⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠂⠀⠀⠀⢺⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠿⠀⠁⠀⠀⠀⢀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⢐⣏⣀⠀⠀⠀⣴⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⠠⣄⠀⣿⣿ ⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⡯⠁⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⣥⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠋⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⢀⣤⣄⠀⣴⣷⠂⠀⢰⣿⣿ ⣿⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⢰⠛⢙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣿⣷⡀⠀⠸⣿⣿⡌⣿⣿⡃⠀⣾⣿⣿ ⡾⣿⣿⣿⣥⠀⠀⠀⠀⠀⠠⡄⠀⠰⠋⣁⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⢻⣿⣿⡄⠀⣿⣿⣷⠾⣻⣿⣷⣬⣿⣿ ⠙⢟⡿⣻⣷⣦⣄⠀⠀⠀⣠⣀⠀⠀⢸⡿⠛⢸⣿⡏⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣦⢻⣿⣿⡀⣽⣿⡿⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠙⢿⣿⣧⣄⠀⠛⢻⠀⢠⣯⣭⢠⣮⣿⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⣿⣿⣎⣿⣿⣧⣿⣷⣾⡿⠛⠁⠁⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠴⡄⠿⣿⡇⣾⣿⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠀⠙⠛⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⣮⠈⠀⢠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⡀⣠⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣇⣊⣉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢝⣻⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣝⡛⠛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣈⣻⣿⣋⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠁⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿ ⢳⣀⠀⠈⠛⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⠿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣢⠀⠀⠁⠀⠈⠻⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣁⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠀⠿⠛⣉⣿⣏⣽⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣉⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠁⠸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣁⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⠸⡯⣿⡿⡇⠀⠀⣹⣿ ⠀⠀⢀⣿⣇⠀⠀⠀⠀⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠒⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠗⠋⠀⠀⠀⢹⣿⣿⠇⠀⠀⣻⣿ ⠀⠰⣾⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣝⡼⢻⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢿⣿ ⠀⣾⣿⣿⣿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⡠⠀⠀⢀⣾⣿⣟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣀⣼⣿⣿⣧⠀⣀⠀⠀⠀⠀⠀⠈⣾⣿⣿⠍⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⣾⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠽⠀⠂⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⣽⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠸⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠜⢽⠡⣤⢀⣿⣿ ⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⢠⣷⣜⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⢀⣤⡄⠀⣴⣶⠂⠀⢸⣿⣿ ⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⣿⠍⡻⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢀⣤⣄⠈⢻⣿⣷⡀⠀⢸⣿⣿⠘⢿⣿⡇⠈⣿⣿⣿ ⡿⣿⣿⣦⡗⠀⠀⠀⠀⠀⠠⣥⠓⠼⠉⢑⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⢻⣿⣷⡄⠀⣿⣿⣧⢿⣿⣿⣷⣽⣿⣿ ⠉⠻⡟⡻⣶⣶⣄⠀⠀⠀⣀⣀⠀⠀⢰⣿⠛⢰⣿⡟⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⢿⣿⣿⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠁⠀⠙⠿⣿⣷⣄⠀⠻⢻⠀⢠⣯⣥⢀⣮⣿⠁⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⣿⣿⣾⣿⣿⣧⣿⣷⣾⡿⠋⠀⠁⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⡇⠀⠸⣤⡾⣿⡏⣾⣿⠏⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠈⠁⠙⠻⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣧⡄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢦⠁⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⠀⢠⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢐⣇⣛⡉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣝⣻⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣬⣽⡛⠛⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⣿⣿ ⢳⣀⠀⠈⠹⡏⠛⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣢⠀⠀⠀⠀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢀⣴⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣽⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠈⠿⠛⣉⣿⣿⣿⣿⣿⠀⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢀⣿⣿⣿⣿⠁⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⡀⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⣿⣿⡿⡇⠀⠀⣽⣿ ⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣁⠀⠀⠀⠀⠈⠓⠚⠚⠒⢿⣷⣾⣷⠚⠒⠒⠲⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⢷⣾⡿⠗⠛⠀⠀⠀⣸⣿⣿⠇⠀⠀⣿⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢀⣟⣸⢿⠃⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⢿⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⢹⣽⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠠⠀⠀⢀⣾⣿⡗⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣀⣼⣿⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⣺⣿ ⠀⣹⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠿⠀⠁⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⣸⣿ ⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⣤⠀⣿⣿ ⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣧⣜⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠀⠀⢀⣤⡄⠀⣴⣶⠀⠀⢰⣿⣿ ⣾⣿⣿⠋⡇⠀⠀⠀⠀⠀⠀⢰⢋⠛⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣀⠈⢻⣿⣧⡀⠀⢸⣿⣿⠀⣿⣿⡆⠀⣾⣿⣿ ⡾⣿⣿⣮⣇⠀⠀⠀⠀⠀⠠⡄⠒⠢⠋⢐⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡈⢿⣿⣷⡀⠀⣿⣿⣇⢯⣯⣿⣧⣼⣿⣿ ⠙⣟⡟⡫⣷⣶⣄⠀⠀⠀⣁⣀⠀⠀⢠⣿⠟⢠⣿⡿⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣝⣙⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣎⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠀⠀⠙⠿⣿⣷⣄⠀⠸⢛⠃⢀⣦⣭⠀⣮⣿⠁⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠋⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣶⣾⠿⠋⠀⠁⠉⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠿⣿⡇⠀⠸⣤⠸⣿⡏⣼⣿⡏⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣷⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠋⠀⠘⠁⠙⠻⠌⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⡄⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⢶⠁⠀⢤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣤⡀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢘⣛⡛⠉⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣙⣿⣿⢿⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣬⣝⡛⠓⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣐⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣏⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿ ⢳⣀⠀⠈⠩⡍⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⢿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠾⣿⣿ ⠘⢧⣢⠀⠀⠁⠀⠀⠹⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⢠⣴⣿⣤⣤⣧⣼⣿⣬⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠀⠟⠛⣉⣿⣯⣿⣿⣿⠈⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢉⡇⠀⢀⣽⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠴⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢸⢻⣿⡿⠇⠀⠀⣹⣿ ⠀⠀⢀⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣅⠀⠀⠀⠀⠈⠓⠚⠚⠲⢿⣷⣾⣷⠚⠒⠒⠒⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡟⠗⠚⠀⠀⠀⢸⣿⣿⠇⠀⠀⣻⣿ ⠀⢰⣾⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡞⣸⢧⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⢹⣼⣿⣿⣤⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⢀⡠⠀⠀⢀⣾⣿⣗⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣀⣴⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠉⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠾⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⠈⠁⠀⠀⠀⢀⣾⢿⢷⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⣸⣿ ⢠⣿⣿⣿⡯⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⣤⠀⣿⣿ ⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣫⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⣧⣜⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣆⠀⠀⠀⢠⣤⡀⠀⣴⣶⠂⠀⢰⣿⣿ ⣾⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⢰⢛⠹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⢿⣿⣦⠀⠀⢹⣿⣷⠀⢽⣿⡁⠀⣿⣿⣿ ⡾⣿⣿⣶⡇⠀⠀⠀⠀⠀⠠⡌⠃⠠⠂⢑⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡈⣿⣿⣷⡀⠸⣿⣿⡆⢮⣿⣿⣧⣸⣿⣿ ⠉⣿⡟⡛⣷⣶⣄⠀⠀⠀⣁⣀⠀⠀⢠⣿⠟⢰⣿⡿⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣝⣙⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣎⣿⣿⣷⢀⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠸⢻⠃⢀⣯⣭⠀⣮⣿⠁⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡝⣿⣿⣼⣿⣿⣾⣿⣶⣼⠟⠋⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠿⣿⡏⠀⠸⣤⠸⣿⡏⣼⣿⡏⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠋⠀⠘⠁⠙⠻⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢦⠁⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣠⢀⣠⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢈⣎⣛⣋⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⣙⣿⣿⢿⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣬⣝⡙⠛⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⣼⠀⢾⠀⢾⣴⠈⣿⡆⢰⡇⠀⢸⠀⢾⣯⠐⢬⡆⢰⡇⠀⢻⠀⢶⠠⢾⡇⠀⠀⠀⡇⠀⢸⠁⡆⡇⠀⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣃⣸⣀⣻⣀⣻⣰⣶⣿⣇⣸⣇⣀⣸⣀⣻⣯⣙⣀⣇⣸⣇⣀⣸⣀⣿⣸⣿⣇⣀⣆⣀⣇⣀⣸⣀⣃⣇⣠⣰⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿ ⢷⣀⠀⠈⠩⡏⠻⣿⣿⣿⠿⠿⡿⠿⢿⢿⠿⠿⠿⠿⢿⡿⠿⠿⡿⡿⢿⡿⢿⠿⡿⠿⢿⢿⠿⡿⢿⡿⠿⣿⠿⠿⡿⠿⢿⠿⢿⢿⠿⣿⠿⠿⡿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⢿⠿⠿⡿⠿⡿⠿⠿⠿⢿⠶⠿⣿⣿ ⠈⢧⣢⠀⠀⠁⠀⡌⠿⣿⢄⠒⡇⢀⣸⢸⠀⣻⠀⡇⢸⡇⢸⠀⡇⠀⢸⣇⠘⡀⠃⡇⢈⢸⠀⡇⢸⡇⢘⣿⡇⢸⡇⠀⢸⠀⣻⡄⢰⣿⠀⣃⡇⠀⢸⠀⠀⣿⠀⡇⢸⠀⡧⠄⢸⠀⣃⡇⠀⢸⡇⣿⠀⣻⠀⡇⢸⣿ ⠀⠀⣿⡆⠀⠀⠀⣠⣶⣿⣤⣤⣧⣼⣿⣼⣤⣭⣤⣥⣾⣷⣬⣴⣧⣧⣼⣿⣤⣧⣤⣧⣼⣼⣤⣧⣬⣧⣬⣿⣧⣼⣧⣤⣼⣤⣭⣧⣼⣿⣤⣿⣧⣴⣬⣤⣤⣿⣤⣧⣼⣦⣥⣦⣼⣤⣿⣧⠦⠼⣧⣿⣤⣭⣤⣥⣾⣿ ⠀⠀⢹⣿⠀⠀⠀⠨⠿⠛⣉⣿⣿⣿⣿⣿⠃⠀⢸⡏⢹⠙⡏⣿⡉⢉⡏⢹⠙⠋⣙⣿⠋⣙⡏⠙⢹⠉⡙⡏⢹⠉⠉⣩⠙⠋⣿⡏⠉⡏⢉⢻⠋⣉⣿⠉⡏⣿⠉⢹⠉⡙⡏⢉⢻⠹⢩⡇⠀⢠⣿⣿⣿⣿⠃⢸⣿⣿ ⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⢸⡇⢸⢠⠀⣿⡇⢸⡇⢠⠀⠀⠼⣿⠂⠈⡇⠀⢸⠀⡄⣧⠀⢸⠀⠼⡇⢸⣿⠁⡃⠃⢰⢸⠀⠼⣿⠀⡄⡏⢐⠸⠀⣤⡇⢠⣾⡆⣼⠁⠀⢼⣿⣿⡿⡃⠀⠀⣹⣿ ⠀⠀⡀⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣍⠀⠀⠀⠀⠈⠓⠚⠚⠲⣿⣷⣾⣷⠚⠒⠒⠒⣿⣷⣶⣿⣶⣾⣶⣷⣿⣶⣾⣶⣶⣷⣾⣿⣶⣷⣶⣾⣾⣶⠶⠛⠒⠓⠓⠚⠲⠶⣿⣷⣾⡿⠓⠊⠀⠀⠀⢰⣿⣿⠇⠀⠀⣻⣿ ⠀⢐⣾⣿⣿⠀⠀⠀⠈⢽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣟⣸⣿⠃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⣿ ⠀⣼⣿⣿⣿⠀⠀⠀⠀⠸⢛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⠠⢤⣀⡀⠀⠀⢀⣾⣿⣟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⢀⣼⣿⣿⣧⠀⣀⡀⠐⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣺⣿ ⠀⣸⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣻⡰⠁⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⢀⣽⣿ ⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⡼⢼⠡⣤⡐⣿⣿ ⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⣿⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣷⣼⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠢⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⢠⣤⡀⠀⣴⣶⠂⠁⢰⣿⣿ ⣾⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣺⠻⢻⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣔⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⢿⣿⣧⠀⠀⢸⣿⣷⢈⢽⣿⡀⠀⣿⣿⣿ ⣿⣿⣿⣶⡷⠀⠀⠀⠀⠀⠰⠭⠀⠾⠉⢉⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡈⢿⣿⣷⡀⠸⣿⣿⡆⢞⣿⣿⣯⣹⣿⣿ ⠙⣿⣿⡟⣷⣶⣤⠀⠀⠀⢀⣀⠀⠀⢠⣿⠿⢠⣿⣿⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣙⡁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣎⣿⣿⣷⢀⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠘⢛⠇⢀⣮⣭⠄⣮⣿⠇⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡽⣿⣿⣼⣿⣿⣾⣿⣶⣾⠿⠋⠈⠁⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⢠⢤⠸⣿⡿⢸⣿⡟⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⢿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠘⠁⠙⠛⠄⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣫⠁⠀⢠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣄⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢺⣞⣛⠉⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢝⣿⣿⢿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣽⡛⠛⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⣻⣿⣫⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣤ ䷩ 𝚕𝚒𝚗𝚎 2610 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_27/10/2021:_Murena_for_/e/_and_Red_Hat_Condemned_for_Its_Nationalism/ Racism⠀✐ Posted in News_Roundup at 11:40 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o ⚓ Top_10_free_cloud_services_for_Linux⠀⇛ Cloud service refers to data storage away from users’ local systems and across the span of dedicated servers meant for this. It is an alternative way of storing data online instead of your local machines. At its earliest, in 1983, CompuServe provided 128 KB of disk space that could be used for files storage to its users. This proved to be crucial despite not being enough. In today’s world, the storage field is under active development because of potential threats such as loss of data/information, data hacking or masquerading, and other attacks. However, many companies have come forward with their solutions to Cloud storage and data privacy, strengthening and stabilizing their future. While using any cloud service, note that you cannot upload your data without an internet connection. Furthermore, you will still need an internet connection to either modify or share documents, presentations, spreadsheets, images, audio, video e.t.c with others. Cloud is virtual and provides services to end-users in storage, hosting of apps, or virtualizing any physical space. In today’s world, cloud computing is used by small and large organizations for data storage. There are three main types of services associated with the cloud, namely, SaaS (Software as a Service) that allows users to access other publicly available clouds of large organizations for storing their data, for instance, Gmail, PaaS (Platform as a Service) for hosting of applications or software on other public clouds, for example, Google App Engine which hosts apps of users, laaS (infrastructure as a Service) for virtualizing any physical machine and availing it to customers to make them get the feel of a real machine. o § Desktop/Laptop⠀➾ # ⚓ Star_Labs_Releases_Coreboot_7_Open-Source_Firmware_for_Its Linux_Laptops_with_New_Features⠀⇛ Based on the upstream Coreboot 4.14 release, Star Labs’ Coreboot 7 open-source firmware is now available for the StarBook Mk V, Star LabTop Mk III, and Star LabTop Mk IV Linux notebooks, along with an updated Coreboot Configurator utility. This release comes about three months after Coreboot 6 and brings several new features, including a new option to set the maximum charge level as 60, 80, or 100 percent, as well as a new option to set the fan curve as Aggressive, Normal, or Quiet. o § Audiocasts/Shows⠀➾ # ⚓ Linux_Action_News_212⠀⇛ Major performance milestones are being hit with new code inbound for Linux, Plasma and GNOME desktops are set to run Wayland on NVIDIA’s binary driver, and why the SFC’s new GPL fight could have implications for you. # ⚓ mintcast_372.5_–_The_Tablet_Chronicles⠀⇛ 1:22 Linux Innards 36:00 Vibrations from the Ether 52:41 Announcements & Outro In our Innards section, tablets And finally, the feedback and a couple of suggestions # ⚓ Video_Editing_with_Linux:_The_Most_Important_Part_of_a Video⠀⇛ Next in our video editing series for the Librem 14, Gardiner Bryant explains why audio is critical in video production, capturing good sound, and post- processing using Audacity, an open source sound editing solution. This video will help those looking to level up their audio and overall production. # ⚓ Starlink’s_Linux_Secrets_|_LINUX_Unplugged_429⠀⇛ We attempt a live production over Starlink, and dig into the secrets of this giant Linux network in space. o § Kernel Space⠀➾ # ⚓ Linux_5.14.15⠀⇛ I'm announcing the release of the 5.14.15 kernel. All users of the 5.14 kernel series must upgrade. The updated 5.14.y git tree can be found at: git://git.kernel.org/pub/scm/linux/kernel/git/ stable/linux-stable.git linux-5.14.y and can be browsed at the normal kernel.org git web browser: https://git.kernel.org/?p=linux/kernel/git/stable/ linux-s... thanks, greg k-h # ⚓ Linux_5.10.76⠀⇛ # ⚓ Linux_5.4.156⠀⇛ # ⚓ Linux_4.19.214⠀⇛ # ⚓ Linux_4.14.253⠀⇛ # ⚓ Linux_4.9.288⠀⇛ # ⚓ Linux_4.4.290⠀⇛ o § Benchmarks⠀➾ # ⚓ Intel_Announces_12th_Gen_Core_“Alder_Lake”_CPUs,_Linux Tests_Forthcoming⠀⇛ Intel is using their inaugural Intel Innovation virtual event today to formally announce the highly-anticipated 12th Gen Core “Alder Lake” processors. These first desktop processors built on their “Intel 7″ process and employ a hybrid architecture will be available in retail channels next week. Today we can talk more about Alder Lake specifications and features while our Linux performance benchmarks and support analysis will come once the Alder Lake review embargo expires next week. While there have been many Alder Lake leaks in recent weeks/months and a number of features disclosed back during Architecture Day, today marks the official unveil for the next-gen Intel Core processors. This is a very exciting transition as they have now shifted to their Intel 7 manufacturing process, the hybrid architecture provides a combination of high performance and low power cores depending upon needs, and Intel is at the forefront now in delivering DDR5 memory and PCIe 5.0 to the masses. When it comes to performance, Intel claims Alder Lake can deliver up to two times the performance of prior generation processors for content creation workloads. Meanwhile when it comes to the generational performance uplift for the P (Performance) cores it’s said to be around 19%. o § Applications⠀➾ # ⚓ Best_Free_and_Open_Source_Alternatives_to_Microsoft Dynamics_365⠀⇛ Microsoft’s stance for decades was that community creation and sharing of communal code (later to be known as free and open source software) represented a direct attack on their business. Their battle with Linux stretches back many years. Back in 2001, former Microsoft CEO Steve Ballmer famously tarnished Linux “a cancer that attaches itself in an intellectual property sense to everything it touches”. Microsoft also initiated its “Get the Facts” marketing campaign from mid-2003, which specifically criticized Linux server usage, total cost of ownership, security, indemnification and reliability. The campaign was widely criticized for spreading misinformation. However, in recent years, there has been a partial shift by Microsoft to embrace the open source software paradigm. For example, some of their code is open sourced. Examples include Visual Studio Code, .NET Framework, Atom, and PowerShell. They have also made investments in Linux development, server technology and organizations including the Linux Foundation and Open Source Initiative. They have made acquisitions such as Xamarin to help mobile app development, and GitHub a hugely popular code repository for open source developers. And they have partnered with Canonical, the developers of the popular Ubuntu distro. But many developers remain hugely sceptical about Microsoft and their apparent shift to embrace open source. o § Instructionals/Technical⠀➾ # ⚓ How_to_install_MelonDS_on_a_Chromebook_–_Updated_Tutorial⠀⇛ This tutorial will only work on Chromebooks with an Intel or AMD CPU (with Linux Apps Support) and not those with an ARM64 architecture CPU. # ⚓ How_to_Clean_Up_Flatpak_Apps_to_Clear_Disk_Space⠀⇛ Here’s how to clean up Flatpak apps to reclaim your precious disk space. Follow along. Flatpak (like Snap) packages runs in sandbox mode. By design, it takes a considerable amount of disk space for an individual application, even if it is a smaller one. For example, a simple Test editor or a basic image annotator application can take up more than 100+ MB of storage space. It’s how Flatpak, or even Snap operates fundamentally. It pulls all dependencies for an app and runs independently. The advantage of this design is – you do not need to worry about dependencies, updates. All you need to do is install and run. On the contrary, it takes up huge amount of disk space. And if you are running Ubuntu, elementary OS or any distribution for longer period, you would be surprised that over time, Flatpak keeps on taking up more space. Hence, in this guide, we will give you some commands which you can run it by yourself to clean up flatpak apps. # ⚓ How_To_Install_Fail2Ban_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Fail2Ban on Debian 11. For those of you who didn’t know, Fail2Ban is an intrusion prevention framework written in the Python programming language. This service will help prevent unwanted logins by banning nefarious IP addresses from gaining access to your server. Whereas, other basic functions are monitor log files, searches for predefined patterns, and temporarily block IP addresses. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of Fail2Ban on a Debian 11 (Bullseye). # ⚓ How_eBPF_Streamlines_the_Service_Mesh [Ed: Disclosure at the bottom reminds people that Linux Foundation is basically buying such articles]⠀⇛ There are several service mesh products and projects today, promising simplified connectivity between application microservices, while at the same time offering additional capabilities like secured connections, observability, and traffic management. But as we’ve seen repeatedly over the last few years, the excitement about service mesh has been tempered by practical concerns about additional complexity and overhead. Let’s explore how eBPF allows us to streamline the service mesh, making the service mesh data plane more efficient and easier to deploy. # ⚓ How_to_Create_File-Sharing_with_ONLYOFFICE_Docs_and Seafile⠀⇛ File sharing, as the act of distributing and providing access to different types of files over the Internet, has become something that everyone is familiar with. The fast development of file-sharing services makes it extremely easy for us to share whatever we need with friends, family, or co- workers. For example, a couple of clicks is enough to instantly share a funny video or picture with someone who is halfway around the world. One of the most popular services for file sharing and synchronization is Seafile. In this article, you will learn how to integrate Seafile with ONLYOFFICE Docs to create a collaborative file- sharing environment on Linux. # ⚓ How_to_Delete_One_or_More_Lines_in_Vi_and_Vim⠀⇛ Editing text files directly from the Linux terminal can be tough, especially if you’re using a complicated text editor like Vi or Vim. Beginner users have a tough time wrapping their heads around command-line text editors and often find it hard to memorize the key bindings used to perform basic operations. Even deleting lines in Vi and Vim can be a nerve- wracking job for newcomers. But using a rudimentary tool like a text editor doesn’t have to be so hard. Here’s how you can remove one or more lines from a text file using Vi and Vim. # ⚓ How_to_Install_Firefox_93_in_Linux_Desktop⠀⇛ Firefox 93 officially released for all major OS e.g. Linux, Mac OSX, Windows, and Android. The binary package is now available for download for Linux (POSIX) systems, grab the desired one, and enjoy browsing with new features added to it. # ⚓ How_to_Install_OpenNMS_Network_Monitoring_Solution_on Debian_11⠀⇛ OpenNMS is a free and open-source Open Network Management System written in Java. It is a network monitoring application that gathers critical information from local and network hosts using the SNPM protocol. It can be installed on Linux and Windows operating systems and provides a web-based interface to monitor network traffics through a web browser. It offers a rich set of features including, Provisioning, Service Monitoring, Event Management, Charting support and Performance Measurement. In this post, we will show you how to install OpenNMS on Debian 11. # ⚓ How_to_Install_Zabbix_Monitoring_Tool_on_Debian_11/10⠀⇛ Zabbix is a free, open-source, popular, and feature-rich IT infrastructure monitoring software developed using PHP language. It is used to monitor networks, servers, applications, services as well as cloud resources. It also supports the monitoring of storage devices, databases, virtual machines, telephony, IT security resources, and much more. # ⚓ How_to_Install_Zabbix_on_RHEL/CentOS_and_Debian/Ubuntu⠀⇛ Zabbix is an Open Source, high-level enterprise software designed to monitor and keep track of networks, servers, and applications in real-time. Build in a server-client model, Zabbix can collect different types of data that are used to create historical graphics and output performance or load trends of the monitored targets. The server has the ability to check standard networking services (HTTP, FTP, SMTP, IMAP, etc) without the need to install extra software on the monitored hosts. # ⚓ How_to_Reset_Forgotten_Root_Password_in_Ubuntu⠀⇛ User roles on a Linux operating system are hierarchy-based. The root user sits on the iron throne and is able to control the actions of all other users. It is the administrative/ authentication power of this root user that controls the actions of any other user with access to the Linux system. # ⚓ How_to_Set_Date_and_Time_on_Rocky_Linux_8_Desktop_and Server⠀⇛ Here are the two ways to set a date and time on Rocky Linux 8 or AlmaLinux using the command terminal and graphical user interface. There are many processes on the Linux operating system that requires the correct system date and time. Also, to update the system properly and other processes like cronjobs we must need the up-to-date time & date. However, Linux or any other OS automatically syncs the system time from the server, in case not or you want to change the timezone manually then let’s explore how to do that. # ⚓ How_to_install_PostgreSQL_on_Debian_11?⠀⇛ PostgreSQL is one of the best open source solutions for relational database management. So, many developers use it as an alternative to MariaDB or proprietary solutions like Oracle. That’s why, today in this post, you will learn how to install PostgreSQL on Debian 11 quickly and easily. # ⚓ How_to_install_complete_Kali_Linux_on_USB_drive_|_FOSS Linux⠀⇛ Kali Linux, previously known as BackTrack Linux, is a Debian-based open-source Linux distribution designed for advanced penetration testing and security auditing. This operating system has many tools for diverse information security undertakings, including penetration testing, reverse engineering, security research, and computer forensics. Kali Linux is a multi-platform elucidation that information security pros and hobbyists can use for free. It is designed to satisfy the needs of penetration testing and security auditing professionals. # ⚓ Installing_NFS_Server_and_NFS_Client_on_Ubuntu_20.04_– ByteXD⠀⇛ NFS server is also known as Network File System server, was developed by Sun Microsystems in 1984. NFS was designed to share files and folders between Linux/Unix systems. After its initial success, NFS version 2 became public, and then everyone could use this to exchange files. It is a distributed file system protocol that allows the client computer to access files over the network. The server requires to validate the client computer, and then after successful validation, files and folders are shared amongst each other. However, the data is not encrypted. Because NFS transfers are not encrypted, it’s not recommended to be used over the internet. NFS server allows you to mount your local files over a network and remote hosts, to interact with them as they are both mounted locally on the same system. NFS serves the same purpose as SMB(Server Message Block), but it is faster as compared with SMB. Currently, there are three NFS protocol versions: NFSv2, NFSv3, NFSv4. o § Games⠀➾ # ⚓ Google’s_Stadia_Pivots_To_Being_Some_White_Label_Game Streaming_Platform_For_Others_To_Use⠀⇛ The saga of Google’s Stadia product has been long, winding, and mostly disappointing. The initial launch of Google’s platform, billed as a Netflix- style video game streaming service, was underwhelming and plagued with Obamacare-like rollout issues, failed promises, underperforming adoption rates, and a paltry catalogue of games on the platform. Other than that, the launch of Stadia went off without a hitch. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_Connect_Arrives_for_iPhone,_At_last._Here’s_How to_Try.⠀⇛ Long awaited KDE Connect is now available for iPhone (iOS >= 15). Here are the details. # ⚓ KDE:_Multi-Axes_Made_Easy⠀⇛ Today we want to introduce the last of the new features we are implementing into the 2.9 release which we have recently finalized. To demo this new feature, let’s use an example contributed by one of our users. This example is based upon the measurement data from a solar cell. The so-called “incident photon to current efficiency” (IPCE) tells us how many incoming photons are converted into free electrons in the cell. This conversion efficiency, together with the generated current and their dependency on the wavelength of the incoming light, are the usual subjects of studies and optimizations for solar cells. Consider the example where we want to plot the IPCE and the current density in the same plot and to see their behavior as a function of the wavelength. Your first idea may be to just lay out the curves for the plot like this… o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ On_Free_Software,_Red_Hat,_and_Iran [Ed: Context here]⠀⇛ I was visiting the Fedora Council ticket tracker when I noticed this ticket up for discussion. The ticket’s purpose is minor and appears inconsequential. It involves adding some legal text to the Fedora Accounts system. The change is related to Export Administration Regulations (the “EAR”) as maintained by the United States Department of Commerce. And the change is not actually a change, but a clarification of a policy that has always been in effect. I am opposed to the impact of Export Administration Regulations by the United States as it pertains to free and open source software. I am a strong believer that the impact of these regulations are most harmful to all free & open source software communities at an individual, human level. When I saw this discussion at the Fedora Council level, it offered me an opportunity to reflect on my own feelings about these regulations, and also to share an opinion on how I believe Fedora Linux could truly live up to its certification as a Digital Public Good to ensure a more equitable world. [...] Firstly, it creates confusion, doubt, and feelings of ill intent. These laws and regulations are meant to impact governments and nation-states. In a Free & Open Source community such as ours, these regulations impact individual people. Not governments or nation-states. As an example, a Fedora community member, Ahmad Haghighi, was recently permanently removed from the Fedora Community. In a few quick clicks, Ahmad’s legacy in the project was erased. As a precedent, even if someone’s contributions were not “supposed” to be accepted in the first place, it does not sit well with me that any one person’s legacy of contributions can so easily be removed from project records. Secondly, it challenges the vision and foundations of the Fedora Project. Particularly our vision statement and the Friends Foundation. When I contribute to the Fedora Project, I do not see people as a citizen of this-country or that-country. I see them as my peers and fellow Fedorans, helping meet that shared vision of creating “a world where everyone benefits from free and open source software built by inclusive, welcoming, and open-minded communities.” As an American citizen, I know my country makes such discriminations about large groups of people based only on their nationality, but as a contributor to Free & Open Source communities, I see people by their individual character and intention to be a part of our shared vision. But how can we truly aspire to this vision if we are consciously making deliberate exclusions, even if they make little to no sense in our own context? This geographic restriction policy sits in contrast to the vision and purpose we spell out “on paper”. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ Nine_Raspberry_Pis_power_this_entire_office⠀⇛ Monterail decided they needed a bigger office, and they wanted that office to be smarter, so they turned to Raspberry Pi to make it happen. It was a real leap of faith because the team couldn’t find a similar Raspberry Pi project quite this big, so they didn’t have much to go on. Spoiler: their courage paid off. # ⚓ How_I_made_an_automated_Jack-o’-lantern_with_a Raspberry_Pi_|_Opensource.com⠀⇛ It’s almost Halloween, one of my favorite days and party times. This year, I decided to (pumpkin) spice up some of my decorations with automated motion sensing. This spooktacular article shows you how I made them, step by step, from building and wiring to coding. This is not your average weekend project—it takes a lot of supplies and building time. But it’s a fun way to play around with Raspberry Pi and get in the spirit of this haunting holiday. # ⚓ Engaging_Black_students_in_computing_at_UK_schools_— interview_with_Joe_Arday⠀⇛ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Moto_G100_Android_Smartphone_returns_to_all-time_low with_$100_discount_to_$500_–_9to5Toys⠀⇛ # ⚓ How_To_Take_A_Scrolling_Screenshot_On_Android_12⠀⇛ # ⚓ Android_12_release_roadmap_for_the_ASUS_Zenfone_7, Zenfone_8_and_ROG_Phone_series_announced_|_Nasi_Lemak Tech⠀⇛ # ⚓ Infinix_Smart_6_launched_with_UNISOC_SoC,_5000mAh battery,_and_Android_11_GO_Edition⠀⇛ # ⚓ Infinix_Smart_6_With_Dual_Rear_Cameras,_Android_11_ (Go_Edition)_Launched:_Price,_Specifications_| Technology_News⠀⇛ # ⚓ Pikmin_Bloom,_the_latest_from_Niantic,_to_begin rolling_out_to_Android_users_today_|_Android_Central⠀⇛ # ⚓ How_to_Use_Android_Recovery_Mode_|_WIRED⠀⇛ # ⚓ PUBG_Mobile_1.7_beta_latest_APK:_Direct_download_link for_Android_devices⠀⇛ # ⚓ Want_to_Remove_Unnecessary_Files_on_Your_Android Phone?_5_Options_You_Must_Try⠀⇛ # ⚓ Android_Auto_has_a_hidden_Easter_egg_that’s_never gonna_give_you_up⠀⇛ # ⚓ How_to_Get_Android_12_Widgets_on_Any_Phone_Right_Now_ (2021)_|_Beebom⠀⇛ # ⚓ Infinix_Smart_6_with_Android_11_Go_Edition,_5,000mAh battery_launched:_price,_specifications_–_Pricebaba.com Daily⠀⇛ # ⚓ Motorola_Android_11_update:_List_of_eligible_devices &_release_date⠀⇛ # ⚓ Kodak_CA_Pro_Android_TV_Series_With_40W_Sound_Output Launched_in_India,_Available_via_Flipkart_|_Technology News⠀⇛ # ⚓ Samsung_Galaxy_Buds_2_review:_Solid_earbuds_for Android_–_SoundGuys⠀⇛ # ⚓ LumaFusion_set_to_come_to_Android_and_Chrome_OS_– 9to5Google⠀⇛ # ⚓ ASUS_is_looking_for_beta_testers_for_ZenFone_8_Flip’s Android_12_update⠀⇛ # ⚓ When_is_Android_12_coming_to_Xiaomi_phones?⠀⇛ # ⚓ How_To_Find_The_Privacy_Dashboard_In_Android_12⠀⇛ # ⚓ Motorola_Android_11_update:_List_of_eligible_devices &_release_date⠀⇛ # ⚓ Redmi_Note_11_appears_on_GeekBench_with_Dimensity_810 &_Android_11_–_Gizchina.com⠀⇛ # ⚓ Chrome_For_Android_Adds_Three_New_Widgets⠀⇛ # ⚓ Google_Pixel_6_&_Pixel_6_Pro_review:_The_best_Android phones_you_can_buy_|_CNN_|_CNN_Underscored⠀⇛ # ⚓ The_40_best_free_Android_games_for_your_phone_or tablet_|_Stuff⠀⇛ # ⚓ Best_Android_app_deals_of_the_day:_DEAD_EYES,_and more_–_9to5Toys⠀⇛ # ⚓ Google_Adds_Sweet_New_Android_12_Weather_Widget Option⠀⇛ # ⚓ Xiaomi_optimizes_MIUI_Android_12_development_version –_Gizchina.com⠀⇛ # ⚓ Lilbits:_Raspberry_Pi-powered_storage_server,_Android 12′s_new_Internet_tile,_and_Palm’s_new_earbuds_– Liliputing⠀⇛ # ⚓ Samsung_prepares_Android_12_beta_for_Galaxy_Z_Fold_3, Flip_–_9to5Google⠀⇛ # ⚓ Best_Android_apps_of_2021_–_CNET⠀⇛ # ⚓ Best_Android_phone_for_2021:_Which_one_should_you buy?_–_TechRepublic⠀⇛ # ⚓ Qualcomm_Just_Upgraded_A_Bunch_Of_Its_Chips_For_2022 Android_Phones⠀⇛ # ⚓ Murena_smartphones_and_cloud_will_protect_our privacy⠀⇛ More than ever the market is demanding a new approach for digital products: more and more people around the world want something different, more ethical, more sustainable, with real guarantees about personal data protection. Four years ago, I wanted to break free from Google and Apple, and therefore we created the “eelo” project, with the simple idea that a different mobile operating system and associated cloud services like email or cloud storage could be possible in this world. Followed by an amazing community of supporters, contributors and now users, the project progressed quickly, and became a reality by the end of 2018. The same year, we had to suddenly abandon our initial project name for a temporary name: /e/. Sometimes, temporary things last longer than expected. And despite being hard to pronounce, difficult to search, and largely criticized by many people, /e/ as a brand name had the benefit to be very singular and helped us appear different. In the end it conveyed the idea that we’re doing something special. […] Nevertheless, as we are reaching more and more people and progressively catching interested from a mainstream audience, we have to introduce a new, strong brand, easier to use, easier to refer to and easier to share with people. The goal of this brand is to have a strong name to call our products, intended to be used by a large number of users in many different countries and cultures. It took some time, since we had many different candidates, both from internal suggestions and from our community. We wanted something that would both convey our project’s values, and that could be within the same lineage of our initial project name. We also had to secure this new brand making sure it was not already in use in the same field of activity, and by entering a long trademark registration processes. o § Free, Libre, and Open Source Software⠀➾ # ⚓ Global_communication_in_open_source_projects⠀⇛ I’m really glad that we have some very active people in FreeDOS who are working on translating messages in all these programs. There are a few folks who contribute to FreeDOS by translating messages from one language to another and sharing those message files so we can use them in the FreeDOS distribution. FreeDOS is a small operating system with low memory constraints, so actually our biggest challenge has been technical. In a more modern system like Linux, you can provide message translation through a service like catgets or gettext. Both are programming libraries where the program says, “I need this string [text] in the user’s preferred language,” and the library gives the program that string. This is an example of internationalization, by providing translations in different languages. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ More_Stories_Behind_the_Podcasts:_Slate’s Latest_Curated_Collections_on_Pocket⠀⇛ Slate and Mozilla’s Pocket have extended their ‘Behind The Podcasts’ collaboration, partnering on a series of new Pocket Collections to provide podcast and Pocket fans with even more opportunities to explore the behind- the-scenes stories that inspired some of Slate’s most successful podcasts. This November, Pocket readers can look forward to all-new collections curated by Slate’s podcast hosts, coinciding with new seasons of One Year, Decoder Ring and the highly anticipated sixth season of Slow Burn, one of the most- popular podcast series in Slate’s portfolio, garnering more than 65M+ downloads since its launch in 2017. The curated Pocket Collections, which offer deep-dive reads, down-the-rabbit-hole research, and commentary straight from the hosts’ notes, are the perfect ‘companion pass’ to round out new episodes of Slate’s fan favorites. # § FSF⠀➾ # ⚓ Beatriz_Busaniche_Speaks_Up_in_Defense_of_Richard Stallman⠀⇛ I am Beatriz Busaniche from Argentina, and I have been a free software and human rights activist for 20 years. I’m writing because I am very proud to consider myself a longtime friend of Richard Stallman. He has stayed in my home many times. I have organized many of his conferences here in Argentina, and we have shared events, social gatherings, and political and public activities. In all these years Richard has always behaved in a totally respectful, warm, and generous way to me, my family, and my friends. Richard has made huge contributions to the world of technology. He laid the foundation for the culture of free software, which has grown into a movement that is crucial to our world today. He has helped us to think critically about what we do and how we do it. Our movement is forever in his debt, and we must acknowledge that we have not met our responsibility to appreciate Richard as a human being. Those of us who are lucky enough to be well acquainted with him know that he is a sensitive, loving person, with weaknesses and imperfections like anyone. He can make mistakes, just like any of us. Yet, he has an extraordinary capacity for logical thinking, and is able to change his position when presented with clear and reasonable arguments. Sometimes, however, he expresses his ideas in an unusually direct way that may seem strange to some. As a feminist, I have always worked to challenge stereotypes and over- generalizations about people. I believe that we should be inclusive of those with differences and, above all, fight for justice and the rights of all people. I feel that Richard has been treated unfairly in recent months, and I am deeply ashamed for not having raised my voice in his defense more firmly before this. # § Programming/Development⠀➾ # ⚓ Qt_6.2.1_Released⠀⇛ I am happy to announce we have released the Qt 6.2.1 today. # ⚓ Qt_6.2.1_Released_With_200+_Bug_Fixes_–_Phoronix⠀⇛ It’s been just shy of one month since Qt 6.2 debuted as the first Qt6 Long-Term Support (LTS) release and ported many of the remaining modules over from Qt5. # ⚓ Qt_6.2_and_Windows_11⠀⇛ # ⚓ webOS_OSE_for_Qt_6.2_Verified [Ed: What became of Palm or Palm OS remarries Qt now that it is proprietary software (both of them; this isn't "Linux" or even "free software" but privatisation)]⠀⇛ # § Python⠀➾ # ⚓ Alternative_Python_Implementation_“Pyston” Plans_For_Greater_Performance,_64-bit_ARM⠀⇛ Pyston as the alternative Python implementation open-sourced originally by Dropbox is forming ambitious plans for a bright future. While Dropbox continued developing Pyston publicly from 2014 to 2017, they stopped supporting it with having moved their performance-sensitive code to other languages. But the original developers then restarted work on it and released Pyston 2.0 in 2020. Pyston 2.0 was made closed-source along with the follow-on 2.1 release but then Pyston 2.2 this year returned it to being open-source. Then in August it was announced the Pyston developers joined Anaconda to continue their work on this high performance Python implementation. # ⚓ Pyston_roadmap⠀⇛ We’ve spent some time recently thinking about the future of Pyston, our faster implementation of Python, and wanted to share what’s on our mind. For updates please check out our wiki. * § Leftovers⠀➾ o ⚓ Most_Americans_Distrust_Partisan_Redistricting,_Prefer Independent_Commissions⠀⇛ o ⚓ Before_Shooting,_IATSE_Film_Crew_on_“Rust”_Walked_Off_Set_to Protest_Conditions⠀⇛ o ⚓ The_E_Terminal_Return⠀⇛ Phillip appeared: I see you’re a modern married man. How can you tell? Your clothes are wrinkled. That could be true for a bachelor. No, they pay for wash-and-fold by the bag. They could be poor. No, vanity is totality, appearance obligation, they laundromat it themselves, you machine wash at home and get brainwiped from drying. I hang it on a line outside. Yes, except when you forget because listening is required, you wear the wrinkled badge of courage of the modern feminist man. Sometimes I rebel. Harmlessly, when your socks mismatch. What should I do? As you are, why add more suffering? I see: say nothing and drink alone unseen. Its best, love disguised as peace. The indeterminate illusion of eternity is finite even when you see through it. Enjoy, why not? I want a dinner of sautéed mushrooms and Veuve Clicquot, cioppino and Pouilly-Fuissé, Renoir and Chateau Margaux, Mozart at midnight. Breakfast eggs fried over bacon at dawn’s riverbank sandbar campfire by the hauled out canoes, fresh coolness beckoning another paddle down the shimmering burbling ribbon to light’s wide horizon, somewhere beyond nightfall, behind the thrumming of crickets, prophesying. o ⚓ Scammers_Are_Using_Fake_Job_Ads_to_Steal_People’s_Identities⠀⇛ It has become a ubiquitous internet ad, with versions popping up everywhere from Facebook and LinkedIn to smaller sites like Jobvertise: Airport shuttle driver wanted, it says, offering a job that involves picking up passengers for 35 hours a week at an appealing weekly pay rate that works out to more than $100,000 a year. But airports aren’t really dangling six-figure salaries for shuttle drivers amid some sudden resurgence in air travel. Instead, the ads are cybercriminals’ latest attempt to steal people’s identities and use them to commit fraud, according to recent warnings from the FBI, the Federal Trade Commission and cybersecurity firms that monitor such threats. The U.S. Secret Service, which investigates financial crimes, also confirmed that it has seen a “marked increase” in sham job ads seeking to steal people’s personal data, often with the aim of filing bogus unemployment insurance claims. o ⚓ Houston⠀⇛ o ⚓ Jean-Luc_Mélenchon_Welcomes_the_Animosity⠀⇛ Paris—As an early evening drizzle enveloped the Stalingrad neighborhood of northeastern Paris, 22-year- old Léo Bewa and a dozen other activists gathered outside a public housing complex to knock on doors. They planned to register residents to vote, but the main reason for their organizing was to talk about the presidential campaign of Jean-Luc Mélenchon, the left-populist from the party La France Insoumise, or France Unbowed, making his third consecutive bid for the Élysée Palace. o § Science⠀➾ # ⚓ Another_victim_of_serial_killer_John_Wayne_Gacy’s_has_been identified_using_DNA⠀⇛ The identification of Alexander came together when the sheriff’s department teamed up with the DNA Doe Project, a nonprofit that uses genetic information to locate relatives of dead people who have not been identified. The organization compared the DNA profile from the unidentified victim’s remains to profiles on a genealogy website to find potential relatives. That led it to Alexander’s family, and Alexander’s mother and half-brother provided their DNA for comparison. o § Education⠀➾ # ⚓ “The_University_of_Puerto_Rico_Is_Not_for_Sale!”⠀⇛ “They are stealing our present. The UPR is not for sale,” read a large banner at the gates of the oldest and largest of the 11 campuses that make up the University of Puerto Rico system. Early in the morning on Monday, October 18, students gathered to join the protests in front of Puerto Rico’s Capitol in San Juan, holding colorful signs: “They violated our past”; “They are stealing our present”; “They are mortgaging our future.” This story was produced for Student Nation, a program of The Nation Fund for Independent Journalism dedicated to highlighting the best of student journalism. For more Student Nation, check out our archive or learn more about the program here. StudentNation is made possible through generous funding from The Puffin Foundation. If you’re a student and you have an article idea, please send pitches and questions to [email protected] o § Hardware⠀➾ # ⚓ There’s_Not_A_Cassingle_Thing_Missing_From_This_Cassette Deck_Masterclass_|_Hackaday⠀⇛ For [ke4mcl], this whole cassette craze of late is not a new discovery so much as it is a personal nostalgia machine. Since [ke4mcl] sees a lot of basic questions go unanswered, they made an incredible beginner’s guide to all things cassette deck. This concise wealth of information covers everything from terminology to operation, basic maintenance like repairing the belt and lubricating the motor, and appropriate cleaning methods for the various parts. Yep, we’re pretty sure this covers everything but the pencil winding technique, which you probably already knew about. o § Health/Nutrition⠀➾ # ⚓ ‘Cloak_and_dagger’_military-intelligence_outfit_at_center of_US_digital_vaccine_passport_push⠀⇛ # ⚓ Deadly_US_Sanctions_Are_Exacerbating_the_Pandemic Globally⠀⇛ # ⚓ House_Introduces_a_Sweeping_Booster_Seat_Safety_Law_to Protect_Children_in_Car_Crashes⠀⇛ Members of Congress today are introducing a law that would establish the most sweeping safety rules for booster seats in more than two decades after determining that the makers of the car seats misled parents about their risks and endangered children’s lives. The new legislation, called the Booster Seat Safety Act, was prompted by a ProPublica investigation last year. The act’s chief sponsors — Reps. Raja Krishnamoorthi, D-Ill., and Katie Porter, D-Calif. — say it will address gaping holes in federal regulations that have allowed booster seat manufacturers to make up their own side-impact crash tests and decide what passes. # ⚓ Breaking:_FDA_Panel_Recommends_Pfizer_Covid-19_Vaccine_for Kids_5_to_11⠀⇛ The Food and Drug Administration’s independent advisory panel on vaccine safety unanimously approved the Pfizer-BioNTech Covid-19 vaccine for children ages 5 to 11 on Tuesday, paving the way for nearly all school-aged students in the U.S. to have protections from the deadly virus available to them in the coming weeks and months. With just one abstention, the advisory panel voted 17-0 to approve the vaccine for younger children following a thorough review of data provided by the drug makers and outside review. # ⚓ Opinion_|_Expand_Medicare_or_Say_Hello_Again_to_Senate Majority_Leader_Mitch_McConnell⠀⇛ Ask any nurse and they will tell you: dental, vision and hearing care are fundamental aspects of health care. And yet right now, West Virginia Sen. Joe Manchin is a major impediment to finalizing the Build Back Better reconciliation bill in Congress, including a Medicare expansion plan that is wildly popular. # ⚓ Melbourne:_The_Longest_in_Lockdown⠀⇛ Then came the global COVID-19 pandemic.  Like the nuclear fallout anticipated in Nevil Shute’s On the Beach, the menace had to eventually head down under and do its bit of gathering.  But there was fierce resistance in the country.  The lockdown formula became the policy de jour and there was no greater example of this than Melbourne. In 2021, the Herald Sun would look with envy across the pond to note that Auckland in New Zealand has taken the honours of the EIU’s essentially irrelevant assessment.  Melbourne had suffered a slump, slumming in eighth spot.  The EIU sternly noted that, “The pandemic has caused huge volatility in our biannual liveability index, which ranks 140 cities across five areas: stability, health care, education, culture, and environment, and infrastructure.”  But Melbourne’s Lord Mayor Sally Capp, despite noting the “devastating impact” of lockdowns on the city, could still brightly note that “we remain one of the 10 most liveable cities in the world”. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Pseudo-Open Source⠀➾ # § Openwashing⠀➾ # ⚓ Microsoft_War_Stories_|_Coder_Radio_437⠀⇛ Chatting about the week’s .NET news leads us into a blue-tinted tale of woe. When Microsoft taketh, they also giveth. But is it enough? # § Security⠀➾ # ⚓ Hacked!_How_finding_my_dream_home_almost_led_me to_a_financial_nightmare [Ed: Mozilla is spying on Firefox users and it wants their passwords too... with server-side sync... in the name of security of course (ignore the NSA leaks; that's just "old news")]⠀⇛ My husband and I had relocated to a new city and had been renting for two and a half years. We were finally ready to buy our own place and stop throwing money away on rent, and we had a deadline — the end of our lease. But, unfortunately, right at the time we started to look last year, the housing market started going absolutely bonkers. Very few houses on that market were what we were looking for, and everything was moving so quickly that houses were selling before they even hit the market. It was an exciting time, but also really frantic. We really felt the pressure. We knew we had a deadline so once we found something, we just needed to move. It felt like there was no room for error or even time to process. # § Privacy/Surveillance⠀➾ # ⚓ If_Courts_Won’t_Protect_People’s_Phones At_The_Border,_Congress_Needs_To_Act_Now⠀⇛ Invasive searches of people’s phones at border crossings and international airports have become standard operating procedure for US border control agencies. The usual justifications have been made: national security and preventing contraband from crossing the border. # ⚓ License_Plate_Reader_Company_Continues Expansion_Into_Private_Neighborhoods_With The_Help_Of_Some_Useful_Cops⠀⇛ The use of automatic license plate readers by law enforcement has steadily increased over the past decade. The theory is a never ending documentation of vehicle movements results in more solved crimes and recovered stolen vehicles. Assertions about law enforcement efficiency have driven other tech acquisitions, ranging from repurposed war gear like Stingray devices to facial recognition software. # ⚓ The_Surveillance_State:_It_Knows_Almost Everything_About_Us,_We_Know_Almost_Nothing About_It⠀⇛ When considering this concept, Edward Snowden’s name comes to mind. Readers will recall that Snowden was an NSA contractor when he discovered that that agency had collected personal information on masses of people around the world and in particular on those in the US. The Constitution (remember that quaint founding document from the revolutionary history of the US?) protects those in the US from unreasonable searches and seizures of our personal information in the Fourth Amendment and establishes our right of free expression that is enshrined in the First Amendment. At least that is what some learned in eight-grade civics class. Following the Vietnam War era, the US Congress limited the government’s ability to pry into the lives of those in the US. That period, in the late 1970s, was the high point of reining in the government’s ability to spy on those in the US without a warrant and further limited the government’s ability to conduct “dirty tricks’ and sabotage of individuals and groups, as it had done through the FBI’s counterintelligence (COINTELPRO) spying program. # ⚓ Resisting_the_Menace_of_Face Recognition⠀⇛ Fortunately, people around the world are fighting back. A growing number of communities have banned government use of face recognition. As to business use, many communities are looking to a watershed Illinois statute, which requires businesses to get opt-in consent before extracting a person’s faceprint. EFF is proud to support laws like these. Let’s begin with the ways that face recognition harms us. Then we’ll turn to solutions. Face recognition violates our human right to privacy. Surveillance camera networks have flooded our public spaces. Face recognition technologies are more powerful by the day. Taken together, these systems can quickly, cheaply, and easily ascertain where we’ve been, who we’ve been with, and what we’ve been doing. All based on a unique marker that we cannot change or hide: our own faces. # ⚓ Facebook_Faces_a_Public_Relations_Crisis. What_About_a_Legal_One?⠀⇛ But to win a lawsuit accusing the company of misleading investors, regulators would have to prove that executives had intended to hide or lie about problems. Regulators would also have to prove that the information revealed by Ms. Haugen, or turned up in an investigation, could have changed trading or voting decisions by shareholders if it had been shared. It would be even more difficult to hold top executives personally responsible. Regulators would have to demonstrate that Mr. Zuckerberg or other executives had explicit knowledge that Facebook was hiding or lying about information that could sway investors. # ⚓ Data_Protection_in_Kenya:_how_is_this right_protected?⠀⇛ Our new paper turns to Kenya’s Data Protection Act to lay the groundwork for a truly rights- centric approach to data protection in Kenya. # ⚓ Supreme_Court_of_India_says:_Investigate Pegasus!⠀⇛ The Supreme Court has pronounced a judgment regarding the use of Pegasus, constituting a committee of technical experts to examine the allegations of unauthorised surveillance using the Pegasus spyware. The committee of technical experts is monitored by Supreme Court Justice R. V. Raveendran (retd.) who will be assisted by Mr Alok Joshi, a former IPS officer, and Dr. Sandeep Oberoi. The committee has been directed to submit its report expeditiously and the matter will be taken up 8 weeks from 27th October, 2021. IFF has provided legal assistance to two petitioners – Mr Rupesh Kumar Singh and Ms Ipsa Shatakshi. Mr Arvind Datar, Senior Advocate, represented them before the Supreme Court. [...] The Supreme Court pronounced its decision on 27th October 2021. Considering the importance of protection of journalistic sources for press freedom, and the potential chilling effect snooping techniques may have, the Court constituted a committee of technical experts to examine the allegations of unauthorised surveillance using the Pegasus Spyware. The committee’s functioning will be overseen by Justice R. V. Raveendran (retd.), former Judge, Supreme Court of India. Mr. Alok Joshi, former IPS officer, and Dr. Sandeep Oberoi, Chairman, International Organisation of Standardisation and the International Electro­- Technical Commission, have been tasked with assisting the overseeing judge. The Technical Committee, whose bios the Court provided, shall comprise of: (Paragraph 60): “1. Dr. Naveen Kumar Chaudhary, Professor (Cyber Security and Digital Forensics) and Dean, National Forensic Sciences University, Gandhinagar, Gujarat. Dr. Chaudhary has over two decades of experience as an academician, cyber security enabler and cyber security expert. He specializes in cyber security policy, network vulnerability assessment and penetration testing. 2. Dr. Prabaharan P., Professor (School of Engineering), Amrita Vishwa Vidyapeetham, Amritapuri, Kerala. He has two decades of experience in computer science and security areas. His areas of interest are malware detection, critical infrastructural security, complex binary analysis, AI and machine learning. He has many publications in reputed journals. 3. Dr. Ashwin Anil Gumaste, Institute Chair Associate Professor (Computer Science and Engineering), Indian Institute of Technology, Bombay, Maharashtra. He has been granted 20 US patents and has published over 150 papers and authored 3 books in his field. He has received several National awards including the Vikram Sarabhai Research Award (2012) and Shanti Swarup Bhatnagar Prize for Science and Technology (2018). He has also held the position of Visiting Scientist at the Massachusetts Institute of Technology, USA.” Amongst other things, the Court has directed the Committee to enquire, investigate, and determine whether the Pegasus Spyware was acquired by the Union Government or any State Government, and whether the spyware was used on phones or other devices of the citizens of India to access stored data, eavesdrop on conversation, intercept information and/or any other purpose [Paragraph 61(A)]. The Committee has also been asked to make recommendations regarding enactment or amendment to existing law around surveillance to secure the right to privacy as well as regarding establishment of a mechanism for citizens to raise grievances on suspicion of illegal surveillance of orders [Paragraph 61(B)]. In order to achieve these ends, the Committee has been authorised to devise its own procedure, conduct investigation as it deems fit, take statements of any person in connection with the enquiry, and crucially ‘call for records of any authority or individual’ (Paragraph 62). o § Defence/Aggression⠀➾ # ⚓ Mo_Brooks_Says_He’d_Be_“Proud”_of_His_Staff_If_They_Helped Plan_January_6_Attack⠀⇛ # ⚓ Judge_Dumps_Felony_Manslaughter_Charges_Brought_Against_An Arrestee_After_A_Deputy_Ran_Over_Another_Deputy⠀⇛ Felony murder is a truly bizarre artifact of the American justice system. It’s simply not enough that there are thousands of laws that can be used to charge people who have allegedly broken them. But felony murder (and its offshoots, which include other crimes like manslaughter) allows prosecutors to charge people for crimes they didn’t commit. # ⚓ “Devastation_and_Anger”_in_Sudan_as_Military_Coup_Halts Country’s_Democratic_Transition⠀⇛ We look at the attempted coup in Sudan, where the military, led by General Abdel Fattah al-Burhan overthrew the transitional government Monday, detaining Prime Minister Abdalla Hamdok and other political leaders. As protesters flooded the streets of Khartoum demanding the government be handed back to the civilians, Sudanese soldiers opened fire on them, killing at least 10 and wounding scores more. The United Nations has condemned the coup, and the United States has suspended a $700 million emergency aid package for Sudan. “No one is in support of this coup,” says Walaa Salah, human rights lawyer and activist who attended the ongoing protests and spoke with Democracy Now! by phone from Khartoum on Tuesday. “Military rule is a regression.” We also speak with Isma’il Kushkush, a Sudanese American journalist who lived in and reported from Khartoum for years, who says, for most Sudanese citizens, “the important thing is to see the transfer into a full civilian government, to see elections.” # ⚓ The_Short,_Quixotic_History_of_North_Korean Internationalism⠀⇛ All tourists in North Korea, which includes me at the end of 2016, are accompanied by state- sanctioned guides. Their job, ostensibly, is not to monitor you but, much like every other tour guide, to show you all the best sights and make sure you stick to the itinerary. Inevitably, you are also shepherded around a very select portion of the country: Most Western tourists only see Pyongyang, the nation’s capital, where the elite live; Chinese day-trippers usually see only Sinuiju, a border city accessible via a bridge to the neighboring Chinese city of Dandong. # ⚓ Why_Biden_Should_Continue_Withdrawing_After_Afghanistan⠀⇛ One month after the Afghanistan pullout, it is still unclear whether we witnessed the beginning of a series of military withdrawals—as part of Biden’s proclaimed end to the era of regime change wars—or if Afghanistan will remain a mere one-off. # ⚓ Opinion_|_A_Few_Early_Thoughts_On_the_American_Coup_of 2024⠀⇛ As an eyewitness, I can recall the events of January 6th in Washington as if they were yesterday. The crowds of angry loyalists storming the building while overwhelmed security guards gave way. The slavishly loyal vice-president who would, the president hoped, restore him to power. The crush of media that seemed confused, almost overwhelmed, by the crowd’s fury. The waiter who announced that the bar had run out of drinks and would soon be closing… # ⚓ The_Department_of_Justice_Is_Letting_the_Coup_Plotters_Get Away⠀⇛ Early yesterday, Rolling Stone published an explosive report alleging that two of the people who helped plan the January 6 “Stop the Steal” protests had extensive planning meetings with members of Congress or their staff. These two organizers appear to be cooperating with the January 6 Select Committee, the congressional task force investigating the Capitol attack, which is more than I can say for most of the Trump cronies who actually served in government. # ⚓ Invasions_of_Empire_and_the_Masquerade_Ball_of_Language⠀⇛ The reader will probably remember Abbottabad 2011, the bin Laden raid, the showdown. Obama’s Counterterrorism chief, John Brennan, told the press Navy SEALs were in a firefight with UBL, and that “while bin Laden had vowed to go down fighting, in his last moments alive the master terrorist hid behind a woman.” As if anticipating criticism for killing the one guy who might have known about future 9/11s, Brennan added that UBL would have been taken had they been able to. He soon walked these details back. A video feed of the raid was said to have gone awry, leaving the narrative to hearsay accounts, and soon several different versions of what happened at the ‘showdown’ were reported. SEALs reached out to the public, 60 Minutes interviewed raiders, the “journalistic” Zero Dark Thirty was made, with the “cooperation” of the White House. There is even the local Pakistani media coverage that told a different tale. But it’s still uncertain what actually took place that early morning in Abbottabad. But there’s another version of those events, KBL–Kill Bin Laden: A Novel Based on True Events by novelist JohnWeisman, which maintains close access to SEAL team members and Weisman, a writer praised by Seymour Hersh, has written about them before. Some facts can only be related as fiction rather than fact, and are truer as a result. In KBL, Weisman gives an account of ‘what actually happened’ at Abbottabad that is disturbing and riveting. SEALs coming up the staircase, facing UBL’s slightly ajar door, we get: # ⚓ FBI_Raids_Chinese_Point-of-Sale_Giant_PAX_Technology⠀⇛ U.S. federal investigators today raided the Florida offices of PAX Technology, a Chinese provider of point-of-sale devices used by millions of businesses and retailers globally. KrebsOnSecurity has learned the raid is tied to reports that PAX’s systems may have been involved in cyberattacks on U.S. and E.U. organizations. # ⚓ Shifts_Since_Fahrenheit_11/9⠀⇛ The first shift in society that must be noted is that we got five years closer to the end of it. We went backward, not forward, on climate change and it seems that all leaders across the world lack the urgency to save us from this crisis. It is possible that technology will develop to mitigate the crisis for some, but this quest for a technological future largely remains a satire, with billionaires flying to space thinking they are the solution rather than the problem. The only thing that is delaying the end of humanity is indigenous resistance. In the past 10 years, these communities have stopped an astounding 25% of U.S./Canadian emissions through protest. Their reward is further genocide upon their communities. Go figure. The solution to the end of the world is not technocratic capitalism, which will still use every resource for private profits until we run out of them. The second change in society is a rather surprising one for the globalist neoliberal era. This is a return of nationalist sentiment. Joe Biden continues Donald Trump’s strategy of mobilizing an idea of America. Joe Biden decided to end a forever war and this appeared to largely be because Trump promised to. Biden was honest enough that he blamed the Afghan people for the war on his way out the door. The Pentagon budget went up again, with eyes to China, with Biden echoing Trump’s America First rhetoric. Similarly, Biden has successfully implemented a brutal nationalist immigration policy where Trump never could do cleanly. When it comes to China, where Trump’s nationalist tariffs failed, Biden has upped the ante, appearing to threaten war with China over Taiwan. Biden has been unwilling to deliver on his own campaign promises, butchering negotiations on his signature Build Back Better plan.. This plan was its own version of nationalism embodied in rebuilding America. As it was stripped it was revealed that it would also increase emissions, and therefore would only be fleeting relief for the working class. Remember that Trump ran a campaign on infrastructure but only became interested in building a wall. Biden is a “better’ Trump. # ⚓ Colin_Powell:_Willful_Victim_of_the_Central_Intelligence Agency’s_Deceit⠀⇛ Powell believed he could deal with the CIA, just as he believed he had dealt with Vice President Cheney’s efforts to prepare his speech.  The Cheney draft of a speech, written by his chief of staff, Lewis “Scooter” Libby, was a total distortion, and Powell ignored it.  But Powell was no match for the manipulation of CIA director George Tenet and deputy director John McLaughlin.  They lied to him, and he never forgave them. Tenet and McLaughlin played key roles from September 2002 to March 2003 in manufacturing intelligence to support a decision to go to war.  They gave deceitful briefings to various congressional committees; they sponsored a specious National Intelligence Estimate in October 2002; they instigated an unclassified “White Paper” on the basis of the estimate to distribute on Capitol Hill before the vote to authorize force; and they assisted Cheney’s desires.  Powell knew that Cheney had made numerous trips to the CIA to make sure that the intelligence would corroborate Bush’s decision to go to war. # ⚓ How_the_US_enabled_Ethiopia’s_bloodletting,_training_its military_while_playing_innocent_observer⠀⇛ # ⚓ 2_Polish_troops_hurt_as_migrants_try_forcing_Belarus_border |_Federal_News_Network⠀⇛ Officials in Poland said Monday that two soldiers were lightly hurt when a group of some 60 migrants tried to force their way across the border from Belarus. The Border Guards office said the troops — who have been deployed to help protect the European Union’s eastern border from growing migration pressure — were treated at a hospital for facial injuries following the events Sunday near the village of Usnarz Gorny. They said in a statement that the migrants were throwing stones and wielding branches. That part of the border is in a dense forest that also includes bogs. Most of the border with Belarus runs along the Bug river. A video showing men trying to break the razor wire border fence with a branch and helmeted Polish troops watching from nearby was posted on the Border Guards website. o § Transparency/Investigative Reporting⠀➾ # ⚓ The_Whistleblower_And_Encryption:_Everyone_Has_An_Angle, And_Not_Everyone_Is_A_Policy_Expert⠀⇛ Over the weekend, the Telegraph (not the most trustworthy or reliable in a batch of UK news organizations that have long had issues with accuracy in reporting) claimed that the latest (and most high profile) Facebook whistleblower, Frances Haugen, was prepared to come out against encryption. This (quite rightly) raised the hackles of multiple encryption experts. As people were getting pretty worked up about it, the Telegraph (silently, and without notice) changed the headline of the piece (from “Facebook whistleblower warns ‘dangerous’ encryption will aid espionage by hostile nations” to “Facebook whistleblower warns company’s encryption will aid espionage by hostile nations”) as well as the actual text of the story, to suggest a slightly more nuanced (but still not great) view — effectively saying she supported encryption, but was concerned that Facebook would use encryption as a “see no evil” kind of blindfold to problems on its platform. o § Environment⠀➾ # ⚓ ACTION_ALERT:_The_New_Climate_Denial:_Don’t_Worry,_Do Nothing⠀⇛ Upon the release of the latest dire report from the UN Intergovernmental Panel on Climate Change (8/9/ 21), the Washington Post (8/10/21) published a strongly worded editorial under the headline, “Climate Doubters Lose One of Their Last Remaining Arguments.” # ⚓ Report_Examines_‘Net_Zero’_Climate_Strategies,_Finds Corporate_Plans_Lacking_in_Lead_up_to_COP26⠀⇛ On Sunday, COP26, the 26th United Nations climate change summit, will kick off in Glasgow, Scotland, in what John Kerry, the U.S. special envoy on climate, has called humanity’s “last best chance” to curb the climate catastrophe. Already, politicians and major corporations, including oil and gas producers, are hard at work promoting the idea that the 2015 Paris Agreement’s goals can be met if the financial world coalesces around “net- zero” climate initiatives. But talk about “net zero” has been met with skepticism by many of those on the frontlines of climate change and those advocating on their behalf. A report issued today by advocacy groups Corporate Accountability, Corporate Europe Observatory, Global Forest Coalition, and Friends of the Earth International takes a look at climate strategies marketed by a half-dozen major polluters and finds that the plans come up lacking because of their heavy reliance on “net zero” strategies that presume that the institutions can continue emitting greenhouse gases as long as they are someday actively removed from the atmosphere.  # ⚓ Will_We_Take_the_Path_to_a_Livable_Future_or_Will_Rich Corporations_Trash_the_Planet?⠀⇛ For the past several decades, Noam Chomsky has been one of the most forceful and persuasive voices confronting injustice, inequity, and the threat posed by human-caused climate chaos to civilization and the Earth. I was eager to know Professor Chomsky’s views on the roots of our current dire predicament and on humanity’s prospects for emerging from this crisis into a livable future. He very graciously agreed to speak with me by way of a video chat. The text here is an abridged version of a conversation we had on October 1, 2021. Professor Chomsky, now 92, is the author of numerous best-selling political works, translated into scores of languages. His critiques of power and advocacy on behalf of the political agency of the common person have inspired generations of activists and organizers. He has been institute professor emeritus at the Massachusetts Institute of Technology since 1976. His most recent books are Consequences of Capitalism: Manufacturing Discontent and Resistance, with Marv Waterstone, and Climate Crisis and the Global Green New Deal: The Political Economy of Saving the Planet,with Robert Pollin and C.J. Polychroniou. # ⚓ Worst_Polluters_Spending_Over_Two_Times_More_on_Border Militarization_Than_on_Climate_Action⠀⇛ As the climate emergency wreaks havoc and displaces growing numbers of vulnerable people around the globe, the world’s richest countries and biggest greenhouse gas emitters are responding in a dangerous manner—by prioritizing border militarization over efforts to mitigate fossil fuel pollution and adapt to a hotter planet. “This militarization of borders is partly rooted in national climate security strategies that since the early 2000s have overwhelmingly painted migrants as ‘threats’ rather than victims of injustice.” # ⚓ Climate_Change_Has_Exposed_the_Decline_of_the_American Empire⠀⇛ Thirteen thousand feet high on the far side of the Himalaya mountains, we have entered the past and the future at the same time. We are a medical expedition and also a pilgrimage, consisting of doctors, nurses, Buddhist clerics, supernumeraries like me, and a large staff of guides, muleteers, and camp tenders. We are bound for the isolated villages of Upper Dolpo, a remote region of northwestern Nepal, land of the snow leopard—both the actual animal and the eponymous nonfiction classic by Peter Matthiessen. We are traveling the same trails Matthiessen walked in 1973. # ⚓ Latest_UN_Climate_Report_Delivers_‘Another_Thundering_Wake- Up_Call’⠀⇛ Countries’ current climate pledges put the world “on track for a catastrophic global temperature rise” of about 2.7°C, United Nations Secretary- General António Guterres warned Tuesday, calling a new report released ahead of a key summit “another thundering wake-up call.” “The era of half-measures and hollow promises must end.” # ⚓ Opinion_|_Critical_Climate_Races_for_Governor_in_Virginia and_New_Jersey⠀⇛ With tight races for Governor in two states, Vote Climate U.S. PAC is issuing their first- ever, Gubernatorial Voter’s Guide in Virginia and New Jersey for the elections on Tuesday, November 2, 2021, rating candidates on climate change. There is a major divide between candidates on climate change in both critical Gubernatorial races. Climate-action voters could make a difference if they turn out and vote climate. # ⚓ Climate_Movement_Hails_‘Mind-Blowing’_$40_Trillion_in Fossil_Fuel_Divestment_Pledges⠀⇛ Over the past decade, nearly 1,500 investors and institutions controlling almost $40 trillion in assets have committed to divesting from fossil fuels—a remarkable achievement that climate campaigners applauded Tuesday, while warning that further commitments and action remain crucial. “Divestment has helped rub much of the shine off what was once the planet’s dominant industry. If money talks, $40 trillion makes a lot of noise.” # ⚓ ‘Really_Fantastic’:_Europe’s_Largest_Pension_Fund_Announces Fossil_Fuel_Divestment⠀⇛ Climate campaigners are cheering Wednesday in response to the news that Dutch pension fund ABP—the fifth-largest in the world—is divesting its assets from fossil fuel producers. “This is really fantastic, after all these years of campaigning, we finally succeeded,” said Liset Meddens, director at Fossielvrij NL, calling the development “a huge victory for the climate, human rights, and all life on Earth.” # ⚓ ‘A_Political_Scam,_Not_a_Serious_Plan’:_Groups_Blast Australia_Climate_Pledge⠀⇛ Prime Minister Scott Morrison’s government on Tuesday announced Australia’s plan for net-zero emissions by 2050—a plan that includes no further ambition toward 2030 targets, relies on unproven carbon capture technology, and does not phase out fossil fuels. “We need to slash emissions today, tomorrow, this year, and this decade—not in 2050.” # ⚓ Opinion_|_Mobilizing_Climate_Finance_to_Avoid_Catastrophe⠀⇛ Rich countries have put the world on the brink of climate catastrophe. They have gotten away with decades of inaction on reducing emissions, and on providing finance for the world’s poorer countries to do the same and to support their frontline communities in coping with increasingly severe climate impacts. # § Wildlife/Nature⠀➾ # ⚓ Opinion_|_Wildfires:_Heartbreaks_and_Healing_Places⠀⇛ Wildfire impacted folks mostly from Chico in Butte County, the North Central California region hard hit by climate fires, will carpool together to paint a giant street mural with paint made from wildfire ashes and charcoal from burned trees on their properties. We will protest against the financiers of fossil fuels and PG&E for the last big chance before Cop26 starts on Halloween day. On October 29 in San Francisco in front of BlackRock HQ, the largest financial investor in fossil fuel projects and major shareholder of PG&E is the perfect target to make our stand to #ProtectTheSacred. Their profitable investments set our communities on fire, killed my neighbors, and wrecked lives.  o § Finance⠀➾ # ⚓ Democrats_Eye_Billionaire_Tax_With_Potential_Backing_From “Centrists”⠀⇛ # ⚓ New_Poll_Finds_Broad_Support_for_Strikes_Across_the Country⠀⇛ # ⚓ Virginia_Democrats_Sue_USPS_Over_Delays_That_Could_Impact State_Governor_Race⠀⇛ # ⚓ Social_Infrastructure_Bill_Has_Been_Gutted._Progressives May_Not_Let_It_Pass.⠀⇛ # ⚓ Can_Billionaires_Save_the_World?⠀⇛ # ⚓ A_Forensic_Look_at_Jerome_Powell’s_“Pants_on_Fire” Explanation_for_His_$1_Million_to_$5_Million_Stock_Sale⠀⇛ The story went viral and forced the Federal Reserve to offer a preposterously lame excuse for what was obviously a desire by Powell to reduce his exposure to the stock market, despite his having access to more insider information than any other human on the planet. The same day that Kuttner’s story ran, Mike Derby, a reporter for the Wall Street Journal, wrote that a Fed representative had characterized the large Vanguard sale as “for family expenses.” # ⚓ Reconciliation_Framework_‘Not_Enough’_to_Push_Through Infrastructure_Bill,_Progressives_Warn⠀⇛ U.S. House progressives led by Reps. Pramila Jayapal, Alexandria Ocasio-Cortez, and Cori Bush dug in their heels Tuesday as right-wing Democrats attempted to salvage a $1.2 trillion infrastructure bill while sidelining the more ambitious Build Back Better package championed by the party’s left wing and President Joe Biden until after the weaker bipartisan legislation is passed. “It’s not enough for me. And there are more of us.” # ⚓ Phil_Knight’s_Big_Tax_Dodge:_A_Q&A_With_Tax_Attorney_Bob Lord⠀⇛ # ⚓ The_Strategic_Brilliance_of_‘Striketober’⠀⇛ Yet, this is precisely what we are seeing, as during the month of October, over 100,000 workers have either threatened to strike or actually have walked off the job to demand wage increases, improvements to their work conditions, and basic human dignity. Dubbed ‘striketober’ by activists and pundits alike, this strike wave is occurring across the country, in various industries. # ⚓ McDonald’s_Workers_Join_‘Striketober’_and_Walk_Out_Over Sexual_Harassment⠀⇛ Amid of wave of worker walkouts that supporters are collectively calling “Striketober,” McDonald’s employees in at least 12 U.S. cities took to the streets Tuesday to raise concerns about how the fast food giant has handled sexual harassment and to demand a union. “No matter what McDonald’s says, not much has changed for workers like me.” # ⚓ Democrats_Urged_to_Seize_‘Historic_Chance’_on_Billionaire Wealth_Tax⠀⇛ “The billionaire wealth tax merits an extra push since it is the most powerful tool on the table for tackling the wealth inequality that is undermining our economy and threatening our democracy.” o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Campaigning_“From_the_Middle_Out”_Won’t_Save_Democrats⠀⇛ While we don’t know what sort of Build Back Better bill Democrats will end up passing, we do know that it will be a shadow of President Biden’s original plan. The core of the climate agenda is out. Free community college is out. The extension of Medicare to cover vision, hearing, and dental is under threat. Senator Kyrsten Sinema (D-Ariz.) perversely seems intent on killing the plan to lower prescription drug prices, a reform even Republican voters support. Instead of the “Roosevelt moment” Biden promised, we’ve suffered another tawdry chapter about the power of deep-pocketed interests and the pervasive corruption of our politics. # ⚓ Pelosi_and_Hoyer_to_Progressives:_Just_Pretend_Democrats Are_Winning_(Even_If_Corporate_Lobbyists_Are)⠀⇛ Democratic leadership advised House progressives behind closed doors Monday night that they better start acting like they are getting a major win even if the reality is that President Joe Biden’s signature domestic infrastructure plan seems on the verge of “being gutted beyond recognition” thanks to an aggressive assault by corporate lobbyists and the obstructionism of a small handful of right-wing lawmakers within the party. “If we don’t act like we are winning, the American people won’t believe it either,” House Majority Leader Steny Hoyer (D-Md.) told Democrats during a private meeting, according to Politico. # ⚓ Conor_Lamb_Is_a_Centrist_in_Sheep’s_Clothing⠀⇛ Last weekend, Representative Conor Lamb, a frontline Democrat from Pennsylvania who’s running for the Senate in 2022, vowed to support carbon- free energy payments, a key climate provision Senator Joe Manchin is currently trying to strip from Democrats’ social spending package. Lamb officially jumped in the race in August to replace retiring Republican Senator Pat Toomey, in what is expected to be one of the most contentious contests in next year’s midterm elections. # ⚓ ‘Bottom_Line,’_Says_Bernie_Sanders,_Deal_Must_Include Medicare_Expansion,_Lower_Drug_Prices⠀⇛ As congressional leadership pushes Democrats to “act like we are winning” even as a few corporate- backed party members and business lobbyists water down the Build Back Better bill, Senate Budget Committee Chair Bernie Sanders reiterated Tuesday that the package must expand Medicare and include reforms to lower prescription drug prices. “Congress must finally have the courage to stand up to the greed of Big Pharma.” # ⚓ Watch:_Bernie_Sanders_Argues_‘We_Must_End_the_Greed_of_Big Pharma’⠀⇛ U.S. Senate Budget Committee Chair Bernie Sanders plans to deliver a live, online address Tuesday night arguing that “we must end the greed of Big Pharma.” The speech—scheduled for 8:00 pm ET at live.berniesanders.com—comes as Sanders (I-Vt.) and other progressives in Congress are fighting for a Build Back Better package that allows Medicare to negotiate with the pharmaceutical industry for lower prescription drug prices and expands the federal healthcare program to cover dental, hearing, and vision services. # ⚓ ‘Manchin_Wasn’t_Done’_Killing_Climate_Action:_Coal_Baron Objects_to_Methane_Fee⠀⇛ Progressives are fuming amid reports that right- wing Democratic Sen. Joe Manchin is pushing his party to weaken or remove the reconciliation bill’s proposed fee on methane pollution, even as scientists warn that humanity’s fate depends on rapidly slashing emissions of the potent greenhouse gas. “As anyone with a leaky roof will tell you, making sufficient investments early on is key to avoiding catastrophic costs down the line.” # ⚓ How_One_Ballsy_Senator_Stole_a_President’s_Gummy_Candy⠀⇛ What have we instead? Joe Manchin of Virginia, a once-little-known-senator Democratic senator essentially holding the Democratic Party hostage. He is also rejecting the purported will – not to forget the needs– of 80% of Americans who approve of the most progressive, far-reaching program drawn up by legislators in two generations. Manchin is as pig-headed, as resolute, as overconfident as any Republican. And he’s usurped Harris’s role as the clinching vote. (His party can’t handle him or his Arizona cohort Kyrsten Sinema.) # ⚓ Sunrise_Movement_Corrects_Manchin:_US_‘Has_Done_More_Than Any_Other’_to_Cause—Not_Solve—Climate_Crisis⠀⇛ As activists with the Sunrise Movement confronted Sen. Joe Manchin in Washington, D.C. Tuesday—their seventh day of a hunger strike for climate justice—the leader of the youth-led green group shot down a claim by the fossil fuel-funded West Virginia Democrat that the United States leads the world in tackling the planetary emergency. “If the U.S. doesn’t pass massive climate action this fall, it is too late. This is one of our last chances.” o § Misinformation/Disinformation⠀➾ # ⚓ Billionaire_political_meddlers,_disinformation_agents launch_‘Good_Information_Inc.’_to_fight_disinformation⠀⇛ o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ A_Guide_To_The_U.S._Government’s_Appeal_In_The_Assange Extradition_Case⠀⇛ On October 27, the High Court of Justice in the United Kingdom will hear the Crown Prosecution Service argue on behalf of the United States government that a lower court improperly blocked the U.S. from extraditing WikiLeaks founder Julian Assange. # ⚓ The_PATRIOT_Act_And_The_Whistleblowers_Who_Challenged_Mass Surveillance_After_9/11⠀⇛ [Editor’s Note: To mark the 20th anniversary of the rise of the American security state after the September 11th attacks, The Dissenter continues a retrospective on this transformation in policing and government.] # ⚓ US/UK:_“Drop_the_charges,_stop_the_extradition_and_free Julian_Assange,”_says_Amnesty_head⠀⇛ Ahead of the US appeal hearing on the extradition of Julian Assange Amnesty International’s Secretary General has called on US authorities to drop the charges against him and the UK authorities not to extradite him but release him immediately. o § Civil Rights/Policing⠀➾ # ⚓ “Worked_to_Death”:_IATSE_Film_Crew_on_“Rust”_Walked_Off_Set to_Protest_Conditions_Before_Shooting⠀⇛ We look at how the tragic shooting death of cinematographer Halyna Hutchins during the filming of “Rust” last Thursday on a set in New Mexico is drawing attention to cost-cutting decisions and overall safety in the film industry. Yahoo News is reporting the gun that killed Hutchins had been used by crew members just hours beforehand for live-ammunition target practice. The film’s lead actor and producer Alec Baldwin later shot the revolver after he was reportedly handed it by the first assistant director, David Halls, who told him it was a “cold gun,” meaning it was not loaded with live ammunition. Halls was fired in 2019 from his position as assistant director on the movie “Freedom’s Path” after a gun “unexpectedly discharged” and injured a crew member. All of this happened after some of the unionized IATSE below- the-line crew members had walked off the set of “Rust” earlier on the day of the shooting to protest their housing, payment and working conditions. New Mexico is a “right to work” state, so producers were able to hire nonunion replacements and continue working on the film. We speak with Dutch Merrick, prop master and armorer for over 25 years and past president of IATSE Local 44 Property Craftspersons, Hollywood, who notes, “Hollywood handles firearms every single day,” and calls the process “carefully regulated.” Despite safety protocol and expertise, he says, Hollywood crews are getting “worked to death” with 80- to 100-hour workweeks, which he suggests played into the accidental shooting. # ⚓ Former_Black_Panther_Russell_“Maroon”_Shoatz_Freed_From Prison_After_49_Years⠀⇛ # ⚓ Why_I_Opposed_the_Patriot_Act⠀⇛ Today marks the 20th anniversary of the US Patriot Act. This legislation, rightfully, has long been critiqued for sweeping in unprecedented government surveillance. The anniversary is an opportunity to also reckon with how the Patriot Act distorted our democracy’s checks and balances—and what needs to be done to realign them. # ⚓ Confronting_Ignorance_and_Ignorant_Confrontations⠀⇛ People respected him so they’d ask about the pain or discomfort they were experiencing or seeing in their children or babies. My father loved to help people, and oftentimes people were worried because they didn’t know, “how bad is it?” They found his expertise reassuring. Everyone knows that two aspirin will not cure everything, and they aren’t a diagnostic tool, but it is a troubleshooting step; using nonsteroidal anti-inflammatory drugs to respond to minor aches and pains is like unplugging your router or modem when your internet is not working. # ⚓ Honoring_Elliot_Harmon—EFF_Activism_Director,_Poet, Friend—1981-2021⠀⇛ Elliot understood how intellectual property could be misused to shut down curiosity, silence artists, and inhibit research—and how open access policies, open licensing, and a more nuanced and balanced interpretation of copyright could reverse those trends. A committed copyleft activist, he led campaigns against patent trolls and fought for open access to research. He campaigned globally for freedom of expression and access to knowledge, and his powerful articles helped define many of these issues for a global community of digital rights activists. This photo was taken shortly before Elliot went to speak on top of a truck at a Stop SESTA/FOSTA rally in Oakland. Elliot’s formidable activism touched upon every aspect of EFF’s work. In his early days with us, he continued the work that he began at Creative Commons campaigning for the late Palestinian-Syrian activist, technologist, and internet volunteer Bassel Khartabil. He also ran a successful campaign for Colombian student Diego Gomez, fighting against that country’s steep copyright infringement laws and advocating for open access and academic freedom. Following the same values, Elliot spearheaded EFF’s Reclaim Invention campaign urging universities to protect their inventions from patent trolls. He went on to help steer our campaign to get the FCC to restore net neutrality rules, framing the issue as a matter of free speech and calling on “Team Internet” to join him in the fight. In all of these efforts and more, Elliot brought a natural sense of how to build and nurture community around a shared cause.  # ⚓ Hitler_can_now_dine_in_italian_restaurants⠀⇛ A few weeks ago, the world noticed that Italy was about to “bring in the strictest COVID-19 measures in Europe”. Starting on October 15th, that is, Italy “would become the first European country to require the so-called green pass – the digital or paper proof of vaccination, immunity or a negative test in the past 48 hours – in all places of work, both private and public.” [...] On one hand, both Italians and foreign visitors are safe. It’s pretty unlikely that they will bump into Hitler in any public place in Italy. On the other, there are two classes of concrete problems here. One is public health, and paradoxically it may be the smaller one: most places here do ask to show Green Passes, but almost none actually verifies that name and age on a Green Pass match the person who shows it. So yes, anybody infected could sneak without getting caught into many public spaces, with those cards. That may not be a lot of people. The No-vax, no- green-pass crowd is a noisy but dwindling minority in Italy, not to mention that some of them are dumb enough to make Green Passes the last of their problems. The main problems are that first, those fake passes are valid everywhere in Europe, not just Italy, and it seems similar passes are available in Poland and Russia. Second, there is almost the same thing I mentioned months ago. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Team_Biden_Finally_Gets_Around_To_Staffing_U.S._Telecom Regulators⠀⇛ It was the longest delay in staffing U.S. telecom agencies in Presidential history, but a White House announcement states the administration will promote interim boss Jessica Rosenworcel to be permanent FCC boss, while appointing former Tom Wheeler advisor and consumer advocate Gigi Sohn to fill the third empty Democratic Commissioner seat. Sohn played a major role in both the crafting of net neutrality rules (since demolished by telecom sector lobbyists during the Trump era) and the FCC’s broadband privacy rules (also since demolished by telecom sector lobbyists during the Trump era). # ⚓ Senate_Urged_to_Quickly_Confirm_Net_Neutrality_Advocates_to FCC_Posts⠀⇛ “There’s no time to waste and so much to get done.” “Finally! Now let’s get this agency back to work.” o § Monopolies⠀➾ # ⚓ The_Facebook_Papers:_Docs_Reveal_Tech_Giant’s_Complicity_in Hate,_Lies_&_Violence_Around_the_World⠀⇛ Thousands of internal Facebook documents leaked to media outlets continue to produce damning revelations about how the social media giant has prioritized its profits over user safety. The Facebook Papers have provided fresh evidence of how the company has let serious problems fester on its platform, including hate, misinformation, and human trafficking, and failed to invest in moderation outside English-speaking countries. The former Facebook product manager who shared the documents, Frances Haugen, is pressing lawmakers to more tightly regulate the company’s activities and testified Monday before the British Parliament ahead of scheduled meetings with officials in France, Germany and the European Union. Facebook CEO Mark Zuckerberg says the leaked documents paint a “false picture” based on cherry-picked evidence, but we speak with UCLA information studies professor Ramesh Srinivasan, who says they confirm what many critics have warned about for years. “This new form of digital capitalism that I believe Facebook is trailblazing is one that is playing with our intimate emotions on every single level.” # ⚓ FTC_Study_Highlights_How_‘Big_Telecom’_Privacy_Practices Are_Even_Worse_Than_‘Big_Tech’⠀⇛ I’ve noted for a few times that the very obvious dysfunction in “big tech” has proven to be the gift that keeps on giving for “big telecom.” While tech giants like Google, Amazon, and Facebook get the entirety of (often very justified) attention for dodgy business practices and terrible judgement, telecom has basically been forgotten in the DC Policy conversation. While lawsuits and Congressional posturing all focus on expanding oversight of “big tech,” “big telecom” and “big media” have been able to lobotomize most of the oversight of its own businesses, despite engaging in all the same (and sometimes worse) dubious business practices. # ⚓ What_About_International_Digital_Competition?⠀⇛ Antitrust has not had its moment since the 1911 breakup of Standard Oil. But this past year, policymakers and government leaders around the globe have been taking a hard look at the technology markets. ‘Break up Big Tech’ is the newest antitrust catchphrase. On both sides of the Atlantic, policies have been introduced to foster digital competition. Congress has introduced several competition and anti-trust bills, including a bipartisan package that passed out of committee. The Biden administration has nominated antitrust advocates to key positions: Lina Khan as chair of the Federal Trade Commission, Jonathan Kanter as the Assistant Attorney General for Antitrust at the Department of Justice, and Tim Wu at the National Economic Council. And across the Atlantic, the European Commission is marking up two key pieces of legislation, the Digital Markets Act and the Digital Services Act, that would create new rules for digital services and enhanced competition in the technology sector.    Early this summer and on his first international travel trip, President Biden headed to Brussels to talk about creating a new U.S.- EU Tech and Trade Council (TTC) and a Joint Technology Competition Policy Dialogue (JTCPD). There have been few details aside from the initial press releases on what policy approaches would be considered. However, it is a clear sign that there is a transatlantic appetite for tackling competition in the technology space. But what would an international competition policy look like? # ⚓ European_design_protection_–_worth_your_money? [Ed: Monopolies fees collected by EU agency, EUIPO, which then uses_the_money_for_corruption]⠀⇛ Every company that spends money and resources on research, development and marketing for its products needs assurance that competitors (or other third parties) cannot take advantage of its innovation. Profiting from innovation requires a good business model and an IP strategy is an important part of that business model. Unlike trademarks, patents and copyright – which are well known and commonly used – design protection is sometimes forgotten or underestimated. However, the design of products, packaging, logos, drawings and artwork plays a key role in distinguishing new products from those of competitors. # ⚓ Tesla_Amps_Up_Fight_With_Rivian,_Cites_Battery_Secrets Theft [Ed: Copying is not theft and it's not a crime to just know something you learned somewhere; Musk pretended to be sharing with his “all out patents are belong to you” post; look at him getting all litigious now.]⠀⇛ Tesla Inc. escalated its trade secrets fight with Rivian Automotive Inc., accusing the maker of electric pickups of continuing to poach its employees and stealing “highly proprietary” battery technology. # ⚓ Your_mom_was_right:_Facebook_is_bad_for_you!⠀⇛ Two whistleblowers have revealed that Facebook is well aware of the real world harms it causes to its users and to democratic ideals worldwide, but it chooses to prioritise profit over doing the right thing. We wrote to the Parliamentary Standing Committee on Information Technology asking them to initiate an inquiry into the revelations made, specifically about India and to call the relevant stakeholders to testify before it. # § Patents⠀➾ # ⚓ UK:_DABUS:_AI’ll_Be_Back [Ed: Every serious court and patent office has repeatedly rejected this provocateur, likely a publicity stunt by Surrey University; but patent litigation firms love to distort the outcome for their radical for-profit agenda]⠀⇛ In a hotly awaited decision, the English Court of Appeal has ruled that AI-based machines cannot be named as inventors, upholding the original decision of the High Court and Comptroller general. Dr Stephen Thaler has become well known in the intellectual property field ever since filing patent applications for two inventions: one entitled “Food Container” (GB18116909.4) and the other entitled “Devices and Methods of Attracting Enhanced Attention” (GB181816.0). However, despite its title, it is not the subject matter of the invention that has been attracting attention, but the named inventor: ‘DABUS’, an AI machine owned by Dr Thaler. # ⚓ Counsel_expect_STRONGER_Patents_Act_to_drop_again soon [Ed: Corrupt_and_bribed_politician_Coons_as_merely a_mole_of_the_litigation_profiteers_who_try_to_buy_laws through_him]⠀⇛ Sources say Senator Chris Coons could reintroduce an amended STRONGER as soon as this week, possibly as a counter to the Restoring the America Invents Act # ⚓ Samsung_Patent_Board_Challenges_OK_Despite Confidentiality_Pact⠀⇛ Samsung Electronics Co. convinced two Federal Circuit judges that a confidentiality agreement concerning licensing negotiations doesn’t bar it from filing patent office challenges. # ⚓ Apple’s_Tribunal_Wins_Against_Camera_Patents_Upheld on_Appeal⠀⇛ The board found all the challenged patent claims were invalid because they were anticipated or obvious. # ⚓ The_U.S._Court_of_Appeals_for_the_Federal_Circuit assesses_the_equitable_powers_of_a_legislative_court: the_Court_of_Appeals_for_Veterans_Claims.⠀⇛ The case involves the plight of Bruce R. Taylor, a Vietnam era Army veteran seeking compensation for disabilities resulting from his service. Before serving two tours overseas, Mr. Taylor volunteered to serve his country in a unique fashion—as a test subject. In 1969, the Army sought soldiers on which it would test toxic chemicals such as nerve gas. The Army’s purpose was to learn how its soldiers would function when exposed to agents that combatants might experience in service. Soldiers were given doses of an array of toxic substances and subjected to training exercises to measure performance. As a result of Mr. Taylor’s participation, he suffers from disabilities that the VA found eliminate his ability to work. In accordance with statute, the VA awarded Mr. Taylor monthly compensation. # ⚓ A_Unified_Patent_Court_for_Europe_–_Coming_Soon? [Ed: No, stop_printing_lies_as_headlines]⠀⇛ Europe may soon have its Unified Patent Court and Williams Powell is ready to assist you. With attorneys qualified for the European Patent Litigation Certificate (which gives UPC rights of representation) and as a Patent Attorney Advocate & Litigator (which gives rights of representation in the UK Courts) we are well-placed not only to obtain IP protection but to conduct IP litigation, both in Europe and in the UK. # ⚓ Kathi_Vidal_nominated_as_USPTO_director [Ed: Another 'bought' Director for the litigation lobby?]⠀⇛ The White House officially announced its intention to nominate the Winston & Strawn partner to the position today, confirming rumours # ⚓ Next_UPSTO_Director:_Kathi_Vidal [Ed: More aggressive lawyers instead of scientists in USPTO? The patent extremists are happy, so that’s a bad sign already; lobbying_buys_nominations]⠀⇛ President Biden has nominated leading patent litigator Kathi Vidal as the next USPTO director. Vidal is currently at Winston & Strawn, leading the company’s Silicon Valley office. She was previously with Fish & Richardson. [Announcement] Vidal has all the qualifications. Bachelor’s and Master’s degrees in electrical engineering (starting college at age 16); JD from Penn (EIC of the law review); Federal Circuit clerkship (Judge Schall); registered patent attorney; and litigated patent cases in courts across the country, including the PTAB. She represented Chamberlain whose garage door opener patents were obliterated by the eligibility revolution of Bilski–Mayo- and-Alice. At the same time, Vidal has represented many accused infringers. # ⚓ The_English_High_Court_applies_German_law_on_EPC_2000 claims_in_Royalty_Pharma_v_Boehringer [Ed: By Bristows of_Team_UPC]⠀⇛ On 8 October 2021, His Honour Judge Hacon (sitting as a Judge of the High Court) handed down his decision in an action brought by Royalty Pharma Collection Trust (“Royalty Pharma”) for approximately €23 million in royalty payments from Boehringer Ingelheim GmbH (“Boehringer”) (Royalty Pharma Collection Trust v Boehringer Ingelheim GmbH [2021] EWHC 2692 (Pat)). The action relates to products sold by Boehringer containing the active pharmaceutical ingredient (“API”) linagliptin for the treatment of type 2 diabetes. Boehringer manufactures the API in Germany. Some API is also formulated, labelled and packed into products in Germany, but some is exported by Boehringer to other countries. Boehringer entered into a non-exclusive licence with Prosidion Limited in 2005. The agreement had a somewhat unusual governing law and jurisdiction clause in that it was governed by German law but provided that the Courts of England and Wales have jurisdiction over any dispute. The agreement was assigned from Prosidion to Royalty Pharma in 2011 and was amended in 2015 (but not with respect to the jurisdiction or governing law clauses). Royalty Pharma claimed outstanding royalties pursuant to the amended agreement. One of the patents licensed by Royalty Pharma to Boehringer was the German designation of EP 1 084 705 (“EP 705”), and it is this patent which formed the subject of the dispute. # ⚓ Dutch_court_rejects_Ericsson_motion_for_anti-antisuit injunction,_but_Apple_may_still_be_enjoined_if_need_be: another_jurisdiction_adopts_Munich_approach⠀⇛ Ericsson means business, and it’s not going to undervalue its patents in the renewal of its license agreement with Apple. Earlier this month, Ericsson filed a declaratory judgment action–on its own FRAND compliance–in the Eastern District of Texas. I’ve now become aware of a decision the Rechtbank Den Haag (Court of The Hague) published (in Dutch) last week. Judge D. Nobel denied an Ericsson petition for an anti-antisuit injunction against Apple. It may be counterintuitive, but all things considered the decision is clearly better for Ericsson–though it’s “the loser” at first sight–than for Apple. As matter of fact, Apple itself has a history of bringing cases that serve a strategic purpose even if a court rejects a motion or complaint (such as when it demonstrated to the rest of the industry that it would enforce its design rights around the globe, even though it ultimately failed everywhere but in its home court). [...] Claim 1 of EP 705 is in the EPC 2000 form and covers a class of effectors of particular enzymatic activity for use in lowering the blood glucose level of mammals for the alleviation of diabetes. The German courts have ruled that EPC 2000 claims correspond to purpose-limited product claims and can be directly infringed via an act in s.9(1) German Patents Act 1980. Case law further indicates that the subject-matter of such claims lies in the suitability of the substance “for” a certain medical use. In order to determine whether an infringer’s product is “for” the treatment of the indication specified in the claim, the German courts have developed the doctrine of sinnfällige Herrichtung. If the product of the claim is sufficiently tied to (or “earmarked for”) the use specified in the claim, the requirement of sinnfällige Herrichtung is satisfied. [...] It is interesting to consider whether the same decision would be reached if Hacon HHJ had had to apply English law rather than German law. # ⚓ Dissent_in_PTAB_edict_could_spur_surge_of_Arthrex- extension_bids [Ed: Fake 'journalists' (lobbyists funded by patent litigation firms) cherry-picking dissenters rather than case outcomes in an effort to tilt media coverage in favour of the side which actually lost]⠀⇛ Stakeholders could try to use Judge Pauline Newman’s dissent in Mobility Workx to extend USPTO director review to PTAB institution decisions, say sources # § Copyrights⠀➾ # ⚓ MPA_Wants_Cryptocurrency_Exchanges_To_Help_Identify Online_Pirates⠀⇛ The Motion Picture Association would like the US Government’s executive cybersecurity order to be optimized to identify operators of pirate sites and services. Among other things, the order should require U.S.-based IaaS providers, including hosting services, DNS servers, reverse proxies, and cryptocurrency exchanges, to robustly verify the identities of foreign customers. # ⚓ Former_UFC_Star_Paige_VanZant_is_Hunting_Down_Photo Pirates_on_Discord⠀⇛ Former UFC star and Dancing With The Stars runner-up Paige VanZant is reportedly making more money from selling pictures and videos of herself online than she ever did with the MMA organization. Unsurprisingly, some fans refuse to pay for her content so in response, VanZant has now gone to court in the US to force Discord to hand over their personal details. ䷩ 𝚕𝚒𝚗𝚎 5824 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.27.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_27/10/2021:_XOrg_Server_21.1_and_Makulu_Shift_Ubuntu_Variant_Released⠀✐ Posted in News_Roundup at 5:43 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Best_Linux_desktop_for_2021:_Which_one_should_you_buy?⠀⇛ Linux on the desktop is a thing to behold. It’s not only incredibly powerful and secure, but it’s also flexible enough to become exactly what the user needs. And although you can successfully run Linux on just about any type of desktop machine (running lightweight Linux distributions on older hardware), to really get the most out of modern-day variants, it’s best to have hardware up to the task. Linux doesn’t require nearly the hardware needed to run Windows 11 or macOS, but why not give the open- source operating system extra power, so you can run more applications and services. So, why not send your money to companies that support open source in return? Which desktops are best suited for the task? Let’s take a look at the five best options you have for 2021. o § Kernel Space⠀➾ # ⚓ Maintaining_Yocto_Project_Documentation_–_Bootlin’s_blog⠀⇛ For many years, Bootlin has been a strong user and a contributor to the Yocto Project, delivering numerous customized embedded Linux distributions and Board Support Packages based on Yocto Project and OpenEmbedded to its customers, for a wide range of hardware platforms and architectures. In 2021, we have been able to bring this engagement further, as Bootlin engineer Michael Opdenacker has been given the opportunity to work as a maintainer for Yocto Project’s documentation, thanks to funding from the Linux Foundation. Since the mourning of Scott Rifenbark, the former maintainer, in early 2020, the project was in need for someone to fill this role. # ⚓ Qualcomm_MSM_DRM_Driver_Improvements_Submitted_Ahead_Of Linux_5.16_–_Phoronix⠀⇛ The MSM DRM driver for supporting the open-source display/graphics support with Qualcomm Snapdragon SoCs has submitted their main feature pull request to DRM-Next ahead of the upcoming Linux 5.16 merge window. The MSM DRM driver changes for Linux 5.16 aren’t too exciting but do include a few items worth mentioning. First up, Embedded DisplayPort (eDP) support has been added to MSM’s DisplayPort sub- driver for newer SoCs having native eDP output. # ⚓ Apple_Silicon_GPIO_Driver_Queued_Ahead_Of_Linux_5.16_– Phoronix⠀⇛ Along with the Apple Silicon PCIe driver, another new driver for supporting Apple Silicon (primarily with a focus on the Apple M1 for now) with the upcoming Linux 5.16 cycle is a new pinctrl/GPIO driver. Queued overnight into the linux-pinctrl.git’s “for- next” branch is the 500+ lines of code driver developed by Arm’s Joey Gouly and Corellium’s Stan Skowronek for bringing up the pinctrl/GPIO support for Apple SoCs. # ⚓ Nintendo_Switch_Controller_Driver_Finally_Set_For_Linux 5.16_–_Phoronix⠀⇛ After stalling last year when it was queued up in HID’s “for-5.10/nintendo” branch only to not make it into HID-next at the time, that threshold has now been crossed with the latest Nintendo Switch controller driver now ready for introduction in Linux 5.16. This open-source driver enables the Nintendo Switch Joy-Con and Pro controllers to work under Linux with a mainline kernel driver. # § Graphics Stack⠀➾ # ⚓ xorg-server_21.1.0_released⠀⇛ This is the final release of X server 21.1. There has been just one fix since the second RC and at this time there are no known regressions since the 1.20 release series. I expect that increased usage after the final release may still uncover something interesting, so there is a potential for subsequent 21.1.1 patch being released in the coming weeks rather than after the usual interval of several months. Notable changes since 1.20 include: - The meson support is now fully mature. While autotools support will still be kept for this release series, it will be dropped afterwards. - Glamor support for Xvfb. - Variable refresh rate support in the modesetting driver. - XInput 2.4 support which adds touchpad gestures. - DMX DDX has been removed. - X server now correctly reports display DPI in more cases. This may affect rendering of client applications that have their own workarounds for hi-DPI screens. - A large number of small features and various bug fixes. Note that since 21.1 series XWayland is released separately and thus this release does not include it. # ⚓ X.Org_Server_21.1_is_Here_After_More_Than_Three_Years of_Development⠀⇛ More than three years after X.Org Server 1.20, released in May 2018, X.Org Server 21.1 finally has been released. The X.Org Server has a long history behind it. It’s the reference implementation of the X Window system first released in June 1984 by its author Robert W Scheifler at Massachusetts Institute of Technology (MIT). X.Org Server is an open source and freely distributed implementation of the X Window System, provided by the X.Org Foundation. It’s part of the X.Org software, the popular X Window System used in many POSIX operating systems, including almost all Linux distributions. # ⚓ X.Org_Server_21.1_Released_With_Variable_Rate_Refresh In_Modesetting_Driver,_Other_Work_–_Phoronix⠀⇛ X.Org Server 21.1 is now officially available as this first xorg-server update in three years and what began development as X.Org Server 1.21 prior to the versioning change. X.Org Server 21.1 brings GLAMOR acceleration for the Xvfb, Variable Rate Refresh (VRR / FreeSync / Adaptive-Sync) support within the generic xf86-video-modesetting driver assuming the underlying DRM/KMS kernel driver supports VRR, much better Meson build system support, X Input 2.4 is integrated that adds support for touchpad gestures, the DMX DDX (Distributed Multihead X) code has been removed, improved display DPI reporting, and a wide variety of other minor improvements and bug fixes. # ⚓ NVIDIA_495.74_Proprietary_Drivers_Released⠀⇛ NVIDIA Corporation introduced the first stable release of the new branch of the proprietary NVIDIA 495.74 driver. At the same time, an update was proposed for the NVIDIA stable branch 470.82.00. The driver is available for Linux (ARM64, x86_64), FreeBSD (x86_64) and Solaris (x86_64). o § Applications⠀➾ # ⚓ Top_6_CAD_viewers_for_Linux⠀⇛ Computer-Aided Design (CAD) uses computers to assist in the creation, modification, analysis, or optimization of a design. The software is used to increase the designer’s productivity, boost the quality of a design, improve communications through documentation, and create a database for production or manufacturing. CAD is an essential part of many streams of engineering. It is professionally used in architecture, auto parts design, aeronautics, interior design, and space shuttle research. Several professional-grade Computer-Aided Design programs like SolidWorks and Autodesk AutoCAD are not natively supported on the Linux platform. So, in this article, we will be looking at the top- performing CAD programs available for Linux. Besides reviewing the available programs, we have also provided the installation instructions for each software. Furthermore, we will give you links to the respective software website to learn more about other distros’ installation procedures. o § Instructionals/Technical⠀➾ # ⚓ Anticipating_Your_Memory_Needs_–_Further_learnings⠀⇛ # ⚓ bkr_job_status ⠀⇛ # ⚓ What_packages_are_Needed_to_build_the_Kernel_|_Adam_Young’s Web_Log⠀⇛ In my quest to automate the testing of the Linux Kernel, I need to automate the build of the Linux Kernel. To build the Kernel, you need the requisite packages. What are they? Let’s find out. I am staring with a Baremetal Fedora Image. It has 344 packages installed already. I’m going to assume that this set is available when I do my automated build as well, or that the needed packages will get pulled in by dependencies. If not, I will find out when my automation fails to run and I will add them at that point. Most Fedora and CentOS based documents on building the Kernel have you do a group install of the “Development Tools” yum package group. I don’t want to do this for two reasons. First, I want to use the beaker format which just lists the packages in the job description. Second, I want to minimize the non-required packages, and Development Tools is general purpose group for coding; not everyone needs everythingm, and I don’t want to put non- essential packages on the system. # ⚓ Yaru-colors:_Give_Ubuntu_folders_a_colourful_Touch_–_Linux Shout⠀⇛ We have a default theme Yaru on Ubuntu 20.04 LTS and in other recent versions of Ubuntu Linux, to give a new feel we can change the accent color of this default theme using Yaru-colors. Well, there are lots of customized themes available to install & apply on Ubuntu, however, what if you don’t want to change the default look of your Linux. I mean the one your getting via Yaru. But still need some new touch & feel on your system. Then try out Yaru-Colors, it will be the visual theme (style of widgets, colors, icons, and GNOME Shell) for official them Yaru of Ubuntu. It is increasingly polished and closely follows the line marked by GNOME. However, not everyone likes the combination and, changing the right thing, Yaru Color is an ideal complement to get away from the characteristic orange, but keep the essence of the distribution. # ⚓ Android_9_on_Linux_|_Linux.org⠀⇛ Many people would sometimes like to have access to Android. In this article, I will cover the steps to install Android 9 on a Virtual Box machine. Having access to Android on your system can make it easier for accessing apps that are only available on Android. # ⚓ How_to_install_the_latest_version_of_Minetest_on_a Chromebook⠀⇛ Today we are looking at how to install the latest version of Minetest on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_Can_You_Install_Google_Browser_on_Debian?⠀⇛ Google Chrome is a widely used web browser in the world. Google Chrome is fast and secure as well. However, it is not an open-source web browser. Hence, Debian comes with a pre-loaded Chromium browser, and not a Chrome. Chromium is an open- source browser. If you still want to install the Google Chrome browser on Linux, this article is for you. Installing Chrome on Linux has a little twist as it’s not an open-source browser. So let’s check out how you can easily install Chrome browser from a Linux terminal. # ⚓ How_to_Install_and_Set_Up_PM2_on_Linux_Servers⠀⇛ Deployment is one of the most crucial and conclusive stages of software development. A proper deployment strategy is vital in delivering the best experience to your users while utilizing your services efficiently. However, this process also brings its own set of challenges with it. Node.js, the open-source JavaScript runtime, is a popular choice for building the backend infrastructure of your application by allowing you to run JavaScript outside web browsers. But what if your Node.js application crashes in production? Find out how you can avoid such scenarios in this article. # ⚓ Create_and_assign_Users_to_Oracle_Databases_–_Unixcop⠀⇛ Hi There ! In this write up, we will discuss about how to create & assign users to the oracle DB As always, begin by connecting to your server where Oracle is hosted, then connect to Oracle itself as the SYSTEM account. The SYSTEM account is one of a handful of predefined administrative accounts generated automatically when Oracle is installed. SYSTEM is capable of most administrative tasks, but the task we’re particularly interested in is account management. # ⚓ How_to_Start_Weblogic_Admin_and_Node_Manager_without password_–_Unixcop⠀⇛ After installing Oracle Weblogic, it’s necessary to give username & password every time it’s prompt. It’s sometime a hassle, for some extent, we don’t want to provide username & password every time. Hello guys ! Today we will learn, how to start the weblogic Admin Server & Node Manager without providing username & password every time. While starting the Admin Server (or) Managed Servers for the first time after the domain creation you must have been prompted for the username and password, In order to handle it, there is a task we need to do. # ⚓ How_to_install_OpenTTD_on_Elementary_OS_6.0_–_Invidious⠀⇛ In this video, we are looking at how to install OpenTTD on Elementary OS 6.0. # ⚓ How_to_reset_weblogic_Admin_user_Password_–_Unixcop⠀⇛ Hi there ! In today’s write up, we will get to know, how to reset the weblogic console/admin password in case you forgot that. This might be a shot article. If you want to learn more about weblogic, please refer to my previous tutorial about instllation & configuration weblogic 14c server on centos 8 from here https://unixcop.com/ oracle-weblogic-14c-on-centos-8/ To reset the password, we first need to go the weblogic domain home. # ⚓ How_to_Create_database_on_Oracle_Database_–_Unixcop⠀⇛ SQL statement is a more manual approach to creating a database than using Oracle Database Configuration Assistant (DBCA). One advantage of using this statement over using DBCA is that you can create databases from within scripts. Hi guys ! In this write up, we will learn, how to create database on oracle database using the manual approach (CMD) When you use the CREATE DATABASE statement, you must complete additional actions before you have an operational database. These actions include building views on the data dictionary tables and installing standard PL/SQL packages. You perform these actions by running the supplied scripts. To Create the database, we have to work through step by step, we will discuss about these below. Seat tight and hold your breath ! # ⚓ Automate_SAP_HANA_System_Replication_in_Cluster_on_IBM Power_Virtual_Servers_in_One_Hour [Ed: SUSE's Web site has become too focused on selling SAP instead or promoting Free software]⠀⇛ # ⚓ How_to_install_Go_(Golang)_in_Arch_Linux/Manjaro_– Citizix⠀⇛ This tutorial will help you install Go(Golang) on a Manjaro/Arch Linux system. This guide can also work for other Linux systems like Debian or Ubuntu or Redhat based systems. Go is a statically typed, compiled programming language designed at Google by Robert Griesemer, Rob Pike, and Ken Thompson. It’s has always been said to be an easy language for developers to learn quickly. Golang is very useful for writing light-weight microservices, infrastructure like networked servers and also tools and systems for developers. It can alsobe used for generating APIs that interact with front-end applications. If you want to build a small functional microservice quickly, then Golang is a great tool to use. # ⚓ Give_Ubuntu_Folders_a_Colorful_Makeup_with_Yaru-Colors⠀⇛ Yaru-Colors is a theme project to bring different colors to Ubuntu’s Yaru theme. Here’s how to install it. Yaru is the default theme for Ubuntu, backed by the community. It is the user interface theme that has been used in Ubuntu since 18.10. The name “Yaru” follows the Japanese influence on Ubuntu’s theme naming and it means “to do.” But what is theme? In short, a theme is what determines the colors, borders, shadows, size, and shape of individual elements on the screen. # ⚓ How_to_Install_SaltStack_Minion_on_CentOS_8/_RHEL_8_– Unixcop⠀⇛ Salt (sometimes referred to as SaltStack) is Python-based, open-source software for event-driven IT automation, remote task execution, and configuration management. Supporting the “infrastructure as code” approach to data center system and network deployment and management, configuration automation, SecOps orchestration, vulnerability remediation, and hybrid cloud control. SaltStack minion is the agent software that is installed on the managed node. Used to execute and run the commands on that node and report back to SaltStack master server. # ⚓ How_to_Install_SaltStack_Master_on_CentOS_8/_RHEL_8_– Unixcop⠀⇛ Salt (sometimes referred to as SaltStack) is Python-based, open-source software for event-driven IT automation, remote task execution, and configuration management. Supporting the “infrastructure as code” approach to data center system and network deployment and management, configuration automation, SecOps orchestration, vulnerability remediation, and hybrid cloud control. SaltStack Master is the server node, it is the central server that controls all the Salstack Minions. Master server holds the Inventory and Public Keys of Minions and perform remote execution on them. The Salt master daemon, used to control the Salt minions. # ⚓ Generate_File_of_Specific_Size_on_Linux_(With_Commands)_– Linux_Nightly⠀⇛ Generating files of a specific size can be useful for testing purposes. There are several different commands in Linux that can create files of certain sizes. Check out the commands and examples below to learn how. # ⚓ How_To_Install_Brave_Browser_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install Brave Browser on AlmaLinux 8. For those of you who didn’t know, Brave is a free and open-source web browser developed by Brave Software, Inc. based on the Chromium web browser. Brave is a privacy- focused Internet web browser, which distinguishes itself from other browsers by automatically blocking online advertisements and website trackers in its default settings. Brave is also called a “crypto browser” because it uses the Ethereum blockchain that is used to secure user data. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Django web framework on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_to_install_Go_in_Fedora_and_Rocky_Linux/Centos/RHEL_– Citizix⠀⇛ This tutorial will help you install Go(Golang) on a Fedora or a RHEL based system i.e. Centos/Rocky Linux/Alma Linux/RHEL. This guide can also work for other Linux systems like Debian and Ubuntu besides the Redhat specifics like the running the yum commands. Go is a statically typed, compiled programming language designed at Google by Robert Griesemer, Rob Pike, and Ken Thompson. It’s has always been said to be an easy language for developers to learn quickly. Golang is very useful for writing light-weight microservices, infrastructure like networked servers and also tools and systems for developers. It can alsobe used for generating APIs that interact with front-end applications. If you want to build a small functional microservice quickly, then Golang is a great tool to use. # ⚓ How_to_install_MX_Linux_21_–_Invidious⠀⇛ In this video, I am going to show how to install MX Linux 21. # ⚓ Yarn_Introduction_and_Tutorial⠀⇛ Yarn is an abbreviation of “Yet Another Resource Negotiator” and is a package manager of various software programs. The best thing about yarn is that it permits you to share and utilize code securely and rapidly among distinct developers all around the globe. If you want to create your own software and you are facing difficulty in it then Yarn will help you to use the solution of other developers. When you are using Yarn and there is an existing issue in it then we will report it and when the issue is resolved then you can again use the updated yarn. Module or package is the means to share a code. The package consists of a code along with all its description in the “package.json” file. # ⚓ How_to_install_the_Tsurugi_Linux_distribution_– TechRepublic⠀⇛ Digital forensics and incident response are complementary activities that not only require solid knowledge of operating systems and the internet, but also a lot of tools, depending on the desired goal. One investigator might want to simply recover a file from a forensically acquired hard drive, while another might want to do a full analysis of a system and check multiple items about it. Tsurugi Linux allows doing all of this. # ⚓ How_to_Convert_Between_Linux_Packages_Using_Alien⠀⇛ Do you want to convert a Linux package to some other format? Perhaps the package you’re looking for isn’t available for your distro but you still want it no matter what. Or maybe you are a developer and want to save your time by quickly repackaging your program to other formats without having to build the package again. Fortunately, Linux has got the tool you need. With Alien, you can easily convert your existing Linux package to other formats through the command line. Let’s start by installing the tool on your system first. # ⚓ How_to_Boot_into_Rescue_Mode_or_Emergency_Mode_in_Ubuntu⠀⇛ Ubuntu and other Linux distributions often might get broken due to many reasons. Sometimes, you may just lose access to your operating system or forget the root password. In those circumstances, chances are that you would probably think of erasing your current OS and reinstalling the Ubuntu OS again. In addition, to back up the data you might also use the GParted tool. But, all the above solutions are really time-consuming and not so much techy-geeky to recover an unbootable Linux OS. Instead of reinstalling, you can boot into rescue mode or emergency mode in Ubuntu to fix the system. Please follow the methods mentioned below carefully if you’re a newbie to Ubuntu and had already got your system broken. o § Games⠀➾ # ⚓ Godot_Engine_–_Multiplayer_in_Godot_4.0:_ENet_wrappers, WebRTC.⠀⇛ Howdy Godotters! Time for yet another status update on networking in Godot. This time, we are going to dig a bit deeper into the low-level territory, showing some of the new ENet features exposed in Godot 4, and the effort of bringing WebRTC on all Godot-supported platforms. # ⚓ Release_candidate:_Godot_3.4_RC_2⠀⇛ The upcoming Godot 3.4 release will provide a number of new features which have been backported from the 4.0 development branch (see our release policy for details on the various Godot versions). With this second Release Candidate, we have frozen feature development and are nearly ready to release the stable version. If you already reviewed the changelog for RC 1, you can skip right to the differences between RC 1 and RC 2. # ⚓ Vintage_Arcade_Used_Negative_Voltage_To_Turn_Volume_Up_To 11_|_Hackaday⠀⇛ When [Nicole Express] got her hands on the logic board for the 1986 SNK arcade game Athena, she ran into a rather thorny problem: The board expected to be fed negative five volts! [Nicole]’s analysis of the problem and a brilliant solution are outlined in her well written blog post. [Nicole]’s first task was to find out which devices need negative voltage. She found that the negative five volts was being fed through a capacitor to the ground pins on the Mitsubishi M151516L, an obscure 12 W audio amplifier. After finding the data sheet, she realized something strange: the amp didn’t call for negative voltage at all! A mystery was afoot. To fully understand the problem, she considered a mid-1980’s arcade and its cacophony of sounds. How would a manufacturer make their arcade game stand out? By making it louder, obviously! And how did they make their game louder than the rest? # ⚓ Paradox_needs_a_bit_more_time_to_finish_Crusader_Kings_III –_Royal_Court_|_GamingOnLinux⠀⇛ Crusader Kings III, the popular strategy game from Paradox is expanding with the upcoming Royal Court DLC but it’s just not ready yet. Announced on Tuesday, October 26, Paradox said plain and simply that “we are not, at the moment, entirely satisfied with Royal Court’s progress, especially regarding its stability” and so it’s going to release at some point during 2022 but they’re not giving us a date as to when just yet. With this being the first CKIII expansion, Paradox said it will include “a set of features entirely new to the CK series, including cultural evolution and language” and so they are continously experimenting with it. # ⚓ Little_Big_Adventure_1_&_2_get_open_sourced_under_the_GPL⠀⇛ Little Big Adventure 1 and 2 are two classic titles originally developed by Adeline Software International and now they’ve both had their engine source code officially released. # ⚓ Mind-bending_puzzler_Superliminal_is_getting_a_multiplayer mode_|_GamingOnLinux⠀⇛ Superliminal is a pretty great puzzle game all about using the ambiguity of depth and perspective and to celebrate a year since the Steam release it’s getting multiplayer. In the main single-player game, you interact with various objects in the world based on your position and how you’re looking at them. It enables you to grab these items, make them big or small and use them to overcome some pretty fun puzzles. The new mode is an “experimental” Battle Royale that will be “available through the holiday season” (whatever that means). o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_Connect_Your_iPhone_to_Linux⠀⇛ One of the biggest benefits of being all-in with Apple’s ecosystem is integration. My text messages automatically appear on my Mac and sharing files from iOS to macOS is a breeze. Even the clipboard integrates my mobile devices with my desktop. Now, a project called KDE Connect brings much of that tight integration to Linux. # ⚓ I’m_livestreaming_Kalendar_development!⠀⇛ Today (Wednesday 27th Oct) at 18:00 CEST I will be streaming some Kalendar development live on YouTube and on KDE’s Peertube instance. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ Makulu_Shift_Ubuntu_Variant_Released⠀⇛ We have just released the much awaited Beta build of Shift ( the Ubuntu Variant ), It is marked as a stable Build that can be used as a daily Runner. # ⚓ First_Shift_Patch_sent_out⠀⇛ We have just sent out the First big Patch for the new Makulu shift ( Ubuntu Variant released earlier today ). This patch now completes the Desktop Manager and makes some significant changes. Please keep in Mind that Shift Ubuntu is a build we are now constantly working on and updating, therefore you will notice a lot of changes over a short period of time, so expect many updates. ISO’s will also regularly get updated on the Website. You can see the Full video of what’s new in the latest patch here : # § FSF-Approved⠀➾ # ⚓ Release_announcement:_Trisquel_9.0.1_Etiona_security update⠀⇛ Images are available at https:// trisquel.info/download or directly at https:/ /cdimage.trisquel.info/ and its mirrors. This minor update to the 9.x “Etiona” series is intended to provide an up to date set of ISO images, both for use as an installation medium and as a live environment with newer packages. # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾ # ⚓ Min_Browser_»_PCLinuxOS⠀⇛ Min Browser has been updated to 1.22.0. Min is a fast, minimal browser that protects your privacy. # ⚓ Zoom_»_PCLinuxOS⠀⇛ Zoom desktop has been updated to 5.8.3.145. Zoom is a meeting client for the Linux desktop. # ⚓ Signal_Desktop_»_PCLinuxOS⠀⇛ Signal Desktop has been updated to 5.21.0. Signal is Private Messenger for Linux. # § SUSE/OpenSUSE⠀➾ # ⚓ SUSE_heads_for_the_Edge_Computing_with_SUSE_Linux Enterprise_Micro_5.1⠀⇛ Once upon a time, we got Linux distributions because they were the Swiss-Army Knives of operating systems. They came with every program you might ever need. You can still get those, of course. But, lately, businesses have been wanting lightweight, secure Linux distros for cloud and edge computing containers and virtual machines (VM)s. To meet that demand, the latest business-class Linux is SUSE’s new SUSE Linux Enterprise Micro 5.1 (SLE Micro). # § IBM/Red Hat/Fedora⠀➾ # ⚓ Assess_resource_consumption_with_Ansible_callback plugins⠀⇛ When you need metrics about playbook execution, callback plugins can help you drill down into the data and troubleshoot issues. # ⚓ Red_Hat_OpenShift_4_Migration:_Modernizing_your_cloud platform⠀⇛ So you’re still using Red Hat OpenShift 3 in your production environment, and everything is running smoothly. “Why should I update to Red Hat OpenShift 4? Version 3 works just fine,” you might say. Maintenance Support for Red Hat OpenShift 3.11 ends June 2022, followed by a final two- year end-of-life phase. You might not be sure how to start your migration to Red Hat OpenShift 4 or understand what it offers. In this post, we’ll walk you through some new features and benefits to help you get started. # ⚓ Red_Hat_Developer_roundup:_Best_of_October_2021⠀⇛ We’re baaack (just in time for Halloween) with the monthly highlights from our developer experts working at Red Hat. This month features hands-on introductions to VS Code for Java extension 1.0, the new developer console for Red Hat OpenShift 4.9, and Helm Chart for Red Hat JBoss Enterprise Application Platform. We also have a quick guide to using Multipath TCP (included with Red Hat Enterprise Linux 8) to cut through the noise in your network. Keep reading for these highlights and more. # ⚓ Announcing_Service_Binding_Operator_1.0_GA_|_Red_Hat Developer⠀⇛ In the context of Kubernetes, the exposure of Secrets for connecting applications to external services such as REST APIs, databases, and event buses is manual and bespoke. This action is usually referred to as binding. The process of configuring and maintaining the binding is error-prone and can lead to challenges and debug failures. Indeed, each service provider suggests a different way to access their Secrets, and each application developer in turn consumes those Secrets in a custom way for their applications. Service Binding Operator 1.0, now in general availability (GA), expands the developer capabilities available on Red Hat OpenShift. As we’ll see in this article, Service Binding Operator makes it easy for developers to connect their applications to backing services like REST APIs, databases, event buses, and others, providing a consistent and predictable experience. # ⚓ Send_S3_data_to_Telegram_with_Red_Hat_OpenShift Serverless_Functions⠀⇛ Red Hat OpenShift Serverless Functions is a framework with tooling to support function development. The framework is built on top of the open source Knative project. It has been available in Tech Preview since Red Hat OpenShift 4.7 and is available on 4.6 (EUS) as well. The central tool in OpenShift Serverless Functions is the kn func command, a plug-in extending the Knative kn command- line interface (CLI) to enable function development on the Knative platform. Development of this plug-in is led by Red Hat through the Boson Project. This open source project has generated interest in the Knative community because function development capabilities atop Knative have been long- awaited and highly anticipated. The Boson Project has been officially donated to the Knative project and its community. Let’s take a look at some of the new features added recently to OpenShift Serverless Functions. To demonstrate these capabilities, we will implement a simple Quarkus function that consumes data from an AWS S3 bucket and sends it to a Telegram chat. # ⚓ IT_careers:_10_ways_to_prove_yourself_during_remote work_|_The_Enterprisers_Project⠀⇛ If an IT professional achieves a big win in her home office in the country, does it make a sound? Perhaps you’re aware of the term “proximity bias:” the unconscious human tendency to favor what is closest to us. Veteran remote workers have long been aware of the predisposition for – and, in many cases, a clear cultural practice of – valuing more highly those employees who physically come into the office every day. People now navigating a hybrid work environment for the first time may also see this dynamic. “It can be difficult to prove your value in a remote work situation because no one can see you and get a visual sense of how you’re performing,” says Cliff Milles, lead technical recruiter at Sungard Availability Services. This can be a particular challenge for IT leaders. “In more senior positions there is more emphasis on relationship-building, stakeholder management, and leading by example, which then sets the tone and culture for others,” says Lars Hyland, chief learning officer of Totara Learning, a provider of enterprise learning, engagement, and performance management technology. # ⚓ 4_IT_leadership_tips_for_turbulent_times_|_The Enterprisers_Project⠀⇛ Even as many IT teams delivered results with little disruption in the last 18 months, the pandemic brought into focus the importance of soft skills in technology leadership. This is where businesses need to invest the most time in the remaining weeks of 2021 and beyond. Technical expertise has always been a given in IT roles, but the ability to motivate staff, help build their skills, and look after their emotional wellbeing requires a different set of capabilities entirely. Successfully blending the two elements is the ultimate challenge of any tech leader. Here are some key areas to focus on to ensure future success for your IT teams. # ⚓ ELevate_project_to_simplify_migration_from_CentOS_7 to_RHEL_8_based_distributions⠀⇛ AlmaLinux distribution developers based company CloudLinux in response to a premature folding support CentOS 8, presented tools ELEVATE , to simplify migration of operating systems on CentOS 7.x distributions built on packet-based RHEL 8, preserving applications, data and settings. The project currently supports migration to AlmaLinux, Rocky Linux, CentOS Stream and Oracle Linux. The migration process is based on the use of the Leapp utility developed by Red Hat , which is supplemented with patches that take into account the specifics of CentOS and third-party distributions built on the RHEL package base. The project also uses an extended set of metadata describing the steps for transferring individual packages from one branch of the distribution to another. # § Debian Family⠀➾ # ⚓ Sparky_6.1_RC1_ARMHF⠀⇛ Sparky 6.1 Release Candidate 1 ARMHF for single board machines RaspberryPi is out. It is based on Debian Bullseye packages and build using the pi-gen script. The system works on Linux kernel 5.10.63 and is available, as before, in two versions: – Openbox – with small set of applications – CLI – text mode only to do it yourself user: pi, password: sparky root user password: toor # ⚓ Bluez_5.62_compiled_in_OpenEmbedded⠀⇛ EasyOS 3.1 has package bluez5 version 5.54. There have been improvements since then, so I have compiled 5.62 in OE. o § Devices/Embedded⠀➾ # ⚓ Tiny_SBC_runs_Linux_on_new_RAM-equipped_Allwinner_RISC- V_SoC⠀⇛ MangoPi is prepping a tiny “MangoPi-MQ1” SBC with the new Allwinner F133-A (D1s), a spin-down of Allwinner’s D1 that adds 64MB RAM. Both SoCs use the XuanTie C906, one of several RISC-V cores that Alibaba T-Head is now open sourcing. A MangoPi project from Beijing Wadora Technology Co. has announced a Linux-driven MangoPi-MQ1 SBC equipped with a new Allwinner F133-A (D1s) SoC. Allwinner’s F133-A is a slightly scaled down version of the Allwinner D1 SoC, which powers Sipeed’s Nezha SBC. Both SoCs are equipped with a RISC-V architecture XuanTie C906 core, which last week Alibaba’s T-Head subsidiary announced is being open sourced along with several other cores (see farther below). # ⚓ Raspberry_Pi_4_achieves_Vulkan_1.1_conformance,_gets_up_to 60%_GPU_performance_boost⠀⇛ Khronos has just granted Vulkan 1.1 conformance to Raspberry Pi 4 SBC, and following the implementation of various optimizations and new features such as geometry shaders, the v3dv Mesa driver delivers up to 60% higher GPU performance in Unreal Engine 4. Iglia started Vulkan driver work for Raspberry Pi 4 almost two years ago, with the triangle demo showcased in February 2020, followed by Vulkan 1.0 conformance in November 2020, and now the driver is certified conformant to Vulkan 1.1. While many GPUs are conformant, the Raspberry Pi 4 is only joined by a couple of complete platforms including several NVIDIA Jetson modules (Vulkan 1.2), and possibly some Intel and Google platforms shown as “Confidential” at this time. # ⚓ CompuLab_IOT-GATE-RPI4_gateway_targets_industrial_control and_monitoring⠀⇛ Compulab IOT-GATE-RPI4 is another industrial gateway based on the Raspberry Pi CM4 module that offers a different feature set and form factor compared to solutions like TECHBASE iModGATE-AI gateway or QWave Systems CatsPi Industrial carrier board. Designed with industrial control and monitoring in mind, the IOT-GATE-RPI4 gateway offers multiple RS485, RS232 and CAN FD ports, Ethernet, 4G LTE/4G, WiFi 802.11ac, and Bluetooth 5.0 connectivity, as well as a wide -40°C to 80°C operating temperature range, plus a wide input voltage from 8V to 36V as well as PoE support. # § Open Hardware/Modding⠀➾ # ⚓ ESP32_Clock_Takes_Time_to_Give_Weather_Info,_Too⠀⇛ It’s fall in the northern hemisphere, so [Mike Rankin]’s kids are back in school and have returned to consulting him every morning about the weather and what they should wear. Since he’s no meteorologist, [Mike] built a beautifully dim and diminutive clock that does all the work for him, plus much more. It glows a lovely dark orange that’s perfect for the nightstand and those early morning interrogations. In default mode, this clock displays the time, CO2 level, room temperature, and humidity in that eye-friendly orange. But wave your hand in front of the time of flight sensor, and it goes external, displaying the low and high temperatures for the day, plus the weather conditions forecast. After a few seconds of that, it goes back to default mode. The ESP fetches the time from an NTP server, then gets the weather from the OpenWeather API. The indoor weather comes from a combination sensor on the board. # ⚓ 3D_Printed_IoT_Weather_Station_Dashboard⠀⇛ This is my dashboard for my 3D Printed IoT Weather Station project, you can build your own by following my build guide. # ⚓ I_Upgraded_My_3D_Printed_Weather_Station_Using_Your Suggestions⠀⇛ Today we’re going to be making some upgrades to my previously built IoT weather station using suggestions that you guys made in the comments section. We’ll see how well the weather station performs after the upgrades and I’ve included a link to the public Thingspeak channel, so you can have a look at the most recently recorded data. # ⚓ Add_Mycelium_To_Your_Mesh_Networks⠀⇛ In many parts of the world, days after a good rainfall, it’s fairly common to see various species of mushrooms popping up out of the ground. These mysterious organisms aren’t the whole story, though. The living being is a vast network of hidden fibers, called mycelium, spreading through the ground and into any other organic material it can colonize. Its air of mystery and its vast reach are the inspiration for entire Star Trek shows and, of course, projects like this LoRa-based mesh network called Mycelium. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Future_proof:_Fairphone_has_gone_5G⠀⇛ It is not new news that we strive to make the most of the materials used in our products. We’re moving closer to a circular economy by using materials from more responsible sources, emphasizing reuse and recycling, and designing our phones to last as long as possible. We do this for a simple reason: the longer you use your phone, the smaller your environmental footprint. But we want to take this one step further and future proof your phone. The only way to do this is to provide you with a 5G device – a tech spec of the future – for Fairphone 4. o § Free, Libre, and Open Source Software⠀➾ # § Events⠀➾ # ⚓ Virtual_Conferences:_a_love-hate_relationship⠀⇛ I love conferences. Now, that most conferences are either virtual or hybrid (both virtual and on-premises), people often say that it must be heaven for me. I can visit many more conferences and give many more talks. Well, it is not just this simple. Virtual conferences are a love-hate relationship for me. Of course, there are some advantages, but also disadvantages. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Tired_of_spam?_A_burner_email_account_could_be the_answer.⠀⇛ Have you ever been in that situation where you need to give your email address over, but you don’t want to? There could be a security reason. Can you trust who you’re sharing with not to spam your inbox? Are you certain they won’t expose you to data breaches due to lax security on their part? Can you protect your email from being sold in lists, used for ad tracking and targeting or even be uploaded to platforms like Facebook to track and target you there? Or it could be a case of inbox fatigue. Or maybe you just don’t want your email associated with some entities and in their database? Enter the burner email account. # § FSFE⠀➾ # ⚓ Router_Freedom_at_risk:_Latvia_allows_restrictions_to consumers’_rights⠀⇛ Latvia’s reform of the telecom law weakens Router Freedom in the country. The national regulator, SPRK, has allowed ISPs to restrict the use of personal routers on the grounds of “technological necessity”. We explain why this is problematic and what impact it can have for end-users’ rights. Router Freedom is the right end-users have to choose and use their own modems and routers to connect to the Internet. Since 2020, European countries have been in a process of implementing this right within a reform of EU telecommunications law. In this context, Latvia has created a risky precedent against end-users’ rights by allowing internet service providers (ISPs) to determine restrictions on the use of personal routers and modems based on “technological necessities”. The FSFE has engaged with the Latvian regulator, SPRK, to stress the necessity to change the law as it represents a big loss for consumer rights. # § Programming/Development⠀➾ # ⚓ A_Clang_compiler,_a_hidden_visibility,_and_a_weak symbol⠀⇛ The LLVM packaging team recently ran into a compiler problem. A build of the LLVM package with Clang, with link-time optimization activated, failed validation. This article steps through how we explored, identified, and ultimately fixed the problem. * § Leftovers⠀➾ o ⚓ The_Animal_Years⠀⇛ Discussing why anthropomorphism came to dominate early animation, and why that trend never really faded away, while rubber-hose animation quickly did. o § Science⠀➾ # ⚓ Product_release_cycles_are_killing_the_environment,_techies tell_British_Computer_Society⠀⇛ o § Health/Nutrition⠀➾ # ⚓ Four_COVID_vaccine_shots._-FDA_(No_thanks.)⠀⇛ Now the FDA is saying we might “need” a fourth. I’m not going to do it. The third, for me, was the weirdest. The side effects lingered for about a month before they went away. They involved burning sensation in my arm, slight chest pain, fatigue, some memory problems, and hot flashes, and while it seems to be over with, I don’t think I’ll be getting a fourth shot. I can’t risk this getting worse each time. How many of these things are you supposed to take? How much are the side effects going to continue escalating? And at what point has it either “worked” or not “worked” well enough that you don’t need any more doses for the foreseeable future? [...] If they wanted to throw gasoline on the anti-vaxxer fire that was already raging, I can’t think of a better way to do it. This sends the message that no matter how many doses you take, your phone will be buzzing off the hook anyway and it’ll be the government stating that you need more. [...] It’s bad enough to have to make choices like this when you’re almost 40 and half your life is probably over anyway, and certainly your prime years, but children? This is going somewhere I had hoped it wouldn’t. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Security_updates_for_Wednesday⠀⇛ Security updates have been issued by Debian (mosquitto and php7.0), Fedora (python-django-filter and qt), Mageia (fossil, opencryptoki, and qtbase5), openSUSE (apache2, busybox, dnsmasq, ffmpeg, pcre, and wireguard-tools), Red Hat (kpatch-patch), SUSE (apache2, busybox, dnsmasq, ffmpeg, java-11- openjdk, libvirt, open-lldp, pcre, python, qemu, util-linux, and wireguard-tools), and Ubuntu (apport and libslirp). # ⚓ Linux_Foundation:_confidential_computing_market to_reach_$54_billion_in_2026 [Ed: ZDNet writing more Linux_Foundation ‘spam’ today. They’re paid to do this. They paint_surveillance_as_“security” and_“confidential”.]⠀⇛ # ⚓ Kali_Linux_Wordlist:_What_you_need_to_know⠀⇛ wordlist can be referred to as a password dictionary since it is a collection of passwords stored as plain text. Kali Linux is the most advanced penetration testing distribution. It is primarily designed for penetration testing and digital forensics hence funded and maintained by Offensive Security. Most Kali Linux wordlists can be downloaded online, including those provided in this article. In addition, there are a collection of common and uncommon passwords that are still or were once used by real people. Remember, you can also create your wordlist if you prefer to or stick to the ones already compiled. Wordlists are derived from data breaches such as circumstances where the company gets hacked. Data stolen from the hacked companies are leaked on websites such as Pastebin or sold on the dark web. # ⚓ FBI_Releases_Indicators_of_Compromise Associated_with_Ranzy_Locker_Ransomware⠀⇛ The Federal Bureau of Investigation (FBI) has released a Flash report detailing indicators of compromise (IOCs) associated with attacks using Ranzy Locker, a ransomware variant first identified targeting victims in the United States in late 2020. # ⚓ Warehouse_belonging_to_Chinese_payment_terminal manufacturer_raided_by_FBI⠀⇛ US feds were spotted raiding a warehouse belonging to Chinese payment terminal manufacturer PAX Technology in Jacksonville, Florida, on Tuesday, with speculation abounding that the machines contained preinstalled malware. PAX Technology is headquartered in Shenzhen, China, and is one of the largest electronic payment providers in the world. It operates around 60 million point-of-sale (PoS) payment terminals in more than 120 countries. # § Privacy/Surveillance⠀➾ # ⚓ License_plate_scanners_were_supposed_to bring_peace_of_mind._Instead_they_tore_the neighborhood_apart.⠀⇛ License plate readers are rapidly reshaping private security in American neighborhoods, bringing police surveillance tools to the masses with an automated watchdog that records 24 hours a day. With “safety-as-a-service” packages starting at $2,500 per camera a year, the scanners are part of a growing wave of easy- to-use surveillance systems promoted for their crime-fighting powers in a country where property crime rates are at all- time lows. Once found mostly in gated communities, the systems have — with help from aggressive marketing efforts — spread to cover practically everywhere anyone chooses to live in the United States. Flock Safety, the industry leader, says its systems have been installed in 1,400 cities across 40 states and now capture data from more than a billion cars and trucks every month. “This is not just for million- dollar homes,” Flock’s founder, Garrett Langley, said. “This is America at its core.” # ⚓ Here’s_the_FBI’s_Internal_Guide_for Getting_Data_from_AT&T,_T-Mobile,_Verizon⠀⇛ A newly obtained document written by the FBI lays out in unusually granular detail how it and other law enforcement agencies can obtain location information of phones from telecommunication companies. Much of the information reiterates what we already knew about law enforcement access to telecommunications data—how officials can request location data from a telecom with a warrant or use court orders to obtain other information on a phone user, for example. But the document does provide insights on what exactly each carrier collects, a more recent run-down of how long each telecom retains certain types of data for, and images of the tool the FBI makes available to law enforcement agencies across the country to analyze cell phone tower data. Ryan Shapiro, executive director of nonprofit organization Property of the People, shared the document with Motherboard after obtaining it through a public record act request. Property of the People focuses on obtaining and publishing government records. # ⚓ How_the_FBI_Gets_Location_Information⠀⇛ Vice has a detailed article about how the FBI gets data from cell phone providers like AT&T, T- Mobile, and Verizon, based on a leaked (I think) 2019 139-page presentation. # ⚓ Google_said_it_had_successfully_‘slowed down’_European_privacy_rules,_according_to lawsuit.⠀⇛ Google said in an internal document that it had successfully “slowed down” European privacy rules in collaboration with other tech companies, according to a legal filing released on Friday. Ahead of a 2019 meeting with other major tech companies, Google said in a memo that it had “been successful in slowing down and delaying” the European Union’s ePrivacy Regulation process and had been “working behind the scenes hand in hand with the other companies,” according to the filing. # ⚓ More_than_100,000_people_have_had_their eyes_scanned_for_free_cryptocurrency⠀⇛ More than 100,000 people have had their eyes scanned in return for a cryptocurrency called Worldcoin, as a project to distribute digital money more widely around the world accelerates. Worldcoin has distributed about 30 iris-scanning hardware devices, which they call “orbs,” to early users on four continents, who get rewards for signing up more people. Orbs take photos of a user’s eyeballs, creating a unique code that can be used to claim free digital tokens. o § Environment⠀➾ # ⚓ Plastic_industry_pollution_to_overtake_coal_in_US_by_2030, report_says⠀⇛ Plastic pollution usually conjures images of grocery bags blowing in the wind or nurdles lodged in a seabird’s stomach. But soon, plastic pollution may take on another meaning, as a new report forecasts that the industry’s greenhouse gas emissions in the US will outpace those of coal by the end of the decade. o § Civil Rights/Policing⠀➾ # ⚓ EU_fines_Poland_€1_million_per_day_over_judicial_reforms⠀⇛ # ⚓ U.S._FTC_needs_rulemaking_to_protect_privacy_and_civil rights_–_Access_Now⠀⇛ Today, Access Now joined Free Press and partner organizations in calling on the U.S. Federal Trade Commission (FTC) to initiate a rulemaking to protect privacy, promote civil rights, and set data protection standards. This call aligns with Senators’ request for the same rulemaking process. How data is collected, processed, and shared has a direct impact on economic opportunities and falls squarely within the FTC’s authority. Companies use personal data to enable and even perpetuate discriminatory practices against people of color, women, members of the LGBTQ+ community, religious minorities, people with disabilities, and other marginalized groups. # ⚓ Where_the_EU’s_DSA_is_heading_—_and_where_it_needs_to_go_– Access_Now⠀⇛ The EU Digital Services Act (DSA) is an ambitious proposal with the potential to empower people in today’s online ecosystem. It is the first legislative proposal worldwide that seeks to establish systemic regulation of “Big Tech” platforms like Facebook or Google to address their impact on public discourse. If done right, the DSA could be an effective tool for preventing the spread of illegal content, protecting fundamental rights, and correcting the power imbalance between users and platforms. Done wrong, however, the DSA could harm the vulnerable communities it is supposed to help, and erode the freedom of expression and opinion — not just in the EU but around the world. So where does this promising regulation stand now? And what needs to happen to ensure its efficacy? We look at the introduction of the DSA, how the negotiations have progressed, and where we need to go from here to safeguard human rights. o § Digital Restrictions (DRM)⠀➾ # ⚓ Disney+_streams_to_Linux-based_VIDAA_Smart_OS⠀⇛ Disney+, a world-renowned streaming application, and VIDAA, a Linux-based smart TV operating system, announced that Disney+ will be coming soon to VIDAA Smart OS-powered Hisense and Toshiba smart televisions, with the latest firmware version. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Marxist_Astronomy:_The_Milky_Way_According_to_Anton Pannekoek_–_The_Public_Domain_Review⠀⇛ Can a person’s experiences on earth alter how they perceive the stars? Lauren Collee peers through the telescope of Anton Pannekoek, the Dutch astronomer whose politics informed his human approach to studying the cosmos. # ⚓ William_Baillie-Grohman’s_*Sport_in_Art*_(1913)_–_The Public_Domain_Review⠀⇛ William Baillie-Grohman’s text on the art of hunting reproduces 243 illustrations and 400 years of arcane knowledge related to the pursuit of animals. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 7750 ➮ Generation completed at 02:41, i.e. 69 seconds to (re)generate ⟲