𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, July 13, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Thu 14 Jul 02:39:39 BST 2022
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/2022/07/13/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
  Previous bulletins in IPFS (past 21 days, in chronological order):

QmXFr24fsod4hN7dFFg3cke2MTRCdpmXGmrzBy4E9SuDmx
QmTweJ4nXQtfXHVgJZdLDGsqQhGfYUadfZnLsNyG957hjX
QmaWVVRETtCzr9u3pkbf9NmBNErxp6EwwuuRbbGaNBDbxs
QmRnbEP8kvfDSZqPYikywBMxdJ2dsMPv4ujj2tKn8HPofU
QmRdcPDNXG7La9xrpj9Te3TGetenUACvpQoAsNtm1XNbZY
QmWvpCp84jsz33ggJ9VGNJLVVweLbvAgZC4QSMMpMtjws4
QmTanxCbrRzbMhGwCHPd6tznN3vqohgB6ksoqtyCiMnDFL
QmSGNyqayw9Kb8GtH2D4DicRMEG9NuJ9kQEJo4KgFc1NeH
QmcVu8iJ8yJqBwWTWX3TYY3ChamvbJm15Ne1VJxfTjdLY6
QmSDCize8znng3qFHzA4NgsDaeV7fzdXZrj1CKRp5JBbgK
QmW2xppCHSDJtWfjB5RvaKrsEtS7w97YEMS3ePee6oW9Mp
QmSGhRVAV44sV2y4ZAiDWo9kvmhjvgBBfpAKFP6AdRx6Pc
Qmf7RX5zTm8khR5YEXJ6a48wsPiHG9zDm63S7nvMHXK1PE
QmZQcpV8gJiG7uwAzM2U75TrNyBfZY4RZNaGfhLLDxdSqB
QmajcAdRfWtgWFRoBM7yDJL3X8EJ5w8Wxf6CNnraP2EQo6
QmateHRg7s96CyDx4BcnezZSfn66P9YWrKiMv5VvFfNyEU
QmehYSPymw58ozer2trPYvEomCKmEguPNgE3qdCbXcmNW9
QmP3Nw5usXTHPhcMx8yZ9TYsWzwSKRw9BNnbjhkoJ88gpe
QmNt7g1pzLJJDE5MHZ21wEEuyos1W3DFP2LTSjB2FLPJPi
QmXniW6uykwhxPzQFCih3ywbRTbNtozdD9MTkKJWNUUis7
Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF


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

⦿ [Meme] Steven J. Vaughan-Nichols Defending Crime Again | Techrights

⦿ Why the EPO Bubble Matters | Techrights

⦿ When EPO Does Not Control and Coerce the Judges — Part IV — No End in Sight for a System of “Institutionalised Injustice”? | Techrights

⦿ The EPO Bubble — Part I — An “Unprecedented Surge” | Techrights

⦿ There Are Probably Over a Million Gemini Pages Already (Static, Not Generated on Demand) | Techrights

⦿ [Meme] The Year is 2032: ILOAT Tells Campinos That He Broke the Law, Repeatedly | Techrights

⦿ When EPO Does Not Control and Coerce the Judges — Part III — ILOAT Judgment No. 4551 | Techrights

⦿ IRC Proceedings: Tuesday, July 12, 2022 | Techrights

⦿ Obscene Lack of Justice at the European Patent Office (EPO) | Techrights

⦿ [Meme] Legacy of UEFI ’Secure’ Boot: BSD and GNU/Linux Users Now Have to ‘Jailbreak’ Their PCs (Desktops/Laptops, Just like Apple iPhones) | Techrights

⦿ There’s No F***ing Debate With “the F***ing President” (What António Campinos Calls Himself!) | Techrights

⦿ [Meme] “There is No Crueler Tyranny Than That Which is Perpetuated Under the Shield of Law and in the Name of Justice.” | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/07/13/defending-microsoft-crime/#comments
		http://techrights.org/2022/07/13/epo-bubbles-matter/#comments
		http://techrights.org/2022/07/13/epo-institutionalised-injustice-in-action/#comments
		http://techrights.org/2022/07/13/epo-unprecedented-surge/#comments
		http://techrights.org/2022/07/13/geminispace-size-2022/#comments
		http://techrights.org/2022/07/13/iloat-a-decade-late/#comments
		http://techrights.org/2022/07/13/iloat-ruling-a-decade-late/#comments
		http://techrights.org/2022/07/13/irc-log-120722/#comments
		http://techrights.org/2022/07/13/lack-of-justice-at-the-epo-2/#comments
		http://techrights.org/2022/07/13/legacy-of-uefi-secure-boot/#comments
		http://techrights.org/2022/07/13/no-epo-debate/#comments
		http://techrights.org/2022/07/13/reaking-laws-to-uphold-laws/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/07/13/debian-11-4-0-tour/#comments
		http://techrights.org/2022/07/13/free-software-in-dod/#comments
		http://techrights.org/2022/07/13/linux-mint-21-beta/#comments
		http://techrights.org/2022/07/13/microsoft-patch-tuesday/#comments
		http://techrights.org/2022/07/13/rust-loss-of-people/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 84

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/defending-microsoft-crime/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/defending-microsoft-crime/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Steven_J._Vaughan-Nichols_Defending_Crime_Again⠀✐


Posted in Deception, Microsoft at 8:34 pm by Dr. Roy Schestowitz


                 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇SJVN shilling Microsoft⦈
 Microsoft, according to SJVN, “hasn’t been evil for about eight years now” in
this piece that’s hours-old. Article full of lies, distortion, and revisionism
       (retirement is well overdue, get off the Linux_Foundation money).


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_crime⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_crime⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_crime⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_crime⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_crime⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_crime⦈_


Summary: An unbelievably misleading article, full of errors, has been published
by Steven J. Vaughan-Nichols; he also helped_shield_Bill_Gates_(Jeffrey_Epstein
enabler)_by_defaming_Richard_Stallman in a site funded by Microsoft, IBM, and
their front group ‘Linux’ Foundation


⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⡥⢹⠋⠋⣹⡟⡙⡛⠟⠋⢻⢋⣿⢘⢹⣻⡏⠸⠁⠐⢋⣻⢋⢋⠻⠋⠛⡙⠃⡈⣻⡇⠋⢻⡿⠛⣿⡇⣿⠘⢛⢻⢻⢛⠛⣻⡟⠛⢛⢻⢛⢸⡟⣛⠛⡛⠟⠙⢛⢹⣿⠛⠛⡙⡟⡟⡟⡙⣙⠛⢻⣿⣿⣿⣿⣿⣿
⣷⣤⣼⣤⣶⣼⣷⣤⣷⣼⣦⣼⣼⣿⣼⣼⣼⣧⣧⣧⣤⣦⣼⣼⣤⣼⣤⣶⣤⣧⣧⣼⣧⣦⣼⣷⣤⣼⣧⣤⣴⣼⣼⣤⣬⣶⣽⣧⣤⣼⣼⣤⣼⣷⣤⣆⣤⣦⣴⣼⣼⣿⣤⣶⣤⣧⣤⣧⣧⣤⣦⣼⣿⣿⣿⣿⣿⣿
⡟⡛⠟⡛⠛⠛⢻⢛⢻⠛⡟⡛⡛⠟⣿⢙⢙⢻⠛⠟⠛⠟⢻⣿⢛⠙⠛⡛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣥⣦⣥⣤⣼⣼⣨⣤⣤⣥⣧⣇⣸⣿⣬⣼⣼⣤⣤⣤⣦⣼⣷⣬⣤⣤⣕⣸⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⢛⠻⢿⡟⠻⠛⡟⠻⠿⠿⠻⠿⡟⠻⠻⠛⠛⠛⠻⠻⠛⢻⠟⠟⢻⠛⠛⡿⠛⠛⠟⠛⡟⠟⠛⠛⡟⠛⠟⠟⠻⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣷⣾⣷⣶⣷⣷⣶⣶⣴⣾⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣷⣦⣴⣶⣧⣶⣶⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⣀⣈⣈⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣂⣀⣃⣘⣀⣃⣀⣘⣃⣀⣀⣂⣀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⢿⡿⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⢻⣿⣿⣿⣿⠟⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠛⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿
⣿⢠⠘⢃⠀⣏⠈⡟⢩⢹⡉⣉⡟⢩⠙⡟⠩⢹⠏⣩⠙⡇⢨⡇⢨⣿⡇⢈⡉⢏⠉⣉⡁⣿⠀⡉⢻⠋⠍⢋⢙⣉⠉⡏⢹⣿⠀⣏⠉⡉⢹⣿⡿⢠⠘⣯⠀⣽⠉⣉⡁⢹⠋⡍⣏⠉⠙⣿⣏⠉⠙⡏⢉⡉⡿⢉⡅⢸
⣟⣘⣄⣸⣀⣛⣀⣇⣘⣻⣃⣛⣇⣘⣀⣏⣒⣠⣄⣙⣠⣇⣘⣇⣘⣻⣇⣘⣁⣞⣀⣻⣃⣻⣀⣃⣼⣀⣒⣟⣘⣻⣆⢀⣿⣿⣀⣛⣀⣇⣘⣿⣃⣲⣂⣙⣀⣻⣀⣻⣃⣸⣀⣛⣇⣐⣀⣿⣇⣐⣀⣃⣘⣃⣣⣈⣃⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠉⢹⠏⠉⡽⠤⡿⠷⠀⣿⠿⠀⣧⠀⡿⠿⢿⣿⡍⢩⢍⡿⠿⠿⡿⠿⠿⠋⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⢿⡿⠿⢿⠿⠿⣿⠷⠀⣿⣧⠀⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢸⡀⢸⠀⢿⠀⡇⠸⠀⡇⠸⠇⣿⠀⡇⠨⠤⣿⡇⢰⠜⠃⠩⠀⡧⡈⢸⠀⢿⣿⠀⠥⢼⠆⠀⢿⠀⡇⢨⠀⡷⢈⠤⡁⢊⠈⠥⡇⠸⠀⣿⣿⠀⡇⢸⡀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣷⣿⣶⣶⣶⣿⣶⣶⣾⣶⣶⣶⣶⣿⣶⣾⣿⣶⣶⣶⣷⣶⣶⣷⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⣶⣀⣲⣿⣷⣶⣿⣶⣶⣿⣶⣶⣿⣶⣶⣾⣿⣶⣶⣿⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⡟⠛⡟⠛⠛⣿⣿⠛⣿⣿⣿⡿⢿⡟⢻⣿⣿⣟⠛⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠈⠇⠈⠇⣾⠀⡄⢹⠀⣟⠀⠤⡅⢠⡇⢸⠁⠄⢹⠀⡄⢹⠀⡟⢡⡌⢣⠀⠁⠱⢠⠁⠄⢡⠈⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣆⣸⣇⣸⣯⣤⣥⣼⣤⣥⣄⣠⣧⣨⣥⣬⣤⣉⣽⣄⣡⣼⣤⣵⣌⣡⣾⣄⣼⣀⣿⣤⣩⣭⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣌⣧⣝⣥⣭⢽⣥⡁⣨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣴⣥⡾⡤⡯⢬⠥⢽⣿⣿⣿⣿⣿⡋⠙⢛⠛⠛⠙⡏⠛⢻⡋⠛⢛⠛⡏⠛⠛⠉⡟⣻⠙⠛⢛⠛⢛⠛⢻⠛⡙⠛⡟⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣶⣶⣾⣿⣿⣿⣿⣿⠿⠿⠿⠟⠿⠟⠿⠿⠿⢿⠿⠿⠿⠿⡿⡿⢿⠿⣿⠿⠿⠿⡿⠻⠿⡿⠿⠿⠿⡿⠟⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣶⣶⣶⣶⣶⣾⣿⣷⢴⡶⣷⣿⣶⣾⣶⣶⣦⣴⣶⣷⣶⢾⣷⡶⡶⣶⣷⣶⣿⢶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣤⡀⢀⢀⠀⠀
⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠫⣿⣿⣿⣿⣿⣿⣿⣤⣤⣬⣥⣠⣤⣤⣧⣥⣴⣼⣤⣤⣤⣷⣀⣧⣤⣶⣠⣤⣦⣤⣼⣴⣯⣤⣤⣬⣼⣤⣦⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀
⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣯⣩⣋⣯⣽⣁⣉⣋⣇⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⡤⠾⠿⠿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠊⡙⣿⣿⣿⣿⣿⣿⡗⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣤⣤⣼⣤⣤⣯⣤⣿⣦⣤⣿⣤⣾⣶⣤⣾⣤⣤⣴⣤⣶⣤⣼⣤⣤⣤⣤⣧⣮⣤⣬⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣉⣏⣸⣀⣉⣇⣉⣁⣹⢉⣉⣭⣻⣍⣉⣟⣹⣍⣉⣉⣩⣉⣏⣱⣏⣉⣉⣍⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀
⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣟⣛⢻⣛⠛⢹⢙⡟⠟⢛⡻⠛⢹⢛⡟⠻⢛⠟⠛⣯⣝⡛⢛⢻⢛⡟⠻⠛⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠟⠿⢿⠿⠟⠿⢿⠻⠿⠿⣿⠿⠿⠻⠿⠿⢿⠿⡿⠿⠛⡟⢿⢿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣶⣾⣾⣶⣶⣷⣼⣶⣶⣶⣾⣶⣾⣶⣶⣶⣾⣶⣷⣶⣶⣷⣿⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣯⣮⣦⣯⣷⣵⣿⣯⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣥⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠿⢿⠿⡿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢈⠿⡄⣿⢻⢿⣭⣿⣫⡟⣯⡻⡟⣭⣿⣫⡝⣯⢨⡇⣽⣿⡟⢭⣿⡯⠝⣿⢻⡟⣟⢭⣿⣿⡿⣫⡟⡟⣫⡟⣯⢻⣟⣭⢻⣿⡟⣭⣻⡟⣿⣻⢻⣽⢻⢻⣝⢿⢫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣼⣶⣧⣿⣼⣾⣛⣿⣿⣧⣛⣵⣟⣳⣿⣝⣣⣿⣼⣧⣻⣿⣿⣛⣼⣜⣫⣿⡧⣼⣿⣛⣼⣿⣷⣝⣻⣧⣿⣧⣿⣼⣯⣛⣼⣿⣧⣛⣽⣿⢡⣿⣼⣛⣿⣜⣛⣿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣟⢿⢟⣿⣿⡿⣻⢟⣿⢻⢿⣟⢸⣿⣿⣿⢛⣿⢻⣿⡟⣿⢻⣿⢸⣿⢻⡟⡿⣻⡟⡟⣻⡟⣿⣿⢸⣟⣿⢺⡟⣿⢻⣻⣿⣿⣿⢟⣿⢻⢛⣟⢿⢻⣟⣿⢻⣟⢿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣓⣼⣝⣻⣸⣜⣛⣿⣷⣝⣮⣛⣻⣜⣻⣸⢿⣿⣿⢨⣛⣼⣜⣫⣿⣸⣿⣜⣿⣼⣇⣷⣝⣛⣧⣿⣟⣓⣼⣸⣿⣿⣸⡇⣛⣼⣟⣢⣿⣿⣾⣛⣿⣸⣿⣸⣜⣫⣿⣜⣛⣿⣜⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣻⡻⣟⣿⢟⡟⣿⣻⡟⣿⣿⣿⢻⡟⣿⢻⡟⣿⢘⣟⢿⢻⣟⣿⢛⣟⢿⣟⣿⣿⣿⡟⣿⢸⣿⡿⣻⡻⡟⣿⢻⣟⣿⢻⡇⣿⢻⡟⣿⢻⡟⣿⢻⣟⣿⣿⣿⢻⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣛⣣⣿⣜⣾⣧⣛⣻⣇⣿⣿⣿⣙⣣⣿⣿⣇⣿⣘⣛⣾⣜⣛⣿⣸⣿⡎⣼⣿⣿⣘⣃⣿⣸⣿⣧⣛⣻⣧⣛⢸⣇⣛⣸⣇⣻⣸⣧⣛⣽⣇⣿⣸⣛⣂⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⣿⣿⣿⣿⣿⣑⣿⣿⡇⠀⠠⡯⠀⠀⠠⣂⢤⣤⡤⡤⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣋⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣏⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠂⠒⠶⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠏⠀⠀⠀⠀⠀⡔⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠹⣿⣿⣿⣿⣶⣀⠀⠀⡀⠀⢰⣿⣿⡿⠁⢀⠀⠐⠒⠒⠀⠄⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠱⣿⡷⠾⣧⠀⢤⣤⢷⣿⣿⡿⠿⣟⠻⢷⣶⣿⡁⢣⣘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⢿⣸⣿⣿⣷⣶⣷⣶⣿⣿⣖⣿⡀⢳⣈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠴⠈⠉⠉⠉⠉⠁⠀⠀⡀⢠⣤⡈⢧⠀⢣⠉⢿⣦⣀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⠄⠀⠀⠊⠀⠀⠀⠀⠀⣈⣁⣤⣜⣷⡀⢣⢈⣿⣿⡀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡁⢀⡠⢶⣶⣿⣿⠿⠿⢿⣟⣿⣛⣿⣇⠈⢆⠘⣿⣿⣄⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢰⣿⢹⣿⣯⡀⠐⠀⣀⣸⣼⣿⣿⣿⡄⠘⡄⠹⣿⣿⣧⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠛⠙⠉⠍⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢋⡉⠉⠙⠛⠛⠛⠉⠋⠃⠀⠀⠐⠒⠒⠂⠀⠀⢿⡿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣠⣤⣤⣤⣤⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⣿⣿⢿⠿⡿⣿⣿⣟⣿⢿⣿⣿⠿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⡿⢿⢿⣿⡿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠿⢹⢹⣛⣿⡿⡻⠟⡿⡻⡏⡟⣿⡟⢻⢟⡿⣻⢻⢻⢻⢟⠿⡋⣿⢟⢿⢩⣏⡟⡏⣟⣻⢹⡛⡟⣻⡟⡻⣟⢻⡟⣻⣛⡿⡻⣿⠩⡿⡻⢻⡟⢻⢹⡛⡿⡻⣿⢫⡿⡻⡿⡛⣻⢿⠿⡟⡟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣾⣾⣾⣿⣷⣷⣿⣷⣷⣷⣷⣿⣾⣷⣾⣷⣿⣾⣾⣷⣾⣿⣷⣿⣾⣾⣾⣿⣾⣷⣿⣾⣾⣷⣷⣿⣷⣷⣟⣹⣷⣿⣿⣷⣿⣿⣾⣷⣷⣾⣷⣿⣾⣚⣷⣷⣿⣾⣷⣷⣷⣷⣿⣾⣦⣷⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⢝⢛⡟⢻⢛⡏⡛⡟⣻⠛⡟⢻⡿⠝⡟⣻⢹⣿⠋⣟⡟⡟⢻⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣾⣷⣾⣶⣷⣶⣷⣾⣶⣷⣾⣷⣿⣷⣾⣾⣷⣿⣮⣮⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢠⠀⢠⡠⣠⡤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣤⠀⣤⣤⣤⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⣿⣿⠍⠂⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⢿⣦⢹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠶⠶⣸⡿⣿⣀⣰⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢻⠿⣿⣿⣿⣿⠿⠿⠋⢋⣥⣶⣽⣿⣿⣯⣀⠀⢈⢠⣼⠻⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡆⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⢠⠿⣿⡟⣿⣶⣤⣴⣎⣛⣯⣽⣿⣿⣿⣿⣿⣿⣿⠓⠲⠤⢨⠈⠉⠛⠛⠛⠛⣻⠛⢛⢓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⢹⣿⣿⣿⣿⡇⠀⠀⠀⣶⣶⡆⠀⠀⣰⣶⡆⠰⠿⠁⠀⢿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣍⡀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⣼⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠸⠿⠿⠿⠿⠇⠀⠀⠀⣿⢻⣿⡀⢠⡿⣿⡇⢰⣶⠀⣠⣼⣶⣿⠙⣿⣿⣿⢋⣿⣿⣿⣯⣍⠀⢋⣬⣭⣬⠈⠉⣀⣤⣤⣀⠀⢀⣀⣿⣯⣀⣂⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⠈⢿⣷⣿⠃⣿⡇⢸⣿⢠⣿⠁⠀⠚⠀⣿⠏⠋⣾⡟⠁⠈⢻⣿⠆⢿⣯⣉⠉⠀⣾⡟⠉⠉⢻⣷⡈⠛⣿⡟⠛⠛⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠘⣿⠇⠀⣿⡇⢸⣿⠈⢿⣷⣤⣤⠀⣿⠀⠀⢹⣿⣆⣀⣸⣿⠀⣀⠙⢻⣷⠘⣿⣇⠀⠀⢠⣿⡇⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠛⠻⠿⠇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠉⠀⠀⠛⠛⠁⠀⠛⠀⠀⠀⠩⠿⠿⠛⠁⠀⠛⢿⣿⡛⠀⠙⠿⣿⣾⠿⠟⠀⢸⣿⡇⠀⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠯⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠛⠙⠟⠛⠛⠛⠛⠛⠛⠙⠹⠛⠛⠛⠛⠛⡏⣿⠉⠙⠛⠻⠛⠋⠛⠛⠟⠻⠛⠟⢻⠉⠉⠋⠛⠛⠛⠟⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫
⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣬⣤⣬⣤⣬⣤⣤⣥⣽⣬⣤⣤⣤⣤⣤⣥⣥⣤⣤⣤⣤⣼⣯⣼⣥⣥⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⡟⠛⠉⠛⠟⠻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠤⠤⠤⠤⠼⠤⠼⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣟⢻⠛⡟⡛⠿⡟⠻⠿⠛⠟⠻⠿⡟⠻⠟⢻⠿⠿⠿⢿⢿⠿⡿⠿⣿⠛⢛⠿⠿⢿⠿⠿⢿⡟⣿⢻⠿⢿⣿⢻⣿⠿⢿⠿⠟⢻⣿⡟⢻⠿⠟⠻⢿⣿⡟⢻⡟⢿⡟⠻⠛⡟⡿⠿⠿⢿⠿⢿⠿⠿⠿⡟⠛⠛⣿
⣿⣿⣿⡄⣀⢀⡇⡆⠀⡀⠀⡀⠂⢀⠀⡀⠐⣀⢠⠐⣰⠀⡀⣄⠀⡀⢰⣟⠀⢈⠀⢸⠀⣐⠀⣸⡇⣤⢠⡀⢸⣿⠘⢃⠐⣐⠀⣀⢸⣟⠃⣀⠐⡀⠐⢠⡟⢀⡀⡇⢸⡇⢠⡄⡇⣇⠒⡀⣆⠐⣀⠀⣁⠂⡀⢰⠀⣿
⣿⣿⣿⣿⣿⣿⡏⠉⠹⠿⠿⠿⣿⠉⠉⠿⠿⠿⠻⡿⠻⡿⠻⠉⠿⠻⠿⠿⣿⡟⠙⡛⡀⠟⠉⠻⢋⠙⣿⠉⠟⢙⠙⢹⢹⢹⠟⢿⠿⠻⣿⠉⢉⠿⠿⠿⠿⠿⠏⠹⠻⠿⠿⢿⡏⠉⠙⠿⠏⡏⠟⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣰⣆⣀⣀⣰⣿⣀⣀⣃⣘⠀⣀⣄⣁⣀⣀⣀⣀⣀⠄⠁⣿⣃⢀⣉⣀⣁⣉⣰⣈⣠⣿⣀⣤⣸⣀⣸⣸⣠⣈⣠⣀⣀⣿⣀⣶⣀⣀⣀⣆⣀⣀⡀⠀⢀⣸⣸⣇⣀⣀⣀⣆⣇⣀⣀⣀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡹⠛⠟⠛⡟⠛⠟⠋⢙⠛⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣤⣈⣅⣀⣇⣇⣀⣁⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⡀⣀⡀⣀⢀⣀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⣯⢹⡟⣿⣹⢿⢿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡆⣶⣴⠆⣶⡆⡖⡆⡖⠆⣶⡆⡖⢲⡆⠀⡆⡶⠆⠐⡖⢰⢰⠂⡖⡆⠐⣶⢰⢲⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡶⢶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⣿⢿⡄⣿⡇⣇⡇⣜⡆⣿⡇⡏⢸⡇⠀⡇⣽⡆⠀⡇⢸⢸⡁⣇⡇⠀⣿⢸⣸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⢠⢠⢠⢠⢤⢠⢤⢠⠄⡤⡄⡤⡄⢀⣤⣠⡤⠀⣤⢠⡄⡄⡄⢠⠀⡄⡤⡄⡄⡄⡤⡄⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⢸⢺⢸⢸⢸⣿⢸⢸⢸⣞⢸⠂⡇⡇⡳⡄⢸⣿⣿⡗⠀⣿⣾⡇⡇⡇⢸⠀⡇⡇⡇⣿⡇⡳⡄⠀
⡀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⢘⡘⢈⡋⠘⣘⠘⣋⠘⡘⢘⠃⣛⢁⣙⢁⡀⠛⣈⢁⢀⠉⢃⡃⣃⠛⣘⠃⣃⢙⢁⣃⢃⢙⠁⠀
⣷⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⢹⢸⡅⠀⡏⡇⣿⡇⡇⣿⢀⣿⢸⣽⠸⣟⠀⣿⢸⣼⠀⢸⡅⣿⡇⣿⢿⣯⢸⢸⣽⢸⣾⠀⠀
⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠸⠾⠸⠀⠀⠷⠃⠿⠃⠧⠻⠼⠻⠸⠹⠸⠟⠀⠿⠸⠻⠀⠸⠀⠿⠃⠟⠞⠷⠸⠸⠼⠸⠹⠀⠀
⠉⠛⢻⣿⡇⠀⠿⠿⠞⠓⠻⠿⠿⠒⠻⠿⠾⠚⠃⠸⠿⠿⠷⠚⠻⠿⠟⠛⠛⠻⠟⠛⠀⠀⠀⢸⣿⣿⣟⡇⠀⠀⢰⢲⢰⢲⢰⢰⣲⢰⠂⣞⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣴⣿⣟⠀⣶⣶⣶⣶⣶⣿⣿⣷⣶⣾⣿⣷⡟⣷⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣸⣿⣿⣿⡇⠀⠀⢸⣹⢸⢯⢸⢸⣹⢸⡁⣌⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡻⣿⡁⠀⠀⢠⢠⢠⢠⣤⢠⢠⢤⢤⠄⡄⢡⠄⡤⡄⡄⢠⣤⣤⣤⣤⣤⠄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠧⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⠿⠟⠃⣛⡃⠀⠀⢸⡿⣾⢸⣿⢸⢘⢦⢸⠀⡇⢸⠂⡗⡇⡇⢸⣿⢸⣿⡇⣿⠂⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⢛⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣶⣿⣿⣿⡇⠀⠀⢈⡁⢁⢈⡉⣈⡈⣉⢈⣀⢉⡈⠁⠉⠁⠉⠈⠉⠈⠉⠁⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣇⢸⢸⡇⣿⠄⣿⣽⡧⠸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⠹⠸⠞⠷⠿⠆⠿⠻⠷⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣻⣟⣛⣛⣻⣻⣛⣛⣛⣿⣛⣛⣛⣣⣿⣟⣛⣛⣛⡛⢛⣛⡛⡛⢛⣛⣋⣠⣿⣿⡛⡛⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⢃⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠃⠙⠨⠊⠀⠁⠅⠊⠈⠐⠁⠁⠁⠀⠛⠑⠙⠀⠃⠀⠛⠻⠉⠠⠉⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠰⠐⢂⠂⠐⠠⠶⠖⠀⠶⠶⠐⠶⠴⠰⠢⠴⠖⠶⠆⠠⠶⠂⠐⠐⠖⠐⠠⠤⠦⠲⠠⢲⠁⠀⠀
⣿⣿⣯⣿⣿⣟⣿⣿⣿⣿⡿⡿⣿⣿⠻⣿⣿⡿⠟⡿⣿⠙⠃⣼⣿⣧⠜⣿⣿⣿⣿⠟⢻⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠈⠀⠀⠈⠀⠈⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠭⠭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣉⡙⡍⢉⡙⣉⡙⡅⢨⠋⣉⠻⠋⣉⣹⢋⣉⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⢛⡛⣛⢛⢛⣛⡛⢿⣿
⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢬⣤⣥⣬⣧⣬⣤⣧⣬⣦⣭⣼⣦⣭⣼⣤⣥⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣭⣭⣭⣬⣭⣥⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⢻⢋⢹⠭⡿⠿⢿⠿⢿⠿⠿⡿⠿⢿⠿⠿⡟⠩⠟⠹⣿⡿⡿⢿⠿⠉⠿⢿⢭⡿⠿⡿⠹⢿⢹⡿⠿⡏⠹⠿⡏⢹⠿⠿⡿⡿⢿⠿⡿⠿⡿⠿⣿⣿⠿⢿⠉⡿⠿⢿⠭⡿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⡘⣼⢸⠀⣇⠻⣻⢰⣧⠸⢃⡗⠌⣹⠸⢃⡇⢸⣇⠸⣿⣧⠀⡌⣸⠀⡇⢸⢸⡇⠍⣻⠸⢿⢸⡀⠅⡇⠸⢂⡇⢸⡸⢇⣧⠀⡌⣸⡀⠅⡇⢸⣿⣇⠸⢻⠀⡏⢭⢸⠀⡇⢸⢸⠀⡗⠌⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⡍⡟⠩⢙⣿⡏⡏⢹⢹⠭⠍⣏⠩⢽⣿⠀⣽⠉⡏⣩⠋⠍⣻⢩⡅⣿⣯⢨⡍⣩⠙⡏⣭⣿⠋⠍⣻⡙⣹⡏⣭⢹⢉⡍⢛⠩⢽⠉⡏⢩⢹⡏⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣧⣿⣬⣴⣿⣷⣼⣦⣿⣬⣧⣷⣭⣾⣿⣦⣿⣤⣧⣿⣧⣥⣾⣬⣦⣿⣿⣼⣷⣬⣼⣧⣿⣿⣧⣥⣮⣼⣬⡇⣥⣾⣦⣥⣷⣬⣼⣤⣧⣼⣼⡃⠭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⡿⠿⢿⠿⢿⠿⢿⢿⡿⣿⠿⠿⡟⠹⡯⢽⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡘⢟⣇⠿⣸⠀⣿⠀⣿⡘⡇⣿⢸⢃⣿⠸⡇⢸⡘⢇⣇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⣤⣄⠐⢶⣄⣉⣻⠦⠤⡓⣒⣂⠩⠥⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡄⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣮⣿⣿⣿⣷⠶⠿⠟⠉⠙⢶⣾⣿⡙⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠙⠋⠉⠉⠙⠋⠀⠀⢻⡇⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⢀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠐⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 345

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/epo-bubbles-matter/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/epo-bubbles-matter/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Why_the_EPO_Bubble_Matters⠀✐


Posted in Europe, Patents at 6:48 pm by Dr. Roy Schestowitz


Video_download_link | md5sum fefb99cd466d10e2c40c8af69607239d
EPO Quality and Compliance Down Sharply
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/war-on-patent-quality.webm


Summary: The EPO‘s numbers, which Benoît_Battistelli arrogantly bragged about
(granting more monopolies by disregarding the EPC), are falling sharply under
António_Campinos and they’re hoping that European_software_patents disguised as
“4IR” or “Hey Hi” (AI, amongst other misused or misleading buzzwords) will
somehow prevent the bubble from imploding; today they pretended — yet_again
(warning: epo.org link) — to cherish the EPC using their_enlarged_kangaroo
court and they’re working to replace common courts with more kangaroo courts by
breaking the law, violating constitutions, and corrupting international
conventions


EARLIER today we started_the_series that we first introduced at the start_of
the_week. The series concerns an “open secret” that EPO staff is well aware of.
The EPO is running out of steam because of corrupt management, not in spite of
it. It is being destroyed from the inside and in the process it takes down the
European economy, curtails justice in Europe, harms the reputation of the EU,
and destroys the lives of thousands of employees’ families. History might look
back kindly at Jorge_Campinos, whereas his son, who refers to himself as “the
f***ing president”, will be remembered as little but a high-profile criminal
who boasted about his crime while regulators stood by, clapping and bagging
bribes_from_the_criminal.


“Overview and some background information is included in the long video above,
assuming the audience isn’t familiar or barely familiar with the EPO and with
patent law.”In just a few years António the criminal is undoing a lifetime of
his dad’s (Jorge) legacy. More details to come. “Organised_crime” aptly
describes what we’re witnessing here. It's_outright_plunder.


Overview and some background information is included in the long video above,
assuming the audience isn’t familiar or barely familiar with the EPO and with
patent law.


Expect at least a dozen parts and about a dozen videos to come about this
crucial topic and still-ongoing crisis. █



                    ䷩ 𝚕𝚒𝚗𝚎 412

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/epo-institutionalised-injustice-in-action/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/epo-institutionalised-injustice-in-action/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_IV_—_No_End_in_Sight
for_a_System_of_“Institutionalised_Injustice”?⠀✐


Posted in Europe, Patents at 1:42 pm by Dr. Roy Schestowitz


Series parts:


   1. When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_I_—_ILOAT_134th
      Session:_Two_More_Bittersweet_Victories_for_EPO_Staff
   2. When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_II_—_ILOAT
      Judgment_No._4550
   3. When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_III_—_ILOAT
      Judgment_No._4551
   4. YOU ARE HERE ☞ No End in Sight for a System of “Institutionalised
      Injustice”?
                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tyranny_quote⦈_
What would Baron Montesquieu have made of the EPO’s dysfunctional legal system
and its abject failure to protect the fundamental rights of staff, leaving them
 without any effective defence against the tyranny of managerial despots like
                            Battistelli and Topić?


Summary: The EPO’s management continues to operate in violation of the law with
impunity, knowing it can take a decade for any sort of independent ruling to be
issued and even then nobody will be held accountable


At the ILOAT, the wheels of justice continue grinding slowly through the toxic
legacy of the Benoît_Battistelli era.


In doing so, they are gradually adding new material to an already impressive
collection of cases exposing the appalling “legal_no-man’s_land” which existed
at the organisation during that time.


“Instead of making a credible effort to recommend proper and equitable redress
for the complainants, Mahoney and his kangaroo committee simply rubber-stamped
the impugned measures.”Following the 134th session, it has now been confirmed
by means of two more judicial rulings that Battistelli and his minions were
guilty of a series of further egregious breaches of the fundamental rights of
EPO staff, in particular the right to freedom of association.


Due to the disgraceful inaction of Battistelli’s successor, António_Campinos,
and the chronic dysfunctionality of the EPO’s internal justice system, these
breaches were permitted to persist for the best part of a decade before the
victims could obtain a final judicial decision striking down the impugned
measures.


            🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇António Campinos and Željko Topić⦈
   Due to the disgraceful inaction of António Campinos (l.), and the chronic
dysfunctionality of the EPO’s internal justice system, breaches of fundamental
rights perpetrated by Battistelli and his minions, including Željko Topić (r.),
  were permitted to persist for the best part of a decade before the victims
              could obtain any kind of redress before the ILOAT.


It’s important to note that despite the manifestly unlawful and tyrannical
character of the measures quashed by the ILOAT in Judgments nos. 4550 and 4551,
these very same measures were previously given a clean bill of legal health by
the EPO’s Internal Appeals Committee (IAC) under the stewardship of Sir_Paul
Mahoney, a former Judge at the European Court of Human Rights.


                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sir_Paul_Mahoney⦈_
  Sir Paul Mahoney, former Judge at the European Court of Human Rights, whose
    appeals committee was responsible for upholding a significant number of
             unlawful measures subsequently quashed by the ILOAT.


Instead of making a credible effort to recommend proper and equitable redress
for the complainants, Mahoney and his kangaroo committee simply rubber-stamped
the impugned measures.


The only discernible effect of the IAC’s contribution to the affair was to add
a further layer of delay to the procedure thereby obstructing the wholly
legitimate attempts of EPO staff to obtain justice in a timely manner.


In the case of Judgment No. 4550, Michael Lund had to wait over eight years to
obtain a ruling at the ILOAT which established that the premature termination
of his IAC appointment had been unlawful.


Likewise, in the case of Judgment 4551, Laurent Prunier and his co-litigants
had to wait over nine years before the totalitarian censorship imposed by
Battistelli and his “bulldog” Topić in June 2013 was finally declared unlawful.
During this time, one of the three complainants passed away and the complaint
was pursued on her behalf by a designated successor.


“The only discernible effect of the IAC’s contribution to the affair was to add
a further layer of delay to the procedure thereby obstructing the wholly
legitimate attempts of EPO staff to obtain justice in a timely manner.”By a
curious twist of fate, Judgment No. 4550 has potentially far-reaching
implications for the_EPO’s_notoriously_dysfunctional_internal_justice_system.


The findings of the Tribunal in this case imply that ever since 1 April 2014,
the composition of the EPO’s IAC has been inherently irregular due to the
unlawful restriction imposed on the CSC’s powers to nominate members by means
of CA/D 2/14 (Battistelli’s so-called "Social_Democracy").


In the words of the Tribunal, this unlawful restriction “substantially
undermined, in various respects, the quality of the effective representation of
staff on that body [i.e., the IAC]“.


The inescapable legal consequence of ILOAT Judgment no. 4550 is that every
opinion issued by the EPO’s IAC since 1 April 2014 is fatally vitiated by the
irregular composition of the body which issued it.


Under normal circumstances such a dysfunctional state of affairs in the
governance of a public body would qualify as a major scandal. But this is the
EPO we are talking about here so don’t hold your breath waiting for the
"captured_media" to report on it.


Notwithstanding the media silence, there can be little doubt that Judgments
Nos. 4550 and 4551 represent significant interim legal victories for EPO staff.


However, at the same time it is abundantly clear that the quality of “justice”
delivered by the ILOAT leaves a lot to be desired.


“Notwithstanding the media silence, there can be little doubt that Judgments
Nos. 4550 and 4551 represent significant interim legal victories for EPO
staff.”The derisory level of moral damages awarded by the Tribunal for what
amount to serious breaches of the fundamental rights of staff means that such
judgments cannot realistically be expected to have any deterrent effect on the
EPO’s managerial and governing circles.


The Tribunal’s extraordinary leniency towards the EPO when it comes to imposing
financial sanctions is difficult to justify.


This kind of unwarranted “kid-glove_treatment” signals to the powers-that-be at
the EPO that they need have no fear of any real consequences should they
persist in their errant ways.


Ultimately, it is to be feared that the net effect will be to bolster the
arrogance and complacency of Campinos and his minions during his second term of
office.


After all, if Campinos feels inclined to continue trampling on the fundamental
rights of EPO staff in the manner of his predecessor, he can do so in
confidence that any alleged breaches will only be sanctioned by the ILOAT – if
at all – long after he has departed.


“Ultimately, it is to be feared that the net effect will be to bolster the
arrogance and complacency of Campinos and his minions during his second term of
office.”And even then, the costs to the EPO will be negligible. Financial
sanctions at the level of a several hundred Euros are quite literally “peanuts”
to an organisation which boasts of an annual budget of €_2.4_billion. (warning:
epo.org link)


Under these circumstances, it’s clear that the system of redress available to
EPO staff fails to provide timely and effective protection of their fundamental
rights and that, consequently, it is not fit for purpose.


Unfortunately, in the absence of any discernible political will to rectify this
situation, it looks like EPO staff are stuck with their intolerable system of
“institutionalised injustice” for the foreseeable future. █


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣛⡼⠓⠺⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⣟⢶⣶⢲⣶⠢⢰⡷⡆⠸⣼⢖⠴⡶⣲⣶⣶⡶⣰⣷⡶⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠗⠚⢧⣛⠀⠀
⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀
⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⡆⡧⣤⡄⡄⣤⠀⡦⡄⢠⠄⡤⡄⡄⡤⡄⡄⣤⠀⣤⢤⠀⡆⣤⢠⣠⣤⢠⡄⣤⡀⢰⢸⢠⣤⢠⡄⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢁⠁⠈⠁⠁⠉⠀⡉⠁⠈⡀⠉⠀⠈⠀⠈⠁⠉⠀⠉⠈⠀⠈⠊⠈⠈⠉⠈⠁⠑⠁⠈⠉⠈⢉⠈⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠹⠱⠿⠸⠁⠿⠞⠏⠾⠮⠏⠇⠰⠯⠀⠿⠸⠇⠏⡯⠺⠗⠏⠧⠸⠇⠇⠿⠸⠇⠸⠼⠏⠶⠽⠾⠾⠁⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣠⣀⣀⠀⣀⢀⣠⢀⡀⣄⣠⠀⣀⣠⠀⢀⣀⢀⠀⢀⡀⣀⢀⡄⢠⣀⡀⣀⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠚⠘⠛⠁⠛⠀⠛⠘⠃⠛⠚⠈⠚⠘⠀⠘⠃⠋⠃⠘⠃⠘⠑⠃⠘⠃⠃⠐⠃⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⢢⣤⢠⡔⣤⡦⢠⢢⢸⠀⣤⢠⢤⢰⡄⡴⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠈⠉⠀⠁⠁⠉⠀⠉⠈⠐⠉⠉⠉⠈⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀
⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀
⠀⠀⣭⢧⡤⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⢤⡼⣭⠀⠀
⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣾⣦⡀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢈⣩⡟
⠀⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⡉⠉
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠆⢠⣤⣿⣿⣿⠛⠛⢿⣷⣼⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⢿⣿⣿⣿⣿⣿⢻⣿⣿⢾⣷⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣹⣿⣿⣿⣴⣿⣿⣿⣿⣍⡛⣿⡏⢵⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⣻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⠟⣽⣿⣿⠃⠈⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠙⠿⣿⣿⣷⣶⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣽⠛⠫⠛⣭⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⣿⣷⣤⣬⣍⠛⠉⡐⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠷⠟⠋⠀⢸⡶⠭⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣫⣠⣾⣷⠀⠉⠛⠿⣿⡟⢁⣾⣿⣿⠛⠁⠀⠀⠀⠀⢈⣁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢯⣿⣿⡇⠀⠀⠀⠀⠀⠛⠟⣾⡇⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣧⠀⠀⢀⠀⠀⠀⠀⣩⠁⠀⠀⠀⠀⠀⠀⠸⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⡿⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠻⠿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀
⣿⢼⡧⣿⢼⡧⣿⢽⢽⡯⣿⢼⡯⣿⢽⡯⣿⣽⣯⣯⣽⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣭⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣯⣽⣽⣯⣿⣽⣯⣿⣽⣯⣯⣽⣽⣯⣿⣽⣯⣿⣽⣯⣯⣽⣽⣯⣿⣽⣯⣿⣽⣯⣯⣿⣿⣯⣿⣽
⣿⣺⣗⣿⣺⣟⣟⣻⣻⣗⣿⣺⣗⣿⣺⣗⣿⣺⣿⣿⣿⣾⣷⣿⢾⡷⣿⢾⡷⣿⣾⣷⣷⣿⢾⡷⣿⢾⡷⣿⢾⡷⡷⣾⢾⡷⣿⢾⡷⣿⢾⡷⣷⣾⢾⡷⣿⢾⡷⣿⢾⡷⣷⣿⢾⡷⣿⢾⡷⣿⢾⣷⡷⣿⣿⡷⣿⢾
⠉⠉⠉⠋⠙⠉⠋⠙⠉⠋⠛⠙⠋⠛⠙⠋⠛⠙⠛⠛⠛⠛⠛⠛⠙⠋⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠀⢀⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣠⠀⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀
⠀⣿⠶⠆⣿⢰⡇⣿⢳⡟⢻⣾⡟⢻⣴⣿⣷⣺⣿⡧⣿⢻⡆⠀⢾⡇⢈⣩⣾⢻⣦⣗⢸⣿⡟⠛⣿⠀⢠⡞⢻⣾⣟⠀⢸⣷⠶⣿⣿⢰⣷⣿⣿⡟⣧⣾⣿⣾⡟⣿⡆⠀⣿⠤⣿⣿⣾⡟⣿⣿⢻⡗⣿⢳⣿⣷⠀⠀
⠀⠛⠛⠛⠛⠛⠋⠛⠈⠛⠛⢹⡟⠛⠘⠛⠋⠛⠛⠛⠛⠘⠃⠀⠈⠛⠛⠁⠛⠛⠋⠛⠛⠛⠃⢈⠛⠂⠈⠛⠛⠙⠛⢀⡘⠛⢀⡛⠛⠛⣛⢛⢚⢳⢛⡛⡛⡛⢣⢻⣣⣦⣛⣠⣛⣛⣿⣿⣿⣛⣼⣟⣻⣾⣷⣿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⡀⡠⣠⣠⣰⣠⣤⣤⣶⣶⣶⣶⣿⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣴⣶⣴⣵⡟⡿⣮⣭⣯⡜⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡂⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣥⣨⣿⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠦⠤⠤⠤⠥⠤⠴⠿⣿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣾⣿⡾⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠁⢢⣀⣈⠉⠉⠁⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣟⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠁⠉⠉⠙⠛⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣧⣶⣦⠀⠀⠀⠀⠴⣿⣿⣿⠟⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣻
⣿⣿⣯⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢻⣿⣽⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡿⢿⣿⢿
⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢾⣿⣞⣿⣻
⣿⣽⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣯⣿⣽
⣿⣾⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⣿⣼⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⠀⠀⠀⠈⠒⢛⣷⣒⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⣿⣾⣿⣿
⠛⠛⠛⠉⠿⠷⡶⠷⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 679

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/epo-unprecedented-surge/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/epo-unprecedented-surge/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO_Bubble_—_Part_I_—_An_“Unprecedented_Surge”⠀✐


Posted in Europe at 4:10 pm by Dr. Roy Schestowitz


Series parts:


   1. YOU ARE HERE ☞ An “Unprecedented Surge”
                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Battistelli_at_JURI⦈_
Back in March 2017 Benoît_Battistelli proudly boasted_to_the_JURI_Committee_of
 the_European_Parliament [PDF] that his reform measures at the EPO had secured
                 an “unprecedented surge” in granted patents.


Summary: New 12-part series about the deflating “grant bubble” at the EPO


Back in March 2017, the Legal Affairs Committee (JURI) of the European
Parliament held a session dedicated to discussing “the_latest_state_of_play_on
the_Unitary_Patent”.


“Despite the EPO management’s eagerness to publicise this “new high mark” in
the Office’s history, not everybody was drinking the corporate Kool-Aid.”On
that occasion, the then President of the (non-EU) European Patent Office Benoît
Battistelli gave a presentation to the assembled MEPs during which he proudly
boasted to his ill-informed and poorly briefed audience that his reform
measures at the EPO had resulted in an “unprecedented surge” in granted
patents.


This “achievement” was also trumpeted on the EPO’s_official_website (warning:
epo.org link) where great pains were taken to emphasise that the increase in
granted patents had been achieved without any compromise in respect of quality.


     “The EPO granted approximately 95 900 patents in 2016, an increase of
     40% over 2015, and the highest ever number. This increase was
     possible following a series of reforms improving quality processes
     and enhancing efficiency, which ensure high productivity without
     compromising on quality.”


Despite the EPO management’s eagerness to publicise this “new_high_mark”
(warning: epo.org link) in the Office’s history, not everybody was drinking the
corporate Kool-Aid.


Many observers were sceptical about the EPO’s extravagant claims that such a
dramatic increase in output could be achieved without detrimental effects on
the integrity of the “end-product”.


“Many observers were sceptical about the EPO’s extravagant claims that such a
dramatic increase in output could be achieved without detrimental effects on
the integrity of the “end-product”.”Although nobody dared to confront
Battistelli openly in March 2017, by June 2018 some German Patent attorneys
were starting to openly_express_concerns about a perceived decrease in the
quality of patents issued by the EPO.


But, secure in the EPOnian ivory tower of immunity/impunity, Battistelli and
his team contemptuously dismissed any criticism of their “achievements”.


By means of oppressive managerial methods pioneered_at_France_Télécom, the
Corsican despot and his successor António_Campinos ensured that the number of
grants continue to climb throughout 2017 (+10.1%), 2018 (+20.8%) and 2019
(+8.0%).


          🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Haseltine_Lake_Kempner:_patent_bubble⦈_
    Between 2015 and 2019 the number of patents granted annually by the EPO
                             effectively doubled.
                  Source: Haseltine_Lake_Kempner_(hlk-ip.com)


The official statistics show that between 2015 and 2019 the number of patents
granted annually by the EPO effectively doubled, rising from 68,401 in 2015 to
a peak of 137,784 in 2019.


“The official statistics show that between 2015 and 2019 the number of patents
granted annually by the EPO effectively doubled, rising from 68,401 in 2015 to
a peak of 137,784 in 2019.”As we shall see in the next part, the number of
grants started to drop in 2020 and the latest figures from 2021 suggest that
the EPO’s “grant bubble” – initially engineered by Team Battistelli and
subsequently maintained by Team Campinos – is in the process of deflating. █


⠀⠀⠀⠀⢄⡢⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⡱⣱⢱⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡠⡳⡹⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠭⠭⠖⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣭⠈⠉⡏⢹⢩⢹⢩⢹⠩⢹⡇⡏⡍⣿⠨⢨⢹⠉⢹⡇⠤⡏⠏⡏⡍⠍⡏⠍⡏⢹⠉⠉⣭⣿⡇⣢⡏⠉⢩⡇⢹⠉⠉⡍⡍⡏⢙⢩⢹⢸⡮⠉⣿⡿⢿⠉⢙⠭⠩⠉⡇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⡿⣿⣿⣿⣷⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣹⢰⢰⣢⣁⡇⣎⢔⣿⣜⣟⣇⢎⣰⣰⣸⢰⣰⣁⣇⣆⣆⢎⡡⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⡟⠛⢛⢿⡍⡏⠉⠟⢹⡟⠻⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⡛⠟⠟⠟⠟⣟⠟⡿⡻⢻⢻⡻⠻⡟⣿⡟⢻⡻⢛⠟⡟⡟⢻⢻⡛⠟⠟⣟⠟⡟⡟⢛⡛⢟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣿⣷⣿⣾⣿⣾⣿⣿⣿⣾⣿⣾⣶⣾⣾⣶⣷⣷⣿⣾⣿⣷⣶⣷⣿⣷⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⡿⡿⢿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣷⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣛⠉⠻⠟⠋⢉⠰⣏⣼⣐⣧⣀⣀⣀⠁⢸⠿⠛⠉⠀⡷⢶⣷⡀⠙⢿⣿⣿⣿⣿⣿
⢀⠠⡀⠄⡀⡀⠀⠧⠀⠠⢘⠀⠀⣭⠀⢀⣤⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣷⣦⣿⣿⣿⣿⡟⠙⠙⠓⠈⠉⠙⠻⣿⣇⣿⣿⣿⠿⡿⢿⣿⣿⣯⢾⠐⡀⠀⢠⡀⠀⠀⠀⠀⠀⠙⠆⠀⣀⢤⢿⣿⣦⡀⠙⢿⣿⣿⣿
⠈⠀⠀⠁⣿⠇⠀⣆⠀⡴⢘⡄⠈⠋⠀⢸⣿⣷⣤⣤⠅⠀⡾⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠿⢷⡋⡀⠀⠀⠀⠀⠒⠿⢿⣿⣿⣿⠿⡇⠇⠁⠡⠽⠂⠇⢱⣀⢀⡀⠀⠢⣀⢸⣷⣦⣶⣷⢀⠈⠀⠈⠻⣿⣦⠀⠹⣿⣿
⡇⠀⠀⠀⠋⠀⡀⡟⠂⠃⠀⠸⡅⡤⠆⠈⡻⣿⣿⠋⠁⠐⠃⣤⠈⢿⢿⣿⣿⣿⠀⠀⠀⠀⢸⣏⡀⠀⠀⠐⣄⠑⠀⣀⠈⢈⣩⠀⠿⠀⢀⠰⠄⣷⡇⢠⣿⣿⣦⡄⣾⡿⢯⢋⢝⠛⠻⢖⣄⡀⠀⠀⢙⢿⣷⣄⠈⠻
⡇⢠⠀⢀⠀⠀⠋⠇⠀⠀⠀⡀⠀⡗⠀⢀⣀⣻⣿⡄⠀⠂⠑⠷⠮⠛⠚⡛⠟⠙⠖⠂⣿⣿⣿⣿⣧⣴⠀⠀⢀⠑⢄⠀⢁⣿⣿⣵⡿⣿⣼⣫⣿⢿⣿⣾⣿⣿⠛⣿⣿⠋⢸⡷⡡⣆⠀⠀⣀⣙⠁⢺⣫⡔⠠⣿⣷⠀
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠃⠀⠀⠀⠀⠀⡐⠀⠀⠁⠰⢶⡆⠀⠀⠀⣤⣤⣤⠀⣠⢠⣉⡆⠀⢸⣿⣿⣫⠀⣻⣿⣿⡄⣘⣿⣿⣿⣿⠴⢿⠿⠀⢸⣿⣝⣵⣧⡀⠸⣿⠗⡮⠔⠋⠀⠈⠁⠀
⣷⣷⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣿⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡱⢚⢩⠉⠏⡍⢸⠉⡏⢽⡏⠍⡏⢉⠍⢹⢩⡃⡏⢹⢽⡏⢹⣩⣿⡹⢉⡍⡏⢽⢹⠉⡯⢝⠉⡩⢘⠉⢩⢩⠍⢙⠩⢸⡏⢹⠏⡏⡭⢽⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣮⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣽⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⣷⣼⣼⣦⣭⣮⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⢻⣽⠿⠛⣻⣛⡻⢿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣾⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⣭⡭⣭⣭⠭⢭⣭⠭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡛⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⣦⢮⣤⣤⠤⣬⣤⠤⣮⣿⣦⣿⡦⠦⠴⣽⣼⣴⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⢸⣿⣿⣿⣿⣿
⣿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣯⣿⣿⣬⣥⢯⣤⣠⠤⣤⣤⠤⣬⣿⣤⣽⠴⣤⣤⣤⣽⣦⡤⣴⠤⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣦⣥⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢯⣤⣠⣤⡤⣤⣤⢬⣿⣤⣿⣥⣤⢤⣤⣶⣼⣥⣧⣦⣤⣤⣦⣷⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣤⣾⣼⣤⣦⣤⣤⣧⣥⣤⣤⣶⣤⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⡏⠋⠋⠋⠋⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⡿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡏⣹⠛⢻⣿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡟⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⡏⠉⣿⡟⠛⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⠉⠉⡉⡉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠋⠁⠀⠉⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠨⠁⠀⠀⠀⡀⣠⠠⠆⠉⢰⡆⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⢀⡀⡇⢰⠀⡇⣿⠀⠀⣈⢸⡇⡇⢨⠀⠂⢸⣿⣿⣿⣿⣿
⣿⣿⣦⣦⣦⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢀⡀⠒⢠⠀⡆⢰⢸⡇⣿⢸⡇⡇⢸⠀⡇⣿⢰⡆⣿⢸⡇⡇⢀⠀⠂⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⠁⢸⠀⡇⢸⢸⡇⣿⢸⡇⠇⢸⠀⡇⣿⢸⡇⣿⠸⠃⠇⢸⠀⡇⢸⣿⣿⣿⣿⣿
⣿⣿⠍⡉⡉⡉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⡀⣀⠀⠀⠀⠀⠀⡀⢀⢠⡄⣿⢸⡇⠟⠸⠀⡇⢸⢸⡇⢿⢸⡇⡆⢰⠀⡇⢿⢸⡇⣿⢸⡆⡇⢸⠀⡇⢸⣽⣭⣥⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⢛⠟⠋⠉⣀⢀⠀⡄⢠⢠⡆⣤⢰⡆⡶⢸⠀⠇⢸⠸⡇⣿⢸⡇⡁⢨⠀⡇⢸⠸⢇⢛⠘⡃⢓⠘⡀⢃⠘⡈⢸⠘⡈⣃⢃⠘⡄⢡⠉⡄⢱⠈⠆⠰⠀⠆⠆⠀⢘⡧⢤⠦⣼⣿
⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠭⠦⠴⢤⠥⡭⢈⠅⡡⠈⠀⠁⠈⠀⠁⠀⠀⠂⡐⢀⠃⡈⢀⠂⡀⢀⠀⠂⠐⠀⠂⠐⠀⠠⡸⢘⠀⡃⢘⠀⡁⢈⠄⡱⠀⠄⠡⠈⠄⠠⡠⢄⠠⡰⢀⠆⡸⢀⠇⡰⢠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⡟⠛⣿⡟⠛⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⡟⠹⣿⣿⣟⣛⣿⣿⠏⣿⣩⣍⣹⣿⣿⠙⢹⣿⣿⣿⣿⣿⡯⢹⣿⣿⣋⣉⣻⡏⠋⣿⣛⣛⣻⡏⠻⠝⣿⣿⣿⣤⣬⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡯⠄⣿⡯⡨⣿⣿⣿⣿⣿⣿⡢⣿⣿⣿⣿⣿⣿⢅⢼⣿⣿⣿⣿⣿⡧⠪⣿⣿⣿⣿⣿⡯⡂⣿⣿⣿⣿⣿⣿⠕⢽⣿⣿⣿⣿⣿⡧⣼⣿⣿⣿⣿⣿⡯⠬⣿⣿⣿⣿⡧⠸⢔⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 850

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/geminispace-size-2022/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/geminispace-size-2022/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ There_Are_Probably_Over_a_Million_Gemini_Pages_Already_(Static,_Not_Generated
on_Demand)⠀✐


Posted in Free/Libre_Software, Protocol at 3:50 am by Dr. Roy Schestowitz


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


Summary: Gemini space (or Geminispace) has grown to the point where it is not
trivial to assess its full extent, but Lupa (data source of the above graph) is
still trying


About three years ago Gemini started with only one or two pages. It grew over
the years as more and more capsules came online (doubling in number over the
past year alone) and it’s getting hard — not to mention expensive — to keep
abreast of it all. It’s not cheap to crawl and re-crawl millions of pages.
Limitations are imposed on the maximum number of URLs retrieved per capsule,
even for capsules that are still growing (ours is approaching 42,000 pages and
there are at least half a dozen capsules with over 10,000 pages in them,
probably over a dozen capsules in fact).


It seems safe to say that there are already over a million Gemini pages
already. We just lack the capacity to keep track of them all. We can
extrapolate a bit.


According to these_latest_statistics based on Lupa, Geminispace continues to
expand. From what I’ve observed here in Techrights, traffic from Lupa, the
crawler, decreased a bit earlier this year. Yes, a few months ago Lupa was
slowing down a bit, so it looked like there was a decline (we’ve been posting
no_less_than_before) and judging by the frequency we_find_new_articles/pages_in
Gemini, compared to past_months, there’s definitely an uptick in activity. In
fact, so_far_today we’ve seen almost 2 new articles per hour. There’s no
authoritative, centralised entity which tracks the growth of Geminispace, and
none is desirable either. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⠋⣿⡽⣿⠛⣿⠋⣿⢛⢻⡟⣿⣽⣹⢹⡫⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣟⣛⣛⣻⣿⣭⢿⡿⠋⡏⢿⡹⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠿⠿⡿⣿⣿⡿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠻⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⢐⣶⣿⡇⣿⣿⣿⣿⣿⣿⣴⣤⣤⣿⣿⣿⣣⣧⣽⣾⣿⣿⣥⣦⣯⣾⣮⣠⣧⣠⣦⣾⣿⣴⣬⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⢃⣵⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⣀⣦⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣴⣿⡄⠀⠀⠀⠀⠀⠀⢠⣦⣦⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡻⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⡿⣯⣪⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣯⣸⣿⣏⣮⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣯⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠙⠀⠀⠻⠉⠈⠙⠉⠻⢿⣿⣿⣿⣿⣿⡟⠛⠉⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠛⢿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠉⠉⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣧⣼⣿⣿⣿⣿⢿⣋⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⢯⣶⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠏⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⡻⢼⣿⡆⣿⣿⣿⠏⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢫⣓⣿⣿⣿⡇⣿⣿⡟⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣽⣿⣿⣿⣿⡇⣿⣿⣧⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⢫⢻⣤⣷⡿⣟⣟⣷⣽⣿⡿⡟⡝⣷⣿⣾⡿⡟⡝⣧⣾⣾⡿⡟⡝⣧⣼⣾⣿⡻⡽⣵⣽⣾⢿⣻⡽⣯⣼⣾⢿⢫⢹⣴⣷⣿⢟⢯⢿⣥⣷⣿⣟⢯⢯⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣒⣽⣾⣿⣿⣷⣩⣴⣾⣿⣿⣷⣫⣶⣿⣿⣿⣗⣫⣶⣿⣿⣿⣗⣪⣷⣿⣿⣿⣏⣮⣷⣿⣿⣿⣏⣮⣷⣿⣿⣿⣞⣵⣾⣿⣿⣿⣰⣽⣾⣿⣿⣿⣱⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 934

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/iloat-a-decade-late/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/iloat-a-decade-late/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Year_is_2032:_ILOAT_Tells_Campinos_That_He_Broke_the_Law,
Repeatedly⠀✐


Posted in Europe, Patents at 1:38 pm by Dr. Roy Schestowitz


       🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Gary Oldman: But I was the f***ing president⦈
  Can you punish him 10 years after committing crimes, lying, and engaging in
                           highly abusive behaviour?


Summary: As EPO dictator, António_Campinos can now see that Benoît_Battistelli
gets away with serious violations, knowing that nothing will happen until after
retirement (no consequences for those who break laws)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⡿⢛⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠁⢴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠛⠛⡿⠿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣶⣿⣿⣇⡀⢉⣿⣷⣶⣤⣤⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠞⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣤⣤⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠉⠉⠉⠏⠉⠛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠗⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠟⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢻⡇⠁⠀⠀⠀⣀⣀⣀⣤⣤⣀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡍⢰⣶⣶⣶⣶⡆⣶⣶⣶⣿⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣶⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⡇⢹⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡇⢸⣿⡇⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣰⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠏⠁⠀
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠩⠾⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⠿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⠓⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠟⠿⠿⣿⣅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣶⣾⣿⢀⠉⢻⣿⣶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣶⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡉⠉⠉⠹⠋⠙⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⡿⠇⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠐⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⣿⠉⠀⠀⠀⠀⣀⣀⣀⣤⣤⡀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡌⢰⣶⣶⣶⣶⡆⣶⣶⣶⣿⣷⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣶⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⡏⢹⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡇⢸⣿⡇⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⣇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠛⠛⠉⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠟⠷⠀⠀
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠱⠾⠿⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⡿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠿⠃⢨⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣤⣶⣶⡎⠙⠻⣶⣤⣄⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣶⣿⣿⣿⣿⣷⣾⣩⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡰⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡉⢁⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠿⠛⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣠⣤⣶⣶⣾⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⢀⣀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡟⠃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡄⢰⣶⣶⣶⣶⡦⣶⣶⣶⣶⣶⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⡇⢻⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡇⢸⣿⡇⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠉⠀
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠾⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠛⠻⣾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣿⣟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣀⣶⣿⣯⣅⣩⡿⢿⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠜⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠘⣀⣤⣽⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⢋⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⠛⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣡⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣾⡍⢰⣶⣦⣰⣶⡆⣶⣶⣶⣶⣶⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⡏⢻⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡇⢸⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠏⠉
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⠋⠁⠀⠰⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢠⣶⣿⣿⣿⣶⣶⣄⣴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⣾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣀⣠⣾⣿⣿⣿⣯⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠀⠀⠀⠀⠀⣾⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠁⠁⠉⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⠇⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⣀⣠⣢⣁⣆⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡌⢰⣾⣿⣿⣿⣿⣿⣷⣶⣾⣷⠟⠁⢰⣶⡆⠀⠀⣶⣶⣴⣶⣶⡆⢰⣶⣆⣷⣶⣶⣿⢻⣯⣷⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⡿⢿⣿⣿⣿⣿⣿⡏⠁⠀⠀⢸⣿⡇⣀⣴⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡇⢸⣿⡏⠻⢹⣿⣇⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠛⠿⠿⠛⠛⠛⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣟⣈⣻⣿⣿⡉⠉⠀⠀⠀⠐⢛⡛⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣴⣾⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⢀⡀⢸⣧⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⡿⠟⠙⣿⣿⣿⣿⣿⣿⣧⠀⣹⣿⣿⣈⣿⣿⣿⡆⠀⠀⣼⣿⣾⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣰⣿⢿⣿⣿⣿⠟⣁⣀⣤⡾⢻⣿⢿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢸⡇⣼⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⠇⠀⠸⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡀⢰⣿⣿⣿⣿⣟⣶⣶⣶⣶⣶⣴⣿⢶⣶⡆⠀⠀⣶⣶⠀⣶⣶⡎⢱⣶⡆⢰⣶⣶⣶⢀⣠⣶⡿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠋⢸⣿⡇⠀⠀⢹⣿⣆⣿⣿⣇⣼⣿⡇⢸⣿⣿⣿⣿⣿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡇⢹⣿⡟⣿⢻⣿⡏⠋⠀⠀⢸⣿⡇⢀⣴⣾⣿⣿⣿⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⣷⣿⣼⣿⣧⣤⣤⣤⣼⣿⣿⡿⢟⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠈⠘⠿⠿⠿⠿⠿⠛⠋⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠋⢻⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠄⣀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⢟⠻⢿⣿⣿⣿⡿⠿⠿⠛⠉⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣄⣤⣽⣿⣿⡇⠀⠀⠀⠀⠀⣨⣭⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠐⣿⣿⣿⣷⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠙⠻⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⢀⠀⢸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠏⠙⣿⣿⣿⣿⣇⣿⡇⠀⣿⣿⣿⢻⣿⣿⣿⣿⠇⠀⢀⣾⣦⣾⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠘⢿⣿⣿⣿⣿⣧⢠⣿⣿⣿⣾⣿⡿⠟⠃⠀⣠⡞⢱⣿⣿⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣤⣴⣶⠿⠋⠀⠛⢀⣿⡇⠀⡛⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⣶⣶⡈⢿⣿⣿⣿⣿⡾⣶⣶⣶⣶⣶⢀⣠⣴⣶⡆⠀⠀⣶⣶⠀⣶⣶⡶⢳⣶⡆⢰⣶⣶⣶⠀⢠⣶⡿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢸⣿⣿⣿⣿⣿⣿⣾⣿⣇⣶⣿⠟⢸⣿⡇⠀⠀⢹⣿⣆⣿⣿⣇⣼⣿⡇⢸⣿⢿⣿⣧⣾⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡏⢻⣿⡿⣿⢻⣿⡟⠟⠀⠀⢸⣿⡇⠀⢀⣸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣾⣿⣿⣿⣿⡻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣹⣿⡇⠈⢸⣿⡇⢀⣀⠀⢸⣿⣧⣶⣿⠿⣿⣿⣿⠸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠀⠈⠙⠋⠿⠿⠿⠿⠟⠋⠉⠀⠀⠿⠿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠁⣽⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣤⣄⢀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠾⣿⣿⣿⣿⣿⡿⠟⠿⠟⠛⠁⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⡆⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠈⣋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢴⣾⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣇⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⠀⣾⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⡇⠿⢿⣿⣿⣿⣿⣷⢰⣦⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⠀⠀⣾⣿⣿⣯⣿⣾⣿⣶⣦⠀⠀⢠⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠛⠘⣿⣿⣿⣿⢸⣿⡀⠀⣿⣿⣯⢹⣿⣿⣿⣿⠃⠀⢠⡟⣲⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠏⠁⠀⠀⠈⢿⣿⣿⣿⣿⡇⣴⣿⣿⣿⣼⣿⡿⠛⠁⢀⣠⠟⠀⠉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⠿⠋⠁⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⣶⣾⣿⣿⣿⣿⣿⣷⡆⣶⣶⣶⣶⣶⠀⣠⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡞⢱⣶⡆⢰⣶⣶⣶⠀⢠⣶⡿⢿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠇⢻⣿⣿⣿⣿⣿⣿⢸⣿⡇⣴⠾⠋⢸⣿⡇⠀⠀⢹⣿⣆⣿⣿⣇⣼⣿⡇⢸⣿⢿⣿⡇⣸⣿⣧⣸⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡆⢸⣿⡟⢻⣿⡟⠿⢸⣿⡏⠋⠀⠀⢸⣿⡇⠀⣀⣼⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣸⣿⣿⣿⣿⡻⣿⣷⡽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⡇⠀⢸⣿⡇⡀⠀⠀⢸⣿⣧⣾⡿⠿⣿⣿⣿⠸⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡛⠛⢫⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠀⠈⠉⠉⠿⠿⠿⠟⠛⠋⠁⠀⠀⠉⠉⠉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠂⠈⠀⠁⠙⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⣀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢩⣏⠉⠙⠻⣿⣿⣿⣯⠀⠀⠀⠀⠀⠠⠴⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣤⣤⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣰⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣶⣶⣶⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢿⣿⢻⣿⣿⣿⣿⣿⣷⡀⣀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⠈⠙⢛⣿⣿⣿⠿⠃⢻⣃⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⡀⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠋⠀⠀⠈⢿⣿⡇⣿⡇⠀⢸⣿⣿⡇⣿⣿⣿⣿⠟⠀⢀⡾⠁⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠎⠀⠀⠀⠀⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⢰⣾⣿⣿⣷⣿⡿⠋⣁⣀⣤⠎⠁⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⠟⠋⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡍⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⣆⣴⣶⡆⢰⣶⣶⣶⠀⢠⣶⡿⢿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⢿⣿⣿⣿⣿⣿⡏⣿⢸⣿⡇⠀⣀⠀⢸⣿⡇⠀⠀⢹⣿⡆⣿⣿⣏⣼⣿⡇⢸⣿⢿⣿⡇⠸⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡎⢹⣿⡟⢻⣿⡏⣿⢸⣿⡇⠞⠁⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⣧⣀⣭⡿⣿⣿⡽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⢀⣤⣾⣿⣿⣿⠸⣿⣿⣿⢀⣿⣿⣻⣿⣿⣿⣿⣟⣺⣿⣇⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠚⠛⠁⠉⠉⠉⠀⠉⠉⣉⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠉⠙⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⢀⢀⢀⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⠋⣩⣭⡉⠉⠙⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣧⣤⣤⣬⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠹⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⠟⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠉⢿⣿⡆⢸⣿⠀⠉⠛⣿⣿⣿⠿⠛⠃⠓⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠈⣿⣷⠈⣿⡀⠀⢸⣿⣿⡟⢠⣤⣶⣿⣿⡆⠀⠀⣡⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡸⣿⡇⠀⠸⣿⣿⣷⢼⣿⣿⣿⡿⠁⠀⣰⠏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣿⣷⢰⣦⡻⢿⣷⣿⣿⠟⠉⣀⣠⡔⠋⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣷⣿⣷⣶⣶⡆⣶⣶⣾⣶⣶⠀⠀⢰⣶⡞⠁⠀⣶⣶⠀⣶⣶⡆⢰⣶⡆⢰⣶⣶⣶⠀⢠⣶⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⡇⣏⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⡆⣿⣿⣧⣾⣿⡇⢸⣿⢿⣿⡇⠸⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡟⢿⣿⡟⢻⣿⡇⠛⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⣇⢀⣉⡻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣿⣿⠘⣿⣿⣿⢀⣿⣿⠛⣿⣿⢸⣿⣇⣸⣿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢟⠛⠟⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠳⠛⠉⠁⠀⠉⠉⠉⠈⠉⠉⢀⣹⣿⣿⣿⣿⣿⣿⣾⣯⢽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄⠀⠀⠉⢘⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⡠⠄⢀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⡃⠀⣀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠲⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⡿⡿⣟⠛⠶⠿⣿⣿⣿⣿⡿⠋⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⠿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡟⠛⣿⣿⠘⣿⡟⠙⠿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⢹⣿⡀⢿⣇⠀⠀⣠⣼⣿⠍⠉⠀⠀⣀⣀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣸⣿⠀⠀⢿⣿⣿⠄⠀⣴⣿⣿⣿⠃⠀⢠⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⡇⢀⠈⢿⣿⣆⢠⣿⡿⠋⠁⠀⣠⠏⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣾⣿⣷⣹⣶⣆⣰⣶⡆⣶⣶⣶⣶⣶⠁⠀⢰⣶⡾⠀⠀⣶⣶⠀⣶⣶⡆⢰⣶⡆⢱⣶⣶⣶⠀⢫⣷⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡏⡋⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⡆⣿⣿⣧⣼⣿⡇⢸⣿⢿⣿⡇⠸⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⡿⣿⣿⡿⢿⣿⡇⠄⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⣧⢀⣉⡻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⡇⠸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠘⣿⣿⣿⠙⣿⣿⣿⠀⣿⣿⠛⣿⣿⠸⣿⣇⣸⣿⣇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠻⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠙⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⢤⠿⠋⠁⠀⠉⠉⠉⠈⠉⠉⠀⠉⢉⣠⣭⣿⣿⣯⣾⠘⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠉⠘⣿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣠⡄⣤⣀⣀⣠⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠃⠀⢀⣿⡇⠀⣼⣿⣿⣿⣿⠛⠛⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⢸⣿⣇⢰⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⣯⡛⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣻⣫⣭⠉⠉⠉⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣀⣀⣀⣀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢫⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣷⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠶⠦⣶⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢻⣿⣿⣿⣿⣦⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣷⣶⡆⢰⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡶⢳⣶⡆⢰⣶⣶⣾⢿⣿⣷⡿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⡄⣿⣿⣇⣼⣿⡇⢸⣿⢿⣿⡿⡿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⡇⢹⣯⡻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣽⣿⡟⢻⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⣠⣾⣿⣿⣿⠘⣿⣿⣿⠀⣿⣿⠛⣿⣿⠸⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠙⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠉⠛⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⣡⣾⣿⠇⠉⠉⠁⠀⠉⠉⠉⠈⠉⠉⠀⠉⠉⢀⣭⣿⣿⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⢿⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⣀⣴⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣧⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⠀⠀⡀⠀⢀⢠⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⠀⢸⣿⣿⣿⣿⣿⠛⠀⢠⣶⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⢸⣿⣿⣄⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣯⠛⣿⣿⣿⣿⣿⣿⠟⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣿⣿⣟⣻⣫⢍⠉⠉⠉⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣍⣀⣀⣀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣩⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⣴⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣏⣉⡉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣶⣿⣿⣿⣷⣶⡆⢰⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡞⢱⣶⡆⢰⣶⣶⣾⣿⣿⣷⡿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⣄⣿⣿⣇⣼⣿⡇⢸⣿⢿⣿⣿⣿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⣷⡟⢻⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⣧⢿⣯⡻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⢀⣴⣿⣿⣿⣿⠘⣿⣿⣿⠀⣿⣿⠛⣿⣿⠸⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠙⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⡈⠉⠁⠀⠀⠀⣈⣭⣷⣿⣿⠃⠉⠉⠉⠀⠉⠉⠉⠈⠉⠉⠀⣉⣉⣴⣯⣿⣟⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠛⣿
⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⣿⣿⣿⣿⣧⣤⣀⣴⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣓⠀⠀⠀⠀⠀⢠⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠆⠀⠀⣾⣿⠀⢀⣿⣿⣿⣿⣿⡟⠃⠀⢠⣶⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⣿⣿⡄⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠳⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⡇⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣟⠛⢿⣿⠿⣿⣿⣿⡿⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⠛⢛⣭⡉⠉⠁⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣾⣿⣯⣁⣀⡀⢀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣛⣉⡉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣷⣾⣿⣿⣿⣷⣶⡆⢰⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡞⢱⣶⡆⢰⣶⣶⣷⣿⣿⣷⡿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⣄⣿⣿⣇⣼⣿⡇⢸⣿⢿⣿⣿⣿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡟⢻⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⣯⣿⣯⡻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⡇⠸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⢀⣠⣾⣿⣿⣿⠘⣿⣿⣿⠀⣿⣿⠛⣿⣿⠸⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣄⡀⠈⠉⠁⠀⠀⠀⢈⣉⣥⣿⣿⠃⠉⠉⠉⠀⠉⠉⠉⠈⠉⠉⠀⠉⠉⣠⣭⣿⡛⠩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠙⣿
⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠘⠋⠁⠀⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣠⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢀⢠⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠀⢸⣿⡇⠀⣾⣿⣿⣿⣿⡟⣠⣡⣰⣾⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣷⢰⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⢸⣿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣏⠛⢿⡿⣻⣿⣿⣿⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⡟⠛⣫⣍⠉⠉⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣍⣀⣀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢫⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣴⣿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣟⣛⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢠⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣶⣿⣿⣿⣿⣷⣶⡆⢰⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡞⢱⣶⡆⢿⣶⣶⣶⣿⣿⣷⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⣄⣿⣿⣇⣼⣿⡇⢸⣿⢿⣿⣿⣿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠷⣾⣷⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡟⣿⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣘⣿⣿⣿⣯⡻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠙⠛⠿⣷⣿⡇⠀⠀⠀⠀⢠⣾⣿⣧⣼⣿⡇⢸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⣠⣾⣿⣿⣿⠘⣿⣿⣿⠀⣿⣿⠛⣿⣿⠹⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣍⣛⣛⡉⠀⠀⠈⠉⠁⠀⠀⠀⠈⢉⣡⣾⣿⠇⠉⠉⠁⠀⠉⠉⠉⠈⠉⠉⠀⠉⠉⢠⣯⣟⠛⢭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢻
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠾⣿⡿⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⣠⣴⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣷⣶⣿⣿⣿⣇⡘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣱
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣿⣿⡇⠀⣾⣾⣿⣿⣿⣿⡷⣂⢀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡟⢀⠀⠀⠀⡜⣿⣿⣿⢸⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢳⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣍⠙⠿⠋⣹⣿⣿⡟⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣋⣩⣥⡀⠀⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣯⣀⡀⡀⠀⣬⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⢿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣾⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣾⣿⣿⢷⣶⡆⢰⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣿⣿⣷⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⣆⣿⣿⣇⣼⣿⣿⢻⣿⣿⣿⣿⣿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣴⣄⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣷⡟⢹⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠁⣿⣿⣻⣿⣿⣿⣿⡻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⣴⣿⣿⣿⣧⣼⣿⡇⢸⣿⣇⣸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⣠⣾⣿⣿⣿⠸⣿⣿⣿⠀⣿⣿⠛⣿⣿⠿⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠛⠿⢿⣿
⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣯⣤⡀⠉⠛⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⣡⣾⣿⠇⠉⠉⠉⠀⠉⠉⠉⠈⠉⠉⠀⠉⠉⠘⣏⠻⢿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠹
⠀⠖⠶⣶⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣿⣷⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣐
⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⢂⣜⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⡔⣿⣿⣿⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠅⠀⠀⠀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⡈⠻⣟⢹⣿⣿⣿⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣟⡛⣭⡀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣄⣰⣿⣿⣿⣿⣿⣿⣅⣀⣀⠀⢠⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣾⣿⣿⢰⣶⡆⢰⣶⡆⣶⣶⣶⣶⣶⠀⠀⢰⣶⡆⠀⠀⣶⣶⠀⣶⣶⡆⢰⣶⣦⣶⣶⣾⣷⣿⣿⣷⡿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⣆⣿⣿⣇⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣴⣶⣶⣄⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣷⡟⢸⣿⡇⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⡻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣾⣿⣾⣿⣿⣿⣿⣇⢸⣿⣇⣸⣿⠇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⣠⣾⣿⣿⣿⠸⣿⣿⣿⢀⣿⣿⠛⣿⣿⣿⣿⣇⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠋⠛⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⠁⠀⠉⠛⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⣡⣾⣿⠇⠉⠉⠉⠀⠉⠉⠉⠈⠉⠉⠀⠉⠉⢹⡯⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠂⠀⠀⠀⠀⠀⢹
⠀⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣰
⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⡇⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡆⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⡿⠉⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡄⠀⢰⣿⣿⣿⣻⢫⣥⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣯⣀⣀⣀⠀⣬⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣤⣾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣽⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⢈⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣴⣿⣾⡍⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠛
⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣻⣧⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⡀⢀⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⠀⣀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⢠⠀⡄⠀⢰⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠏⠁⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢰⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣇⠀⠀⣼⣿⣿⣿⢿⢟⡋⠉⠉⠉⠉⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣄⢠⣿⣿⣿⣿⣿⣾⣝⠀⠀⠀⠀⣘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣿⣿⣧⣼⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠟⡿⣿⣿⠿⠿⠇⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣀⣠⣤⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣌⡷⢷⢦⣤⣤⢤⠠⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡻⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠘⢻⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠟⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⠻⠿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢁⣠⡀⣀
⠀⠀⠀⠀⣻⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡄⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢾⣿⣿⡏⢠⠀⡄⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⣾⣿⣿⡿⣻⢛⣍⠉⠉⠉⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⢀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⣿⣿⣿⣿⣿⡿⣤⣾⣿⣿⣶⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠛⠻⠿⠿⠿⢟⣛⣀⣀⣘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣴⣶⡄⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣌⡻⢿⣶⣦⣤⡤⡤⠤⠄⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠘⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠉⢁⡄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⢀⠀⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣇⢠⣼⣼⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⢀⠀⠀⢸⣿⣿⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠳⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣸⣿⣿⣿⢿⠿⡛⠋⠉⠉⠉⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣾⣏⠀⠀⠀⠀⢀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣁⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣭⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⠞⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣠⣄⠉⠁⠀⠀⠈⠃⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠻⣶⣶⣤⣀⣀⣀⡀⠀⠤⠖⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣘⡙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⢿⢸⣿⢸⣿⡇⣿⣿⠿⠘⣿⣿⣿⣿⣿⣿⣿⡿⣏⢢⣖⢸⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⣿⢿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣮⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⢸⣿⣾⣿⣧⣿⣿⣶⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⢸⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣿⣾⡋⢸⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣛⢻⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⢀⣶⣿⡏⢸⣿⢸⣿⣇⡀⣶⣆⣻⣿⢿⣿⡇⣿⣇⣿⣿⢸⣿⣛⡛⣿⣯⣿⣿⣿⣻⣿⢸⡿⠟⠻
⣿⣿⣿⣽⣿⣿⣾⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⣏⠀⠀⠀⠈⠉⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⢉⣵⣿⣿⠋⠁⠈⠉⠈⠉⠉⠁⠈⠛⠋⠁⠈⠻⣧⣿⣿⣯⣵⣬⣿⣿⣧⣿⣿⣿⣿⣿⣼⣿⣼⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢀⠀⠀⠀⢰⣿⣿⣇⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠈⠀⠀⠀⡜⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⢠⣿⣿⣿⡿⡿⠿⠛⠛⠛⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⣼⣿⣿⣿⣷⣦⣯⠃⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣗⣩⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⢠⣤⣀⡀⠀⠀⠀⠀⠀⣀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣮⡈⠋⠛⠿⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⢿⢸⣿⢸⣿⡇⣿⣿⠿⠀⢻⣿⣿⣿⣿⣿⣿⡿⣏⢳⣖⢸⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣾⢻⣿⡿⠟⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣮⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣧⣿⣿⣶⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡛⢸⣿⣷⡆⡻⣿⣿⣿⣿⣿⡇⣿⣟⣿⣿⢸⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣛⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⢹⣿⢸⣿⣇⡀⣶⣆⣿⣿⢻⣿⡇⣿⣏⣿⣿⢸⣿⣟⡛⣿⣯⣿⣿⣿⣿⣿⢸⣿⠿⠟
⣿⣿⣿⣽⣿⣿⣾⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠈⠉⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⣠⣿⣿⠏⠈⠉⠈⠉⠙⠁⠈⠛⠛⠁⠈⠉⠡⣿⣿⣯⣵⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣼⡗⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡀⠀⠀⠀⣿⣿⡀⡜⣾⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠠⠀⠀⠀⠀⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡯⠫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢰⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⣸⣿⣿⣿⢿⠿⠛⠋⠉⠉⠙⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣿⣿⣿⣿⣶⣾⣟⠀⠀⠀⠀⢀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣟⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⢿⢸⣿⢸⣿⣇⣿⣿⠿⠀⠀⣿⣿⣿⣹⣿⣿⣿⣯⢳⣟⢸⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣿⣿⣿⡇⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣺⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⣋⣾⣿⣷⡄⠻⣿⣦⡿⢻⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣻⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢿⣿⣇⡀⣶⣆⣿⣿⢸⣿⠁⣿⣿⣿⣿⢸⣿⣟⡓⣿⡏⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣾⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⠀⠈⠉⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⢉⣯⣼⡏⠈⠉⠉⠁⠈⠛⠛⠁⠈⠉⠀⠉⠙⣿⣷⣾⣿⣿⣧⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⠀⠀⠄⣼⣿⣇⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠃⠘⠀⠀⢀⢻⣿⣿⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⡘⣼⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠈⠈⢨⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢨⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣼⣿⣿⣿⣶⣴⡗⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣀⣄⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⢸⣿⢸⣿⣷⣿⣿⣿⡀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣷⣟⣹⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⣿⣿⡟⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣺⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢺⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣿⡿⠻⣿⣦⡐⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⢸⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣟⡁⣶⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣟⡛⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣾⣿⣮⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣯⢯⡁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⣩⣿⡿⠉⠁⠈⠛⠛⠁⠈⠋⠀⠉⠉⠉⢿⣿⣿⣿⣧⣿⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⠀⠀⠀⣼⣿⣇⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠺⠀⠀⢠⢻⣿⣿⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⠘⣼⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠘⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢨⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣼⣿⣿⣿⣶⣴⡗⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣀⣄⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⢸⣿⢸⣿⣷⣿⣿⣿⣀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣷⣟⣹⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⣿⣿⡟⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣺⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣿⡿⠻⣿⣦⡰⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣟⡁⣶⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣟⡛⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣿⣿⣮⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣯⢯⡁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⣩⣿⡟⠉⠁⠈⠛⠛⠁⠈⠋⠀⠉⠉⠉⢿⣿⣿⣿⣧⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣈⠀⠀⢸⣿⡅⣤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢰⢿⡄⠀⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣺⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢅⣱⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣾⣾⣼⠀⠀⠀⠀⢘⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⢺⣿⣿⣿⣿⣿⣰⣄⣿⣿⢿⢸⣿⣿⣿⣿⣷⣗⣸⣿⣶⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣆⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⣴⣿⣷⣦⡐⢸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢺⣿⣺⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣗⡛⣷⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣟⡛⣿⣏⣿⣿⣿⢺⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⠝⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⢨⣿⣿⠃⠈⠛⢛⡁⠘⠙⢠⡿⠉⠉⠙⣿⣿⣿⣧⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⢀⡀⠀⢰⣿⣧⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⢺⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠈⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠣⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣾⣿⣿⣛⢋⣍⠁⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣷⣀⣀⣠⣀⣬⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⢾⣿⣿⣿⣿⣿⣸⣷⣿⣿⣿⢸⣿⣿⣿⣿⣷⣖⢸⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣿⣿⣆⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⢿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⣄⣻⣿⣦⡀⢸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡺⣿⣆⣿⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⣹⣿⡇⠈⠛⠛⢁⡘⠛⠀⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⣾⣧⣰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣤⣷⠀⠀⣿⣷⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⣿⣿⣿⣋⣍⡉⠉⠈⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣷⣂⣐⣠⣄⣤⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⢸⣿⣿⣿⣿⣷⣖⢸⣿⡆⣿⣧⢸⣿⣴⣿⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣿⣿⣆⢸⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⢿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣼⣿⡟⣿⣿⣾⣿⢸⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⣻⣿⣧⡀⢸⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢻⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡰⣿⣇⣻⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⢉⣿⣷⠊⠛⠛⠥⠜⠿⠠⣿⣯⠉⠙⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⡄⠀⠀⠀⢈⣛⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢰⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⠂⠀⢸⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠘⠂⠐⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⡻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣵⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣿⣿⣿⣻⣩⢡⠀⠀⠈⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣶⣀⣊⣤⣤⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⢸⢿⣿⣿⣿⣷⣖⢼⣿⡆⣿⣧⢸⣿⣠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣟⣿⣆⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⢿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣼⣿⣟⣿⣿⣾⣿⢻⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⢻⣿⣧⡀⢸⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢹⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣾⣇⣻⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⣹⣿⠎⠛⠛⠡⠼⠟⠤⣿⣯⠉⠙⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⢀⠈⠀⠀⠀⡛⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⢰⣿⣇⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⠀⠀⢸⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠆⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⣿⣿⣏⣭⣠⠀⠀⠉⠙⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣶⣀⣤⣤⣤⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⡀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣦⣶⣾⣿⡎⣿⣧⢸⣿⣠⣾⡟⣷⡆⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣟⣿⡆⢸⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⣹⣿⡿⣿⣿⣾⣿⢿⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⠻⣿⣧⡀⢸⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣹⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣾⣇⣻⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢼⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠉⠀⠙⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⣹⣿⡏⠛⠛⠡⢜⡿⡤⣿⣯⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⢠⠘⠀⠀⠈⣻⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⢀⠀⠂⣰⣿⢰⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡿⣴⣏⠀⠀⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣏⣴⡄⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣼⣿⣿⣿⣿⣿⣦⣤⣥⣤⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⠉⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣸⣿⣿⣿⣿⢢⣶⣾⣿⡆⣿⣧⢸⣿⣠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⡆⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⡿⣿⣿⣾⣿⣿⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⠻⣿⣧⡀⢸⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣾⣇⣻⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⣹⣿⠏⠛⠛⠁⠘⠛⠀⢛⣿⡉⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠⠀⣾⡇⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⢣⣾⡅⠀⢸⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠈⠋⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣭⣆⡄⠀⠀⠈⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠉⠉⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⢀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣸⣿⣿⣿⡇⢲⣶⣼⣿⡆⣿⣧⢸⣿⣠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣟⣿⡆⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢻⣿⡷⣿⣿⣾⣿⣿⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⢻⣿⣦⡀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡷⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣾⣇⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠙⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⢉⣽⣿⠊⠛⠛⠁⠘⠿⠠⣿⣏⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⢠⣿⣆⡞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⢰⣾⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⠈⠙⠆⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣏⣵⣤⠀⠀⠀⠙⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢲⣖⣸⣿⡆⣿⣧⢸⣿⣤⣿⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣿⣿⣆⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠛⢿⣿⣷⣿⣿⣿⣿⢻⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⣻⣿⣦⡀⢸⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡯⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡸⣿⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢹⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⣩⣿⡇⠈⠛⠛⠁⠘⠟⠠⣿⡉⠙⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀⣀⠀⡀⠀⠀⠀⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⣰⣿⣧⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡇⣴⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⡇⠉⠻⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣣⣮⣾⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣏⣵⡤⠀⠀⠀⠘⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢇⣾⣿⣿⣿⣿⣿⣦⣤⣤⣤⣴⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢹⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⡂⢲⣶⣴⣿⡆⣿⣧⣼⣿⣾⣿⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣆⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠙⢻⣿⡿⣿⣿⣾⣿⢹⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⣤⣿⣿⣦⡀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡿⣷⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⣽⣿⠃⠈⠛⠛⠁⠘⠛⢠⣏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⢹⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣾⣿⢸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⢀⣶⠂⠀⣼⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡥⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⣮⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⣆⡄⠀⠀⠀⠉⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⣿⣿⣷⣦⣤⣤⠤⣲⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣠⣾⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢉⣈⣩⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢨⡭⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⢸⣿⣾⣶⣤⣄⣠⡈⢀⠀⣤⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⡀⢻⣿⣿⣿⣿⣿⣷⣤⣛⠻⡿⡿⣿⠿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣆⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⣤⣿⣿⣦⡀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢹⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡻⣷⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⢈⣽⣿⠃⠈⠛⠛⠁⠘⠛⣤⡍⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡆⢀⠀⠀⠀⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⠃⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⡄⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣥⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣥⡄⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣠⣥⡤⢄⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⢀⣼⣿⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣏⣥⣬⣩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠈⣿⣿⣿⣿⣿⣷⠀⢀⣤⣄⣼⣿⠋⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣇⡘⢿⣿⣿⣿⣿⡷⣿⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣆⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⣤⣿⣿⣦⡀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡻⣷⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢹⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣾⣻⠿⡿⢀⠈⠉⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⢈⣽⣿⠃⠈⠛⠛⠁⠘⢿⣤⡍⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣾⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⣾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡆⠀⠁⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡛⣩⡉⠁⠀⠈⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣅⣀⣃⡠⠤⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⡟⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⡟⠋⠛⠿⠟⢻⣿⣯⣽⣤⢨⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠸⣿⣿⣿⣁⣴⣶⡀⠀⣤⣽⣿⣟⣛⠛⡟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣿⣿⣆⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⣻⣿⣦⡀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢻⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⡿⢿⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⣰⣾⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣸⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⠇⠈⠉⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⢉⣿⡯⠈⠛⠛⠁⠘⠛⣤⡍⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⣾⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⣿⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡛⣩⡉⠁⠀⠈⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣅⣀⣁⡠⠤⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⠿⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⡟⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢸⣿⣿⣿⡟⠋⠛⠿⠟⢻⣿⣯⣽⣤⢨⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠸⣿⣿⣿⣁⣴⣶⡀⠀⣤⣽⣿⣟⣛⠛⡟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⣿⣿⡆⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⣻⣿⣦⡀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢹⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⡿⢿⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⣰⣾⣆⣿⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣽⣿⣿⣿⣿⣿⣽⡿⠿⠇⠈⠉⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⢉⣿⡿⠈⠛⠛⠁⠘⠻⣤⡍⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⣾⣅⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡿⢸⡦⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⠉⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠀⠀⠀⣴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢛⣍⠉⠀⠈⠉⠙⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣯⣀⣀⣀⡀⢤⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⢀⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣄⣠⣿⣿⣿⣿⣿⣿⠟⠋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣖⡀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣯⣼⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠸⣿⣿⣷⣞⠛⠙⠛⠛⠛⣿⣿⣿⣥⣤⣨⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣁⣤⣾⣷⠀⢀⣼⣿⣿⣿⠟⠿⠿⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢹⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⡆⢸⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣾⣿⢸⣿⣧⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⠻⣷⣾⡃⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣶⣆⣿⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⠋⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⣡⣾⠟⠛⠁⠈⠛⠀⠻⣏⠉⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⠀⠀⠀⡀⢰⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡿⠐⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣩⣦⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣬⣤⠤⢲⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⣰⣿⣟⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⢀⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢰⣦⣾⣿⣿⣿⣿⡿⣿⠋⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣿⣿⢿⣿⣿⣿⣿⣷⣿⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⢸⣿⣿⣿⠏⠈⣈⡉⠉⠙⣿⣿⣷⣷⣦⣤⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠸⣿⣿⣿⣶⣾⣿⣧⠀⣴⣿⣿⣿⣿⣛⣛⣛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣎⢸⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⠻⣷⣶⡇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡏⣿⡏⣿⣿⠸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣶⣦⣿⣿⢸⣿⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⠟⡁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⢁⣾⠟⠋⠁⠘⠋⠀⠛⣯⠉⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡟⣦⣴⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⡇⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⣫⢉⠁⠀⠈⠉⠛⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣅⣀⣀⣀⠠⢬⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⢰⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⣴⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢀⣄⣼⣿⣿⣿⣿⣿⣿⠛⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⢸⣿⣿⣦⡿⠘⠙⠛⠛⠛⣿⣿⣯⣧⣤⣬⣥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⣿⣿⣿⣤⣴⣿⣷⠀⢠⣿⣿⣿⣿⠛⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⡏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣦⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⠻⣷⣦⡾⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡟⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣶⣆⣿⣿⢸⣿⠀⣿⣏⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⡿⠁⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⣬⣿⠋⠁⠈⠉⠀⠛⢻⡍⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡿⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡇⠸⠿⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠐⠇⠀⠀⠰⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣩⣦⠄⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⠄⢒⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⣠⣿⣿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⣴⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢁⣦⣾⣿⣿⣿⣿⣿⢿⠏⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⡟⣿⣿⣿⣿⣿⣿⡃⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣿⣿⣿⡿⠁⢁⣉⠉⠉⢹⣿⣿⣾⣶⣰⣶⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣆⢀⣾⣿⣿⣿⣏⣙⣛⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⣆⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣷⡄⠻⣷⣦⣾⢿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡏⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣶⣆⣿⣿⢸⣿⠀⣿⣇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠿⠟⠁⡉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⢨⣿⡟⠁⠘⠋⠀⠉⠙⢯⡁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⢀⢀⡀⠀⢠⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡏⠸⠸⠇⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⢐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣩⣠⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣀⣄⣠⠤⢤⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⢠⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣠⣿⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣄⣴⣿⣿⣿⣿⣿⣿⠟⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⡿⣿⣿⣿⣿⣯⣿⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠘⣿⣿⣷⣟⠛⠳⠛⠛⠛⢿⣿⣯⣷⣤⣨⣭⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣧⣤⣾⣷⠀⢠⣼⣿⣿⡿⠛⠻⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⢸⣿⣿⣿⣿⣿⣿⣧⣜⣿⣿⣿⣿⣿⡖⣿⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⡆⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣶⡄⠻⣷⣦⣰⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣇⡀⣶⣆⣻⣿⢻⣿⠀⣿⣇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⠉⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⣿⣿⠁⠈⠋⠀⠙⠛⠋⣥⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⠇⡀⡄⠀⠀⣿⣿⣵⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢸⠀⠇⡇⠀⢠⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⢋⣍⡀⠀⠀⠈⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣀⣐⣀⡀⠠⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⣶⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢃⣄⣼⣿⣿⣿⣿⣿⣿⠿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⣇⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⢻⣿⣿⡿⣿⣿⢃⣀⡀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⢸⣿⣿⣿⣟⣠⣶⡄⠀⣀⡉⠻⣿⡿⠿⢿⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⢿⣿⣿⣿⣶⣦⢰⡄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣄⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⡆⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣶⡄⠻⣷⣦⣀⣼⣿⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⢿⣿⠀⣿⣇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⣹⣿⠇⠈⠉⠀⠉⠋⠉⠑⢬⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡇⡆⡆⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠀⠃⠃⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣡⡦⠄⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣬⣤⠤⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⣼⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⢠⣾⣿⣿⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⡿⠛⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⡿⠻⡹⣿⠿⠟⣿⣿⣣⣄⣀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠘⣿⣿⣿⣟⣴⣶⣆⠀⣤⣬⣽⣟⡛⠻⠿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⢹⡏⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⡿⠇⣾⡟⣿⡆⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣦⡄⠻⣷⣦⣀⣾⣿⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⢿⣿⠀⣿⣇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⡟⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⣹⣿⠇⠈⠉⠀⠉⠋⠉⠁⠨⠉⠙⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⢘⢣⡄⠀⠸⣿⣿⣼⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⠘⠀⠇⠀⢧⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡸⠀⠀⠀⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠁⠀⠀⠀⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠟⠛⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣍⣴⠴⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⣥⡤⠖⣺⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⡿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⠟⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠟⠿⠿⠿⢻⣿⣍⣦⣤⣬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣾⣷⣄⢀⣦⣬⣽⣛⡛⠛⠛⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣽⣟⣿⣿⣿⡏⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⢛⡾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⠿⠇⣾⡟⣿⡆⢸⣿⠇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣦⡄⠻⣷⣦⡀⣸⣿⠀⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⣿⣿⠀⣿⣇⣿⣿⢸⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⡿⠁⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⢹⣿⡿⠈⠉⠀⠛⠙⠋⠁⠈⠏⠉⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⡇⣄⠀⠀⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⠀⠀⢻⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⡿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠆⣾⣿⣿⣿⣥⣴⡰⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠒⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⢀⣾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⣠⣾⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠛⠿⠿⠿⠛⠻⣯⣡⣤⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⡀⣾⣶⣶⣽⣍⣉⣉⣁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⡿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⢻⡾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⠿⠇⣾⡟⣿⡆⢸⣿⡆⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣶⡻⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣦⡄⠻⣷⣦⡀⢸⣿⠁⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⣾⣿⠀⣿⣇⣿⣿⢸⣿⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠁⢈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⢙⣿⣿⠉⠉⠀⠉⠉⠉⠁⠈⠛⠉⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠇⣞⢰⠀⢠⢹⣿⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠎⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⠿⠿⠛⠛⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⣸⣿⣿⣿⣭⣴⡗⠂⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠖⣢⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⠉⣹⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⣶⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠻⠻⣿⣿⠿⠿⣛⢃⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⡀⣴⣶⣶⣼⣍⣉⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣿⣽⡿⣟⡿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⠻⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⠿⠇⣾⡟⣿⡆⢸⣿⡆⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣦⡄⠻⣷⣦⡀⢸⣿⠃⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⣼⣿⠀⣿⣇⣿⣿⢸⣿⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠁⣈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⠙⣿⣿⠏⠉⠀⠉⠉⠉⠁⠈⠙⠉⠁⠙⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢰⡇⣸⢰⠀⢀⢸⣿⣷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠄⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⡿⠿⠛⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣰⣿⣿⣿⣯⣥⡆⠆⠀⠀⠀⠀⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡤⢒⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣦⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠷⠎⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣷⣾⣮⡀⢰⣦⣤⣤⣇⡀⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⣿⣻⡿⣿⣿⠏⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⠻⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⠿⠇⣶⡟⣿⡆⢸⣿⡆⣿⡟⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣺⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣦⡄⠻⣷⣦⡀⢸⣿⠃⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⣾⣿⠀⣿⣇⣿⣿⢸⣿⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⢈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⠙⣿⣿⠏⠉⠀⠉⠉⠉⠁⠈⠉⠉⠁⠉⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⣶⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⢀⡆⡄⠀⠘⣿⣿⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠈⠀⠇⠀⠁⣿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⢠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⣼⣿⣿⣟⣞⣩⢡⠀⠀⠀⠈⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣀⣀⣄⡀⢤⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣽⣜⡛⠛⣻⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣍⣿⢻⣿⡷⣶⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢷⠛⡾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢠⣾⡟⣷⡄⠀⠀⣿⡟⣷⡆⣿⡿⢿⣦⢸⣿⠿⠇⣶⡟⣿⡆⢸⣿⡆⣿⡿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣇⣭⡅⠀⠀⣿⣧⣿⠇⣿⣷⣾⡋⢸⣿⣦⡄⠻⣷⣦⡀⢸⣿⠃⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢸⣿⣇⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣀⡀⣶⣆⣻⣿⣾⣿⠀⣿⣇⣿⣿⢸⣿⣀⡀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡧⠈⠉⠀⠉⠋⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠈⠉⠈⠉⠉⠁⠈⢙⣿⣿⠏⠉⠀⠉⠉⠉⠁⠈⠙⠙⠁⠉⠁⣼⡿⣿⣿⣿⣿⣿⣿⣿
⠛⠿⠿⣿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣦⣆⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣩⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2315

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/iloat-ruling-a-decade-late/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/iloat-ruling-a-decade-late/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_III_—_ILOAT_Judgment
No._4551⠀✐


Posted in Europe, Patents at 2:17 am by Dr. Roy Schestowitz


Series parts:


   1. When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_I_—_ILOAT_134th
      Session:_Two_More_Bittersweet_Victories_for_EPO_Staff
   2. When_EPO_Does_Not_Control_and_Coerce_the_Judges_—_Part_II_—_ILOAT
      Judgment_No._4550
   3. YOU ARE HERE ☞ ILOAT Judgment No. 4551
                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO censorship⦈
    In Judgment No. 4551, the Tribunal found that “the true reason for the
 requirement of the prior authorisation was to exercise a prior censorship on
                      the content of the communications.”


Summary: EPO censorship of staff communications isn’t compatible with the law,
said a ruling one week ago, but the ruling is nearly a decade late


The ILOAT Judgment which we will look at in this part – No._4551 – concerns a
challenge by a group of three staff representatives to measures adopted by EPO
management in May 2013 (!) for the purpose of preventing EPO staff
representatives from sending mass e-mails to staff.


One of the complainants against these measures was Laurent Prunier, a staff
representative who was viciously targeted and defamed by Benoît_Battistelli and
subjected to another politically-motivated disciplinary procedure by Elodie
Bergot which led_to_his_dismissal_in_2016.


As noted above, the measures impugned in the case of Judgment 4551 date back to
May 2013 (!).


“The Tribunal found that the restrictions imposed by the communiqué of 31 May
2013 were unlawful and breached the fundamental right to freedom of
association.”On 13 May 2013, Battistelli issued Communiqué No. 26 entitled
“When enough is enough – the use of mass emails within the Office”. He
complained that staff representatives were using mass emails increasingly, and
claimed that, in many instances, these emails were polemical and factually
incorrect.


Battistelli announced that he would shortly be setting up rules on mass
communications and he delegated this task to his trusted “Croatian bulldog”,
the_notorious_union-buster_Željko_Topić.


            🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇António Campinos and Željko Topić⦈
 On 30 May 2013, Battistelli’s “Croatian bulldog”, the notorious union-buster
 Željko Topić (r.), issued a communiqué imposing unlawful restrictions on EPO
staff representatives with regard to the use of mass e-mails for communicating
 with staff. These oppressive measures were maintained intact by Battistelli’s
                       successor, António_Campinos (l.).


On 31 May 2013, Topić issued a communiqué decreeing that as from 3 June 2013,
the sending of emails to more than fifty addressees would be restricted and
that prior authorisation would be required. The communiqué noted that there was
a facility for communication by the staff representation and the trade unions
via dedicated intranet pages under their sole responsibility.


The Tribunal found that the restrictions imposed by the communiqué of 31 May
2013 were unlawful and breached the fundamental right to freedom of
association.


According to the Tribunal’s assessment, the communiqué of 31 May 2013 was
unlawful because it set out an indiscriminate limitation on the use of mass e-
mails, without providing specific reasons for this measure which, moreover, was
intended to apply for an indefinite time.


The EPO failed to establish that the prior authorisation was required for
technical reasons, and it provided no evidence that mass emails to more than
fifty addressees could jeopardise the operation of its IT systems.


“The EPO failed to establish that the prior authorisation was required for
technical reasons, and it provided no evidence that mass emails to more than
fifty addressees could jeopardise the operation of its IT systems.”As a matter
of fact, the wording of the two impugned communiqués revealed that “the true
reason for the requirement of the prior authorisation was to exercise a prior
censorship on the content of the communications.”


The Tribunal was satisfied that the content of the mass e-mails which irritated
EPO management did not exceed the limits to freedom of opinion and speech, and
therefore did not justify the imposition of a requirement for prior
authorisation.


     “The [EPO] did not have the power to prevent or to impede
     communications among staff representatives and staff members only on
     the basis that they appeared, according to the Organisation, to be
     “polemical” or “factually incorrect”, or to substantiate “vindictive
     personal attacks”.


     The EPO failed to provide evidence that the communications went
     beyond the bounds of legitimate, though harsh, criticism, and
     trespassed into the realm of gross violations of the rights of the
     Organisation or individuals. In the present case, the measures taken
     by the Organisation were disproportionate.”


The Tribunal recalled that according to its case law, the ability of a body
representing the staff to circulate emails to all staff members is not “a
privilege”. On the contrary, such body “has a legitimate right to avail itself
of this facility, unless there is good cause for restricting it” (Judgment
3156).


“The complainants were collectively awarded costs of € 900 euros.”Although the
Tribunal found in favour of Laurent and his co-complainants, it rejected their
claim for an award of € 20,000 in moral damages for the “serious breach” of
their rights since 2013.


According to the Tribunal, “the annulment of the impugned decision is in itself
a sufficient remedy for any moral injury the complainants may have conceivably
suffered.”


The complainants were collectively awarded costs of € 900 euros.


In the concluding part of this mini-series we will look at the wider
implications of ILOAT Judgments nos. 4550 and 4551 for the_EPO’s_notoriously
dysfunctional_internal_justice_system. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⠛⠟⠛⠛⢿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⡀⠀⠤⢼⣿⣿⣿⣷⣿⣿⣹⣯⣿⣺⣺⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠄⠀⠁⠉⠍⠍⠉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠙⠘⢋⣭⣭⣭⣭⣭⣁⢀⣭⣿⣶⣿⣶⣾⣯⣀⣈⣻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣠⣶⣶⣿⣿⣿⣦⣤⣿⣿⣿⣷⣾⣷⣤⣴⣿⣶⣾⣿⣶⣦⣀⣤⠀⡆⢸⣿
⣿⠀⠀⢸⣷⣿⡿⠛⠛⡛⣛⠛⢿⠛⠿⠿⠛⠛⠛⠛⠛⠛⠻⠛⠿⠿⠿⠟⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠉⠯⠉⠙⢻⣿⣿⠀⠃⠸⣿
⣿⠀⢰⢸⣿⣿⡇⣰⣿⣶⣾⣿⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡥⠀⠀⢀⡠⣠⡀⠀⣀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠢⡻⣿⣶⣦⡄⠀⠀⢌⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆⠸⢼⣿⡟⠀⠀⠘⣿
⣿⠀⢸⠘⢿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⡿⡫⠂⠀⢀⣾⣿⣿⢁⣼⡇⠄⣠⣾⣵⣿⣿⣿⣮⢆⠀⠈⢒⣜⣽⣿⣿⣿⡀⠀⠐⢽⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠈⣿⡇⠄⠀⠀⣿
⣿⠀⣸⢀⣀⣿⠃⠀⠈⢽⡻⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠘⣿⠟⡠⠀⠀⣾⣿⣿⣇⣾⣿⣌⣼⣿⣿⣿⣟⣿⣿⣿⣷⣣⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢼⣿⡄⠀⠀⠀⠂⠀⠀⣿⣿⣽⣿⣿⣿⣭⣿⠀⣈⣁⡇⡇⢸⣿
⣿⠀⣾⢸⣿⣿⣇⠀⢻⣿⡏⢿⣿⣿⣿⣏⡀⠀⠀⠀⠀⣼⣏⡼⠁⠀⠀⣿⣿⣿⣿⣿⣿⣼⣿⣿⣗⠒⠐⢻⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⠾⠀⠀⢊⢻⣇⠀⠀⠀⠀⡀⠦⠹⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠁⡇⢸⣿
⣿⠀⣿⢸⣽⣿⡇⠀⢾⣿⣛⣾⣿⣿⣿⣀⠀⠀⠀⠀⠀⢹⣿⣣⠊⠀⠸⣿⣿⣿⣿⣿⣿⣭⣭⣭⣥⠀⠀⠒⣂⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⢷⣿⠀⠀⠀⡀⡇⠀⠘⢿⣿⣽⣿⣿⣿⠻⣶⣇⣿⠀⡆⢸⣿
⣿⠀⣿⠸⣿⣿⠇⢠⡈⠙⢿⣿⣿⣿⠓⠒⠂⠀⠀⠀⠀⣿⣿⡁⡠⠀⠀⢿⣿⣿⣿⣿⣿⣟⣛⣓⣀⡀⠀⠀⠚⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢈⣼⣿⡀⠀⠀⡐⠀⠀⢰⣦⣈⣛⣛⣿⣿⠀⠹⢟⡿⠀⠀⢸⣿
⣿⠀⡇⠀⠉⠀⠀⠀⠻⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⢻⣷⡯⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠀⠉⠽⠞⠛⣛⣻⣿⣿⣿⣿⣿⣿⠀⠀⡠⣡⣽⡏⡇⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠈⠃⠀⠀⢸⣿
⣿⠀⠂⠀⠀⠀⠀⠀⠀⠹⣟⠉⢉⣿⡇⠀⠀⠀⠀⠀⠘⢸⣿⣿⢊⠀⣶⣿⠟⣋⣩⡀⠈⢈⣀⡀⠀⠀⠀⠀⠀⠀⠉⣉⣁⣀⢈⡉⠙⠻⢿⣧⡀⠐⢳⡿⢿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣀⣀⠀⢀⣀⣀⠀⠀⠀⠙⠀⣘⡛⠃⠀⠀⠀⠀⠀⢀⣈⠉⠀⠊⣸⣫⣴⣿⣿⣿⣯⣤⣤⣉⣙⡳⣄⠀⠀⣴⡾⠛⠉⠀⣔⣛⣻⣿⣿⣷⣯⣗⣀⡈⠃⢠⣶⣄⣀⣀⡀⣀⢐⣂⣶⣶⡶⣶⣶⢲⣶⣤⡶⠶⢶⣾⣿
⣿⣿⣓⣶⣶⣶⣶⣶⣿⣶⣾⣶⣿⣿⣶⣶⣷⠉⠸⠀⢼⡿⢸⣿⣿⣿⣿⣿⣿⣿⣷⡶⣶⣿⣿⣭⣥⢹⡆⢸⡏⣐⣚⣻⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡄⡀⢰⣶⣶⣶⣶⣾⣿⣷⣶⣶⣾⣶⣶⣷⡔⢼⣿⣿
⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠲⠶⠶⠶⠶⠂⣸⡇⢸⣷⠀⠉⣭⣭⣽⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⡿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿
⣿⣿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠬⠬⣿⣷⠘⠛⣙⣛⠛⠿⢿⣿⣃⡿⠭⠙⠉⠁⢀⣿⡇⢸⣿⣇⠀⠀⠀⠒⠚⠛⢻⣿⣿⠿⠟⢋⡍⠉⢨⣿⡭⠯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢲⣿⣿
⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣁⠠⣽⣿⠀⢀⣧⢿⣿⣷⣶⣦⣤⣶⡴⡆⠀⠀⣸⣿⡇⠀⣿⣿⡄⠀⠀⡠⣀⣲⢶⣶⣶⣿⢿⣿⡇⠀⢸⣿⠅⠨⠹⠿⠿⢿⣿⢿⣿⠿⠿⠿⠿⠿⡿⢿⡭⠽⣿⣿
⣿⡿⠆⠀⠀⠀⠀⠐⠒⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠻⣿⣿⣿⣿⡿⣪⡞⠀⠀⣿⣿⡇⠀⢿⣿⡧⠀⢢⡺⣗⣿⣿⣿⠿⣫⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⠈⠁⠀⡀⠀⠹⣿
⣿⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠀⢷⣜⢿⣿⣿⣿⡯⡊⡀⣀⣉⡛⣇⠀⣘⣩⣴⣦⣀⢻⣿⣿⡿⣻⣿⡏⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠗⠇⠀⠀⣿
⣿⠀⢠⢀⣴⣿⡇⠀⠄⠀⠂⠈⠉⠈⠁⢈⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⠿⢀⣴⣶⣯⣽⣟⡻⢷⣿⣿⠳⠿⠿⠇⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠀⠀⠀⣿
⣿⠀⢸⢸⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠿⠿⠶⠶⠶⣾⣿⣿⣿⣿⣿⣷⣽⣯⣤⢠⣤⡀⠀⡀⠀⠀⠀⠀⢠⣤⠠⠄⣠⠤⠀⠠⠤⣤⣤⡄⠄⠤⠀⠀⠠⠤⣴⣿
⣿⠀⠸⢸⣿⣿⡇⠀⢀⠉⠀⣀⣶⣤⣬⡁⠀⠐⠂⠐⠒⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⠾⠿⠿⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡇⠄⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⠄⠈⣿⣿
⣿⠀⠀⠀⠻⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⢈⠻⣿⣿⣿⡀⠛⢛⣛⣛⣋⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣀⣀⣀⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⣈⣉⣁⢀⣿⣿
⣿⠀⠀⠀⣴⣾⡇⠀⠠⣸⣿⡿⠿⣿⣿⡟⠛⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⣜⢿⣿⣿⣶⣦⣈⢛⠛⠒⠻⠿⠿⠟⣛⣋⣍⠀⠀⠀⣿⡇⠠⠤⠀⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠤⠀⠠⡄⣾⣿
⣿⠀⠀⢀⢹⣿⡇⠀⠘⣿⣿⣷⣤⣶⣟⣶⡾⠏⠉⠁⠀⠀⠀⠀⠀⣀⣤⣾⢸⣿⣿⣧⡙⢿⣿⣿⣿⣿⡶⠿⢿⣿⣿⣶⣿⠟⢁⣴⠀⢠⣿⣇⠀⠈⢋⣉⠉⢿⣿⣿⡿⠿⢿⣿⠿⢿⠿⣿⣿⣿⣏⣉⣉⣉⡈⡉⣿⣿
⣿⠀⡀⠀⣼⣿⡇⠀⠀⠀⢛⢿⣿⣽⣿⠦⠃⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠁⣾⣿⣿⣿⣮⡢⡙⢿⣿⣿⡇⠀⠸⠲⣿⡟⠁⣠⣿⣿⣧⡄⠀⠀⢀⣤⣀⣀⡈⠉⠉⠉⠀⠐⠂⠀⠀⠀⠀⠐⠿⠂⠄⠀⠀⠀⠀⠐⣾⣿
⣿⠀⡇⠀⠙⣿⡇⠀⠀⠀⠀⢢⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠅⠀⣿⣿⣿⣿⣿⣿⣎⡀⠙⠻⠧⠤⠴⠖⠋⠠⣺⣿⣿⣿⣿⣿⠀⠀⠀⠋⠻⣿⣿⣷⣤⡀⠀⠒⣂⣀⣀⣀⣀⡀⠤⠀⠀⠀⣶⣤⠀⠀⢨⣿
⣿⠀⡇⡀⢴⣿⡇⠀⠀⠀⠀⠀⠨⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⡀⣿⣿⣿⣿⣿⣿⣿⠦⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠘⣿
⣿⠀⡇⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡿⠿⠿⣿⣿⣿⡿⢇⠀⠀⠀⠀⠀⠀⠀⢕⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿
⣿⠀⠁⠨⢰⣿⣇⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣉⣀⣁⣀⣀⣈⣉⣉⣉⣁⣀⣠⣀⣀⣀⣀⣀⣉⣀⣉⣉⣭⣭⣍⣥⣄⣀⣀⣀⣀⣀⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣾⠀⠀⠀⣿
⣿⠀⠀⠀⠈⠻⠿⠿⠿⣿⡿⠛⠻⢿⣿⡿⠿⠿⠛⠋⠛⠛⠛⠛⠛⠛⠋⠙⢻⡻⣿⠿⠿⠏⠛⠿⠿⠿⠿⠿⠟⠙⠻⠿⣿⣿⣿⣿⠏⠙⢿⠿⠿⠿⠿⠿⠉⠙⣿⢿⣿⡿⣿⠿⠉⠙⣿⣿⡿⠿⠿⠿⠋⠉⠀⠀⠀⣿
⣿⠀⠀⡒⠒⠒⠒⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠄⠄⢀⠀⠀⠁⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠒⠒⠀⠀⠀⣿
⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣾⣦⡀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢈⣩⡟
⠀⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⡉⠉
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠆⢠⣤⣿⣿⣿⠛⠛⢿⣷⣼⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⢿⣿⣿⣿⣿⣿⢻⣿⣿⢾⣷⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣹⣿⣿⣿⣴⣿⣿⣿⣿⣍⡛⣿⡏⢵⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⣻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⠟⣽⣿⣿⠃⠈⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠙⠿⣿⣿⣷⣶⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣽⠛⠫⠛⣭⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⣿⣷⣤⣬⣍⠛⠉⡐⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠷⠟⠋⠀⢸⡶⠭⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣫⣠⣾⣷⠀⠉⠛⠿⣿⡟⢁⣾⣿⣿⠛⠁⠀⠀⠀⠀⢈⣁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢯⣿⣿⡇⠀⠀⠀⠀⠀⠛⠟⣾⡇⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣧⠀⠀⢀⠀⠀⠀⠀⣩⠁⠀⠀⠀⠀⠀⠀⠸⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⡿⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠻⠿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2530

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/irc-log-120722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/irc-log-120722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Tuesday,_July_12,_2022⠀✐


Posted in IRC_Logs at 2:45 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-120722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-120722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-120722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-120722.gmi
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
 QmfJbwrYhhpxwcezudNA1oj9d6pEXMq7sJUZF9hcwxzSnR #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmUX6igtFHS5VvUzZbj2cvfNrGx4LESg2cRLRpkLBoAeEk (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmYXwaUBjZxwQvoXMr4PmiPvm4vWMfo8khVzDUb7uV17N7 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmTLnuBubD2whtxmi1MHPxyYM8A6nsY7N6ww3pbGPZh3oc social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmcKizFzoGuFquU4ysgj6B4V1uoP1gxNn9ypUBvDnXgZs8 #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 Qmd5p7dQjodYuciUJVnGz48BfBYsEssQRbivdR7PMfh9e6 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmcySCFP9vTdXWWbigQp4Fr4a9nwWsGRc5moMWhFrjK7E5 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmW1xzwDpWSw4P312mW72NMm4meF6iiTVx5K8cVqJw3e8x (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF



                    ䷩ 𝚕𝚒𝚗𝚎 2657

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/lack-of-justice-at-the-epo-2/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/lack-of-justice-at-the-epo-2/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Obscene_Lack_of_Justice_at_the_European_Patent_Office_(EPO)⠀✐


Posted in Europe, Law, Patents at 5:37 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 04611f31d4b2970d10ad33f4c9d7c68c
ILOAT Too Slow to Stop EPO Abuse
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-injustice-system.webm


Summary: Europe’s second-largest institution and biggest patent office, the
European Patent Office (EPO), is intentionally breaking the law while relying
on “institutionalised injustice” or a deficient pipeline of appeals (up to 10
years if not more to finish an assessment by an independent court) while no
actual oversight exists


TODAY we published not one part but two parts of the series about ILOAT and the
EPO‘s “institutionalised_injustice”. We rushed it a bit (final part published a
day earlier than planned) because we wished to proceed to another series, which
is closely related. It demonstrates a state of crisis created by Benoît
Battistelli and perpetuated by António_Campinos for short-term “gains”. By
granting tons of European_software_patents (illegal) they hope to prevent the
bubble from bursting, but that will be the subject of the next video.


“The EPO cannot survive like this.”The reason these two series are connected is
explained above, but the gist of the correlation is, in order to break the law
without facing resistance from examiners the management needed to crush the
staff and make an “example” of innocent people. Management by fear and an
atmosphere or terror, they’ve wrongly assumed, would ‘pacify’ antagonistic
staff. Instead, staff relationships have worsened, the quality of patents has
plunged, and exacerbation in the recruitment is rather_telling. The EPO cannot
survive like this. █



                    ䷩ 𝚕𝚒𝚗𝚎 2711

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/legacy-of-uefi-secure-boot/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/legacy-of-uefi-secure-boot/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Legacy_of_UEFI_‘Secure’_Boot:_BSD_and_GNU/Linux_Users_Now_Have_to
‘Jailbreak’_Their_PCs_(Desktops/Laptops,_Just_like_Apple_iPhones)⠀✐


Posted in Deception, GNU/Linux, Microsoft at 8:25 pm by Dr. Roy Schestowitz


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Mr. GAFAM... Jailbreak⦈
              GAFAM ♥ computers the users (buyers) cannot control


Summary: Pentagon-sponsored garbage like UEFI ‘secure’ (exactly the opposite!)
boot has vindicated us for what we’ve said repeatedly for a decade; it was all
along about obstructing/punishing people who refuse to use Windows_with_NSA
back_doors


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠻⡟⠀⣀⣿⡿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⢀⣴⣿⣿⠽⠟⠄⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡁⠘⠛⢉⠁⠊⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠇⣤⡜⠀⠠⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢩⣤⣤⣷⣧⢀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣿⣿⣿⣿⣿⣬⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⢀⣟⠁⠀⡈⠀⡿⠀⢸⣿⠿⣿⣩⡉⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠐⢤⡠⢴⣷⣿⢇⢰⣏⣹⣤⣼⣧⡆⣾⣷⣻⣿⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢹⣠⣤⣶⣿⣿⣿⣸⣿⣿⣿⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⣤⣀⣀⡀⠀⠀⠛⠛⠛⣿⠿⠿⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⢁⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⢐⣁⣋⢁⢀⢼⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠳⣻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⢛⣿⣿⡿⡟⠒⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⢹⣿⣿⢿⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠻⠽⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠛⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣶⣦⣴⣶⣷⡶⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠢⠏⣠⣾⣿⣿⡿⠿⠛⢻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⢋⡁⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠛⣿⣷⡆⠀⠀⠀⠸⡿⠟⠛⠛⣿⣿⡿⠻⠿⠋⡀⠉⢿⣿⣿⡇⢠⢇⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣵⣿⠟⡿⣇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠈⠁⠀⠀⣰⣿⠟⠀⣄⣠⣏⣀⢀⠸⠛⠉⠉⠻⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣿⠃⠀⠆⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⡷⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠴⠃⠀⠀⠀⠀⠀⠈⠡⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⡠⣰⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⡿⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠓⠛⠾⢷⣶⠂⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠿⣿⣿⠟⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣀⣀⡀⡀⢀⣤⣠⣴⣿⣿⣿⣿⣿
⠀⠀⠀⢘⠿⠀⢀⣠⣶⣿⣾⣿⣿⣿⡿⢿⣿⣾⡌⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠛⠉⢑⣀⣥⣤⣿⣿⣾⡿⣿⡿⠻⣿⣷⡈⠛⠧⠎⠀⠌⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿
⣿⣿⣷⣾⣿⣿⣯⠻⣿⣷⡿⢡⣄⡈⠙⢿⣷⣤⣶⣶⠦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⡷⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣶⠽⠛⢹⣿⣿⣿⣿⠘⣰⣿⣿⣿
⣿⣿⣿⣯⡻⣿⣿⣦⠙⢻⣷⡀⠻⠩⠀⠀⠙⠟⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠠⠊⣴⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⣿⣿⡿⠿⣽⣷⣤⡙⢿⣦⡀⠀⠀⠀⠀⠈⠻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣛⠉⢛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⣴⣌⡹⣶⣿⡿⣿⡿⢻⣿⣿⣿
⢿⣧⣄⠙⠋⢀⠀⠙⢿⣿⡗⡀⠻⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⠿⠿⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠏⠀⠚⠟⠛⢳⣿⠋⠀⠀⢀⣿⣿⣿⣿
⠿⠟⢻⣧⣀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢙⣣⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷⡆⢴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⣂⠀⣠⣾⠿⠿⠛⠟
⠀⢀⠀⠙⠛⠂⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣛⣧⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠌⠠⠟⠋⠀⠀⢀⣠
⠄⠠⠤⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⢄
⠦⠶⢶⣶⣤⣦⣤⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⢰⣷⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣯⣶⣤⠀⢠⣶⣾⣷⣿⣦⡈⠉
⠀⠚⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠀⢼⣿⣿⣿⣿⡿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠉⠉
⠶⠒⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⢁⣴
⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⢠⣿⣿⣿⢸⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⣿⣄⣸⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣏⣽⣿⣿⣿⣿⡿⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡗⢹⣿⣿⡇⢻⣿⣿⣷⣿⣿⣿⣯⣹⣿
⣟⣻⣿⣿⣿⣇⣸⣿⣿⠇⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⡋⢻⣿⣿⣿⣸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠉⠛⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣛⣅⣈⣻⣻⣟⣽⣿⣿⣿⡟⠁⠀⠉⠉⠉⠁⠀⠉⠉⠉⠙⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⣀⡉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⠛⠛⠛⠻⠿⠿⠛⣿⠋⠈⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣝⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠋⢨⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠻⢃⣀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣠⣿⣿⣿⣿⡻⠁⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡀⠛⠋⠀⡩⠞⠀⠀⠀⠀⠀⢀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢠⣶⢅⠡⠛⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣧⣴⣾⡇⠠⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢹⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡛⠀⣼⡇⢠⠀⡀⣀⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⡿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⢸⡇⠸⠦⠀⡈⠁⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡉⢛⣛⢿⡆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣾⣿⣷⣿⢃⢸⣏⣹⣤⣼⣧⡆⣾⣷⣻⣾⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢻⠿⠿⢻⣿⣿⢸⣿⣿⣿⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⣶⣶⣶⣦⣤⡀⠀⣸⣿⣿⣦⠀⠀⠀⢀⣀⣠⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⣠⢐⣒⣋⠁⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠉⠸⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢀⣻⣻⣿⣿⡟⠂⢿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠻⣿⢿⣤⣾⣿⣿⠿⠟⠋⠉⣿⣿⣿⠀⠀⠻⠹⢿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠛⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣶⣦⢬⣿⣷⡶⠆⣿⣿⣿⠏⠉⣿⣿⣿⣿⣷⣶⠆⠀⠸⣿⣿⣿⠀⠞⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠛⠛⢛⣿⣶⠈⠀⠀⠀⠻⠿⠛⠀⢀⣿⡿⢿⡿⠛⠉⠀⠀⠀⢻⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⣼⣿⡿⠄⠄⠀⠀⠀⠀⠀⠀⣸⣿⠃⢠⣁⣠⣀⣠⢤⢶⠛⠉⢁⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣿⣿⠁⠰⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠓⡴⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢼⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⢀⣀⣠⡠⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠳⠛⡿⣶⡶⠀⠀⠀⢠⣦⣤⣤⣶⣿⣿⣿⣿⠿⣿⣷⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⡀⣀⠀⣀⢀⣀⣀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠧⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠻⢿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠓⠉⢁⣀⣄⣴⣿⣿⣽⣿⣿⡿⠿⣿⣧⠙⠻⣄⠓⠀⡘⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢿⣿⣾⠿⣱⣄⠈⠻⣿⣶⣤⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⢶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣯⡿⠋⣽⣿⣿⣿⡿⠙⣰⣿⣿⣿
⣿⣿⣿⡟⢿⣿⣿⣮⠛⢿⣇⠙⠿⠓⠀⠀⠻⢿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⡰⠇⣴⡙⠻⣹⣿⣹⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣷⡿⢿⣿⣶⣌⠻⣷⣄⡀⠀⠀⠀⠀⠐⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣟⣛⠛⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢁⣤⣏⢳⣴⣿⢿⣿⡿⣻⣿⣿⣿
⣿⣇⡈⠛⠋⡀⠀⠙⣿⣿⣧⡨⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⡿⢿⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠋⠀⠛⠿⠛⣼⡿⠋⠀⠉⢀⣿⣿⣿⣿
⠿⠿⢿⣄⣀⠀⠀⠀⠀⠀⠛⠃⠀⠈⢛⣧⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⡀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠛⠁⣂⠀⣠⣿⡿⠿⢿⠿
⡀⠀⠈⠛⠿⠂⠀⠀⠁⠀⢀⣠⣴⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⡇⠼⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠟⠃⠀⠀⣀⣀
⠀⠤⠤⠤⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢬⣉
⡤⠤⢶⣶⣬⣤⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢽⣧⣦⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣧⣦⣤⠀⢠⣶⣶⣾⣷⣆⡁⠀
⠐⠶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠠⢼⣿⣿⣿⣿⡿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⡏⠙⠉
⠶⠆⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡟⢀⣼
⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢠⣿⣿⣿⢸⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⣷⡄⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣏⣿⣿⣿⣿⣿⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⡇⢻⣿⣿⣷⣿⣿⣿⣿⣽⡿
⣿⣻⣿⣿⣿⣇⢹⣿⣿⠇⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠉⠛⠙⢿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣾⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣛⣀⠘⣛⣻⣟⣿⣿⣿⣿⡯⠀⠀⠉⠉⠉⠁⠀⠉⠉⠋⠙⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⣀⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠂⠿⠛⠻⠿⠿⡿⠿⣿⠋⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣿⣿⣿⣿⠀⣿⠿⠛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢀⣠⠆⢸⣿⡻⠉⠀⠀⢀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣿⣿⡏⣇⣘⣿⡶⠥⢞⠄⠀⠀⠀⠀⠀⢈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣿⣿⣿⠱⠋⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⡟⠃⣿⠏⠉⠁⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠈⣿⡆⣧⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⣨⣵⣄⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⢸⣿⠿⣟⣉⡉⠛⠻⠿⠟⣯⢋⡈⢛⡛⢿⣆⡌⣽⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄⠀⠀⠀⠉⠀⣰⣶⣿⢃⢸⣏⣹⣤⣴⣷⡦⣶⣷⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⣠⣾⣿⣿⣿⣿⣸⣿⣿⣿⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣠⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢁⣴⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣟⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⣄⢈⣭⣤⡀⠀⠈⣿⣿⢹⣿⣿⣿⣿⣿⣿⣷⠈⡉⠉⢻⣿⣿⣯⠁⡶⠀⠀⢻⣿⡿⠰⣹⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢉⠩⢻⢿⣿⠛⠀⢀⣿⣿⠀⢻⣿⣿⣿⣿⣛⡏⠘⠀⠀⠈⣿⣿⣿⠀⠀⠀⣀⣸⡿⠁⠀⠻⠙⢿⡿⣿⣿⣿⣯⣭⣿⣿⡿⠙⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣀⣾⣿⣦⣶⣿⠷⠞⠀⢨⣿⠏⠀⢸⣿⣿⣿⣿⠶⠂⠀⠀⣠⣤⣿⣿⣿⣶⣾⣿⡿⠇⠀⠀⠀⠀⠐⠈⡀⠈⢉⣹⣿⣿⣿⢋⡁⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠛⢙⣿⣷⠂⠀⠀⠀⠘⠋⠀⠀⣾⡿⠛⠏⠛⠀⠘⠃⠀⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣷⣿⠟⡯⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠾⢿⡟⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣱⣤⣤⣄⠤⠝⠋⠁⢀⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠁⠀⠇⠀⠀⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢑⣜⣉⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠐⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⢀⡠⠀⠀⠀⠀⢰⣿⣿⣦⣤⣤⣶⣿⣿⣿⣿⣟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿
⠓⠳⠻⣷⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⡋⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣠⣀⣄⣠⣠⣤⣾⣿⣿⣿⣿⣿
⡀⣀⡀⠟⠓⠀⢀⣴⢿⣿⣿⣿⣿⣿⡿⢻⣿⣿⢎⠛⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣀⣀⣤⣶⣶⣿⣿⣿⡿⣿⣿⠛⢿⣷⣄⡉⠤⠈⠀⠄⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡟⢫⣧⣀⠈⠻⣿⣶⣿⠿⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⡛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡷⢟⠋⢸⣿⣿⣿⣿⣉⣰⣿⣿⣿
⣿⣿⣿⣿⣝⣿⣿⣷⡈⠹⣷⣄⠉⠛⠀⠀⠈⠻⢓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡐⠁⢾⣆⠙⣻⣿⣷⣿⣿⣿⣿⣿
⣿⡿⠻⣿⣿⡿⠛⣿⣿⣦⡈⢻⣦⣤⠈⠀⠀⠀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣭⣝⣈⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢀⣲⣦⡝⣾⣿⡟⣿⡿⣱⣿⣿⣿
⣻⣷⣤⡈⠁⠂⠀⠈⠻⠿⢛⣤⠛⠿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⡻⡻⠿⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⡀⠋⠛⠛⢹⡿⠃⠀⠀⢠⣿⣿⣿⣿
⠛⠛⠻⣶⣆⡀⠀⠀⠀⠀⠈⠁⠀⠀⣈⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠀⣰⣿⠟⠛⠛⠛
⠠⠀⠀⠈⠙⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣿⠘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠘⠰⠛⠁⠀⠀⠠⣤
⠂⠐⠒⠂⢀⠀⡀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⡿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⢀⢤⡀⠀⣐⡢
⠖⠒⣩⣭⣴⣶⣤⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢸⣷⣶⣶⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣧⣶⣤⡀⢠⣿⣿⣿⣾⣷⣄⣀
⠈⠙⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠀⢺⣿⣿⣿⣿⡿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣇⡀⠀
⠛⢁⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣼
⣄⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⢸⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣼⣿⣿⡏⣿⣿⣿⡿⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣄⣿⣿⣿⣧⣼⣿⣿⣿⣿⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣟⣽⣿⣿⣿⣧⣼⣿⣿⠇⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⡏⢻⣿⣿⣿⣸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠉⠉⠉⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣿⣧⣌⣿⣿⣿⣿⣿⣿⢿⠟⠈⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⣤⣅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢙⠋⠉⠛⢛⣛⡛⣿⡉⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠋⡅⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⡏⠰⣾⣃⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢣⣷⣿⣿⣿⣿⡿⠉⠾⢋⢀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠿⣿⡿⢿⡿⠋⠚⠄⠀⠀⠀⠀⡀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡿⠋⢸⣿⠀⣔⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠋⠀⠀⠈⣿⠀⠇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣦⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣀⠀⠀⠀⠘⡿⠛⡈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣷⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⣠⣤⡤⠀⣸⣿⠿⣟⣉⡉⠛⠻⠿⠟⣯⢋⡈⢛⡛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⣠⣾⣿⣿⣿⣿⢇⢰⣏⣹⣤⣴⣧⡆⣶⣷⣻⣿⣿⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣤⣀⡀⠈⠉⠹⠿⠷⣾⣿⣿⡿⠟⣻⠉⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⠆⠀⠹⣿⣿⣧⠐⠋⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣟⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⣠⣈⣍⣄⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⣿⣿⣿⣠⣤⣴⠖⠚⠛⢳⡹⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⡉⢻⣿⣿⠛⠀⢸⣿⡇⠹⣿⣿⣿⣿⠿⠛⠿⣠⠤⠲⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡰⣼⣿⣧⣴⣿⡷⠌⠁⣸⣿⠁⢀⣿⣿⣿⣿⣬⠧⠀⠂⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠀⠈⢉⣹⣿⣿⣿⢋⡁⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠙⢛⣿⣷⠀⠀⠀⠀⠛⠟⠓⢾⣿⠟⠻⠋⠁⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣷⣿⠟⡯⣆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠾⢿⡟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣀⣤⣤⣤⣤⠤⠜⠋⠉⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠇⠀⠃⠀⠀⠀⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣼⣷⣤⣿⣄⣀⣼⣉⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⢄⢠⠠⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣹
⠓⠚⠿⢶⡾⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣠⣀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿
⠀⣀⡀⠿⠓⠀⢀⣴⡿⢿⣿⣿⣿⣿⣿⠻⣿⡿⢇⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣀⣀⢤⣶⣴⣾⣿⣿⡿⣿⣿⠛⠻⣿⣦⣈⠀⠀⠀⠦⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠘⣿⣿⡿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣯⠡⣶⣄⠈⠻⢿⣷⣿⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⡛⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢞⠋⠰⣿⡿⣿⣿⣉⣰⣿⣿⣿
⣿⣿⣿⣿⣌⢻⣿⣿⠎⠙⣿⣆⠉⠛⠁⠀⠈⠛⢟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣠⠋⢹⣧⠈⢳⣿⣧⣿⣿⣿⣿⣿
⣿⡿⠛⢿⣿⡿⠛⢿⣿⣷⡌⠹⣷⣤⡀⠁⠀⠀⠀⠙⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣯⣭⣭⣀⣹⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⣰⣦⡜⣷⣿⡟⢿⡿⢫⣿⣿⣿
⣙⣷⣶⡄⠉⠢⠀⠀⠙⠿⣟⣦⠘⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣛⡛⠿⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⡀⠈⠛⠛⢹⣿⠋⠀⠀⢀⣿⣿⣿⣿
⠙⠛⠛⣷⣦⣀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣭⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣧⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣠⠀⢰⣿⠟⠛⠉⠛
⠄⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣯⣽⡀⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠟⠁⠀⠀⠠⢤
⠂⠐⠒⠂⢀⡀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⢄⠀⠀⠀⠀⠀⡠⢄⠀⣐⡢
⠶⠒⣫⣭⣤⣶⣤⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⢰⣷⣶⣶⣤⣤⣤⠀⢠⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣼⣤⣀⢠⣾⣿⣿⣶⣿⣦⣀
⠀⠉⣻⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣇⠀⢺⣿⣿⣿⣿⡿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣇⡀⠀
⠛⢋⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⢀⣴
⣄⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣷⣼⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣄⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠃⢸⣿⣿⣟⣈⣿⣿⣿⣤⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⢺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣷⣼⣿
⣿⣭⣿⣿⣿⣷⣼⣿⣿⠇⣿⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⡯⢻⣿⣿⣿⢸⣿⣿⣿⡇⡀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣽⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠉⠉⠉⢿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣽⣤⡌⣻⣿⣿⣿⣿⣿⡿⠟⠂⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⢙⡉⠉⠙⣛⣛⡙⣻⣏⠀⠀⣤⣶⡀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠿⠿⠿⣿⣿⡿⡏⠸⣿⣅⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢠⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⠏⣿⠿⠿⠿⠿⢿⡻⠉⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⡟⠃⢰⣿⠀⡆⡰⠀⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠈⣿⡀⢛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠠⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣟⣀⠀⠀⠀⠘⡿⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⠀⢀⣤⣴⣤⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⡿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⡿⠅⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡙⢛⣛⢿⡆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢛⣩⣿⣿⣿⣿⣿⣷⣿⢃⢰⣏⣱⣤⣼⣧⡆⣾⣷⣻⣿⡿⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠘⠛⠇⣿⣿⣿⡿⠛⣿⢹⣿⣿⣸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀⡀⠀⠀⢠⣤⠀⣰⠂⠀⠘⣿⣿⣷⠐⠃⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⠀⠀⠀⠀⢀⣿⣿⣿⣤⠤⠶⠞⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠒⠒⠂⠀⢺⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢖⠓⠚⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠐⠺⡿⠶⣇⡀⠀⣿⣿⢘⣿⣿⣿⣿⣿⡿⡿⠦⠂⢺⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠋⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣴⣿⣈⣀⣈⡠⠀⣿⣿⠸⣿⣿⣿⣿⣯⠀⡀⠀⠀⠀⣤⣆⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠿⠟⣿⣯⡅⠉⠀⠰⠿⠯⠀⢿⣿⣿⣿⠝⠰⣇⡀⠀⠀⠈⠹⠿⠿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢷⣤⣿⠏⠈⠁⢰⡾⠟⣛⣀⠀⢀⡀⠀⠀⢈⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠁⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠁⡿⠀⠀⠀⠀⢀⣿⣿⣦⣤⣶⣶⡾⠻⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣰⠀⠀⠀⠀⠀⠈⠁⠂⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⡄⢀⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠣⢶⣆⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⡀⠀⠀⠀⠀⢀⢀⣴⣶⣶⣿⣿⣿
⠀⠀⠸⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠘⢿⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡒⠒⢀⣀⣀⣠⣾⣿⣿⣿⣿⡿⠿⣿⣇⠘⠛⡈⠋⢀⡙⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣼⣿⢃⣄⠈⠻⣿⣦⣥⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡷⢶⣶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣮⡿⠟⣽⣿⣿⣿⡷⠟⣠⣿⣿⣿
⣿⣿⣿⣟⢿⣿⣿⣬⠛⢿⣇⠙⠿⠶⠀⠀⠻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⡠⠂⣶⠈⠻⣹⣿⣹⣾⣿⣿⣿⣿
⣿⣿⢿⣿⣷⡿⢿⣯⣤⡈⠛⣷⣄⠀⠂⠀⠀⠀⠐⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣟⠻⠫⠹⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⢁⢠⣉⣷⣴⣿⣿⣿⡿⣻⣿⣿⣿
⣿⣧⡀⠛⠋⡁⠀⠻⣿⣿⣦⡈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠿⢿⢿⣷⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠏⠀⠾⢿⠿⢸⣿⠋⠀⠉⢁⣿⣿⣿⣿
⢾⠿⢿⣄⣀⡀⠀⠀⠈⠉⠺⠛⠀⠈⠻⣦⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⡄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠁⡤⠀⣠⣿⡿⠿⠿⠿
⠀⠀⠈⠛⠿⠆⠀⠀⠑⠀⠀⣀⣤⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡛⡇⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠐⠆⢠⠿⠋⠀⠀⢀⣀
⡀⠤⠤⠤⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢬⣉
⣤⡤⢴⣶⣮⣥⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⣹⣧⣭⣧⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣧⣦⣤⠀⢠⣶⣶⣾⣶⣌⠐⠈
⠀⠶⣾⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⢠⢼⣿⣿⣿⣿⡿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠛⠓
⡴⠆⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡗⠀⣴
⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢠⣿⣿⣿⢸⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿
⣷⡄⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣟⣿⣿⣿⣿⣟⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡗⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡟⠻⢿
⡿⣟⣿⣿⣿⣇⢹⣿⣿⠇⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠋⢻⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣾⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠉⠙⠛⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣾⣏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣛⣁⠘⢛⣛⣛⣿⣿⣿⣿⡷⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠋⢉⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⠀⢈⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠿⠟⠻⠿⠿⠿⠿⣿⠛⠉⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣄⣀⣸⣿⠛⣿⠛⣛⢛⡟⢹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠋⠁⠸⣿⡀⣿⣾⡇⢸⡛⠫⠾⠃⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠇⣿⣧⣼⣿⠥⢞⠄⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣄⣠⠀⠀⠀⠀⢸⣿⣿⠡⠊⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣆⠀⠀⠀⢏⠀⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⣠⣿⣧⢂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣾⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠛⣿⣿⣡⣶⣿⣿⣿⣿⠿⠋⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡘⢛⡛⢿⡆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⢻⣿⣿⣿⠁⡟⢰⣶⣿⢃⢰⣏⣹⣤⣼⣧⡆⣾⣷⡻⣾⡿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠀⠘⠁⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⢸⣿⣿⣄⣀⣠⣤⣴⣿⣿⡏⠊⠉⠈⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣦⣤⠿⠿⠛⣙⠋⠁⢹⣿⣿⣿⣧⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠐⠐⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠆⠀⢸⣅⣀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠸⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠬⠿⢗⡄⠀⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣏⣠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠻⠝⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠋⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⣤⣤⡨⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⡉⠀⢙⣿⠀⠀⠀⠉⠛⣿⠿⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠿⠟⣿⣮⠀⠀⢰⠟⢹⣿⣿⣿⣿⣿⠟⠇⣿⡿⠟⠃⠀⠀⠀⠀⠀⠘⠻⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⢸⣿⡗⠀⠀⠀⠀⢸⣿⡿⠀⠈⢁⣴⣾⣿⣷⣄⡀⠀⡀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠺⣿⣿⡟⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⢸⡇⠀⠀⠀⠀⣸⣿⣠⣼⣾⣿⣿⡟⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢀⡄⠀⠀⠀⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠘⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠳⣞⣠⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿
⠀⠀⢿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠹⣷⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⣿⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠂⠀⣀⣀⣰⣿⣿⣿⣿⣿⡿⢿⣿⣄⠛⠋⠹⠆⢀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢱⣿⣿⣿⣿⣿⡿⣿⣿⣿⢛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡻⣿⣿⣵⢟⣠⣄⠙⢿⣷⣮⣡⣴⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢶⣶⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣤⣍⡿⠋⣿⣿⣿⣿⠞⠃⣸⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣷⡜⠻⣿⡄⠛⢿⠆⠀⠈⠻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣬⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⡴⢰⡄⠙⢟⣿⣿⣻⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣾⡿⢿⣯⣤⡘⢻⣶⡀⠀⠀⠀⠀⠀⠚⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡛⠛⠁⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢀⣌⣹⢦⣾⣿⣿⣿⣟⣿⣿⣿⣿
⣷⣄⠈⠻⢏⠀⠈⠻⣿⣿⣆⠹⣿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠿⡿⣿⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠉⠠⠻⠻⠷⣾⡿⠉⠈⠉⢸⣿⣿⣿⣿
⣿⠿⣧⣀⡀⠁⠀⠀⠀⠑⠛⠁⠀⠉⢻⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⠠⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣴⣿⡿⠿⡿⠿
⠀⠀⠙⠻⠷⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⡄⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠀⡼⠟⠁⠀⠀⢀⣀
⠀⠨⠤⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣈⡉
⣤⠤⢴⣶⣮⣤⣤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⢈⢿⣬⣭⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣽⣤⣤⠀⢤⣶⣶⣷⣦⡄⠂⠉
⠰⠶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⢠⢼⣿⣿⣿⣿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡟⠛⢒
⠄⠆⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣾
⠐⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣄⡀⠀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢠⣿⣿⣿⢸⣿⣿⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣦⡀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣟⣿⣿⣿⣿⣿⡛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡟⠻⢿
⡿⣿⣿⣿⣿⡇⢹⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢸⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣷⣷⣾
⣿⣿⣿⣿⣿⣿⣾⣯⡉⠀⠉⠉⠛⣿⣾⡟⣻⣿⣿⣿⣿⣿⣿⣾⡍⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣛⡀⠘⣛⣻⣻⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠙⠋⣉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⡘⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠿⠛⠹⠿⠿⠿⢿⡿⠋⠁⢀⣠⣄⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠃⣹⣿⠠⣧⣼⠁⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠁⠀⠀⠀⠀⠘⣿⣀⣻⣿⣶⣿⣿⡿⢛⣉⠅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀⢀⠀⠀⠀⠀⢿⣿⣿⣿⠿⡛⠉⠞⢋⢉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⡄⠀⠀⠘⠏⠉⠁⠀⠄⡀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⠀⠀⣠⣾⣡⠊⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⠠⠁⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡿⢉⣵⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠋⠙⣿⣿⣿⡟⢋⡷⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⣦⠀⠼⠁⠀⠸⣿⣿⣧⠈⠀⠀⠀⢸⣿⠻⣿⣩⡉⠛⠻⠿⠟⡯⢋⡈⢛⡛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⢀⢀⣠⣿⣿⠿⠐⢾⣶⣿⢃⢰⣏⣹⣤⣴⣧⡄⣾⣷⡻⣾⣿⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⠻⠻⢛⢿⠻⣿⣿⣏⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣀⠀⠀⠀⣠⣾⠄⠂⢸⠃⠀⣿⣿⣿⡄⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠀⠀⣸⣷⣶⠿⣿⣿⣿⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣧⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠰⡻⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠑⢙⠆⠀⢾⣿⢂⣿⣿⣿⣿⣿⠿⠿⢿⣯⣧⣀⠈⠁⠈⠙⠿⠿⢻⣿⣿⣿⡄⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⣴⣔⠤⠀⠀⣸⡿⢸⣿⣿⣷⣽⣿⣀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠛⠋⣹⣦⠀⠐⠟⠁⢸⣿⡿⠿⡿⠋⠘⣲⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⡿⡟⠀⠀⠀⠀⢸⡿⠃⠀⢀⣴⣾⣿⣿⣿⣿⣧⣀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠀⠰⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢘⡇⠀⠀⠀⠀⣸⣦⣴⣾⣿⣿⣿⡟⣛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠁⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⡀⠀⠈⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿
⠳⠞⢦⣶⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⡀⠀⠀⠀⣀⢀⣰⣿⣿⣿⣿⣿
⠀⠀⠸⠇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⡷⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣑⣀⣤⣤⣴⣿⣿⣾⡿⢻⡟⠻⣿⣧⣈⠁⡄⠈⠀⠌⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⢿⣿⣿⣿⣿⣿⣿⡿⣿⠋⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⡟⢰⣆⡀⠙⠿⣷⣦⣾⠶⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡟⠾⠏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⠻⠋⢾⣿⣿⣿⣗⠃⣸⣿⣿⣿
⣿⣿⣿⣯⠛⣿⣿⣦⠉⢻⣧⡈⠚⠃⠀⠀⠙⠟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡜⠡⢶⡈⠛⣾⡿⣼⣿⣿⣷⣿⣿
⣿⡟⠻⣿⣿⡟⠻⣾⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣭⣉⣋⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠎⢀⣠⣬⢳⣾⣿⢻⣿⠟⣼⣿⣿⣿
⢿⣧⣄⠈⠃⠀⠀⠘⠿⡿⣃⡄⠻⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⢛⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠐⠚⠛⠛⣾⡟⠁⠀⠀⣰⣿⣿⣿⣿
⠿⠟⢻⣤⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⣘⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢴⡀⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣴⣿⠿⠛⠻⠛
⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣙⣇⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠼⠛⠁⠀⠀⢠⣤
⠀⠐⠒⠐⠀⡀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⡤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄
⠶⠒⢲⣧⣤⣦⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢰⣶⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⣦⣤⡀⢰⣶⣿⣶⣾⣦⣈⠀
⠀⠛⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠰⢺⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠉⠉
⠒⠂⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠻⣻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⢠⣾
⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣄⣸⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣷⡟⠻
⣟⣯⣿⣿⣿⣧⣸⣿⣿⠃⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⢺⣿⣿⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠉⠙⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣿⣤⢈⣻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⣠⡁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡛⠋⠈⠛⠛⠛⠛⣿⠁⠀⠠⣦⣄⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣶⣀⠀⠀⠈⣿⡿⢿⠿⢿⣿⡿⢟⣋⠅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣅⣤⣤⡸⠋⠞⢋⢝⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⠵⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿⠹⠛⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠋⣻⣿⣣⣾⣿⣿⣿⡏⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡀⠀⣀⠀⠈⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⠃⠀⠀⢸⣿⣿⣇⡀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⡠⣤⡴⠶⠟⠿⠟⠛⠓⠁⠀⢸⣿⠿⣿⣩⡉⠛⠻⠿⠟⣯⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⣉⣥⣴⡞⠁⠀⠀⠀⠀⠀⢰⣶⣿⢃⢰⣏⣱⣤⣼⣧⡆⣾⣷⡻⣾⡿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠟⠋⣿⣇⠀⣶⣆⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⣤⣀⠀⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⡿⠿⣿⣆⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⡄⠈⣿⣿⣿⣀⣀⣽⣿⣧⣶⣿⣿⡆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⣠⣿⣽⣧⣉⠉⠉⠙⢻⡿⠿⣿⣿⡀⠀⠀⠀⠀⠰⣻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠃⠛⠃⢸⣿⡇⢸⣿⣿⣿⣿⣿⡿⠟⠋⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠻⠙⢿⡿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣦⣴⣄⠄⠀⢘⣿⠇⢸⣿⣿⣿⣿⢆⣀⣤⣦⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠄⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠛⣽⣶⠀⠿⠋⠀⢸⣿⠿⣿⡟⠉⢫⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⣿⡟⠀⠀⠀⠀⣼⠟⠀⠈⣠⣶⣿⣿⣿⣿⣿⣿⡄⡄⠀⠀⠠⢀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠀⠐⠀⠀⠀⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢘⡇⠀⠀⠀⠀⣥⣤⣼⣿⣿⣿⣿⡿⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾
⠀⠀⠀⠈⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠳⠼⢦⣴⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣿
⠀⠀⡹⠯⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⡈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣉⣁⣀⣠⣀⣠⣿⣿⣾⡿⢿⡿⠻⣿⣷⣀⠁⠄⠋⠀⠌⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠁⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⠻⣿⣷⡟⢣⣆⡈⠙⠿⣿⣦⣶⡶⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠾⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⡧⠾⠋⢺⣿⣿⣿⣟⠊⣨⣿⣿⣿
⣿⣿⣿⣯⠛⣿⣿⣦⠙⢻⣧⡈⠻⠃⠀⠀⠙⠟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠓⣶⡀⠛⣼⣿⣼⣿⣿⣿⣿⣿
⣿⡿⠻⣿⣿⡿⠛⣿⣶⣄⠉⢿⣦⡀⠀⠀⠀⠀⠀⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣟⣉⣃⠈⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⢀⣤⣬⢱⣶⣿⢿⣿⠟⣽⣿⣿⣿
⢿⣧⣄⠉⠋⠄⠀⠘⠿⡿⣷⣄⠻⢟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢙⠛⠻⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠃⠀⠊⠙⠛⣺⡿⠁⠀⠀⢀⣿⣿⣿⣿
⠿⠿⢿⣤⣄⠀⠀⠀⠀⠀⠛⠁⠀⠀⢉⣢⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡆⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣰⣿⠿⠛⠻⠟
⠠⠀⠀⠙⠛⠋⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣛⣇⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁⠀⠀⢀⣤
⠀⠀⠒⠐⠀⡀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⡿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⠀⠠⢀⠀⠀⠠⠄
⠶⠖⢶⣶⣤⣤⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢲⣶⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣧⣦⣤⠀⢰⣶⣾⣶⣶⣦⣈⠀
⠀⠛⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠰⢾⣿⣿⣿⣿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠉⠉
⠶⠂⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⢀⣼
⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣿⣿⣿⢸⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣄⣸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣄⣿⣿⣿⣯⣽⣿⣿⣿⣿⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣷⡝⠻
⢟⣯⣿⣿⣿⣧⣸⣿⣿⠇⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣻⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣹⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠉⠛⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣻⣤⣈⣻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⣀⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡛⠛⠋⠛⠛⠟⠛⣿⠉⠀⠠⣶⣤⡀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣍⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⡟⠛⠛⣙⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣾⣾⣿⣿⣿⡿⠛⣉⠅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⡻⠋⠞⠋⢉⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⡏⣁⣴⣿⣿⣿⡿⠯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠘⠋⠟⣿⣿⣿⡿⢛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣤⣦⠀⠼⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⣀⣰⣿⣿⠧⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⢇⠻⡽⢻⣿⣥⣤⣤⣶⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣷⣶⣷⣾⣿⡇⠀⠙⠟⠛⠋⠁⠀⠀⢸⣿⠿⣿⣩⡉⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠁⢸⣿⣄⡀⠀⠀⠀⠀⢰⣶⣿⢃⢸⣏⣱⣤⣼⣧⡆⣾⣷⡻⣾⡿⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⢺⣿⡿⠿⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣦⣾⣿⣧⣶⣶⡀⠀⠀⠀⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⢶⣿⣿⣿⡍⠉⢉⠹⢿⣿⣿⣷⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⠿⠁⠈⠀⠀⠁⠀⣸⣇⠀⠀⠀⠀⠀⠸⣻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠘⠃⠁⢰⣿⡇⢹⣿⣿⣿⣿⣿⠿⢿⣤⣤⣭⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣞⡤⠀⢸⣿⠃⢸⣿⣿⣿⣿⢠⣜⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣆⡌⡷⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⢛⣧⠀⠿⠃⠀⢸⣿⣿⣿⣯⠏⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣾⣿⠀⠀⠀⠀⣾⠟⠀⠗⣡⣶⣿⣿⣿⣿⣿⣿⣿⢇⡤⠀⠀⠀⢀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠀⠀⠀⠀⠐⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠸⢇⣤⣴⣾⣿⣿⣿⣿⠟⢻⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠄⠀⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⠷⠿⣴⡆⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣟⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣄⣀⡀⠀⠀⠀⣀⣠⣵⣾⣿⣿⣿⣿
⠀⠀⠿⠁⠂⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⢆⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣁⣀⣀⣀⣼⣿⣷⣿⢿⣿⠟⠿⣿⣆⡉⢪⠈⠂⠠⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡝⢿⣿⣾⠋⣶⣀⠈⠻⢿⣷⣴⣶⣶⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⡤⠟⢁⣿⣿⣿⣿⡟⢃⣼⣿⣿⣿
⣿⣿⣿⣝⢻⣿⣿⡎⠛⣿⣄⠙⠿⠁⠀⠈⠹⠟⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠚⢰⣆⠙⢣⣿⣧⣿⣿⣿⣿⣿⣿
⣿⡟⢿⣿⣿⠟⢻⣿⣶⡈⠹⣷⣄⠀⠀⠀⠀⠀⠙⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣟⣛⡋⢙⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠃⣠⣦⡙⣷⣾⡿⢿⣿⢋⣿⣿⣿⣿
⣿⣤⡈⠙⠣⡀⠈⠛⣿⡿⣆⡘⠿⡃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠀⠘⠋⠛⠃⣿⠟⠀⠀⠀⣸⣿⣿⣿⣿
⠿⠻⣧⣤⡀⠀⠀⠀⠀⠈⠋⠀⠀⠈⣙⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⠰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠀⡀⢀⣾⡿⠟⠛⠛⠛
⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣻⡀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠞⠋⠀⠀⠀⣤⣤
⠀⠰⠄⠂⢀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣤⡄⠀⠀⠀⠀⠀⠤⡀⠀⠀⠤⢀
⠶⠖⢲⣦⣴⣤⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢴⣴⣶⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣵⣤⣤⠀⢰⣾⣿⣾⣷⣄⡁⠀
⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠶⢾⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢩
⠒⠂⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡟⠟⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣠⣿
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢸⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣯⡟⠻
⣟⣯⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠉⠉⠛⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣉⣿⣀⣘⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠉⠉⠉⠁⠀⠉⠙⠉⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢀⣈⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⠛⠛⠘⠻⠻⠛⢻⣟⠁⠀⢐⣶⡆⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⠉⣀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠁⠀⠿⠿⣶⣾⣿⣿⣿⣿⣿⠟⠛⠉⠈⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣤⣦⠀⢠⠆⠀⢹⣿⣿⣇⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠀⠀⠘⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣦⠶⢶⠶⠺⠟⠛⠃⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣏⢭⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⡄⢶⣤⣤⣤⣶⡤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⡿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⠍⠛⠛⠋⠁⠀⠀⢸⣿⠿⣿⣉⡉⠛⠻⠿⠟⣯⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⢘⣿⡿⢷⠆⠀⠀⢰⣶⣿⢃⢰⣏⣱⣤⣼⣧⡄⣾⣷⡻⣾⡿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡉⠉⢉⠹⢿⣿⣿⠂⠀⠀⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⣴⠿⠿⠿⣿⣿⡿⡿⠀⠑⠀⠈⠉⠉⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠆⠀⠀⠀⠀⠸⣻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠓⠁⢰⣿⡇⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⡄⠀⢸⣿⠁⢸⣿⣿⣽⣿⢀⣬⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣨⣻⡷⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⢛⣧⡔⠿⠁⠀⢸⣿⣿⣿⢏⠏⣻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣾⣿⠂⠀⠀⢀⣿⠋⠀⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠀⠰⠀⠀⠐⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺
⠀⠀⠀⣿⠀⠀⠀⠸⢇⣤⣾⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⠠⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠄⠀⠉⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠲⠭⣤⡆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⡀⡀⠀⠀⣄⣠⣥⣿⣿⣿⣿⣿
⠀⠀⡿⠄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢦⡙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣉⣁⣀⣀⣀⣴⣿⣿⣿⠿⣿⠟⠻⣿⣆⡉⠋⡤⠂⠠⡘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠑⣿⣿⣿⣿⣿⣟⣿⣿⣿⠣⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡙⢿⣿⣾⠋⣶⡆⠈⠻⢿⣷⣴⣶⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⢿⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣾⡤⠟⠁⣿⣿⣿⣿⣟⠃⣼⣿⣿⣿
⣿⣿⣿⣟⢻⣿⣿⡎⠛⣿⣄⠙⠿⠅⠀⠀⠙⠟⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠠⣶⠈⢛⣾⣟⣼⣿⣿⣿⣿⣿
⣿⠿⢿⣿⣿⠟⢿⣿⣶⡈⠙⣷⣄⠀⠀⠀⠀⠀⠙⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣟⣛⡋⢙⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⢀⣶⣘⢳⣾⣿⢿⣿⠏⣾⣿⣿⣿
⣿⣤⣀⠙⠣⡀⠈⠻⣿⡿⣂⡘⠿⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠁⠀⠋⠛⠓⣿⡟⠁⠀⠁⣸⣿⣿⣿⣿
⠿⠛⣧⣤⡀⠀⠀⠀⠀⠀⠋⠀⠀⠈⣙⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⠀⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠈⠋⢀⠀⢀⣾⡿⠟⠛⠛⠛
⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⡅⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠾⠋⠀⠀⠀⢠⣤
⠀⠠⠀⠂⢀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⣿⢿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⡤⠀⠀⠀⠀⠀⠠⣀⠈⠀⠢⢄
⠶⠖⢲⣦⣴⣤⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠐⢴⣶⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣦⣤⠀⢰⣶⣿⣶⣷⣦⣀⠀
⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠐⢾⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠉⢩
⠒⠂⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡟⠿⣻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⣠⣿
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⢸⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣷⣄⣸⣿⣿⡟⣿⣿⣿⡿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⠟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣇⣛⠿
⣟⣯⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠉⠋⠙⢿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣿⣄⢘⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⣈⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠘⠻⠛⠛⢻⣟⠁⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⠸⣿⠃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢀⣴⣾⡿⠿⠿⠿⢿⣿⣿⣿⠿⣿⠋⢹⠿⠛⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢠⠆⠀⠘⣿⣿⣿⠐⠋⠀⠀⠀⠈⢀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡷⠾⠿⡿⢿⡿⢟⠁⠂⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣉⣽⣯⣀⣀⣀⡈⠀⠉⠀⠀⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⡇⠀⢠⣿⣧⣀⣀⣀⣠⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣷⣀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠈⣿⣿⣿⠿⠿⠋⠉⠀⢸⣿⠿⣿⣩⡙⠛⡿⠿⠟⣯⢋⡙⢛⣛⢿⡆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣷⣶⣾⣿⣇⣯⠀⠀⢰⣶⣟⢃⢰⣏⣹⣤⣼⣧⡆⣾⣷⡻⣾⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣧⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣤⣿⣿⣿⣿⣦⠤⣖⠚⠹⡿⠿⠀⠀⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣦⣀⠀⠼⠉⠙⠉⠿⠛⠛⠋⠀⠀⠀⠀⠀⣴⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠉⠹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠐⠢⠀⢰⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⠻⠽⢿⣿⣿⣿⣿⣯⣽⣿⣿⡿⠋⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣄⣐⡀⠀⢸⣿⠃⢸⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠪⠻⠿⡆⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⣿⡿⣇⢀⣾⠋⠀⣼⣿⣿⣿⣿⢏⢟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣵⣿⠟⡯⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣸⣿⡇⠀⠀⠀⣿⡟⠉⠿⣔⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⢿⣿⣿⠁⢠⠀⠀⠠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠉⢹⠀⠀⠀⢸⡇⣀⣠⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣐⠀⠀⠀⠀⠈⠉⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠘⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢷⣲⢀⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⢀⣄⣶⣶⣶⣶⣿
⠀⠈⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠻⣿⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠔⠀⠈⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣅⠹⢏⡛⡇⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿
⣿⣷⣿⣿⣿⣿⡻⣿⣿⣵⣟⣧⡄⠙⢿⣷⣮⣣⣤⣬⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣶⡦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣠⣿⣿⠟⣿⣿⣿⣿⡿⠟⢠⣿⣿⣿
⣿⣿⣿⡟⣿⣿⣧⣌⠻⣿⡆⠻⢿⡆⠀⠈⠻⣿⡏⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣬⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡩⢆⣴⠙⠿⣽⣿⣹⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣿⣿⣤⡘⠻⣦⡀⠀⠀⠀⠀⠀⠪⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠇⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡜⠀⣠⡙⢇⣴⣿⣿⣿⡿⣻⣿⣿⣿
⣿⣅⠈⠻⢟⠁⠈⠻⣿⣿⡆⠹⢿⡧⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡿⣿⣷⣶⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⡞⡿⠷⣼⣿⠋⠈⠛⢡⣿⣿⣿⣿
⣿⡿⣿⣀⢀⠁⠀⠀⠈⠁⠞⠃⠀⠁⠺⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣬⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠟⠁⠄⠀⣠⣿⣿⠿⢿⠿
⠀⠀⠘⠿⠷⠆⠀⠀⠁⠀⠀⢀⣠⣴⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⠿⡄⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣴⠿⠋⠀⠀⠀⣀
⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⡉
⣠⡤⣤⣤⣶⣤⣤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⣽⣭⣭⣥⣤⣤⣤⠀⢠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⣧⣤⠀⢠⣴⣶⣿⣶⣄⠒⠈
⠀⠴⣾⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡟⠓⠒
⣤⠄⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡗⠂⣴
⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⢀⣿⣿⣿⢸⣿⣿⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿
⣦⡀⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⡟⣿⣿⣿⣿⣟⡛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⡿⣻⢿
⡿⢿⣿⣿⣿⡇⢹⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣼⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣾⣯⡉⠀⠉⠉⠛⣿⣾⡿⢛⣿⣿⣿⣿⣿⣿⣬⡍⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⢛⡀⠘⢿⣿⣛⣿⣿⣟⣿⡷⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⠀⠀⠉⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠬⠿⠿⠼⣿⣿⡿⢿⡿⠋⠉⢀⣄⡄⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠏⠀⠀⣿⣿⣿⠀⠁⠀⠀⣿⣿⡇⠀⠀⢀⣿⣿⡶⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣷⣴⣶⣶⣾⡿⠿⣿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠛⠛⠉⠉⠉⢁⣀⣀⣀⣀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣾⣿⣾⣷⣿⣾⣿⣿⣿⣿⡿⠏⠊⠀⠀⠀⠀⠀⡀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⠛⠛⢻⣿⡏⠉⢘⠁⠂⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢸⣿⣿⣯⣀⣀⣽⣿⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣦⣤⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠙⣿⣿⣿⣿⠁⠀⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣽⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣷⣶⣿⢃⢸⣏⣹⣤⣼⣧⡆⣾⣷⡻⣾⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⢿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠛⢹⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⣂⣠⣠⣤⣭⡉⠁⠀⠀⠀⠀⠀⠀⣠⣴⣟⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣦⣄⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠃⠈⠉⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠐⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢀⡠⣿⣆⠀⠁⠸⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⢢⠂⢴⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⠀⠀⠀⠻⠝⢿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣌⠀⠀⢸⣿⠀⢻⣿⣿⣿⣿⢋⢫⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⡶⠍⠀⠀⠀⠀⠀⠈⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣿⣤⢠⡾⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⠚⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⣿⣿⠀⠀⠀⠀⣿⠯⠉⠿⢧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠘⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡏⠀⠀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠁⡟⠀⠀⠀⠸⣗⣠⣾⣼⣿⣿⣿⣿⠟⢿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠇⠀⠀⠀⠀⠀⠈⠁⠢⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⢷⣦⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡾⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⢀⢀⣀⣤⣾⣿⣿⣿⣿
⠀⢸⡿⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡎⠹⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠣⢀⣀⣀⣀⣼⣿⣿⣿⢿⣿⠿⢿⣿⣄⠙⢠⡛⠂⣀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠻⣿⣷⣾⢋⣤⣄⠙⠿⣷⣦⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⢷⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣶⡽⠟⢉⣿⣿⣿⣿⡟⠋⣸⣿⣿⣿
⣿⣿⣿⡛⢿⣿⣷⡜⠻⣿⡈⠻⡿⠀⠀⠈⠻⡟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠞⢱⣆⠙⢿⣿⣯⣿⣿⣿⣿⣿⣿
⣿⠿⣿⣿⣾⠿⢿⣷⣦⡈⢿⣦⣀⠐⠀⠀⠀⠈⠫⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⣛⣛⠋⢻⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢠⣼⠙⣦⣾⡿⣿⣿⢛⣿⣿⣿⣿
⣿⣀⠈⠛⠅⠀⠈⠻⣿⣿⣀⠹⢿⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠁⠐⠿⠻⠓⣿⠟⠀⠀⠀⣸⣿⣿⣿⣿
⠿⠿⣧⣄⡀⠀⠀⠀⠀⠘⠋⠁⠀⠈⣛⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⠰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠨⠋⠀⠀⢀⣾⣿⠿⠻⠿⠟
⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣟⢻⠐⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡾⠋⠀⠀⠀⣀⣄
⠠⠤⠤⠄⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣷⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣤⣄⠀⠀⠀⠀⠀⢀⡀⠘⠠⢬⡉
⠤⠖⢶⣦⣥⣬⣴⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠠⢵⣤⣦⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⠀⢴⣶⣷⣾⣶⣌⠉⠀
⠐⠶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠤⢼⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠉⢃
⠦⠂⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣶⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⣡⣿
⠘⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⢠⣿⣿⣿⢸⣿⣿⣧⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣦⡀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡟⣿⣿
⣟⣿⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠉⠙⠛⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣾⡋⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣙⣛⣀⣹⣻⣿⣻⣿⣿⣿⣿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⠀⢀⡉⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠛⠛⠻⠿⠿⠟⢿⡟⠁⠁⢠⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣧⣤⣦⣶⣿⣿⠟⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠋⠉⠉⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⠉⠉⣻⣿⣿⣿⡿⠋⠊⠀⠀⠀⠀⠀⡀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⡏⢐⠁⠂⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢹⣿⣿⣿⣠⣀⣽⣿⡁⠀⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⡋⣳⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠹⣿⣿⣿⣦⡤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣹⣿⣿⣿⣿⣄⣤⣼⣿⣿⣿⡄⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣿⣿⣶⣿⢃⢸⣏⣱⣤⣼⣧⡆⣾⣷⡻⣾⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠻⠿⠟⠛⠛⠁⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠐⠼⠿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣰⣿⣷⣄⠀⠸⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⢳⠀⢲⣾⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢙⠃⠀⠀⠻⠙⢿⡿⣿⣿⣿⣯⣭⣿⣿⣿⠋⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣄⡄⠀⠀⣿⡇⢐⣿⣿⣿⣿⢿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠾⠊⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⣿⣦⡀⣴⠟⠀⢸⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⣿⣿⠀⠀⠀⠀⢸⡿⠋⠟⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡏⠀⠠⠀⠀⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⣯⣁⣰⣴⣾⣿⣿⣿⠟⢻⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠠⠆⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠷⢦⣴⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⡀⠀⠀⠀⠀⢀⣠⣬⣿⣿⣿⣿⣿
⠀⠸⡿⠄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡆⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⠟⢿⣿⣆⠙⠁⣝⠁⣀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠝⢿⣷⣾⠋⣤⣄⠉⠻⣿⣦⣴⣶⣶⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡷⢿⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣴⡯⠟⠉⣿⣿⣿⣿⡏⠋⣸⣿⣿⣿
⣿⣿⣿⣟⢿⣿⣷⡌⠻⣿⣄⠙⠿⠆⠀⠀⠻⡟⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠞⢡⣦⠙⢛⣿⣿⣽⣿⣿⣿⣿⣿
⣿⠿⣿⣿⣾⠿⢿⣿⣦⡈⢻⣶⣄⠀⠀⠀⠀⠀⠘⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣟⣛⡋⢙⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢰⣴⡙⢳⣾⣿⢿⣿⠏⣾⣿⣿⣿
⣿⣤⡈⠙⠃⡀⠈⠻⣿⡿⣆⡹⠿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⡿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠁⠐⠻⠺⠃⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿
⠿⠿⣷⣄⡠⠀⠀⠀⠀⠐⠛⠀⠀⠈⣚⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⠰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠨⠋⠠⠀⢀⣾⡿⠿⠛⠟⠛
⠀⠀⠉⠛⠓⠀⠀⠀⠁⠀⣀⣤⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣟⢻⡘⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠋⠀⠀⠀⣠⣤
⠠⠤⠤⠄⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⡀⠈⠀⠤⣀
⠴⠖⢲⣦⣥⣤⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠠⢾⣴⣶⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⠀⢰⣶⣿⣾⣶⣄⡉⠀
⠒⠳⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⡤⢼⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⡏⠉⢉
⠶⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣶⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⣠⣿
⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢠⣿⣿⣿⢸⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣧⡀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⠟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣯⣟⢿
⣟⣿⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠉⠛⠛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣙⣻⣀⣸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⢀⣈⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠚⠛⠛⠻⠻⠻⠟⢻⣟⠁⠁⢠⣦⣄⠀⠀⠀⠀⠀⠀⢰⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠿⠟⠛⠋⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣻⣿⣿⣿⠉⠉⣿⣿⣇⣀⣀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⢰⠀⣿⣿⡿⡟⠋⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣹⣿⣿⣿⣀⣁⣽⣿⡑⠁⠀⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠇⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣟⠉⠻⣿⣷⣆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢻⣿⣿⣿⣿⡀⣀⣹⣿⣿⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⠿⣟⣉⡉⠛⠻⠿⠟⡏⢋⡈⢛⣛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣯⡉⣁⠄⠿⢿⣷⣿⢃⢰⣏⣹⣤⣴⣷⡆⣾⣷⡻⣾⡿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣼⣄⣤⣤⡙⠋⠉⠉⠁⠀⠀⠠⣸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠙⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣟⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⣐⣼⢿⣢⠀⠸⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠘⠊⠀⠂⢼⣿⡆⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠙⢿⡿⣿⣿⣿⣯⣭⣿⣿⣿⠉⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣬⡄⠄⠀⢸⣿⢸⣿⣿⣿⣻⣏⢥⣥⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠰⠈⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⢽⣶⡀⠠⡾⠃⢸⣿⣿⣿⣿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣷⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢠⣿⣿⠀⠀⠀⠀⠀⣿⠍⢑⡛⣠⣾⣿⣿⣿⣿⣿⣿⢿⠿⠅⠀⠀⠌⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⠰⠀⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⣐⣅⣠⣴⣿⣿⣿⣿⣏⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠷⠦⣴⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣗⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⡀⠀⢀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿
⠀⢐⠿⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⠈⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣉⣀⣤⣄⣠⣼⣿⣿⣿⢟⣿⠟⠻⣿⣦⡈⠠⠛⠃⠠⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡝⢿⣿⣿⠋⣴⣆⠈⠻⢿⣷⣼⣿⢿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⠟⠿⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠮⡟⠁⣿⣿⣿⣿⣏⠉⣼⣿⣿⣿
⣿⣿⣿⣯⢻⣿⣿⡆⠙⢿⣆⠈⠻⠃⠀⠀⠙⢟⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠘⠨⣦⠈⢛⣿⣿⣼⣿⣿⣿⣿⣿
⣿⠟⢿⣿⣿⠟⢻⣿⣶⣄⠹⣷⣄⡀⠀⠀⠀⠀⠙⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣭⣏⡃⢙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⣠⣶⣍⢳⣾⡿⢻⣿⢏⣾⣿⣿⣿
⣿⣤⣄⠉⠃⠀⠀⠙⡿⠿⣧⡘⠿⢗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢛⠛⠟⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠁⠀⠋⠛⠓⣿⠟⠀⠀⠀⣸⣿⣿⣿⣿
⠟⠛⣿⣦⣠⠀⠀⠀⠀⠀⠉⠀⠀⢀⣹⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⠀⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠋⠠⠀⢀⣾⡿⠟⠛⠛⠛
⠄⠀⠈⠙⠛⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣹⡆⢛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠞⠋⠀⠀⠀⢤⣤
⠀⠒⠒⠐⢀⢀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⠿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⣤⡄⠀⠀⠀⠀⠠⣀⠈⢀⣢⠄
⠶⠒⢲⣧⣴⣦⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠐⢲⣶⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣦⣤⡀⢰⣾⣿⣶⣷⣦⣀⡀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠰⢾⣿⣿⣿⡿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠉⢩
⠒⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡟⠻⣻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣠⣿
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣄⡄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⢸⣿⣿⣷⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣷⣄⢸⣿⣿⡟⣿⣿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣄⣿⣿⣿⣯⣿⣿⣿⣿⣿⠟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣶⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣏⣟⣿
⣿⣽⣿⣿⣿⣧⣸⣿⣿⠇⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢾⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠉⠋⠙⢻⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢩⣿⣄⢸⣿⣿⣿⣿⣿⡿⡿⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⣀⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢛⠉⠙⠛⠛⠛⢛⣟⠁⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠾⠛⠛⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⡀⢸⣿⣿⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡁⠸⣿⣿⣿⡇⠇⠸⣿⣿⡿⠯⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣿⣿⣿⣷⣶⣶⣿⣿⠁⠂⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⢿⣿⣿⣿⣿⣿⢿⣿⣧⡀⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠄⢸⣿⣿⣿⣿⡇⠀⢸⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣀⣈⣿⣿⣿⣿⣧⣛⣤⣽⣿⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⣿⣿⣿⡇⣠⢠⠸⣿⣷⣿⢃⢰⣏⣹⣤⣼⣧⡆⣾⣷⡻⣾⣽⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣼⣧⣭⣤⣿⠛⠛⠛⠋⠈⠀⢠⢼⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠉⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣦⣄⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⡀⠀⣹⢛⡟⠁⢸⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠐⢻⠖⢢⢠⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⢄⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣴⡤⠄⠀⢸⣿⣿⣿⣿⣿⢿⣿⢯⣩⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⢤⠐⠈⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣟⣦⡀⠀⣼⡟⢹⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⣿⣿⠀⠀⠉⠀⠈⢿⡟⠛⠿⠋⣡⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠐⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡟⠀⠠⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠁⣿⠀⠀⠀⠀⢀⡟⢁⣀⣿⣿⣿⣿⠟⢿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢀⡆⠀⠀⠀⠀⠀⠉⠁⠢⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢶⡄⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡾⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⢀⢀⣴⣶⣶⣾⣿⣿
⠀⠸⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡬⠹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠈⣀⡀⢀⣰⣿⣯⣿⣿⣿⠿⢿⣿⣄⠙⢀⠛⠀⢀⢻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠻⣿⣷⣶⠟⣤⡀⠙⢿⣷⣦⣰⣶⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⣶⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣴⣿⠿⢋⣿⣿⣿⣿⡯⠛⢰⣿⣿⣿
⣿⣿⣿⡻⢿⣿⣷⡜⠻⣿⡀⠻⢿⠄⠀⠈⠿⡿⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⠴⢠⣄⠛⢟⣿⣟⣽⣶⣿⣿⣿⣿
⣿⡿⣿⣿⣾⡿⣿⣵⣄⠙⢿⣦⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣛⣿⠛⠇⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎⢀⣼⡙⣢⣾⣿⢿⣿⠟⣿⣿⣿⣿
⣿⣀⠈⠛⢍⠀⠘⢻⣿⡿⣀⠹⣿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⡿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⠐⠛⠺⠇⣾⡿⠁⢈⠉⣸⣿⣿⣿⣿
⡿⠿⣷⣄⣀⠀⠀⠀⠀⠐⠛⠀⠀⠈⢻⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣤⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⡀⠀⣴⣿⠿⠿⠿⠟
⠀⠀⠙⠻⠷⠀⠀⠀⠂⠀⢀⣠⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⠀⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠰⠁⡼⠟⠁⠀⠀⣀⣀
⠀⠤⠤⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⠀⠐⠠⢌⡉
⣤⠤⢶⣶⣭⣬⣤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠠⢽⣬⣬⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣦⣤⠀⢠⣶⣶⣿⣶⡌⠉⠀
⠰⠶⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠤⢼⣿⣿⣿⡿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠛⢓
⠶⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⢀⣾
⠐⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣄⡄⠀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣦⡀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣟⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡟⠿⣿
⣿⣿⣿⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠉⠉⠛⣿⣾⡟⣻⣿⣿⣿⣿⣿⣿⣾⡍⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣛⡀⢘⣛⣻⣻⣿⣿⣿⣿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠠⡘⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠿⠛⠻⠿⠿⠿⢿⡟⠁⠁⣠⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⣧⣦⣠⣤⣤⣤⣬⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣿⣿⣿⡀⠀⢰⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣌⡀⢸⣿⣿⣿⡇⠇⠸⣿⣿⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣬⣿⣿⣿⣧⣤⣤⣿⡿⠍⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠊⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣿⣿⣿⣿⣧⢀⠠⡇⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠘⠦⠤⠀⣿⣿⣿⣿⣿⠰⠄⢧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣾⣿⣈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠟⠟⠿⣿⣿⣿⣿⡟⡛⠛⢹⡿⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡈⢛⣛⣿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⡆⠦⠀⣿⣿⣿⣿⡷⠸⠙⢺⣷⣿⢃⢸⣍⣹⣤⣼⣧⡄⣾⣷⡻⣾⡿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⣿⣿⣻⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠐⠂⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⢹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠊⠨⣿⠗⢂⠁⣸⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠋⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣦⣜⡄⣄⠄⠀⢻⣿⣿⣿⣿⡿⣿⣟⠉⣹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠒⠄⠀⠐⠀⠀⠀⠀⠀⠈⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠿⣿⣯⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⣿⣿⠀⠀⠈⠁⠘⣿⣿⠟⠻⠿⣉⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡇⠀⠄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠱⡟⠀⠀⠀⠀⣰⣿⡏⢀⣲⣾⣿⣿⠟⢿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠀⢠⡆⠀⠀⠀⠀⠈⠍⠀⠠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠘⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢶⣆⣤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⢀⢰⣤⣶⣶⣾⣷⣿
⠀⢸⡟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡎⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠢⢀⣀⡀⢀⣼⣿⣯⣿⣿⣿⠿⣿⣿⡀⠛⣟⠷⠀⣈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⠟⣠⡌⠛⢿⣷⣬⣰⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⢶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⣾⣹⠟⢹⣿⣿⣿⣿⡯⠛⣸⣿⣿⣿
⣿⣿⣿⡻⢿⣿⣦⡙⠿⣿⡈⠻⢷⠄⠀⠙⢿⠿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢁⠞⢢⣌⠻⢿⣿⣯⣿⣶⣿⣿⣿⣿
⣿⡿⣿⣷⣾⠿⣿⣥⣄⠙⢽⣆⡀⠀⠀⠀⠀⠐⢯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣻⡛⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡷⠃⣠⣼⡹⣦⣾⡿⣿⣿⢟⣿⣿⣿⣿
⣯⣀⠙⠻⠁⠀⠙⢿⣿⣷⢀⠿⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⡿⣶⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠁⠐⠊⠿⢣⣿⠟⠁⠈⠁⣸⣿⣿⣿⣿
⡿⢿⣧⡠⠀⠀⠀⠀⠉⠱⠟⠀⠀⠙⢳⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣷⣶⡄⢰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠋⢀⠀⢠⣼⣿⠿⠿⡿⠿
⠀⠀⠙⠻⠗⠀⠀⠀⠂⠀⢀⣠⣴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢿⠺⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠺⢂⡾⠛⠁⠀⢀⣀⣄
⠠⠤⠄⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣷⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣀⡀⡀⠀⠀⠀⠀⢀⠀⠐⠠⣌⡉
⡤⠤⢶⣶⣥⣬⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠸⢧⣴⣦⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣷⣤⣤⠀⢰⣶⣶⣿⣦⡍⠁⠀
⠰⠶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⡤⢼⣿⣿⣿⡿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠛⢓
⠶⠐⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⣠⣿
⠘⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣆⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡿⢻⢟
⣿⣻⣿⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣹⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣾⣍⠉⠀⠉⠋⠻⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣾⡉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢙⣛⡀⢙⣻⣻⣻⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠛⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠻⠿⠛⠿⠿⡿⠿⢿⡟⠉⡇⣀⣤⡀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⢿⣿⣷⡇⠂⠀⢰⣮⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⣾⣿⣿⣷⢀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠖⠀⢿⣿⣿⣿⠈⠂⢹⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⣿⣿⣿⣿⠿⠿⢟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⠠⠀⢰⣿⣿⣿⣿⡇⠖⠀⠠⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣉⣛⣃⣸⣿⣿⣿⣿⣇⣘⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠉⠉⢹⣿⣿⣿⣿⢉⡉⠉⠩⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣻⣘⣃⣘⡿⠿⠿⠿⠃⠃⢹⣷⣿⢃⢰⣍⣱⣤⣼⣧⡄⣾⣷⡻⣿⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠒⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠜⢻⠿⢇⠀⢸⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠋⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣦⣜⡅⣤⡄⠀⢸⣿⣿⣿⣿⣿⢿⣿⠍⡁⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣿⣦⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⣿⣿⠁⠀⠀⠁⠘⣿⣿⡟⠋⠿⣉⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⢀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡇⠀⠄⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠁⣟⠀⠀⠀⠀⣰⣿⣟⢁⣺⣶⣿⣿⠟⢿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢠⡇⠀⠀⠀⠀⠀⠈⠁⠠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢷⣦⣠⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⢀⢰⣤⣾⣾⣿⣿⣿
⠀⢸⠿⠄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣎⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠢⢀⣀⣀⣀⣴⣿⣯⣿⢿⣿⠿⢿⣿⣀⠛⠌⠛⠆⣀⢻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿
⣿⣿⣿⣿⣿⣯⠻⣿⣷⣾⢿⣤⡄⠙⢿⣷⣤⣰⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⡵⠟⢹⣿⣿⣿⣿⡟⠛⣰⣿⣿⣿
⣿⣿⣿⡻⢿⣿⣷⡜⠻⣿⡈⠛⠿⠆⠀⠘⠿⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠞⢱⣄⠛⢯⣿⣯⣿⣶⣿⣯⣿⣿
⣿⡿⣿⣿⣾⠿⢿⣶⣆⠙⢿⣦⡀⠀⠀⠀⠀⠈⠨⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣛⡛⠀⢛⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣠⣼⡻⣥⣾⡿⣿⣿⢯⣿⣿⣿⣿
⣿⣀⠈⠛⠁⠀⠘⢿⣿⣿⣄⠹⣿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⡿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠘⠋⠛⠓⣿⠟⠁⠈⠁⣺⣿⣿⣿⣿
⠿⠿⣧⣄⠀⠀⠀⠀⠀⠰⠏⠀⠀⠉⢻⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⣆⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢀⠀⢀⣼⣿⠿⠛⠿⠟
⠀⠀⠙⠛⠟⠀⠀⠈⠂⠀⢀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⢻⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠃⡾⠛⠀⠀⢀⣀⣄
⠠⠤⠄⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣷⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣤⣄⠀⠀⠀⠀⠀⢀⡀⠀⠠⢌⣉
⠤⠔⢶⣦⣥⣤⣤⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠨⢷⣴⣦⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⠀⢰⣶⣶⣾⣶⣌⠁⠀
⠐⠶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠤⢼⣿⣿⣿⡿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠉⢃
⠶⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⣠⣿
⠘⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢠⣿⣿⣿⢸⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣦⡀⢹⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡏⢻⢿
⢟⣻⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣾⣯⡉⠀⠉⠉⠙⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣾⡉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣙⣏⡀⣙⣟⣻⣻⣿⣿⣿⡿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⢀⡈⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠺⠟⠛⠿⠿⠿⠟⢿⡟⠁⡃⣠⣤⡀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠉⠉⠉⢉⣿⣿⣿⡍⠁⠀⣴⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣰⣐⣂⢸⣿⣿⣿⡧⢀⠐⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣉⣁⣈⣿⣿⣿⣷⣬⣀⣽⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠉⠉⠙⣿⣿⣿⣿⠉⢉⠡⠂⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡰⣧⣈⠀⢸⣿⣿⣿⣿⡆⡇⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣤⣼⣿⣿⣿⣿⣧⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣀⣀⢀⡀⢹⣿⣿⣿⣧⢀⣄⡀⠀⢸⣿⠿⣿⣉⡉⠛⠻⠿⠟⡯⢋⡈⢛⣛⢿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⣿⣬⣤⣼⠟⠛⠛⠋⠈⣱⣶⣿⢃⢰⣍⣹⣤⣼⣧⡄⣾⣷⡻⣾⣿⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣠⣄⣀⣀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠀⠀⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠊⢟⠟⢇⠀⠀⣿⣇⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣤⣴⡦⢤⠤⠀⠀⣿⣿⣿⣿⣿⣿⣿⢘⣐⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠟⢿⣶⡀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣿⡻⢛⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣵⣿⠟⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⣿⣿⠃⠀⠀⠀⠀⣿⣿⡟⠁⠹⢉⣴⣿⣿⣿⣿⣿⢿⡯⠀⠀⠀⢈⠍⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠀⠀⠐⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡿⠀⠀⠀⠀⣰⣿⣟⣀⣼⣶⣿⣿⠟⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⠠⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠧⣆⣰⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⠀⠀⠀⠀⠀⢀⢠⣦⣾⣿⣿⣿⣿
⠀⠸⠟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣆⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣀⣀⣀⣠⣼⣿⣷⡿⡿⣿⠟⢿⣿⣆⠉⠀⠈⠀⠠⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠙⢿⣿⣾⠟⣤⡀⠉⠻⣿⣧⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠿⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⡧⡟⠁⣿⣿⣿⣿⣗⠉⢰⣿⣿⣿
⣿⣿⣿⣙⢻⣿⣷⡌⠛⣿⣆⠙⠟⠄⠀⠀⠻⠟⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠚⢠⣶⠈⢋⣿⣏⣽⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⠟⢿⣵⣦⡈⠺⣷⣄⠀⠀⠀⠀⠀⠑⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣛⡋⢙⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⢠⣶⡝⢷⣾⡿⣿⣿⢏⣾⣿⣿⣿
⣿⣤⡈⠙⠃⠀⠈⠻⣿⣿⣄⠜⠿⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠁⠐⠋⠛⠓⣿⠟⠀⠀⠀⣼⣿⣿⣿⣿
⠿⠟⣷⣦⡀⠀⠀⠀⠀⠉⠋⠀⠀⠈⣙⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠋⠀⠀⢀⣾⡿⠟⠛⠛⠛
⠀⠀⠈⠛⠛⠀⠀⠀⠁⠀⣀⣤⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣻⡊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠞⠋⠀⠀⠀⢤⣤
⠀⠰⠆⠀⢀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⣤⡄⠀⠀⠀⠀⠠⣀⠈⠀⠦⠄
⠶⠒⢲⣦⣥⣤⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢱⣴⣶⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⠀⢰⣾⣿⣦⣷⣆⣁⠀
⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠠⢾⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠉⢩
⠺⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡟⠿⣻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣠⣿
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⢠⣤⣤⣄⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⣿⣿⣿⢸⣿⣿⣷⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡄⢸⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣏⢙⠿
⣟⣿⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠉⠛⠙⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣿⣀⣘⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⣈⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠘⢛⠛⠘⠛⢛⡛⢻⡋⠁⠁⢰⣤⡀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠈⡀⠁⢩⣿⣿⣿⠉⠁⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠸⣅⣁⢸⣿⣿⣿⡇⡆⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣤⣤⣤⣬⣿⣿⣿⣧⣬⣀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠈⠉⣿⣿⣿⣿⡍⠉⠡⠂⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠠⠧⣤⠄⢠⣿⣿⣿⣿⡅⠇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣶⣦⣼⣿⣿⣿⣿⣧⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡄⣠⣀⡀⢸⣿⣿⣿⣧⢠⣄⡈⠀⢸⣿⠿⣿⣉⡙⠛⠿⠿⠟⣯⢋⡈⢛⣛⣿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣮⣤⣼⡟⠛⠛⠛⠈⢰⣶⣿⢃⢰⣍⣹⣤⣼⣧⡄⣾⣷⡻⣾⣿⢿⣿⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠐⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠘⢚⣿⠿⢇⠁⣸⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣔⣤⣤⠤⠄⢸⣿⣿⣿⣿⣟⣻⣿⠤⡄⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢻⣭⣤⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠾⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣵⣿⠟⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣼⣿⡇⠀⠀⠀⠀⢹⣿⣿⡟⠉⡻⣀⣴⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠃⠀⠄⠀⠀⠄⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣀⣠⣾⣿⡿⠻⣿⣿⣿⡇⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢰⠀⠀⠀⠀⠀⠀⠉⠐⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠘⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣦⣀⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⢀⢠⣤⣼⣾⣿⣿⣿
⠀⠾⠧⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣶⡌⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢿⣿⣶⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠡⣀⣀⢀⣀⣾⣿⣽⣿⢿⡿⠿⣿⣧⡈⠛⡈⠁⠀⡈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣽⣿⣿
⣿⣿⣿⣿⣿⣟⢿⣿⣶⡞⢣⣄⠈⠻⢿⣶⣤⣶⣦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣴⣮⢽⠏⢹⣿⣿⣿⣿⠞⠃⣸⣿⣿⣿
⣿⣿⣟⠿⣿⣿⣦⠙⢿⣧⠈⠻⠶⠀⠀⠙⢿⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣴⡈⠻⣹⣿⣫⣷⣾⣿⣿⣿⣿
⣿⢿⣿⣷⡿⠿⣿⣷⣀⠛⣷⣄⡀⠀⠀⠀⠀⠑⢾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣟⣛⡛⠀⢟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡗⠁⣤⣏⡕⣴⣿⡿⣿⡿⢻⣿⣿⣿⣿
⣧⣀⠙⠻⡁⠀⠙⢿⣿⣧⣀⠿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠏⠀⠞⠛⠛⢸⣿⠋⠀⠈⢀⣿⣿⣿⣿⣿
⡿⢿⣦⡀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠙⣣⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡄⢴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣿⡿⠿⠻⠿⢛
⠀⠈⠛⠻⠟⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⣧⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠟⠋⠀⠀⢀⣠⣀
⠠⠤⠄⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⣀⠀⠒⠠⢌⣉
⠤⠖⢶⣮⣥⣤⣬⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠸⢥⣴⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⢴⣶⣶⣷⣦⡍⠁⠀
⠲⠶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣇⠤⢸⣿⣿⣿⡿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⠉⣣
⠆⠐⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⡋⣽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣰⣿
⠚⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣾⡆⢠⣿⣿⣿⢸⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⢹⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣽⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡟⠟⠟
⣛⣿⣿⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⢸⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣾⣍⠉⠀⠉⠙⢻⣷⣾⢛⣿⣿⣿⣿⣿⣿⣿⣮⠉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣹⣏⡀⣹⣛⣛⣿⣿⣿⣿⡿⠁⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⠀⢀⠉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠛⠟⠛⠿⠿⠿⠻⣿⠋⢈⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣙⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢠⠀⠤⢿⣿⣿⣿⠀⠀⢰⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠘⠓⠂⠈⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⠻⠿⢿⣿⣿⣿⣿⡿⠯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢀⡄⠠⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠛⠒⠀⢸⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢰⡖⠤⠀⣿⣿⣿⣿⡆⡀⠀⢸⣿⠿⣟⣉⡉⠛⠿⠿⠟⣯⢋⡈⢛⡛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣿⠈⠉⠉⢰⣶⣿⢃⢰⣏⣹⣤⣼⣧⡄⣾⣷⡻⣾⡽⢿⢿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣤⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠁⠸⡻⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⢐⠻⠿⢧⠁⠀⣽⣧⣘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣤⣤⠤⠤⠤⠀⢻⣯⣿⣿⣿⣙⣿⡏⢄⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠻⢿⣤⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡯⠋⣹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⠟⡯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⡇⠀⠀⠀⠀⣿⣿⣿⠋⡸⠉⣤⣾⣿⣿⣿⣿⣿⢿⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠀⠰⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢿⠀⠀⠀⠀⣠⣿⣗⣅⣠⣴⣿⣿⡟⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠴⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠶⠆⣤⡆⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⢀⢀⣄⣾⣿⣿⣿⣿
⠀⠠⠿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡦⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣮⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣈⣀⣀⡀⣀⣰⣿⣿⣼⡿⣿⡿⠻⣿⣆⡈⠣⡀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢹⣿⣿
⣿⣿⣿⣿⣿⣿⡝⢿⣿⣶⠛⣵⣄⠈⠻⢿⣶⣤⣶⣶⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⢾⠗⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⡦⡟⠋⣾⣿⣿⣿⣿⠙⢁⣾⣿⣿
⣿⣿⣿⣟⠻⣿⣿⣆⠙⢿⣆⠉⠛⠃⠀⠀⠛⢿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⣶⡈⠛⣾⣿⣼⣷⣿⣿⣿⣿
⣿⡿⢿⣿⣶⡿⢻⣽⣶⡄⠹⣷⣄⡀⠀⠀⠀⠀⠑⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣟⣛⡃⠙⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢠⣦⣌⢣⣾⣿⢻⣿⠟⣽⣿⣿⣿
⣿⣤⣀⠙⠋⠀⠀⠻⣿⣿⢇⡨⠿⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠻⠿⢿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠐⠈⠛⠋⣾⡿⠁⠀⠀⣰⣿⣿⣿⣿
⠿⠿⢿⣤⡀⠀⠀⠀⠀⠐⠏⠁⠀⠀⢙⣧⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣶⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣴⣿⠿⠛⠛⠛
⠀⠀⠈⠛⠛⠂⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣻⣛⡇⠹⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠼⠛⠁⠀⠀⢀⣴
⠀⠀⠤⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄
⠤⠖⢶⣶⣬⣤⣤⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢸⣦⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣦⣤⠀⢰⣶⣾⣦⣵⣦⡉⠀
⠀⠲⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠠⢼⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠉⠉
⠖⠂⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠿⣻⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡏⢀⣾
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣄⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣷⣄⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣤⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣧⠙⠿
⢟⣻⣿⣿⣿⣇⣸⣿⣿⠇⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣼⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠉⠉⠛⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣛⣀⣘⣟⣻⣻⣿⣿⣿⣿⠏⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠛⠛⠛⠟⠛⠟⠻⣿⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⡆⠠⠘⣿⣿⣿⡅⠀⢠⣿⣿⣶⡾⠛⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠊⠛⠒⠀⢸⣿⣿⡏⡄⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠛⠛⠿⠿⣿⣿⣿⣿⡿⠯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⡄⠠⠄⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠙⠒⠂⠀⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠦⡶⠤⠄⢸⣿⣿⣿⣧⠀⠀⢸⣿⠿⣟⣩⡉⠛⠿⠿⠟⡯⢋⡈⢛⡛⢿⡆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣾⠉⠉⠉⢱⣶⣿⢃⢰⣏⣱⣤⣼⣧⡄⣾⣷⡻⣾⡿⢿⢿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣄⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠀⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠁⠸⣽⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⢐⣿⠻⢦⠁⠀⣿⣧⣘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣌⣄⡄⣠⠄⠀⢻⣿⣿⣿⣿⣝⣿⡇⡀⢼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠜⠻⢻⣤⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡫⠊⣽⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣵⣿⠟⡯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⡇⠀⠀⠀⠀⣿⣿⡿⠋⠨⠁⣤⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠀⠰⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢿⠀⠀⠀⠀⢠⣿⣟⣍⣠⣴⣾⣿⡟⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠼⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠷⠄⣠⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⢀⢀⣄⣶⣶⣿⣿⣿
⠀⠠⠿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡦⠙⢿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣷⣶⣶⣾⣿⣷⣷⣷⣿⣿⣿⣿⣿
⠐⢄⣀⡀⢀⣠⣿⣿⣽⡿⣿⡿⠿⣿⣇⠈⠁⠀⠀⢀⡘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⢹⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢿⣿⣶⠛⣳⡄⠈⠻⣿⣶⣰⣶⡶⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⢶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣴⣇⠿⠋⣿⣿⣿⣿⣿⠈⢁⣿⣿⣿
⣿⣿⣿⣟⠿⣿⣷⣄⠛⢿⣆⠙⠻⠆⠀⠀⠹⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡐⠁⣶⠈⠛⣼⣿⣼⣷⣿⣿⣿⣿
⣿⡿⢿⣿⣶⡿⢟⣵⣤⡈⠻⣷⣄⡀⠀⠀⠀⠀⠑⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⡃⠙⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢀⣤⣌⢣⣾⣿⢻⣿⠟⣽⣿⣿⣿
⣿⣄⡈⠙⠋⠀⠀⠛⣿⣿⣇⡈⠿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⢿⡿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⠒⠛⠛⣺⡿⠁⠀⠀⢰⣿⣿⣿⣿
⠿⠿⢿⣤⣀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠛⣣⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣶⣴⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣴⣿⠿⠟⠛⠿
⠀⠀⠈⠛⠻⠂⠀⠀⠁⠀⠀⣀⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢙⡇⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠟⠁⠀⠀⣀⣰
⠀⠠⠄⠄⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠤⢄
⣤⠤⢶⣶⣬⣤⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢽⣦⣶⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣤⣤⠀⢠⣶⣾⣶⣶⣮⠉⠁
⠀⠶⣾⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠠⢼⣿⣿⣿⣿⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⡏⠉⠉
⠤⠆⢿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠿⣻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⢀⣼
⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⢀⣿⣿⣿⢸⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣷⣄⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣏⣿⣿⣿⣿⣿⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣤⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡇⠟⠿
⡿⣛⣿⣿⣿⣇⢸⣿⣿⠇⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣸⣿⣿⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠉⠙⠉⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⡏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣛⣀⢘⣛⣛⣛⣿⣿⣿⣿⠏⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣈⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠿⠛⠚⠿⠿⠿⠻⣿⠃⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣉⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢠⡆⠤⠘⣿⣿⣿⢀⠀⢸⣿⣿⠛⠁⠀⢀⣿⠏⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠘⠛⠚⠀⢻⣿⣿⡈⡄⢸⣿⣿⢀⠐⠉⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠛⠛⠿⠿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⡄⠠⠄⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠙⠒⠂⢸⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠠⡖⠤⠀⢸⣿⣿⣿⣇⠁⠀⢸⣿⠿⣿⣉⡉⠛⠿⠿⠟⣯⢋⡈⢛⣛⢿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠈⠈⢱⣶⣿⢃⢰⣍⣹⣤⣼⣧⡆⣾⣷⡻⣾⡿⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠒⠒⠀⠀⠀⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢺⡿⠟⠧⠀⢠⣿⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠋⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣄⣤⠤⢠⠄⠸⣿⣿⣿⣿⣿⢭⣿⠅⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠿⣿⣦⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⡶⢃⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⣿⠟⡯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣿⠀⠀⠀⠀⠘⣿⣿⡟⠀⠸⢁⣴⣿⣿⣿⣿⣿⣿⠿⠣⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡏⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠸⡏⠀⠀⠀⠀⣸⣿⣏⣀⣰⣶⣿⣿⠟⢿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⡆⠀⠀⠀⠀⠀⠀⠁⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠘⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢷⡄⣠⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣯⣿
⠀⠸⠿⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣶⣶⣮⣿⣷⣷⣿⣿⣿⣿⣿⣿
⠢⢈⣀⡀⣀⣰⣿⣯⣿⡟⣿⡿⢿⣿⣄⠉⢄⠀⠀⢀⢻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿
⣿⣿⣿⣿⣿⣯⠻⣿⣷⣞⠋⣄⠀⠙⢿⣷⣆⣰⣶⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠦⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣶⣀⠟⢁⣿⣿⣿⣿⡿⠙⢰⣿⣿⣿
⣿⣿⣿⡻⢿⣿⣷⡜⠻⣿⡀⠙⠳⠄⠀⠈⠻⡿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣮⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠚⢠⡆⠙⢧⣿⣧⣿⣶⣿⣿⣿⣿
⣿⡿⣿⣿⣾⠿⢿⣵⣆⡈⢻⠦⡀⠀⠀⠀⠀⠈⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣟⠛⠊⠻⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⢀⡌⡙⣴⣾⡿⣿⣿⢋⣿⣿⣿⣿
⣿⣀⠈⠛⠋⠀⠈⢻⣿⡿⣀⠹⢿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⡿⣿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠀⠀⠊⠛⢓⣿⠟⠀⠈⠀⣺⣿⣿⣿⣿
⡿⠿⣧⣄⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⢒⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣤⢐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠋⠀⠀⢀⣾⣿⠿⠛⠟⠛
⠀⠀⠙⠻⠿⠀⠀⠀⠂⠀⢀⣠⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⢻⠠⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠾⠋⠀⠀⠀⣀⣄
⠀⠠⠤⠤⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣷⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣤⣤⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠁
⡤⠤⢶⣶⣭⣬⣤⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠈⢱⣴⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⠀⢰⣶⣷⣾⣶⡌⠁⠀
⠰⠶⣾⣿⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠤⢼⣿⣿⣿⡿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⡏⠉⢁
⠴⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣠⣿
⠐⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣤⣤⣤⡄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⡇⢀⣿⣿⣿⢸⣿⣿⣧⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣦⡀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣏⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡏⠛⠿
⢟⣻⣿⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢸⣿⣿⣧⢺⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣾⣯⡉⠀⠉⠉⠛⣿⣾⣟⣻⣿⣿⣿⣿⣿⣿⣾⡍⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢙⣫⣀⢘⣛⣻⣻⣿⣿⣿⡿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠋⣨⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⡈⢩⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠛⠓⠻⠿⠿⠟⢿⡟⠁⡅⢀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣋⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⢠⡆⠤⠘⣿⣿⣿⢀⢀⢸⣿⣿⣿⣿⡁⠀⢻⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠈⠛⠊⠀⣿⣿⣿⡉⡤⢸⣿⣿⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⠛⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⡄⠠⠄⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣬⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠙⠒⠂⢸⣿⣿⣿⡇⠀⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠠⡖⠤⠀⢸⣿⣿⣿⣇⠀⠀⢸⣿⠿⣿⣉⡙⠛⠿⠿⠟⡯⢋⡈⢛⡛⢿⣄⡌⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⢰⣶⣿⢃⢰⣍⣹⣤⣴⣧⡄⣾⣷⡻⣾⡽⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⣄⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠂⠀⠀⢰⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢢⣟⠻⢧⠀⢸⣿⢀⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠹⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣄⣤⢤⠀⠀⢸⣿⣿⣿⣿⣟⣸⣯⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠿⣿⣤⠀⠀⢀⣾⢿⣿⣿⣿⣿⣿⣿⠣⣡⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣵⣿⠟⡯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⣿⡿⠀⠀⠀⠀⢸⣿⣿⠿⠀⠨⣠⣶⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⠇⠀⠆⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⣸⣿⣏⣀⣴⣾⣿⣿⠟⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠠⡆⠀⠀⠀⠀⠀⠀⠁⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠘⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠷⢄⣤⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣧⣿
⠀⠸⠇⠀⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣶⣶⣶⣮⣿⣷⣷⣿⣿⣿⣿⣿⣿
⠢⣀⣀⡀⣀⣼⣿⣧⣿⣿⣿⠿⢿⣿⡀⠙⠈⠉⠀⢀⢻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣩⣿⣿
⣿⣿⣿⣿⣿⣯⠻⣿⣷⡜⠫⢄⡀⠙⢿⣷⣄⣰⣶⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠦⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣶⡴⠟⢑⣿⣿⣿⣿⡖⠙⢀⣿⣿⣿
⣿⣿⣿⡻⢿⣿⣦⡘⠻⣿⡀⠙⠗⠄⠀⠐⠻⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣬⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠊⢴⣆⠙⢧⣿⣧⣿⣶⣽⣽⣿⣿
⢿⡿⣿⣷⣾⠿⢿⣵⣄⠉⢛⡦⡀⠀⠀⠀⠀⠀⠨⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣛⠛⠂⠻⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠁⢀⣬⡙⣴⣿⡟⣿⣿⢫⣿⣿⣿⣿
⣧⣀⠈⠛⢅⠀⠘⢻⣿⡷⣀⠹⣿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⣿⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠀⠀⠈⠛⢓⣿⠏⠀⠀⠀⣾⣿⣿⣿⣿
⡿⠿⣧⣄⠀⠀⠀⠀⠀⠐⠋⠀⠀⠉⢂⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⣦⣄⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠀⠀⢠⣾⡿⠿⠛⠟⠛
⠀⠀⠙⠻⠷⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡟⢻⠈⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⠋⠀⠀⠀⣀⣄
⠀⠠⠤⠄⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣷⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣤⣤⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠉
⡤⠤⢶⣶⣥⣤⣤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢵⣴⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣧⣤⣤⠀⢰⣶⣷⣾⣶⡌⠁⠀
⠰⠶⣾⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠤⢼⣿⣿⣿⡿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠉⢁
⠴⠀⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠟⢽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣠⣿
⠐⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⡇⢀⣿⣿⣿⢸⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣦⡀⢸⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣏⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡏⠛⠿
⢟⣻⣿⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⢸⣿⣿⣧⢾⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣾⣏⡉⠀⠉⠉⠙⣿⣾⣟⣻⣿⣿⣿⣿⣿⣿⣾⡉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣙⣫⣀⢙⣛⣻⣻⣿⣿⣿⡿⠇⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⡈⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠛⠓⠻⠿⠿⠟⢿⡟⠁⡅⢀⣠⡀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣉⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⣞⠐⠀⢿⣿⣿⣿⣴⣤⣿⣿⣿⢿⣿⣿⣿⣮⡃⠙⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣓⣍⣉⣁⣸⣿⣿⣿⣼⣦⢿⣿⣿⠘⠉⠁⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠖⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⢰⡀⠂⠀⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣈⣙⣉⣀⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣗⣺⣓⠆⠀⣿⣿⣿⣿⡄⠀⢸⣿⠿⣟⣉⡉⠛⠻⠿⠟⡯⢋⡈⢛⡛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣶⣿⢃⢰⣏⣹⣤⣴⣧⡄⣾⣷⡻⣾⡿⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣤⣤⣄⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠈⢀⠀⠀⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⡽⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⠝⠓⠀⢸⣿⣧⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⡿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠹⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⣤⣄⣄⡤⠀⠀⢘⣿⣿⣿⣿⣿⣸⣿⢐⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⣹⣿⣿⣿⢋⡀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⣻⣶⡄⠀⠀⠾⢻⣿⣿⣿⣿⣿⣛⠁⣠⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣵⣿⠟⡯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⠁⠀⠀⠀⠀⣿⣿⠗⠀⡉⣠⣾⣿⣿⣿⣿⣿⡿⠿⠫⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣾⡟⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡟⠀⠀⠀⠀⣰⣿⣇⣤⣴⣿⣿⣿⡟⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠁⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠆⠄⣴⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣾
⠀⠐⠟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⣿⡷⠖⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣾⣶⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿
⣉⣀⣠⡀⣀⣤⣿⣿⣶⠿⣿⡟⠻⣿⣧⡈⠀⠈⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿
⣿⣿⣿⣿⣿⣿⡝⢻⣿⣶⠋⢰⡄⠈⠙⢿⣷⣤⣶⣶⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠿⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⡛⠁⢿⣿⣿⣿⣷⠉⢁⣿⣿⣿
⣿⣿⣿⣏⠻⣿⣷⣦⠙⢻⣦⠈⠛⠇⠀⠀⠙⢟⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠠⣷⡀⠛⣾⡿⣼⣿⣾⣿⣿⣿
⣻⠟⢻⣿⣷⡿⠻⣽⣶⡀⠙⢷⣄⡀⠀⠀⠀⠀⠁⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣟⣋⡃⠘⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡼⠋⠀⣶⣌⢱⣾⣿⠹⢿⠟⣼⣿⣿⣿
⢿⣦⡄⠙⠃⠀⠀⠙⢿⣿⢇⡈⠻⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠁⠉⠉⣽⠟⠀⠀⠀⣸⣿⣿⣿⣿
⠿⠟⢻⣤⡀⠀⠀⠀⡀⠐⠉⠁⠀⠀⣙⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣴⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣶⡿⠟⠛⠛⠛
⠀⠀⠈⠙⠛⠂⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣻⣛⡇⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠀⠀⠀⢄⣤
⠀⠐⠂⠂⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⠿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⠀⠀⠀⠀⠀⠀⢄⡀⠀⣒⠤
⠶⠖⢲⣦⣤⣤⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢰⣶⣶⣦⣤⣤⣤⠀⢠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣤⣤⠀⢰⣿⣯⣷⣽⣦⣀⡀
⠀⠛⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠠⢾⣿⣿⣿⣿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡇⠀⢈
⠔⠂⣻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡟⠻⣻⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡏⢀⣾
⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣄⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢀⣿⣿⣿⢸⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣷⣄⣸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣄⣿⣿⣿⣇⣿⣿⣿⣿⣿⠟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡟⢺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣧⠙⠿
⢟⣻⣿⣿⣿⣇⣸⣿⣿⠃⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⢺⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠉⠉⠉⢻⣿⣿⣹⣿⣿⣿⣿⣿⣿⣾⣏⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⢉⣻⣄⢈⣻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⡁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠘⠛⠛⠛⠛⣻⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣴⢠⡄⢻⣿⣿⣿⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡗⠝⠶⠂⠸⣿⣿⣿⣸⣭⣸⣿⣿⠟⠃⠁⠅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⠀⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠯⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢀⡄⢠⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠘⠳⠖⠀⢸⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⢰⡦⣤⠀⣿⣿⣿⣿⡆⠀⢸⣿⠿⣯⣩⡙⠛⠿⠿⠟⣯⢋⡈⢛⡛⢿⡆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣶⡏⠉⠉⢹⣷⣏⢃⢰⣏⣱⣤⣼⣧⡄⣶⣷⡻⣾⡽⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣤⣤⣄⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠐⠀⠀⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠱⡹⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢿⠟⢇⡀⢠⣿⣇⣽⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⠿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠋⠹⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣄⣄⡤⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⠠⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⢋⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⠿⢻⣦⡄⠀⠀⣾⢿⣿⣿⣿⣿⣿⣟⠖⢀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣵⣿⠟⡯⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠇⠀⠀⠀⠀⣿⣿⠗⠀⡘⢉⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⣿⠀⠀⠀⠀⢀⣿⣏⣀⣬⣾⣿⣿⣿⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠋⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠶⢆⣀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⢀⡀⣖⣶⣶⣶⣾
⠀⠀⢿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠘⢿⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢳⣧⣤⣮⣿⣶⣶⣷⣿⣿⣿⣿⣿
⠐⠀⢀⡀⠀⣀⣾⣿⣭⣿⣻⣿⠿⣿⣧⠈⠋⠈⠃⠀⡘⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿
⣿⣿⣿⣵⣿⣿⡟⢿⣿⣤⡞⢁⣄⠈⠻⣿⣦⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⢴⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣎⠸⠋⢹⣿⣿⣿⣿⠉⠃⣼⣿⣿
⣿⣿⣿⡝⠿⣿⣯⣄⠙⢿⣇⠘⠻⠄⠀⠀⠙⢿⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠊⣴⡈⠻⣹⣿⢉⣷⣮⣿⣿⣿
⣿⡿⢿⣿⣷⣾⢿⣿⣤⡀⠻⣷⣄⠀⠀⠀⠀⠀⠀⢵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠛⠳⠘⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡜⠁⢠⣈⠓⣴⣿⠿⣿⡿⢩⣿⣿⣿
⣿⣇⡀⠛⠟⠁⠀⠹⣿⣿⡆⠈⠿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⢿⢿⣶⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠏⠀⠊⠋⠛⢰⣿⠋⠀⠀⢀⣿⣿⣿⣿
⢾⡿⣿⣀⡀⠀⠀⠀⠀⠁⠶⠋⠀⠀⠃⢁⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⡄⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢠⣾⡿⠿⠿⠿
⠀⠀⠈⠛⠿⠆⠀⠀⠐⠀⠀⢀⣠⣴⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠟⡇⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠟⠋⠀⠀⢀⣀
⠀⠠⠄⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠠⢍
⣤⡤⢤⣴⣶⣤⣤⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⣹⣧⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣤⣤⠀⢠⣶⣶⣶⣵⣦⠉⠁
⠀⠶⣾⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠠⢸⣿⣿⣿⣿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⡏⠉⠉
⢠⠄⢾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⠀⣴
⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣄⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿
⣷⣄⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣇⣻⣿⣿⣿⣟⡟⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⢺⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⡇⢻⣿⣿⣷⣿⣿⣿⡧⠙⠻
⡿⢿⣿⣿⣿⣇⢸⣿⣿⠃⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⡋⢻⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣺⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠉⠉⠉⢻⣿⣿⢛⣿⣿⣿⣿⣿⣿⣾⣟⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⢙⣁⠘⣛⣛⣛⣻⣿⣿⣿⡗⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠋⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠿⠿⠿⠿⣿⠋⠉⠀⢄⣄⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⢀⡄⣀⠸⣿⣿⣿⣇⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢼⠷⠴⠀⣿⣿⣿⡏⣯⣝⣿⣿⣿⠿⠉⠈⠅⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡻⠁⠘⠀⠀⠀⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⡠⢀⡀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠂⠻⠦⠆⢰⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣤⣠⡀⢸⣿⣿⣿⣷⠀⠀⢸⣿⠿⣿⣩⡙⠛⠿⠿⠟⣯⠋⡘⢛⡛⢿⡄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣷⣶⣶⣾⠉⠉⠉⢹⣶⣿⢃⢰⣏⣹⣤⣴⣦⡆⣾⣷⡻⣾⡽⢿⣿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣯⣤⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠋⢹⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢒⡶⠔⠆⠀⣿⣷⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠻⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⡄⢀⡤⠀⠀⣿⣿⣿⣿⣿⡊⣿⡏⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⢋⡀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣟⣄⠀⠀⢰⡿⣿⣿⣿⣿⣿⣿⡓⠊⣹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣵⣿⠟⡯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⠀⠀⠀⠀⢹⣿⣿⠉⠀⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠾⣿⣿⡟⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠈⢹⡇⠀⠀⠀⠀⣸⣿⣉⣀⣴⣾⣿⣿⡿⢿⣿⣿⣿⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠘⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢴⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣴⣶⣖⣾
⠀⢸⡏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⠻⣷⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡿⣦⣤⣴⣦⣿⣶⣶⣷⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⢠⣿⣏⣿⣿⣿⣿⣿⣿⡀⠹⠋⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢳⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿
⣶⣾⣯⣴⣿⣿⢻⣿⣯⣡⠿⣀⠈⠻⢿⣦⣄⢠⣤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⣴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣴⣩⡿⠋⣿⣿⣿⣿⡿⠻⠁⣾⣿⣿
⣿⣿⣿⠿⣿⣿⣦⠙⢿⣿⠀⠛⡷⡄⠀⠉⢿⣿⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⡱⢠⣄⠙⠟⣽⡟⣻⣦⣾⣻⣽⣽
⣿⣿⣿⣷⣼⣿⣿⣣⣄⠙⢷⣄⠀⠀⠀⠀⠀⠁⢐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠇⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠎⠀⣈⡻⣤⣼⣿⢿⣿⡟⣽⣿⣿⣿
⣿⠁⠙⠿⠟⠀⠐⢿⣿⣷⡄⢻⣿⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣷⣶⣶⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠙⠻⠃⣾⡿⠁⠈⠉⢸⣿⣿⣿⣿
⣿⣿⣆⡀⠀⠀⠀⠀⠉⠩⡞⠀⠈⠑⠳⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣈⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⣴⣿⡿⠿⠿⠿
⠁⠀⠙⠿⡦⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢻⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠁⠀⠀⢀⣄
⠀⣀⣀⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣶⣦⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉
⣀⡠⣤⣤⣶⣴⣤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠈⢽⣭⣭⣥⣤⣤⣤⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣦⣤⠀⢠⣶⣶⣵⣦⡄⠂⠀
⠡⣤⣼⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⢀⣸⣿⣿⣿⣿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡗⠓⢒
⣤⠀⢿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡇⢀⣾
⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢠⣤⣤⣄⡀⠀⣿⣿⣿⡏⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⡆⢀⣿⣿⣿⢸⣿⣿⣧⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿
⣆⠀⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⡟⣿⣿⣿⣿⣟⡛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⡇⢻⣿⣿⡿⣿⣿⣿⡟⠛⠻
⡿⢿⣿⣿⣿⡇⢹⣿⣿⠇⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣷⣸⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣷⣦⣤
⣾⣿⣿⣿⣿⣿⣬⣉⠉⠀⠉⠉⠻⣷⣬⡻⢻⣿⣿⣿⣿⣿⣯⣬⡉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠙⢛⠀⠸⡿⢿⢛⣿⣟⣫⣟⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠛⢉⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠘⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⢽⡿⣿⡿⢿⡿⠋⠉⢀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⣴⠠⠄⢻⣿⣿⣿⢴⣤⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠛⠓⠃⢸⣿⣿⣿⣼⣶⣼⣿⣿⣿⠿⠋⠁⠁⢈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⢆⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠛⠛⠿⠿⢿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢠⡆⠤⠀⢸⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠈⠛⠚⠀⢸⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡷⢲⠶⠤⠀⣿⣿⣿⣿⡇⡄⠀⢸⣿⠻⣿⣉⡉⠛⠿⠿⠟⡏⢋⡈⢛⡛⢿⣄⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⢰⣶⣿⢃⢰⣍⣹⣤⣼⣧⡄⣾⣷⡻⣾⡿⢿⣿⣟⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⡎⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣦⣤⣤⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡷⣏⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠀⠀⠀⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢶⡿⠆⠀⢸⣿⣧⣼⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⠿⡿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠹⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⡄⠀⠤⠀⢈⣿⣿⣿⣿⣷⣤⣿⠐⣄⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⢋⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢻⣯⡆⠀⠀⠾⠛⣿⣿⣿⡿⢿⡯⠀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣵⣿⠟⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⠇⠀⠀⠀⠀⣿⣿⡇⠀⠈⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠃⠀⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢽⠀⠀⠀⠀⢠⣿⣍⣤⣴⣿⣿⣿⣿⠛⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠦⣠⡄⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣾⣿⣿⣿
⠀⡾⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⡌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢻⣷⣶⣾⣮⣿⣇⣶⣷⣿⣿⣿⣿⣿
⠄⣀⡀⠀⣀⣼⣿⣽⣿⢿⣿⠿⣿⣷⡀⠉⠀⠀⠀⡈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢸⡿⣿⣿⣿⣿⣿⢿⣿⣿⠓⣽⣿⣿
⣿⣿⣷⣿⣿⣯⠻⣿⣷⡞⠃⣀⠈⠙⢿⣶⣄⣴⣦⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣾⠼⠛⢸⣿⣿⣿⣿⡖⠁⢰⣿⣿⣿
⣿⣿⣟⠻⢿⣿⣦⠙⠻⣧⠀⠙⠇⠄⠀⠘⠿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢴⡄⠙⢳⣿⢫⣿⣾⣽⣷⣿⣿
⣿⠿⣿⣷⣾⠿⢿⣦⣄⠙⢵⣆⡀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⡛⠈⢓⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁⢠⣄⠙⣴⣿⡟⣿⡿⢣⣿⣿⣿⣿
⣧⣀⠉⠛⠁⠀⠘⢻⣿⡷⣀⠿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⡿⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠈⠙⢳⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿
⡿⢿⣧⡀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⣃⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⡆⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⠿⠟⠛⠛⠛
⠀⠀⠙⠻⠆⠀⠀⠈⠀⠀⢀⣠⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⠟⢣⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⠀⠀⠀⣤⣤
⠠⠤⠄⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠿⢿⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣤⣤⡄⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠀
⠤⠔⢶⣦⣥⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠐⢣⣴⣦⣤⣤⣤⣤⠀⢠⣤⣤⣤⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⢰⣾⣷⣼⣶⡌⠁⠀
⠲⠶⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠤⢸⣿⣿⣿⡿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡏⠉⣡
⠖⠐⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⡦⢼⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠗⢽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡇⣰⣿
⠐⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢠⣤⣤⣤⡀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡇⢀⣿⣿⣿⢸⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣟⣈⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣼⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡗⢺⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡏⠻⠿
⣛⣯⣿⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣾⣍⡉⠀⠉⠉⠻⣿⣾⢛⣿⣿⣿⣿⣿⣿⣿⣾⠉⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⣙⣏⡀⣛⣛⣛⣻⣿⣿⣿⡿⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⢋⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⢀⡈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠿⠿⠿⠟⢿⡋⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢀⡄⢤⢨⣿⣿⣿⣿⣴⣄⣿⣿⣿⠘⢾⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠚⠓⠶⠀⣿⣿⣿⣿⣸⣶⣿⣿⣿⠷⢚⣛⡽⢃⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠈⠉⢉⠐⢖⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣠⠀⡄⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡗⠛⠳⠒⠀⣿⣿⣿⡇⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣷⣀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠶⣶⢤⡄⢸⣿⣿⣿⣿⠀⠀⢸⣿⠿⣏⣩⡉⠛⠻⠿⠟⣯⠋⡈⢛⡛⢿⣆⡌⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣶⣾⡏⠉⠉⢹⣶⣿⢁⢰⣏⣱⣤⣼⣥⡆⣶⣷⡻⣾⡿⢿⢿⣟⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣸⣿⣿⣿⣿⣻⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣶⣦⣤⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣉⣝⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠰⡹⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠺⢛⠏⠂⠀⢸⣿⢦⣿⣿⡿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⡿⣿⣿⣿⣯⣭⣿⣿⡿⠉⠛⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣤⠤⠄⠀⠀⢸⣿⣿⣿⣿⣷⣼⣯⠤⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣿⣿⣿⢋⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠻⢏⣤⡄⠀⠀⠟⢻⣿⣿⣿⡿⣿⠏⠙⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣵⣿⠟⡯⢆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⠀⠀⠀⠀⠈⣿⣿⠂⠀⢐⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣿⣿⠃⠀⠆⠀⠀⠢⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⣰⣿⣤⣤⣶⣿⣿⣿⡿⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠄⠄⣠⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⠜⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⢀⠀⣀⣠⣶⣿⣿⣽
⠀⠰⠿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢶⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢻⣾⣶⣾⣶⣶⣶⣷⣿⣿⣿⣿⣿
⠀⢄⣀⡀⢀⣀⣾⣿⣼⣿⢿⣿⠿⣿⣧⡀⠉⠀⠀⠀⡀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢸⡿⣿⣿⣿⣿⣿⢿⣿⣿⠉⣿⣿
⣿⣿⣿⣾⣿⣿⣯⠻⣿⣷⡞⠣⣄⠀⠙⢿⣶⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⡾⢼⠋⢸⣿⣿⣿⣿⡃⠀⢴⣿⣿
⣿⣿⣿⣏⠻⢿⣿⣦⡙⠻⣧⡀⠛⠇⠀⠀⠘⢿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢴⡄⠙⣱⣿⣣⣿⣶⣿⣿⣿
⣟⢿⠿⣿⣷⣾⠿⢏⣶⣄⠉⢿⣦⡀⠀⠀⠀⠀⠀⠹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣟⣛⣙⠈⢓⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡞⠁⣠⣄⠑⣶⣿⡟⣿⡿⢱⣿⣿⣿
⠿⣧⣀⠙⠛⠁⠀⠈⠻⣿⠷⣀⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠀⠈⠈⠉⢠⣿⠃⠀⠀⢀⣿⣿⣿⣿
⠿⠿⠿⣤⡀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠁⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡦⡆⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠀⢰⣿⠿⠛⠛⠛
⡀⠀⠀⠙⠛⠂⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡟⡗⣳⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⣠
⠄⠠⠤⠄⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠿⢿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⡄⠀⠀⠀⠀⠀⢄⡀⠀⠐⠤
⣤⠤⢶⣶⣬⣤⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⢰⣧⣴⣦⣤⣤⣤⠀⢠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣤⣤⠀⢠⣶⣾⣷⣼⣦⣄⡀
⠀⠲⢿⣿⣿⣿⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠀⢼⣿⣿⣿⣿⡿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡇⠈⠉
⠦⠂⢿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡏⢀⣴
⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢀⣤⣤⣄⡀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⣿⣿⣿⢸⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿
⣿⣦⣸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡇⢀⣿⣿⣿⣀⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⠃⢸⣿⣿⣟⣈⣿⣿⣿⣠⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡗⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⡗⢹⣿⣿⡇⢿⣿⣿⣷⣿⣿⣿⣇⡎⠿
⡿⣛⣿⣿⣿⣇⣸⣿⣿⠇⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⡇⣼⣿⣿⣿⡏⢻⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣧⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠉⠉⠉⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠉⠁⠉⠉⠉⣉⣅⡈⣛⣛⣻⣽⣿⣿⣿⡿⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢀⡈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠛⠓⠿⠟⠿⠛⣿⡋⠈⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠩⠾⢛⢛⡿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⣿⡽⠂⠀⠀⠀⣠⢍⡁⠂⠂⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣰⡆⣦⠐⣿⣿⣿⣿⣿⠡⠚⠁⠀⠀⠀⣀⣀⣀⣼⣶⣶⣶⣶⣶⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠿⠞⠃⣿⣿⣿⣿⡃⠠⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢒⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⡾⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡯⠀⣽⣿⠿⣿⣩⣙⠛⡿⠿⠟⣿⣟⡉⢛⣟⣿⣆⡌⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣭⣴⣶⣿⢇⢸⣟⣹⣤⣼⣷⡧⣾⣷⣻⣿⣿⢿⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⢿⣿⣿⣸⣿⣿⣿⣿⣻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣶⣶⣶⣤⣄⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⢿⣿⣿⣿⡇⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣶⣿⣯⣍⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠨⠿⠁⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣿⣿⣿⣿⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢟⢻⢿⡇⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣷⡤⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⣃⠈⢹⣽⣿⣿⣿⢻⡓⠈⠺⣻⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠿⣿⣿⡿⠉⠀⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣤⡦⡜⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠵⣭⣿⣿⡿⡿⣇⠅⠀⠀⠉⠿⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣿⡧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡲⣾⣿⠿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡟⠀⢰⠀⠀⠹⠶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⡏⠘⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⢽⡐⢘⢝⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⡠⡗⠀⠀⠀⠈⠈⠻⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣷⣶⣿⡅⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠧⠐⠁⠀⠀⠀⠀⠀⠀⠀⠙⢛⠮⠛⢿⠻⢢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣯⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣦⣀⣀⣀⣠⣀⣶⣶⣿⣿⣿⣿⣿⣿
⣰⣿⡷⠞⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣤⣥⣮⣠⣽⣿⣿⣿⣿⣿⡿⢿⣿⣦⣻⣿⡿⣿⣤⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣦⡙⠻⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⠷⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣿⣿⡟⢱⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣮⠻⣿⣏⠻⣿⡿⢀⠈⠻⣿⣏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣤⠟⢿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣷⣌⢿⣷⣄⡙⠿⢠⣤⠈⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣟⡟⢻⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣎⠛⢯⣤⡘⠿⣿⣿⣧⡽⠿⣷⣄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⢿⣿⣿⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣁⠾⠿⠿⢻⣿⠟⠀⢿⢇⣼⣿⣿⣿⣿
⠿⢿⣿⣶⣦⡝⠋⢀⡈⠻⠟⠃⠀⠈⣻⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣔⠿⠋⣼⣷⣠⣿⡿⠟⠛⠿⠻
⡀⣀⠙⠛⠿⠛⣤⡀⠋⠀⣀⣤⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢻⣿⣿⣻⡟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠉⠁⠀⠀⠻⠿⠟⠋⠀⢀⠠⣴⣶
⠴⠾⠷⠆⢀⢀⠈⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠿⢿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣤⡄⠀⠀⠀⢀⣠⣄⠉⣓⣶⣤
⠶⠶⠒⠛⠹⢬⣰⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⡆⢴⣿⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⡁⢀⠀⣿⣿⣿⣿⣿⣦⣁⣀
⠚⠿⣿⣿⡿⢟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣯⡟⠓⡾⠏⠛⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣚⣀⡙⠿⣿⣾⣿⣋⣀⣀⡉⣩
⣿⡟⢫⣷⡾⠿⠛⣋⣿⡿⠏⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠻⣿⣿⣿⣿⣾⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠿⣷⣤⣿⣿⣿⣦⣬⣻⣿⣿⣭⣯⣶⣿
⠾⠻⠿⢻⣶⣶⣾⣿⡟⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣿⠻⣿⣤⣌⠁⣉⣀⡀⠉⣫⣿⣿⣿
⣷⣄⠀⠉⠙⠻⠏⣉⠾⣿⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣯⣽⠅⠀⠀⠀⠀⠀⠀⠀⢉⣱⣿⣿⣗⡼⣿⣿⣷⡛⢟⣿⣾⣿⣿⣿⣿
⣿⣿⣧⣄⡀⢴⡾⢿⣁⡰⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠙⢛⣛⠛⢻⣟⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⣼⣿⣧⠀⠈⣻⣷⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣄⠀⠀⠁⠠⣬⢻⣿⣯⠙⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡊⢉⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠘⠚⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣅⣹⣿⣿⣿⣿⣿⣿⣿⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣠⣶⣎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⢻⣿⠛⢻⣿⣿⡿⢿⣿⣃⣧⣶⣿⣧⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡟⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⣠⢦⣔⢻⣿⣿⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠿⠿⠿⢰⣿⣿⣿⡇⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠛⣛⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⣉⣭⣌⣤⣼⣿⣿⣿⡛⢋⣉⣤⣀⣼⣿⣄⣠⣠⣦⣼⣿⣿⣿⡌⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠔⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣤⣄⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⡉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠄⢙⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢿⠿⢿⣿⣿⣿⡿⣿⡣⠱⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣶⣶⣚⣉⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣮⡿⠁⠸⣿⣿⣿⣿⣿⣶⣿⣛⣫⣻⣿⣿⣿⣿⣷⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠠⠆⠔⠀⠀⠰⠈⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⡿⣿⠿⠛⠋⢛⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⣿⣿⣿⣥⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡎⠀⠘⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠿⣿⣿⡿⠉⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⣰⡶⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣾⣿⣿⠃⠀⠀⠙⡻⠿⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⡇⢀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣾⣿⣿⡿⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡟⠀⡆⠀⠀⠹⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⡉⣿⠳⠉⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠓⠟⠋⠪⠓⢑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣠⡇⠀⠀⠀⠀⠘⢿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⣺⣷⣛⡐⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠣⠔⠁⠀⠀⠀⠀⠀⠀⠉⠘⣙⠟⠻⢟⡯⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⡞⠂⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠘⣿⣿⣄⣀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿
⣰⣿⡷⠟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣠⣥⣦⣘⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⠻⣿⡿⣿⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣌⡙⢿⣿⣯⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣿⣿⡿⢻⣿⣿⣿⣿⡿⠿⣼⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣷⣝⢻⣿⣌⢿⣿⣷⢀⠙⢿⣿⣏⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣬⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣀⡸⠟⢃⣀⠈⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⢟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣏⠻⣯⣄⠙⢿⣿⣿⣆⣿⣿⣧⡀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣁⣾⠿⠿⢻⣿⡟⡡⢿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣬⡑⠓⣀⠉⠿⠿⠃⠀⠙⢿⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣼⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣀⣴⠿⠋⣾⣮⢠⣾⣿⠿⢻⠿⢿
⣀⡈⠙⠿⠿⠷⣤⠈⠃⠀⣀⣠⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⣿⣿⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠁⠀⠀⠿⠿⠿⠋⠀⠀⢀⣴⣶
⡤⠽⠤⠦⠀⢀⠉⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⣤⡄⠀⠀⠀⠀⢄⣐⠛⠲⢤⣁
⡦⠴⠶⠞⠯⢬⣡⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡁⠀⠐⣿⣿⣿⣿⣿⣍⡉⠁
⠲⠷⣶⣾⡿⠟⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢘⣟⡿⠢⣿⠟⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠿⠚⣙⠻⢿⣷⣿⣿⠋⣁⠉⠉⣩
⣶⠞⢏⣧⡶⠿⠟⢫⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⣷⣶⣷⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣟⣧⣄⣿⣿⣷⣤⣝⣿⣿⣯⣛⣯⣵⣿
⡼⠿⡿⣿⣦⣤⣾⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣜⣿⣿⣷⣤⣉⠉⢉⡁⠉⠙⣛⣿⣿⣿
⣧⡀⠈⠙⠻⠿⠟⢉⢿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣈⣹⣿⣿⣿⣿⣿⣿⣿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠋⣡⣿⣿⢇⣾⣿⣿⣦⠻⠿⣣⣶⣿⣿⣿⣿
⣿⣿⣦⣀⡀⢤⡾⣿⣉⡴⣾⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⢻⠿⠿⢻⣿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡏⣰⣾⣧⠀⠙⢻⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣉⠀⠀⠁⢠⡜⢿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡂⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⡿⠛⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠑⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣅⣻⣿⣿⣿⣿⣿⣿⣿⠟⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⢻⢿⠟⢿⣿⣿⡿⣿⣿⣋⣧⣶⣾⣶⠀⠀⠀⠀⠀⠀⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⡄⣤⢐⣿⣿⣿⣿⣤⣼⣿⣿⣿⢁⣭⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠳⠶⠋⣿⣿⣿⣿⣻⣶⣿⣿⢿⠉⢿⣟⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⢀⠄⣄⠀⣿⣿⣿⣿⠀⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⠾⠷⠖⢀⣿⣿⣿⡇⠢⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⢿⠿⢿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡷⣴⢠⡄⢸⣿⣿⣿⣿⢰⠶⣼⣿⣿⣿⣿⠿⠛⠛⠿⠿⣿⡿⠛⠋⠹⢿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣷⣾⡍⠉⠉⠉⠀⣠⣬⣿⣿⣿⠀⠉⠉⠠⠀⢠⣿⣆⡀⠀⢠⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣶⣶⣤⣄⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠶⠶⠿⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠒⠀⠀⠀⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣷⣶⠊⢉⣉⣉⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣘⠧⠙⠂⠘⣿⣷⣾⣿⣿⢿⣿⠿⠟⢽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣬⡄⢀⡄⠀⢀⣿⣿⣿⣿⣿⣴⣿⢴⣲⣺⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢟⣤⡄⠀⠀⠘⠻⣿⣿⣿⡿⢿⡟⠃⣠⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⡇⠀⠀⠀⠀⢿⣿⠟⢀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡟⠀⠠⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⢀⣿⣿⣤⣾⣿⣿⣿⣿⠟⠻⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠁⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠈⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⣠⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡶⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⢀⢀⣀⣰⣶⣾⣿⣾
⠀⠾⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡦⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣷⣾⣿⣮⣶⣶⣶⣷⣿⣿⣿⣿⣿
⠀⣀⡀⠀⣀⣼⣿⣧⣾⠿⣿⡿⠿⣿⣄⠈⠀⠁⠂⢀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠑⣿⢿⣿⣿⣿⣿⡿⣿⣿⡟⢩⣿⣿
⣿⣿⣿⣿⣿⣿⠙⢿⣿⣶⠋⢤⠀⠉⠻⣿⣦⣤⣶⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡶⡦⡟⠁⣿⣿⣿⣿⣿⠉⢠⣾⣿⣿
⣿⣿⣿⣙⠻⣯⣷⡌⠛⢿⣄⠈⠣⠆⠀⠀⠻⡟⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠡⣦⠈⢋⣾⣟⣽⣷⣿⣿⣿⣿
⡿⠿⢿⣿⣶⠿⢻⣷⣦⠈⠺⣷⣄⠀⠀⠀⠀⠀⠐⢵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣟⣛⠃⠘⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠋⠀⣠⡌⢢⣾⣿⢻⡿⠏⣾⣿⣿⣿
⣿⣤⡈⠙⠃⠀⠈⠻⣿⡿⢆⡘⠿⡗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠂⠈⠃⣾⡟⠀⠀⠀⣰⣿⣿⣿⣿
⠿⠟⣿⣄⠀⠀⠀⠀⠀⠐⠛⠁⠀⠈⢀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣶⡿⠟⠛⠛⠛
⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⢟⢚⡆⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⢠⣤
⠀⠤⠄⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣷⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄
⡤⠔⣿⣿⣿⣿⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡄⠙⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣾⣿⣿⣿⡧⡉⠀
⠐⠲⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠛⣿⣿⣿⣷⠄⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣿⣿⣿⠇⠈⠉⢉
⠐⠀⣿⣿⣿⣿⠟⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣘⣿⣿⣿⣿⠤⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⡧⣄⣿⣿⣿⣿⣾⣿⣿⣿⣈⠁⢀⣾
⠐⠙⣿⣿⣿⣿⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⡍⢉⣱⣿⣿
⣷⡄⣿⣿⣿⣿⠀⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠁⢠⣿⣿⣿⣃⣻⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠃⣿⣿⣿⣿⠛⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣹⣿⣿⣿⣇⣟⠛⢿
⢿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠙⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠁⠀⠙⢿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⢉⣛⣀⢙⣛⣿⣻⣿⣿⣿⣿⠛⠋⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠛⠚⠿⠿⠟⠻⡟⠁⠁⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢀⡤⣤⣸⣿⣿⣿⣧⣦⢿⣿⣏⢉⣴⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠈⠳⠿⠈⣿⣿⣿⣇⣷⣾⣿⣿⡘⠻⣟⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⢠⠀⡄⠀⣿⣿⣿⡏⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠷⠖⢰⣿⣿⣿⡇⢷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡶⡶⢤⠄⢸⣿⣿⣿⡇⣴⠶⢸⣿⣿⣿⣿⡿⣟⠛⠛⠻⢿⡿⠛⠉⠩⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣠⣬⣿⣿⣿⣄⡈⠉⠁⠀⢀⣾⣷⣀⠀⣠⣠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⡏⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣶⣶⣶⣤⣤⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⡿⠿⠿⠶⡛⠻⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⡿⣿⣶⣮⣉⣉⣉⣽⣿⡿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠒⠃⠋⠂⠀⣿⣷⣾⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣾⡄⢄⠠⠀⢀⣿⣿⣿⣿⣿⣦⣿⣤⢰⢼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⢯⣾⡄⠀⠀⠸⢻⣿⣿⣿⡿⠻⡿⠃⣠⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣦⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⠃⠀⠀⠀⠈⣿⣿⠇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢏⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⡿⠀⠰⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⣠⣿⣷⣤⣶⣿⣿⣿⣿⡟⠻⣿⣿⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⠖⠀⠀⠀⠀⠀⠀⠀⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡷⣠⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡶⠻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⢀⢀⣄⣴⣿⣿⣿⣾
⠀⠿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡶⡦⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣷⣶⣾⣧⣷⣷⣿⣿⣿⡿⣿⣿
⠅⣀⡀⠀⣀⣼⣿⣿⣿⡿⣿⡿⠿⣿⣆⠈⠡⠠⠀⢀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢼⣿⣿
⣿⣿⣿⣿⣿⣿⡙⢿⣷⣶⠋⢡⡀⠈⠻⣿⣦⣡⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⢾⠖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣶⡧⡛⠁⢿⣿⢿⣿⣿⠈⢁⣿⣿⣿
⣿⣿⣿⣝⠻⣿⣷⣌⠛⢿⣆⠀⠻⠀⠀⠀⠻⠿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠠⣦⡈⠋⣾⡟⣼⣿⣾⣿⣿⣿
⣿⡿⢿⣿⣶⡿⢿⣹⣦⡈⠹⣷⣄⠀⠀⠀⠀⠀⠐⢵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣟⣉⠃⠐⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢠⢴⣌⢣⣾⣿⢹⡿⠏⣾⣿⣿⣿
⢿⣤⡈⠙⠋⠀⠀⠻⣿⡿⢇⡈⠿⡗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⠈⠓⣼⡟⠁⠀⠀⣸⣿⣿⣿⣿
⠿⠿⢿⣄⠀⠀⠀⠀⠀⠐⠚⠁⠀⠈⢐⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⢴⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣶⡿⠟⠛⠛⠛
⠀⠀⠈⠛⠛⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣛⢛⡆⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠁⠀⠀⢠⣤
⠀⠠⠤⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣤⣤⠀⠀⠀⠀⠀⠠⢀⠀⠀⠠⠄
⡤⠖⣿⣿⣿⣿⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡀⠺⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣧⣈⠀
⠐⠲⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠛⣿⣿⣿⣷⠄⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣿⣿⣿⠇⠈⠉⢉
⠲⠂⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣘⣿⣿⣿⣿⠤⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⡇⢄⣿⣿⣿⣿⣾⣿⣿⣿⣌⠁⢀⣾
⠀⠙⣿⣿⣿⣿⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⠐⣿⣿⣿⣿⣿⣿⣿⡍⢉⣵⣿⣿
⣷⡄⣿⣿⣿⣿⠀⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠁⢠⣿⣿⣿⣃⣹⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠁⣿⣿⣿⣿⠓⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣹⣿⣿⣿⣧⣍⢙⠻
⢿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠙⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠁⠀⠙⢻⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⢉⣻⣀⢙⣛⣛⣻⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⣀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠛⠛⠘⠿⠿⠟⢻⣿⠁⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣍⣙⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣠⢠⡄⣾⣿⣿⣿⣤⣼⣿⣏⢉⣹⣭⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠻⠶⠟⢸⣿⣿⣿⣹⣾⣿⣿⡘⠳⣞⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⡄⢠⠀⢸⣿⣿⣿⢀⣸⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠾⠳⠶⠂⣾⣿⣿⣏⠸⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⢴⣦⡄⠀⣿⣿⣿⣿⢰⠶⠄⣿⣿⣿⣿⣿⡿⣟⡛⠛⠻⢿⡿⠛⠋⣩⣽⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⣶⡏⠉⠉⠁⠀⠀⣤⣼⣿⣿⣿⣆⡈⠉⠉⠀⣀⣼⣿⣄⠀⢀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣶⣤⣤⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠷⠚⠻⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⠂⠀⠀⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⠿⣿⣶⣮⣉⣉⣉⣽⣿⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠚⡺⠋⠃⠂⢸⣿⣤⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣮⡄⠄⠤⠀⢘⣿⣿⣿⣿⣿⣼⣿⢄⣦⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣯⣬⠀⠀⠀⠿⣿⣿⣿⣿⠿⣿⡯⢃⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣴⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡏⠀⠀⠀⠀⢹⣿⣿⠏⠀⠔⣰⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠠⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠇⠀⠆⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⢀⣼⣿⣧⣴⣶⣿⣿⣿⣿⠛⢿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠠⡇⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠘⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣀⠀⠀⠀⠀⠀⢀⢀⣄⣴⣶⣾⣧⣿
⢸⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⡶⡌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣧⣶⣷⣶⣷⣷⣿⣿⣿⡿⣿⣿
⢀⣀⠀⠀⣀⣿⣿⣭⣿⢿⣿⠿⢿⣧⡀⠓⡈⠘⠀⡈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣟⠿⣿⣷⡼⠋⣄⠈⠙⢿⣷⣄⣴⣦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣶⠼⠛⠡⣿⣯⣿⣿⡟⠉⣰⣿⣿⣿
⣿⣿⣯⡻⢿⣿⣦⡙⠻⣷⠀⠹⠇⠀⠀⠐⠿⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢴⡆⠙⢻⣿⢧⣿⣾⣽⣿⣿⣿
⡿⠿⣿⣷⣾⠿⣏⣷⣄⠑⢷⣆⡀⠀⠀⠀⠀⠀⠺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣛⠛⠈⢛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡵⠁⢠⣆⡙⣴⣿⡟⣿⡿⢣⣿⣿⣿⣿
⣯⣀⠉⠛⠁⠀⠘⠿⣿⡷⣀⠽⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⣿⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠐⠊⠚⢃⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿
⡿⠿⣧⡀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠙⣃⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⣆⡆⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⣾⠿⠟⠛⠛⠛
⡀⠀⠙⠻⠗⠀⠀⠈⠀⠀⢀⣠⣴⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠟⢳⠐⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠟⠉⠀⠀⠀⣠⣤
⠠⠤⠄⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣷⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣤⣤⡤⠀⠀⠀⠀⠀⠄⡀⠀⠀⠤⠀
⠤⠔⣿⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡄⠅⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣾⣿⣿⣿⣍⡁⠀
⠲⠶⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠛⣿⣿⣿⣷⠀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣿⣿⣿⠇⠉⠉⢡
⠶⠐⣿⣿⣿⣿⠛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⡧⡀⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⣰⣿
⠐⠳⣿⣿⣿⣿⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⡏⢉⣾⣿⣿
⣆⠀⣿⣿⣿⣿⠀⣹⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⢠⣿⣿⣿⣇⣻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠂⣿⣿⣿⣿⠃⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣼⣿⣿⣿⣇⣙⠙⠿
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣏⡉⠉⠁⠀⠹⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⣙⣛⡀⢛⣛⣛⣻⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠉⠀⠈⠙⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⢀⡈⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠿⠿⠿⠿⢿⠟⠈⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣉⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⡴⢤⣤⣿⣿⣿⡷⡶⣿⣿⡀⡩⣷⣿⣽⣿⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠛⠛⠣⣿⣿⣿⣧⣷⣿⣿⡇⠙⢺⣙⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⢠⠀⠤⠀⣿⣿⣿⡇⡠⢽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠓⠚⢀⣿⣿⣿⡇⢳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡗⣶⠶⠆⢸⣿⣿⣿⡇⠖⠖⠸⣿⣿⣿⣿⣿⣟⣿⣭⡍⠉⠙⢻⡟⠉⠁⠤⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣦⣀⣀⣀⣀⣤⣿⣿⣄⣀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣷⣶⣶⣶⣦⣤⣄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⠙⣩⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⢿⣿⣿⣿⣿⣿⠛⢛⣛⣛⣉⣛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⢹⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣧⣤⣤⣤⣾⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠚⡟⠫⠐⠀⣿⣿⣶⣿⣿⡿⣿⣿⠟⢟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣤⣄⠄⠀⠀⣻⣿⣿⣿⣿⣷⣿⣿⡶⢺⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢛⣷⡆⠀⠀⠐⠛⣿⣿⣿⣿⠿⣿⡿⣡⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣷⣶⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣾⣿⡇⠀⠀⠀⠀⣻⣿⠿⠂⠀⣠⣾⣿⣿⣿⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢺⠀⠀⠀⠀⣠⣿⣿⣷⣶⣾⣿⣿⣿⣟⣙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠼⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⡆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⡀⠀⢀⢀⣔⣶⣿⣿⣿⣿
⠻⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣖⡈⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⢹⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⣿
⣀⡀⡀⣀⣼⣿⣿⣾⠿⣿⡿⠻⢿⣷⣀⠑⠄⠈⢀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⢃⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠻⣿⣷⡞⢡⣆⠀⠙⠿⣿⣤⣶⡷⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠺⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡘⠃⢸⣿⣿⣿⣿⣏⢀⣼⣿⣿⣿
⣿⣿⣏⡻⣿⣿⣦⠙⢻⣧⡀⠛⠷⠀⠀⠘⠿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢿⡄⠙⣽⣿⣱⣿⣿⣾⣿⣿⣿
⠿⠿⣿⣿⡿⠻⣿⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠺⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣋⣙⠀⣹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠔⣦⠙⣾⣿⠛⡿⠟⣼⣿⣻⣿⣿
⣧⣄⠉⠛⠀⠀⠙⠻⡿⢇⡀⠻⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⡀⠀⠀⠉⣹⡟⠁⠀⠀⢠⣿⣿⣿⣿⣿
⠿⢻⣦⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢉⣲⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡆⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⡿⠛⠛⠙⠉⠉
⠀⠀⠉⠛⠂⠀⠀⠈⠀⢀⣠⣴⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⣋⣇⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠰⠋⠁⠀⠀⠠⢤⠤
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⡿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⢀⠤⡀⠀⣐⡦⠠
⠶⠒⣿⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡌⠇⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣁⣀⠀
⠛⠲⣿⣿⣿⣿⣀⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⣛⣿⣿⣿⣿⠀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠿⠃⣿⣿⣿⣿⣶⣿⣿⣿⡇⡀⠀⣤
⠂⠈⣿⣿⣿⣿⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠔⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣾⣿
⠉⠓⣿⣿⣿⣿⠘⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡿⣿⣿⣿⣇⠻⣿⣿⣿⣿⣿⣿⣿⣅⣬⣿⣿⣿
⣦⠀⣿⣿⣿⣿⠀⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⠉⠉⠁⢠⣿⣿⣿⣇⣹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿
⣿⣷⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠁⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣾⣿⣿⣿⣧⣍⠙⠻
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⢻⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣯⡉⠉⠁⠀⢹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⣹⣟⣀⣛⣻⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⣀⡁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠛⠋⠛⠛⠛⠛⣿⠋⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢠⢠⣄⢼⣿⣿⣿⣤⢽⣿⠀⡨⣵⣽⣽⣿⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠘⠷⠞⢸⣿⣿⣿⣻⣾⣿⡇⠙⢶⣙⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠿⢿⣿⡟⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⡤⢠⠀⢸⣿⣿⣿⠀⠜⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠶⠂⣾⣿⣿⡏⠰⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢤⣦⡤⠀⣿⣿⣿⣿⢰⠲⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡍⠉⠙⣿⡟⠉⠩⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣀⣴⣿⣷⣄⣀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣶⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣶⣦⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⡉⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⢿⣿⣿⣿⣿⣿⣿⠛⣛⣛⣛⣛⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⠂⠀⠀⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣧⣤⣤⣼⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠘⡞⠛⠋⠄⢸⣿⣧⣼⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣄⠄⡠⠀⢘⣿⣿⣿⣿⣿⣼⣿⣤⡐⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⢻⣦⠀⠀⠀⠾⢿⣿⣿⣿⡿⣿⢏⠉⣱⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣷⣿⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⠀⠀⠀⠀⢘⣿⣿⠋⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⡁⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡟⠀⠀⠀⠀⠐⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡟⠀⠀⠀⠀⣰⣿⣯⣤⣾⣿⣿⣿⣿⠟⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⣴⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡾⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠀⠀⠀⠀⠀⢀⢀⣀⣤⣿⣿⣿⣼
⠠⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣶⡆⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡟⣿⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⢀⣀⠀⠀⣀⣿⣿⣿⣿⡿⣿⡿⠿⣿⣆⠈⠈⠋⠂⢀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿
⣿⣿⣿⣿⣿⣿⡙⢿⣿⣶⠋⢦⡄⠈⠻⣷⣦⣰⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠷⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠦⠛⠁⣿⣿⣿⣿⣿⠉⢀⣿⣿⣿
⣿⣿⣿⡙⠿⣿⣷⣌⠛⢿⡄⠙⠛⠀⠀⠀⠻⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠠⣷⠈⢋⣿⣟⣼⣿⣿⣿⣿⣿
⡿⡿⢿⣿⣾⡿⢿⣹⣦⡈⠺⣶⣀⠀⠀⠀⠀⠀⠐⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣟⣋⡃⠘⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⢠⣶⣌⢳⣿⡿⢻⡿⢏⣾⣿⣿⣿
⣿⣄⡈⠙⠋⠀⠈⠻⣿⡿⢆⡸⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿⠿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⢀⠀⠀⠉⠁⣿⠟⠀⠀⠀⣸⣿⣿⣿⣿
⠿⠿⢿⣀⡀⠀⠀⠀⠀⠐⠋⠁⠀⠈⢒⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢀⣾⡿⠛⠛⠛⠋
⠀⠀⠈⠛⠇⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣟⢘⡆⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠞⠋⠀⠀⠀⢤⣤
⠀⠤⠤⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⣤⠀⠀⠀⠀⠀⠠⢀⠀⢀⣒⠄
⡤⠤⣿⣿⣿⣿⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡀⠖⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣾⣿⣿⣿⣧⣀⡀
⠐⠶⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠛⣿⣿⣿⣷⠆⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣿⣿⣿⢇⠀⠀⢩
⠴⠂⣿⣿⣿⣿⠟⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣘⣿⣿⣿⣿⠤⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⡗⣄⣿⣿⣿⣿⣾⣿⣿⣿⣌⠁⣠⣿
⠐⠻⣿⣿⣿⣿⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣏⠘⣿⣿⣿⣿⣿⣿⣿⡅⢉⣵⣿⣿
⣷⡀⣿⣿⣿⣿⠀⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠁⢠⣿⣿⣿⣇⣻⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣹⣿⣿⣿⣧⣌⣝⠿
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠻⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠁⠀⠙⢿⣿⡟⣫⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⢉⣻⣀⣙⣛⣛⣛⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⣀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠛⠚⠿⠛⠟⢻⡿⠁⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣯⣉⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢀⡄⡄⢰⣿⣿⣿⣠⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠘⠷⠞⠈⣿⣿⣿⣹⣾⣿⡀⠀⡀⠀⣼⣿⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣠⠀⡄⢸⣿⣿⣿⠀⠜⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⠛⠶⠂⢸⣿⣿⣏⠰⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⡶⢤⠀⢿⣿⣿⣿⢰⠲⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠄⠈⢉⣿⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣴⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣧⣶⣶⣦⣤⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣉⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠂⠀⠀⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠈⠙⠻⠻⠿⢿⣿⣿⣿⣤⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠔⣺⢟⠠⠂⣿⣿⣼⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⡤⡄⡀⠀⠀⣻⣿⣿⣿⣿⣧⣿⣷⣦⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⣧⡌⠀⠀⠸⠿⣿⣿⣿⣿⢿⣿⡯⢉⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⠀⠀⠀⢻⣿⠟⠆⡠⣀⣾⣿⣿⣿⣿⣿⣿⣃⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠇⠀⠆⠀⠀⠐⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠉⢸⠃⠀⠀⠀⢀⣾⣿⣥⣴⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠘⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣠⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡶⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⢀⢀⣄⣰⣶⣾⣿⣿
⢿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣿⣶⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⠀⢐⣿⣿⣧⣯⡟⣿⠿⢿⣿⣄⠉⠉⠉⠂⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿
⣿⣿⣷⣿⣿⣿⠻⣿⣷⣜⠏⣤⡀⠙⠿⣷⣆⣠⣶⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⢜⠋⠸⣿⡿⣿⣿⣿⠘⢀⣿⣿⣿
⣿⣿⣿⡙⢿⣿⣶⡌⠻⣿⡄⠙⠷⠀⠀⠀⠻⡿⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⢴⣆⠘⣳⣿⣣⣿⣷⣿⣿⣿⣿
⣿⡿⣿⣿⣾⡿⢿⣷⣦⠈⠻⣦⡀⠀⠀⠀⠀⠀⠢⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣛⣙⠋⢙⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢠⣦⡍⣶⣿⠟⢿⡿⢱⣿⣻⣿⣿
⣿⣀⡈⠛⠋⠀⠈⠻⣿⡿⢆⡘⢿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠁⠉⢡⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿
⠿⠿⣧⣤⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⢚⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⣰⣿⠟⠛⠙⠛⠉
⠀⠀⠘⠛⠿⠂⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣟⢻⡂⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠛⠁⠀⠀⠠⢤⣤
⠀⠤⠀⠄⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣷⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠠⡀⠀⢐⡢⠠
⡤⠤⣿⣿⣿⣿⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡀⠐⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣅⣀⡀
⠐⠶⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⠄⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⠀⣤
⠤⠂⣿⣿⣿⣿⠟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣘⣿⣿⣿⣿⠤⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⡦⣀⣿⣿⣿⣿⣾⣿⣿⣿⣀⢀⣼⣿
⠐⠻⣿⣿⣿⣿⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⡅⣨⣿⣿⣿
⣦⡀⣿⣿⣿⣿⠀⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠁⢠⣿⣿⣿⣇⣹⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿
⣿⣷⣿⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠓⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣼⣿⣿⣿⣏⣍⣙⣿
⣻⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⠻⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣯⡉⠉⠁⠀⠙⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⢉⣻⣀⣙⣛⣻⣻⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⡈⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠛⠛⠚⠿⠟⠟⢻⣿⠁⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⡿⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡉⠁⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣶⣶⣶⣶⣦⡄⠀⠘⠻⡿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⠿⣿⣿⣿⣧⠀⡀⡀⠀⠀⠀⠀⠀⡄⢀⣠⣦⣶⣶⣶⣿⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⡀⢀⠀⣿⣿⣿⡏⢠⢻⣿⣤⣄⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠾⠷⠴⠀⣿⣿⣿⡃⢆⣼⣿⣿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢤⣄⣄⠀⣿⣿⣿⡇⡶⠄⢿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠯⠈⠉⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣾⣷⣶⣶⡏⠉⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⣠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⡎⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢿⣤⣤⣤⣤⣄⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠈⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⢻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣷⣤⡀⠙⠻⠻⠿⠿⠿⣿⣿⣿⣧⣭⣉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⡾⣶⣇⠀⢰⣿⣧⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣈⣀⣄⡀⠘⣿⣿⣿⣿⣿⣷⣿⣱⣆⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣯⡌⠀⠀⠾⢻⣿⣿⣿⣿⣿⡿⠞⣩⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡁⠀⠀⠀⠈⣿⣿⠿⢂⣠⣄⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⠆⠀⠂⠀⠀⠐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠉⣿⠀⠀⠀⠀⢀⣿⣿⣥⣶⣾⣿⣿⣿⣿⠟⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠠⠄⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠛⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢠⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⢀⢀⣀⣶⣶⣶⣶⣾
⣿⡅⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠻⣷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣾⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⡿⢿⣿⡄⠙⢯⠜⠂⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿
⣿⣿⣶⣾⣿⣿⠻⣿⣷⣼⠛⣤⡀⠙⢿⣶⣆⣠⣤⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣯⠟⠋⢼⣿⣿⣿⣿⣟⠙⢡⣿⣿⣿
⣿⣿⣿⡻⢿⣿⣧⡌⠻⣿⡄⠙⠿⠀⠀⠈⠻⡿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣴⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⣶⡀⠛⣼⣿⣼⣿⣶⣿⣯⣿⣿
⣿⣿⣿⣿⣾⡿⢿⣷⣤⠉⢻⣦⡀⠀⠀⠀⠀⠀⠪⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣟⡛⠉⠛⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢀⣰⣌⠛⣾⣿⠳⣿⡟⣿⣿⣿⣿⣿
⣿⣀⠈⠻⢏⠀⠈⠻⣿⣿⠆⡹⣿⡇⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⡿⣿⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠏⠀⠈⠋⠉⣸⡿⠁⠀⠀⣠⣿⣿⣿⣿⣿
⣿⠿⣧⣀⠀⠁⠀⠀⠈⠑⠛⠁⠀⠘⠱⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣦⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⣴⣿⠟⠛⠛⠛⠩
⠀⠀⠘⠻⠷⠂⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⢻⡆⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠸⠛⠁⠀⠀⠠⣤⣤
⠀⠨⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣷⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⡤⠀⠀⠀⠀⠀⢄⠀⠁⢐⠄⡀
⣤⠤⣿⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡄⠿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣁⡀⠀
⠰⠶⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⠄⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣶⣿⣿⣿⠇⠈⠉⣤
⠤⠀⣿⣿⣿⣿⠾⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣸⣿⣿⣿⣿⡤⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⡉⢠⣾⣿
⠐⠲⣿⣿⣿⣿⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣇⣵⣿⣿⣿
⣄⠀⣿⣿⣿⣿⠀⣸⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠁⢠⣿⣿⣿⣇⣹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠒⣿⣿⣿⣿⠟⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣾⣿⣿⣿⣇⣝⡛⠿
⢿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⢾⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣷⣮⣍⠉⠉⠁⠀⠻⣿⣿⡟⣫⣿⣿⣿⣿⣿⣿⣭⡉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⣛⣁⠙⣻⣻⣟⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠀⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠙⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠿⠟⠛⠿⠿⠿⠻⣿⠃⠁⢠⣤⡄⠀⠀⠀⠀⠀⠀⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣋⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃⠀⠀⣿⣿⣧⡤⣿⠿⠿⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠘⣿⣿⣿⣷⣿⣴⡘⢻⣚⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⡄⠠⠀⠀⠀⠘⢻⣿⣿⣿⠿⠋⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠛⠒⠀⣰⣄⣀⠀⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠦⡆⠤⠀⣿⣿⣿⡇⠔⠖⠹⠿⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠂⠀⢈⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣤⣤⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣨⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠠⣾⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⣿⣿⣦⣀⠈⠛⠛⠻⠟⠿⣿⣿⣿⣧⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡾⣾⣏⠀⠀⣿⡷⣬⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣈⣀⡀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣵⣒⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⡌⠀⠀⠸⠛⣿⣿⣿⡿⢿⣿⡖⢫⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⠀⠀⠀⢻⣿⠟⠀⢠⣦⣾⣿⣿⣿⣿⣿⣟⣀⣀⢀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡧⠀⠐⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢸⠇⠀⠀⠀⢀⣼⣿⣵⣶⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠘⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡾⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣾⣿⣾
⢿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⠌⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣾⣾⣿⣷⣷⣷⣿⣿⣿⡿⣿⣿
⣀⣀⡀⠀⢀⣿⣿⣿⣿⡿⢻⣿⠟⢿⣿⡀⠙⠔⠓⠀⠈⢻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿
⣿⣿⣿⣶⣿⣿⣯⠻⣿⣷⡾⢳⣄⠀⠙⢿⣷⣤⣴⣶⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠞⠉⢸⣿⡿⣿⣿⣿⠍⢁⣾⣿⣿
⣿⣿⣿⣿⡛⢿⣿⣶⡌⠛⣿⡄⠋⠷⠀⠀⠈⠻⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠺⣇⠈⣽⣿⣵⣿⣷⣿⣿⣽⣿
⣿⡿⠿⣿⣿⣾⠟⣫⣷⣦⡉⢿⣦⣀⠀⠀⠀⠀⠈⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣏⣙⠀⢛⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢀⣴⣴⡉⣿⣿⠏⠿⠏⣼⣿⣿⣿⣿
⠿⣷⣄⠈⠛⠁⠀⠈⠻⢿⡿⣀⠹⢿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⡀⠀⠈⠉⠸⡿⠁⠀⠀⣠⣿⣿⣿⣿⣿
⠿⠿⠿⣧⣄⠀⠁⠀⢀⠀⠘⠋⠀⠀⠈⢡⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣿⠛⠉⠉⠉⠉
⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣟⣛⣹⡘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠀⠀⡀⠀⠶⠶
⠄⠀⠤⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⣿⠿⡿⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⢀⡢⢄⠀⠐⡒⠠
⠴⠶⣿⣿⣿⣿⢀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣧⣄⡀
⠀⠒⣿⣿⣿⣿⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⡛⣿⣿⣿⣷⠐⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣇⡀⢀⣴
⠦⠂⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣃⣿⣿⣿⣿⣷⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⡆⣄⣿⣿⣿⣿⣾⣿⣿⣿⣄⢠⣾⣿
⠀⠈⣿⣿⣿⣿⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣅⣴⣿⣿⣿
⣷⡄⣿⣿⣿⣿⠁⣸⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⣌⣿⣿⣿⣿⣬⣿⣿⣿⣿⡿⠉⠁⢠⣿⣿⣿⣃⣸⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠋⣿⣿⣿⣿⠉⣿⣿⣿⣿⣁⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣾⣿⣿⣿⣷⣁⡙⠻
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠘⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣉⠉⠁⠀⠉⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣯⣭⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⢉⣠⣍⣙⣻⣿⣥⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⠀⠀⠋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡛⠛⠙⠛⠛⢛⢛⣟⠁⠀⣠⣦⡀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣍⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣤⣤⣠⣿⣿⣿⣴⣼⣿⢿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠛⠛⠛⣿⣿⣿⣽⣾⣿⡄⠶⠦⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡗⢚⣑⣹⣿⣇⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠙⠯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⠿⠛⠋⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⢰⠦⠄⠀⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⡓⠀⢈⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣶⣶⣶⣶⣤⣤⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣾⣷⣬⠙⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢻⣿⣿⣿⣦⣄⠀⠙⠛⠛⠛⠛⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⡾⣾⣏⠀⠀⣿⣇⣼⣿⣿⣿⣿⡿⡛⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣈⣀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣳⣶⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣯⡌⠀⠀⠾⠛⣿⣿⣿⣿⢿⢯⠗⣡⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⡇⠀⠀⠀⠀⢻⣿⠏⠀⣤⣤⣿⣿⣿⣿⣿⣿⢃⣀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣻⠃⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢸⠃⠀⠀⠀⢀⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⠛⠻⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠘⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⢀⢀⣀⣴⣾⣿⣿⣿
⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣦⠙⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢹⣿⣷⣶⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠁⣀⠀⠀⠀⣿⣿⣿⣷⡿⠿⣿⡟⠻⣿⣆⠈⢣⠚⠃⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢹⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣝⣿⣿
⣿⣿⣿⣶⣿⣿⣿⡝⢿⣿⣾⠏⢢⡄⠈⠙⢿⣦⣴⣶⣶⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡟⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢚⠁⢸⣿⢿⣿⢿⣿⠙⢁⣿⣿⣿
⣿⣿⣿⣿⣙⠿⣿⣿⣦⠙⢻⣆⠈⠻⠂⠀⠀⠙⢿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠺⣆⢉⣾⣿⣾⣿⣷⣾⣿⣿⣿
⣿⡿⠿⢿⣿⣷⡟⠻⣿⣶⣄⠹⣿⣤⡀⠀⠀⠀⠀⠁⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣯⣭⣁⣘⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⣸⣶⡉⣿⡿⠙⠿⢋⣿⣿⣿⣿⣿
⡟⢿⣦⡀⠙⠋⠀⠀⠙⠿⣿⣇⡈⠿⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⢛⠛⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⢸⡟⠁⠀⠀⣼⣿⣿⣿⣿⣿
⠛⠿⠟⢿⣦⣀⠀⠀⠀⡀⠈⠋⠁⠀⠀⢙⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣾⡿⠋⠉⠉⠉⠑
⡅⠀⠀⠀⠙⠛⠁⠀⠀⠉⠀⠀⣠⣴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣉⣇⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠠⠾⠶
⠤⠀⠐⠂⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⢀⠢⣀⠀⢐⠂⠤
⠴⠶⣿⣿⣿⣿⠀⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣽⣿⣿⣿⣡⣀⠀
⠀⠈⣿⣿⣿⣿⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⢙⣿⣿⣿⣷⠀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⣿⣿⣿⣿⣷⣿⣿⣿⣇⡀⢠⣶
⠶⠒⣿⣿⣿⣿⠻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⡆⣄⣿⣿⣿⣿⣾⣿⣿⣿⡄⣠⣿⣿
⡀⠈⣿⣿⣿⣿⣤⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣅⣴⣿⣿⣿
⣿⣄⣿⣿⣿⣿⠉⣸⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣿⣿⣿⣿⣥⣿⣿⣿⣿⣽⠏⠁⢠⣿⣿⣿⣃⣸⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠉⣿⣿⣿⣿⠋⣿⣿⣿⣿⣉⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣾⣿⣿⣿⣿⣩⡛⠻
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠈⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣍⠉⠁⠀⠙⠛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣉⣉⡉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⣠⣿⣉⣛⣿⣭⣿⣿⣿⣿⠛⠉⠉⠉⠉⠉⠉⠀⠈⠉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠛⠃⠛⠛⠛⠛⣻⡉⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣤⣤⣰⣿⣿⣿⣴⢺⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠛⠿⠿⣿⣿⣿⣴⣾⣇⣠⡄⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠢⢼⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⣿⣿⣿⡿⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⣿⣿⣿⠃⠸⣿⣿⣿⠿⢿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣗⡚⢀⣿⣿⣿⣘⣢⣿⣿⣯⠽⢿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣷⣾⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠿⢿⠇⠗⠊⠿⠟⣠⡍⠙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⠁⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠈⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡞⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣷⣶⣶⣶⣦⣤⣄⠀⠀⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢿⣿⣿⣿⣌⡉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠀⢸⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣥⡀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠞⣺⠡⠀⣸⣷⣴⣿⣿⡿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⡔⡀⠀⣸⣿⣿⣿⣿⣷⣾⣧⣶⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣅⠀⠀⠐⠋⢿⣿⡿⠻⢻⠟⠢⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⢸⣉⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠃⠀⣀⣀⡀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡇⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠉⡟⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⢻⣽⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣠⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡶⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⣾⣿⣧⣿
⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣶⣆⠙⢿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣶⣷⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⣼⣿⣿⣿⣿⣯⣿⢋⣿⠟⠻⣿⣆⡈⠳⡉⠁⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠈⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣾⣿
⣿⣿⣷⣶⣿⣿⣿⣿⠙⢿⣷⣶⠉⢠⣄⠈⠙⠿⣶⣴⣶⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⡛⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢎⠉⠸⣿⢿⣿⣿⣿⡟⠈⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣛⢿⣿⣷⡎⠙⢻⣆⠈⠻⠂⠀⠀⠙⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠉⠰⢧⠈⣾⣿⣾⣿⣷⣤⣿⣿⣿⣿
⣿⣿⣿⡿⢿⣿⣶⡿⢿⣷⣦⣄⠙⣷⣤⡀⠀⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣯⣥⣈⣩⣥⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣠⢶⡌⣿⡿⠛⠿⢫⣿⣿⣿⣿⣿⣿
⣭⡙⢿⣦⣀⠙⠫⡀⠀⠙⢿⣿⢇⡈⠿⢟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠠⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿
⣉⡛⠿⠟⢿⣤⡀⠀⠀⠀⡀⠀⠋⠁⠀⠀⢙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣆⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠉⠉⠉⠒⠿
⣬⡅⠀⠀⠀⠙⠛⠃⠀⠀⠉⠀⠀⢀⣤⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣏⣸⣈⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠲⠶⠶⢤
⠠⠶⠄⠒⠂⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⠀⠀⠀⠀⠀⣐⠠⡀⠀⠑⠂⠀⣸
⢤⠴⣿⣿⣿⣿⠉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠁⣽⣿⣿⣿⣁⢤⣿
⠀⠀⣿⣿⣿⣿⠺⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠙⣿⣿⣿⣿⠀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣷⣿⣿⣿⠇⣰⣾⣿
⠀⠒⣿⣿⣿⣿⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿
⣄⠀⣿⣿⣿⣿⣴⣼⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⡟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣿⣿⣿⣿⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣥⣿⣿⣿⣿⣽⡿⠁⢠⣿⣿⣿⣃⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣁⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣍⡙⠫
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣍⡉⠉⠁⠀⠙⠛⢻⣿⣿⣟⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⢹⣿⡍⣿⣭⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⡌⢛⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠁⠙⢛⢛⠙⣻⠁⠀⣠⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⣤⣄⠀⣿⣿⣿⣤⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⠿⢷⣿⣿⣿⣴⣿⣏⣋⠩⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⡩⢈⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⣿⣿⣿⡿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠤⠀⣿⣿⣿⢃⠸⣿⣿⣿⣿⣿⣿⠈⠘⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠳⠒⠀⣿⣿⣿⠘⢢⣿⣿⣷⠶⢿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠘⠛⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡿⠿⣿⣿⣿⠿⠟⢻⣿⣷⣴⣶⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡶⣿⣿⣿⡇⡖⠞⠿⠿⣙⠛⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠘⢻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢷⣶⣶⣶⣦⣤⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⡉⠩⠛⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣇⡈⠙⠛⠛⠛⠛⠻⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⢜⡒⠧⠀⢰⣿⣠⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⠀⢸⡿⣿⣿⣿⣧⣾⣃⣠⢾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣍⠈⠀⠀⠟⢹⡿⡟⠛⢻⠍⠉⣤⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠈⣮⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⠏⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠚⢻⣍⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣷⣛⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣶⣾⣿⣾
⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣴⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣶⣷⣶⣷⣵⣷⣾⣿⣿⣿⣿⣿
⣁⡀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣻⡛⣿⡿⠿⣿⣤⡈⠛⠄⠂⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿
⣿⣿⣷⣦⣿⣿⣿⣿⣿⡿⣿⣿⣤⡟⠁⡀⠈⠙⢿⣶⣤⣶⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠋⠸⣿⢿⣿⣿⣿⣿⠉⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡻⢿⣿⣧⣌⠛⢿⣧⠈⠛⠆⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠱⣇⠈⣾⣿⣿⣿⣇⡀⣽⣿⣿⣿
⣙⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣦⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣨⣯⣍⣈⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠠⢤⡈⣾⣿⠛⡿⢹⣿⣻⣿⣿⣿⣿
⣿⣛⠻⣿⣍⠀⠛⠿⡏⠀⠙⢿⣿⣷⣀⢿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⡿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿
⡛⠻⠿⢶⣿⢿⣆⡀⠈⠠⠀⠀⠀⠸⠋⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢸⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠉⠉⠉⠭⠿
⣋⣛⣓⠀⠀⠀⠛⠿⠷⠀⠀⠘⠀⠀⠀⢀⣤⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣏⣸⡉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠴⠦⠦⣽
⠉⠉⣉⣁⠠⠤⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡆⠀⠀⠀⠀⠀⡀⠄⡀⠀⡒⠠⠐⣿
⢉⣀⣿⣿⣿⣿⠄⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠉⣽⣿⣿⣿⡁⣼⣿
⠀⠀⣿⣿⣿⣿⣤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠙⣿⣿⣿⣷⣄⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⠇⣴⣿⣿
⡀⠀⣿⣿⣿⣿⢙⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣷⡄⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡁⠀⣿⣿⣿⣿⣿⣿⣿⣟⡁⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⡟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣻⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣷⢬⣿⣿⣿⣿⢉⣽⡇⢠⣿⣿⣿⣃⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢽⣿⣿⣿⣿⡀⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⢈⣿⣿⣿⣿⣩⣯⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⡙⠟
⣻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣸⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⡉⠉⠁⠀⠙⠟⠛⢿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⢉⣿⡍⣨⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠁⠙⠛⣛⠉⣻⡁⠀⢴⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⣄⣀⢠⣿⣿⣿⣤⢻⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⠿⢾⣿⣿⣏⣧⣿⡍⡉⢽⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣏⡥⢘⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⢿⣿⣿⣿⡿⢿⣿⣴⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⢠⠀⠄⢸⣿⣿⣿⠁⠜⣿⣿⣿⣿⣿⣿⠉⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠳⠒⠘⣿⣿⣿⠐⢀⣿⣿⡆⠚⣿⣿⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠻⠿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⠿⠿⢿⣿⣿⣿⠿⠛⢻⣿⣧⣶⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⡆⠤⠸⣿⣿⣿⡶⠲⠚⠿⢟⡛⠛⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⡃⢀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⠙⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⢍⡈⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣦⣈⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡌⠈⠉⠙⠛⠛⠋⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠐⠒⠠⠀⢸⣿⣠⣿⣿⢿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣐⡀⠀⡀⠀⢸⡿⣾⣿⣿⣦⣿⡃⠠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣁⠈⠀⠀⠟⢷⡿⠟⠛⢿⠟⠈⣠⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⠀⠀⠀⠀⠀⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⠒⢯⣍⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⢴⣶⣮⡛⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣶⣾⣿⣾
⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣷⣿⣶⣷⣶⣶⣧⣿⣾⣿⣿⣿⣿⣿
⢁⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣇⠈⠁⠀⠂⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿
⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⠿⡀⠈⠛⢿⣶⣤⣴⣦⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠋⢸⣿⣿⣿⣿⣿⡿⠈⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⠻⣿⣯⡀⠻⣧⠀⠀⠈⠻⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠱⡇⢉⣿⣿⣿⣿⠃⠀⣽⣿⣿⣿
⢙⣿⣿⣿⣿⣿⣿⣧⣍⣻⣿⣿⣇⡀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠺⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣈⣭⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠠⢄⡘⣿⡿⠻⠏⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⠏⠙⣿⣿⣷⡄⠹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡛⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠨⡿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣍⣻⣶⣤⠀⠉⠂⢀⠀⠙⠹⡿⠷⠀⠉⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠋⠉⠋⠭⠿⣿
⣤⣤⠤⣬⣍⠛⠋⠻⣷⣦⣄⠀⠀⢦⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣬⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠠⠤⠤⣭⣿
⠶⠶⠖⠶⠦⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⢀⠠⠄⠀⢐⠠⠄⣾⣿
⠀⠀⣿⣿⣿⣿⠈⠉⣸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣏⠀⠀⣿⣿⣿⣿⠉⣼⣿⣿⣿⢁⣿⣿
⠀⠐⣿⣿⣿⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠙⣿⣿⣿⣧⣤⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣧⣾⣿⣿
⣄⠠⣿⣿⣿⣿⣈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⡿⢛⣿⣿⣿⣿⣒⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣧⣿⣿⣿⣿⢤⣼⣿⣿⣿⢹⣿⣿⣿⡿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡁⠀⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡇⣿⣿⣿⡟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣹⣿⣿⣿⣞⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣷⠀⣿⣿⣿⣿⠍⣭⣵⢦⣿⣿⣿⣃⣸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡆⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣈⣽⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣯⣌⢙⠫
⣻⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⠛⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠁⠀⠉⠙⢛⠟⢻⣿⣟⣛⣿⣿⡉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠉⢩⣯⡄⣹⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠙⠛⢛⠙⣟⠁⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣠⣀⡀⣼⣿⣿⣇⡤⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⠿⢶⣿⣿⣿⣻⣼⣯⠉⠉⣿⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣩⠀⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⣿⣿⣿⣿⠿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣾⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⡀⠠⠀⣿⣿⣿⡏⠠⢻⣿⣿⣿⣿⣿⣯⠈⠀⠑⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠳⠶⠂⢸⣿⣿⡄⠂⢼⣿⣿⡊⣿⣿⡏⠉⠁⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⠿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠿⣿⣿⣿⡿⠿⠟⣿⣿⣴⣦⡀⠁⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣴⢤⠀⢿⣿⣿⣧⠔⠆⠻⠿⡛⠛⠗⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣴⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣼⣩⣈⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠸⠃⣽⣿⣿⣿⣿⣦⡈⠉⡻⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠉⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣰⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣁⠈⠛⠛⠛⠙⠛⠻⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠔⠀⠀⠀⣾⡇⣼⣿⣿⠻⠿⠛⠟⣳⣾⣿⣤⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⣿⢷⣿⣿⣿⣰⠅⠀⢰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢛⣀⠈⠀⠐⠛⠿⠟⠛⠉⠟⠀⢀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠸⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢫⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠔⠶⣭⣝⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣴⣶⡙⠻⠿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣾⣷⣼⣿⣿⣷⣤⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣔⣴⣾⣿⣿
⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣌⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣷⣴⣶⣤⣶⣴⣷⣷⣿⣿⡿⣷⣿
⠁⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠃⣐⡄⠀⡘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣾⣿
⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠍⠹⣿⠉⠙⠿⣷⣶⣙⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠞⠁⣿⢿⣿⣿⣿⣿⡗⠈⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣷⣮⠉⢲⣦⠀⠀⠈⠻⡿⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢷⠈⣾⣿⣿⣿⠟⠃⠀⣼⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣶⣌⠙⠹⡧⣄⠉⠀⠀⠀⠀⠈⠚⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣴⣥⣀⣩⣤⠀⠀⠀⠀⠀⠀⠀⢰⡝⠀⡰⣆⢿⣿⠿⠿⣿⣷⣀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⡿⣿⣷⣤⡈⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣉⣉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠁⣿⠇⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣏⠉⠙⠿⣟⠀⠈⠻⠿⣿⣦⠌⠙⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣽⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⠛⠭⢿⣿⣿
⣿⣿⠿⠿⠿⠶⢾⣿⣿⣷⣀⢀⡑⠒⢠⣀⠈⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣁⣅⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣤⣤⣸⣿⣿
⣿⡷⠖⠒⠒⠒⠂⠈⠁⠉⠛⠿⠇⠀⡈⠋⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⢐⠀⠀⣿⣿⣿
⣿⠛⣿⣿⣿⣿⣁⡀⣸⣿⣿⣿⣿⣿⡆⣀⣼⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⠦⣿⣿⣿⣿⣿⣿⣿
⣧⡀⣿⣿⣿⣿⣩⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠙⣿⣿⣿⣇⠀⣿⣿⣿⣿⠙⣿⣿⣿⣧⢀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⢠⣿⣿⣿⡿⣿⣿⣿
⣦⡉⣿⣿⣿⣿⠉⠱⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⡿⠈⣿⣿⣿⣿⣚⣂⡀⠀⣼⣿⣿⡟⣿⣿⣿⡆⠒⣿⣿⣿⣿⣾⣿⣿⡿⣿⣾⣿⣿
⣿⣷⣿⣿⣿⣿⣠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡇⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣹⣿⣿⣿⣧⣿⣿⣿⣷⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣷⠀⣿⣿⣿⣿⡿⢉⣥⣶⣿⣿⣿⣃⣸⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡀⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣁⣩⣽⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣇⡈⠙⠏
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠐⠋⠉⠛⠛⡉⡻⣿⣿⡿⣿⣯⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⣭⣤⢉⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⠘⢱⡝⣿⣿⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠋⡉⠋⢹⡋⠀⢰⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣍⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣦⡤⠰⣿⣿⣿⡄⢸⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠛⠷⣿⣿⣯⣶⣿⣆⠀⣻⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⣽⣿⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⢻⣿⣿⣿⠟⢿⣿⣶⣾⣿⡿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣠⠀⠀⠸⣿⣿⡿⠀⠊⣿⣿⣿⣿⣧⣹⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣈⣛⣉⣀⣿⣿⣧⣈⣘⣿⣿⠂⢺⣿⣸⡇⠀⠀⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠛⢻⡇⠀⠀⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠛⠛⢻⣿⣿⣿⠛⠋⢹⣿⣷⣶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢐⣆⠖⡈⡿⠿⠿⠇⠙⠈⠛⣋⠋⠙⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⣠⢀⠙⢛⡻⠿⠻⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⣦⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣈⣠⣮⣾⣦⣌⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢻⣿⣿⣿⣿⣿⣷⣄⡀⠙⠿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠀⣹⡀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠈⠀⠀⠘⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⣿⡇⣸⣿⡏⠙⠋⠉⠉⢠⡄⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣸⡿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⣴⣿⣀⣿⣿⠧⡔⠀⠀⢰⣿⣷⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣓⡄⠀⠈⠁⠙⠛⠛⠋⠀⠀⣀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣶⣎⡙⠛⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣻
⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣼⣍⡉⢻⣿⣷⣶⣤⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣿
⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⡛⢿⣿⣿⣿⣧⣬⣻⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣷⣶⣶⣶⣿⣶⣷⣵⣒⣶⣿⣿⠿⣶⣿
⣤⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣴⢿⣿⣷⣾⣿⠛⢿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⣿⡿⣿⣿⣿⣿⣿⣟⣛⠿⢿⠇⢘⣾⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡾⠿⠿⣿⠟⠻⠿⣿⣦⣉⠉⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠀⣿⣿⣿⣿⣿⣿⣿⡇⠁⠠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠈⠀⣄⡀⠀⠀⠀⠽⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠲⢀⣿⣿⣿⣿⡿⠋⠀⠀⢨⣧⣾⣾
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⣿⣧⣀⠉⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⢿⣷⣴⣷⠀⠀⠀⠀⠀⠀⠘⠀⠀⠶⣸⡿⠙⢿⣿⡅⠀⠀⠰⢾⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⣦⣀⡀⠛⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⣼⣿⣿⣦⣀⡐⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣿⠻⣿⣿⣷⣆⣈⠛⠷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡿⠋⠁⠉⠛⢿⠿⠟⡻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠙⠛⠻⢯⣂⣀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣾⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠲⠶⣄⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣟⣿⣶⣦⣀⡠⠉⠉⠻⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⢀⠀⠁⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⣹⣿⣿⣿⣿⣿⡏⠛⢻⣿⣿⣿⡏⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣇⢀⣀⣿⣿⣿⣿⠡⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡶⣿⣿⣿⣿⣿⣿⣧⣄⣠⣿⣿⣿⣧⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠉⣿⣿⣿⡇⠀⣿⣿⣿⣿⠙⣿⣿⣿⣧⠀⣿⣿⣿⣿⣟⣛⡃⠀⢸⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠤⢼⣿⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣤⡀⠀⣼⣿⣿⡟⣿⣿⣿⡎⠀⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠲⢼⣿⣿⣿⠻⣿⣿⣿⣤⣼⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡧⠤⣿⣿⣿⡇⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡤⣼⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠈⣿⣿⣿⣧⠀⣿⣿⣿⣿⡿⣟⢃⣾⣿⣿⣿⣃⣸⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣹⣿⣿⣿⣧⣀⡈⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠋⠉⠙⣿⣿⣿⣋⣻⣿⣿⣿⣍⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⢛⠛⠹⣿⣿⣿⣿⡏⠉⠉⠉⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠒⠁⠉⠋⢭⣘⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣦⡄⢠⣿⣿⣿⡄⣺⣿⣿⣿⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠙⠛⠳⣿⣿⣷⣷⣿⣄⠀⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⣽⣿⣤⣼⣧⣤⣄⣀⣀⣀⣀⣀⣀⣀⣾⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⢻⣿⣿⣿⠛⢿⣿⣶⣾⣿⡿⢿⣿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣰⡀⠂⠸⣿⣿⡿⠀⢊⣿⣿⠿⣿⣧⢸⣇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣈⣉⣉⣀⣿⣿⣧⣈⣨⣿⣿⠁⢿⣿⢸⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠛⢸⡇⠀⠀⠠⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠛⠛⢻⣿⣿⣿⠉⠉⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣐⣇⣂⣈⡿⠿⠿⠇⠉⠈⠛⣉⠉⠁⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣧⡄⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠙⠭⡏⢿⠛⢿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣦⣄⠀⢘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢑⣁⣦⣶⣾⣷⣦⡉⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⣐⠘⠻⢿⡿⣿⡿⠿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢩⡀⢻⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⢸⣿⡏⠙⠋⠉⠉⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣸⣿⠃⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⢠⣴⣿⣅⣾⣿⠧⠄⠀⠀⢀⡀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣑⣄⠀⠀⠀⠈⢛⠋⠉⠀⠁⣀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡗⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡇⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣬⣙⠛⠛⠛⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢩
⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣈⣏⡉⠙⢿⣿⣶⣦⣴⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣷⣿
⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡿⠿⣿⣿⣾⣿⣤⣝⡛⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣶⣷⣶⣴⣶⣦⣶⣥⣖⣲⣿⣿⠫⢶⣿
⣤⣄⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣾⣿⣶⣮⣽⣿⠟⠿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⣿⢿⣿⣿⣿⣿⣿⣿⣛⠻⢿⠇⢐⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣷⣼⣿⡿⠿⢿⣷⣦⣉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣋⡉⠁⠀⠈⠃⣀⣀⠀⠀⠁⠩⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣿⣿⣿⡧⠋⠀⠀⢡⣣⣶⣶
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣶⣦⡀⠘⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠷⢺⠇⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⠛⢻⣿⣿⠃⠀⠀⠀⠿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡉⠉⠉⠕⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣼⣿⣿⣦⣀⡀⢘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⠉⠹⣿⣿⣶⣶⣤⡀⡙⠻⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠋⠀⠈⠛⠉⠻⠟⠏⣙⡝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣈⠉⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⣢⣦⣤⣲⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣄⣀⡀⠀⠉⠛⠿⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡀⠁⠀⢛⢿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣧⢠⣠⣿⣿⣿⣿⠦⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢰⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠉⣿⣿⣿⡇⠀⣿⣿⣿⣿⠙⣿⣿⣿⣧⠀⣿⣿⣿⣿⣻⣟⣧⡀⢸⣿⣿⣿⣿⣿⣿⠀⠁⣿⣿⣿⣿⣠⣿⣿⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⢸⣿⣿⣿⣷⣀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⢀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣶⣿⣶⠀⣼⣿⣿⡟⣿⣿⣿⡇⠐⣿⣿⣿⣿⣾⣿⣿⣿⢿⣷⣍⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣾⣿⣿⣿⣿⢉⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⡇⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⡇⢹⣿⣿⣿⣿⣉⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠽⠿⠟⢹⣿⣿⣿⣁⣸⣿⣿⣿⠎⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⠛⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣼⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣶⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣹⣿⣿⣿⣧⣄⡈⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠋⢹⣿⣿⣿⡿⢿⣻⣃⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠿⠿⠿⣿⠏⠉⠉⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⢻⠿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⠘⠿⠿⢿⠝⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣠⣤⠄⢸⣿⣿⡇⠄⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⠿⠾⣿⣿⣧⣾⣷⡀⢘⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢨⣿⣧⣄⣸⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⠛⠛⣿⣿⣿⣿⠛⣿⣷⣶⣿⣿⠿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⡄⠀⠀⢻⣿⣿⡏⠀⢹⣿⣿⣿⣿⡀⣺⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣙⣛⡁⣸⣿⣿⣇⣁⣸⣿⣿⠘⣿⡇⢸⡇⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠛⠃⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠛⠛⠛⢻⣿⣿⣟⠛⠋⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⢰⡰⠆⢸⡿⠿⠿⠸⠐⠘⠛⠛⠛⠁⠀⠀⠀⠀⠀⠸⢻⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣯⣀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠙⠩⡟⠿⠟⠹⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣦⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⡇⢀⢠⣤⣶⣬⣿⣦⡌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⠄⠙⢿⡿⣿⠿⡿⢻⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⢸⣿⠏⠙⠉⠉⢉⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣸⣿⠇⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⢀⣴⣿⡁⣼⣿⠆⠄⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢳⡄⠀⠀⠀⠙⠻⠛⠛⠀⠀⢀⣤⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠠⠴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣘⡛⢿⡿⠿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⠛⠻⢿⣿⣶⣤⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢽⣾⢷⣿
⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣴⣾⣿⣿⢦⣶⣏⣉⣛⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣷⣶⣶⣾⣶⣶⣶⣤⣒⣶⣿⣿⠫⢷⣿
⣀⣀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣨⣽⣭⣍⣛⣾⣿⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠄⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⣿⠁⢀⣽⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣛⡛⢿⣿⣿⣷⣦⣍⠋⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠸⡿⠿⠛⠉⠹⠋⠀⠉⠉⠙⠋⢲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⢠⣂⣾⣶
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣤⣀⠀⠺⠶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠿⢶⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⢿⠁⠀⠀⠒⠷⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣍⣉⠙⠻⠿⠓⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣼⣟⣿⣁⠀⠀⠀⠐⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠿⣿⣷⣤⣄⣀⠉⠚⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁⠁⠀⠀⠘⠹⠟⠏⣙⡙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣽⡛⠛⠿⠿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⠆⠠⣤⣤⣢⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠛⠿⢷⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢻⣿⣿⣿⣷⣀⣿⣿⣿⣿⠉⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣇⢀⠀⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠉⣿⣿⣿⡇⠀⢸⣿⣿⣿⠉⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣇⣀⢸⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⢡⣿⣿⣿⡟⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣸⣿⣿⣿⣷⣤⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⢀⣿⣿⣿⡏⠀⣿⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣘⣾⣷⡄⣼⣿⣿⡏⣿⣿⣿⡆⠄⣿⣿⣿⣿⣾⣿⣿⣿⢿⣮⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⣿⣿⣿⣟⣉⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡟⡷⣿⣿⣿⡇⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣷⠀⣿⣿⣿⣿⠉⠽⠿⢻⣿⣿⣿⣁⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣶⣶⡀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣼⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣶⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣸⣿⣿⣿⣇⣀⠈⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠙⠿⣿⣿⣛⣿⣧⣿⣿⣯⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⢿⣿⠿⣿⠏⠉⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⣿⣿⣿⡛⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣀⢀⠀⣿⣿⣿⢀⢸⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠻⠿⣦⣿⣿⣿⣤⣾⡍⠉⣿⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣾⣿⣿⣿⣿⣧⠀⣿⣿⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⢿⣿⣿⣿⡿⣿⣿⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣷⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢀⠀⠀⠸⣿⣿⣿⠃⠘⣿⣿⣿⣿⡇⠀⣿⠁⠀⠈⠁⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡞⠳⠖⠀⣿⣿⣯⠐⠀⣿⣿⡏⣿⣧⠀⣿⠀⠀⠀⠐⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠹⠿⠀⣿⠀⠀⠀⡀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠿⠿⣿⣿⣿⠿⠿⢻⣿⣧⣤⠀⠄⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⡄⢤⠀⣿⣿⣿⡇⠆⠎⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠈⠋⠉⠟⢿⣿⠟⣿⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⣿⡇⢀⣠⣤⣶⣤⣿⣦⣈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠙⢿⡿⣿⡿⣿⠿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠈⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⡄⣿⣿⠟⠻⠟⠛⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⡿⠁⣿⣷⡄⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠉⠉⠻⣷⠿⠛⠁⠀⢀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠘⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⢿⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢂⣴⣿⣿⣿⣶⣶⣿⣄⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣶⣴⣿
⡇⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⣀⣤⣿⣦⡤⣨⣿⡟⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣤⣤⣤⣤⣤⣄⣴⣤⢳⣲⣿⣿⢳⣱⣿
⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢾⣿⠛⠻⢿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣾⡟⠁⠀⣽⣿
⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣶⣶⣿⠿⣿⣿⣾⣿⣇⣉⠛⠟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⢸⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⢨⣿⣷⣷⡶⠆⢿⡟⠛⠛⠛⠛⠲⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⢠⣋⣼⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⣟⠉⠁⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣶⣶⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠒⠷⣳⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣷⣤⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⠀⠀⠀⠀⠀⠀⠸⠃⢸⣿⣿⣿⠗⠀⠀⠀⠀⢼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣦⣤⡁⠀⠁⠘⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠀⠀⠀⠀⠷⠲⠜⠟⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠉⠻⠿⣿⣿⣿⣶⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢤⡄⠀⠀⢀⡀⡀⣀⣰⣾⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⣿⣷⣦⣄⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⠉⠙⠗⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠉⣿⣿⣿⡇⠀⢺⣿⣿⣿⠙⣿⣿⣿⣧⠀⣿⣿⣿⣿⠛⡿⡇⢀⢸⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿⢵⣿⣿⣿⢿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⠁⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⢀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣀⣻⣯⣍⣼⣿⣿⡟⣿⣿⣿⡟⢠⣿⣿⣿⣿⣾⣿⣿⣿⣦⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣷⠂⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⢿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⡇⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⢶⣿⣿⣿⣿⠐⣛⠇⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣺⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠉⢙⣷⢾⣿⣿⣿⣁⣸⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⠟⣿⣿⣿⣿⣴⣶⡖⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣇⠉⠃⠉
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠋⠀⠛⠛⢿⣿⣿⣿⣥⣿⣿⣿⠛⣋⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⢹⣿⣿⣿⡟⠉⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠛⠻⣿⣯⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠅⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⣌⣉⣉⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣴⡠⠀⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠛⠳⢿⣿⣿⣴⣿⡄⠀⣿⡗⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣤⣤⣾⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⢻⣿⣿⣿⡟⣿⣿⣶⣿⣿⠛⠛⣿⡿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⢠⡀⠀⠈⣿⣿⣿⠀⠊⣿⣿⠿⣿⡆⠀⣿⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣙⣉⣀⣿⣿⣧⣈⣀⣿⣿⠃⣿⣇⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠛⠀⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠛⠛⠛⣿⣿⣿⡋⠉⢹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢂⣇⡒⠀⡿⠿⠿⠇⠃⠁⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠸⠟⠿⣿⡟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠈⠈⢈⠉⢹⢻⠃⠘⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠁⠀⣠⣴⣷⣴⣿⣷⣦⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠂⠛⠻⠛⠛⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡆⢸⣿⠉⠉⠋⠉⢉⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⡃⢸⣿⠆⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠈⠿⠟⠉⠀⠀⣀⣴⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣷⡬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣃⢈⣛⡛⠛⢾⡟⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⢿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠿⣿⠿⠿⢿⣷⣿⣧⣤⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣴⡿⠼⣿⣿
⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣶⣶⣶⣶⣼⣿⢉⣙⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⣶⣶⣶⣶⣦⣄⣤⢟⣿⠟⠉⣾⣿⣿
⣀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠿⣋⣙⣛⣳⣿⡿⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣛⠿⠇⠀⣀⣽⣿⣾
⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⡿⠟⠿⢿⣿⣿⣷⣦⣤⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠉⣽⣯⣾⣶⡾⠶⠒⠻⠋⠈⠉⠉⠉⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠁⠀⠀⠂⢠⣾⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢙⡋⠁⣀⣀⣀⠀⠀⠰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠗⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠐⠚⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⠿⠿⠿⠿⠿⢿⣿⠶⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡚⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⢠⡤⠲⠺⣶⣶⣄⣀⣀⣀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠹⠋⠉⢻⣿⣿⠿⠀⠀⠀⠀⠘⠛⠒⠉⠉⠛⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⡉⠈⠀⠀⠈⣻⡛⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠐⢺⣿⣿⠀⠀⠀⠀⠀⣄⣤⣦⣄⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⢿⡷⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠛⢿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⢀⣀⡀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢾⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣹⣿⠟⣿⣿⣿⣿⠙⣿⣿⣿⡇⠀⢸⣿⣿⣿⠉⣿⣿⣿⣧⠀⣿⣿⣿⣿⠛⠛⠻⠤⢸⣿⣿⣿⣿⣿⣿⣀⡀⣿⣿⣿⣿⢾⣿⣿⣿⢿⣿⣿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡉⠉⠀⣿⣿⣿⣿⢀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣀⣀⡈⢳⣾⣿⣿⡏⣿⣿⣿⣧⠁⣿⣿⣿⣿⣾⣿⣿⣿⣤⡹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣤⡶⠶⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⡇⣿⣿⣿⡏⠁⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣴⠄⣿⣿⣿⣿⣤⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠉⠉⠁⢹⣿⣿⣿⣁⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣼⣶⣿⣿⣿⣿⣃⣿⣿⣿⣿⠀⣾⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣇⠀⠈⢉
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠉⠙⠉⠉⠁⢛⣻⣿⣿⡿⠛⢛⣻⣇⡀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠙⠟⠿⠋⠀⠈⢉⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣷⣶⡿⢿⡿⣩⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣄⡤⠀⣿⣿⣿⠀⣸⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠙⠛⠳⣿⣿⣯⣶⣿⡀⢀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣤⣤⣿⣄⣀⣀⣀⣀⣀⣀⣀⡀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢻⣿⣿⣿⠛⣿⣿⣶⣿⣿⠛⠛⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⢠⠀⠀⠘⣿⣿⡟⠀⢹⣿⣿⢿⣿⡆⠀⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣈⣙⣁⣀⣿⣿⣧⣈⣸⣿⣿⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⠋⠀⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⠛⢛⣿⣿⣿⠉⠉⢹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢐⣇⠂⢀⡿⠿⠿⠒⠈⠈⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠻⢿⢿⡿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣿⣿⣿⣿⣿⣿⢿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⠀⡀⢕⢀⠉⢯⣙⡻⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠁⠀⣢⣲⣶⣮⣾⣿⣷⣄⠀⠉⠛⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣷⡾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠃⠛⠻⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡆⢸⣿⠉⠉⠉⠁⢁⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣾⡃⣼⣷⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠙⠿⠛⠉⠀⠀⣀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠂⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⡄⠽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠚⡁⣙⣛⠛⠫⢿⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣿⢿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⡿⠿⠿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣰⡟⢸⣿⣿
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣴⣶⣿⣷⣶⣾⣿⣉⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣦⣴⣴⣶⣤⣄⣨⠏⣿⠏⠙⢾⣿⣿
⡀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡟⣙⣛⣛⣻⣿⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣟⡛⠻⠆⠀⣈⣽⣿⣾
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣾⡿⠟⠿⠿⢿⣿⣷⣶⣤⣌⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠰⡟⠿⠿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠈⠉⣭⣥⣽⣶⡾⠶⠂⠙⠇⠀⠀⠈⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠁⠀⠐⠐⢰⣶⣦⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⡋⠁⢀⣀⣀⣀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠏⠀⠀⠀⠒⠓⣻⣮⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣴⡾⠿⠿⠿⠿⠿⢿⠷⢒⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠛⠁⣀⣤⠀⢂⡗⣶⣦⣀⣀⣀⡉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠓⠂⠉⢉⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠚⢛⠃⠁⠉⠁⢉⣻⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⢿⣿⣿⣿⡯⠀⠀⠀⠀⠀⣠⣤⣤⣄⣶⣯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⠿⢿⡿⠿⠿⠿⠿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢾⣍⣁⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢺⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠈⣉⣉⣿⣿⣿⣿⠟⣿⣿⣿⡇⠀⢸⣿⣿⣿⠉⣿⣿⣿⣧⠀⣿⣿⣿⣿⠛⠛⠃⠠⢸⣿⣿⣿⣿⣿⣿⣀⡀⣿⣿⣿⣿⢺⣿⣿⣿⢿⣾⣿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠛⠛⠋⣿⣿⣿⣿⣀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣀⣀⡀⠀⣾⣿⣿⡏⣿⣿⣿⣧⡁⣿⣿⣿⣿⣾⣿⣿⣿⣤⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⣹⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⡏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠛⠛⠉⣿⣿⣿⣿⠉⣿⣿⣿⣿⠀⣸⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠉⠉⠁⢠⣿⣿⣿⣁⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿
⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣀⣀⡀⣿⣿⣿⣿⡶⣿⣿⣿⣿⠀⣼⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣹⣿⣿⣿⣇⠀⠀⢉
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⢉⠟⠟⣻⣿⣿⣿⣿⣿⡍⠉⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠀⠈⢹⣿⣿⣿⣿⣿⠟⡛⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣁⣴⣾⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣠⣠⠄⢸⣿⣿⡇⠸⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠙⠛⠳⢾⣿⣿⣵⣾⣇⠀⣺⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣧⣄⣸⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠛⣿⣿⣿⡟⢻⣿⣷⣾⣿⣿⠿⢿⡿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⡄⠠⠀⢿⣿⣿⠃⠈⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣙⠛⠀⣸⣿⣿⣀⣀⣿⣿⡇⢸⣿⡀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠛⠃⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠛⠛⠛⣿⣿⣿⡟⠛⠋⣿⣿⣶⣄⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⢶⠰⠀⢻⣿⠿⠷⠂⠃⠙⠛⠙⠙⠀⠀⠀⠀⠀⠀⠀⠻⡿⠻⣿⣟⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣿⣿⣿⣿⣿⣿⡿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⡀⢚⠄⠉⢟⣿⣻⠀⠹⣷⣼⣿⣿⣿⣿⣿⣿⡟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣶⣶⣶⣤⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠚⠀⠁⣤⣶⣷⣶⣾⣿⣷⣄⠀⠉⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⢾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣄⠐⠀⠋⠹⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⣿⡏⠉⠛⠋⠉⣸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⡟⢀⣿⠧⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠻⠟⠛⠂⠀⠀⣠⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠿⠿⠋⠙⢛⠛⠿⣿⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⠿⠿⣿⣾⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣿⠃⢻⣿⣿
⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠁⠀⢨⣧⣶⣶⣶⣾⣿⡋⠙⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⣴⣤⣶⣶⣶⣲⣄⣤⡼⢿⡟⠃⣐⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢿⠟⠛⢛⠛⣿⣿⠿⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⡻⠿⢾⠀⠀⣾⣽⣿⣾
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⡿⠿⠿⢿⣿⣿⣖⠤⣍⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢲⠿⠿⠻⣍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣩⣭⣿⣴⣶⠶⠂⠒⡂⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠀⠀⠀⠐⢂⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠛⠉⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠒⠚⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣀⣤⣾⠿⠿⢿⠿⠿⣿⡷⠦⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠐⠛⠛⢁⢀⣤⠠⠔⠶⢦⣤⣀⣀⣈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠛⠚⠋⠉⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠟⠗⠘⠛⠃⠘⢻⡟⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢴⣶⣿⣿⣶⣿⣿⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢰⣿⣶⣿⣿⣿⣿⣿⣿⣷⣦⡁⠀⢸⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⠉⣿⣿⣿⣧⠀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣴⣿⠿⣿⣿⣿⣿⣉⣿⣿⣿⡏⠀⢾⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⡟⣿⣿⣿⡏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢀⡴⣿⣿⣿⣿⢉⣿⣿⣿⣿⠀⣹⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠉⠉⠁⢠⣿⣿⣿⣇⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣘⣂⡀⣿⣿⣿⣿⠙⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣻⣿⣿⣿⣇⠀⠈⢛
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠙⣛⠹⣿⣟⣿⣫⣍⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠟⠀⠈⣿⣿⣿⣷⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣦⣿⣿⡿⠛⢛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣶⣦⣄⣠⣩⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣠⣠⠀⣾⣿⣿⣇⢼⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⠿⠷⢿⣿⣿⣴⣼⣇⠀⢸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣇⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣿⡿⢿⣿⣵⣾⣿⣿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡄⠠⠀⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⠀⣸⡇⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠛⠚⠀⣸⣿⣿⡐⣀⣿⣿⡇⢹⣿⡁⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠛⠃⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⠿⣿⣿⣿⡟⠛⠛⣿⣿⣤⡄⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣶⠤⠀⢿⣿⣿⡧⠆⠂⠻⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠑⣽⣷⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⣀⣿⢭⢏⠛⣿⣿⡫⠈⢷⣬⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢠⣤⣤⣤⣤⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠻⠛⣻⣟⣷⣵⣷⣮⣿⣿⣆⠀⠉⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⢾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠘⠾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠐⠀⠏⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣷⠀⣿⠿⠛⠛⠛⠛⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⡟⢸⣿⠆⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠙⠿⠟⠋⠀⠀⠀⢀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠑⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣦⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⣙⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡀
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣍⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⡿⠛⠿⠿⠿⣶⣦⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢉⣭⣴⣷⣶⣿⣿⣶⣾⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⢣⣿⣿⣿⣿
⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠉⠉⣻⡁⣴⣶⣤⣽⣟⠛⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⣶⣶⣤⣤⣴⣤⢶⣴⡊⣻⣿⣿⢗⣲⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣿⠿⠿⠿⠟⢿⣿⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⢷⣽⠁⢠⣽⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣠⣤⣿⣶⣿⣿⣷⣿⣿⣄⠈⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣭⣿⣿⢿⣟⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⢛⣛⡛⣿⢤⣤⣤⡄⠨⣯⠁⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠀⠀⢀⣰⣖⣵⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⡿⠋⠋⠀⠀⠀⠀⠀⢴⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠐⢞⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣶⣶⣿⣿⣾⣷⣤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠴⢿⠟⠋⠉⣁⡀⣠⡴⣤⣬⣅⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⠙⠶⠛⠛⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠰⠄⢚⢳⣿⠧⠿⠞⠉⠻⣿⠿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡀⣀⣤⣶⣶⣾⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢁⣤⣴⣷⣶⣶⣶⣶⣶⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⡜⠛⣿⣿⣿⣿⣿⣿⣿⣿⣮⡉⠘⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠁⣿⣿⣿⣿⠿⣿⣿⣿⣷⠀⣼⣿⣿⣿⠉⣿⣿⣿⣧⠀⣿⣿⣿⣿⠛⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣿⣿⣿⣿⠸⠛⠋⣿⣿⣿⣿⣿⣿⣿⣭⣥⡄⣸⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡏⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠐⠿⠂⣿⣿⣿⣿⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠉⠉⠁⢠⣿⣿⣿⣇⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣀⣀⣰⣿⣿⣿⣿⠀⣿⣿⣿⣿⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⢿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢠⣿⣿⣿⣿⡏⣿⣿⣿⣿⣏⣿⣿⣿⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⡘⣿⣿⣿⣿⠋⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠔⠾⡛⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣶⣤⣈⣉⣉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣤⡤⠀⣿⣿⣿⠤⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠛⠿⠷⣿⣿⣯⣶⣿⣀⠀⣻⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣹⣿⣇⣀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⣿⣿⣿⠿⣿⣯⣶⣾⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⢠⠀⠄⠘⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⢀⣿⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠘⠓⠂⠀⣿⣿⣇⣀⣸⣿⣿⠂⢿⣿⡀⣿⠁⠀⠈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠛⠃⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⣿⣿⣿⠛⠛⢻⣿⣧⣤⢀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠰⡦⠦⠘⣿⣿⡿⠶⠓⠈⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠐⠹⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢀⣬⣿⣟⣿⡿⢻⣿⠃⠹⣦⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣿
⠀⠀⣠⣴⣦⣤⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡗⠿⠿⣿⣿⣷⣿⣷⣿⣾⣿⣇⠀⠙⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿
⠀⢠⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠈⠺⢿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠂⠛⠻⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡄⣿⡟⠋⠻⠛⠋⠉⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡼⢁⣿⠣⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠻⠟⠋⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠋⢀⡄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢢⣶⣶⣶⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠘⠛⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣄⠀⠀
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣍⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⠿⢿⡿⠷⣶⡉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣿⣭⣼⣦⣶⣶⣷⣶⣿⣅⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⢼⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠞⠛⠛⢻⣟⢉⣤⣤⣬⣿⡟⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣶⣶⣤⣴⣦⣤⣤⣤⣄⣕⣶⡫⣿⡟⢒⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢆⢸⣿⠨⠿⠿⠷⠽⣿⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡻⠷⢷⡏⠀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⣉⣀⣨⣯⣴⣶⣶⣶⣶⣿⣆⠈⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠟⠻⣿⡋⣭⣭⣍⠉⣭⠉⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⠀⠀⢄⣐⣶⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⡷⠟⠋⠁⠀⠘⠀⢀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠰⢶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣤⣤⣶⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⢴⣶⠿⠟⠛⠙⠉⠉⣩⣭⣉⣉⠉⠑⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠺⠀⠙⠛⠻⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢤⡤⠶⡒⢸⣿⢬⣿⠿⠛⢿⣷⣷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⠀⣀⣀⢜⣴⣾⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⣸⣧⣤⣤⣤⣤⣴⣾⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣠⡎⣿⣿⣿⣿⣿⣿⣿⣯⡙⠉⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠉⠀⣿⣿⣿⣿⠛⣿⣿⣿⣷⣆⣿⣿⣿⣿⠉⣿⣿⣿⣧⠀⣿⣿⣿⣿⠛⠛⠃⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣄⣿⣿⣿⣿⡷⣿⣿⣿⣿⣀⣿⣿⣿⡿⠀⣿⣿⣿⣿⣀⣀⡀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣥⠄⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡏⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⠉⠉⠁⢠⣿⣿⣿⣇⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠻
⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣀⣀⠀⣿⣿⣿⣿⠖⣿⣿⣿⣿⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡦⣿⣿⣿⣿⣸⣿⣿⣿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⡄⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠙⠛⠛⠉⠙⠻⠿⠿⣿⡛⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⢠⣽⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⣷⣦⣌⣀⣉⣹⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4770

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/no-epo-debate/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/no-epo-debate/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ There’s_No_F***ing_Debate_With_“the_F***ing_President”_(What_António_Campinos
Calls_Himself!)⠀✐


Posted in Europe, Patents at 8:03 pm by Dr. Roy Schestowitz


António Campinos keeps ‘f***ing with his staff’ (slang) without asking for
consent


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇CSC, SUEPO, and ILOAT⦈
  The CSC, SUEPO, and ILOAT have been calling out and specifying the illegal
                                    agenda


Summary: The EPO’s in-house criminal António_Campinos (trying to ‘finish the
job’ of Benoît_Battistelli, a Corsican with quasi-Nazi_family_connections) is
only pretending to speak to elected (actually elected, unlike himself) staff
representatives; the substance of the issues is described in 3 long documents


The EPO‘s Central Staff Committee (CSC) has just circulated a bunch of long
documents with images in-line.


The main_document_being_circulated [PDF] is a “[r]eport on the GCC meeting of 5
July 2022: Fixed-term appointments & “Bringing Teams Together”,” and “[t]here
were three documents on the official agenda.” That’s a lot of text. Just
reading the thing properly can take hours, never mind discussing it.


“Once again, the “fucking president” (that’s what he is calling himself) is
leaving far too little time for actual discussion.”“The President had scheduled
one hour for the meeting,” the CSC notes, “although two of the documents on the
agenda were clearly of very great importance:


- Circular 405: Extension & Conversion of fixed-term appointments (GCC/DOC 12/
2022)
- “Bringing Teams Together” (GCC/DOC 13/2022)”


We’re talking about 28 pages of text here (the report anyway)! Just “one hour
for the meeting”? What is this, comedy???


“Campinos is just a ‘tourist’ at the EPO, plundering the organisation and
shielding prior plunderers.”“We sent a written and reasoned opinion to the
President on both documents,” the CSC noted, adding its opinion_on_GCC/DOC_12/
2022 [PDF] and on_GCC/DOC_13/2022. [PDF]


Once again, the “fucking president” (that’s what he is calling himself) is
leaving far too little time for actual discussion. He just wants to pretend
there’s some dialogue and he’ll ignore all the input from people who actually
know the EPO. Campinos is just a ‘tourist’ at the EPO, plundering the
organisation and shielding prior plunderers.


Now that Campinos bought_his_second_term he no longer feels the need to even
pretend that he’s seriously engaging with staff. █


⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢠⠀⠀⠢⡀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⣴⡙⠇⠀⠀⠹⠱⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢼⣼⣟⣿⣿⣿⣿⠄⠀⠀⠰⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠋⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣦⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣤⣀⣸⣿⣷⡆⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠈⠉⠛⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⡀⠀⠴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣘⣿⠿⡿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡍⢻⣿⣿⡗⠀⣿⣿⣿⠡⡠⠌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣠⣧⡈⠧⣼⡿⡶⣿⣿⣿⢠⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡤⡜⠿⢿⣿⣿⡇⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⢻
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⠀⠈⣷⣄⠘⡿⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢰⠄⣾
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢺⣿⣿⡀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣆⠘⡿⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⠈⢻⣿⡇⠀⣾⣯⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠠⣦⣤⣿⣿⡀⠡⠀⣠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠀⠀⠠⢤⣤⣀⣀⠀⠀⠀⠀⠀
⠸⠋⠁⠀⢿⠟⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢠⣆⠀⠸⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠿⢿⠟⠀⠀⢠⣋⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠛⢳⡀⠀⠀⡀
⠀⠠⣶⣦⣴⣆⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⠀⠀⠻⠟⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠁
⠀⢠⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⢰⣧⣤⣿⡀⠀⠀⠀⠀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣇⠀⢠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠛⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠿⣿⠿⢿⠿⡿⠶⠿⠿⠀⠀⣸⣿⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡆⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⢰⡀⠀⠱⣄⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣷⣾⣜⠃⠀⠀⠹⡘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠐⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⢉⠙⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠴⣦⣤⣼⣿⣷⡇⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⠛⢿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣀⠀⠰⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣸⠿⠻⡟⣿⡇⡀⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣷⣾⣿⣷
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⡎⢻⡿⢿⣇⠀⣿⣿⣿⠱⠤⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣷⡄⠣⣼⡿⠶⣿⣿⣿⢰⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣦⡌⠿⠋⣿⣿⡏⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⢻
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⡀⠀⣷⣄⠘⠿⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢰⠀⢼
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣆⠈⡟⠀⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⠉⢹⣿⡇⠀⣶⣆⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠐⢶⣬⣿⣿⡀⠠⠆⣠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠐⠀⠀⠤⠤⢤⣀⡀⠀⠀⠀⠀
⠘⠋⠁⠀⢿⠟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣄⠀⠘⣿⣿⠀⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠏⠀⠀⠐⡍⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠻⣀⠀⠀⠀
⠀⠠⣶⣦⣴⣆⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⠀⠀⠻⠟⠀⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀
⠀⢠⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⢸⣧⣤⣿⡀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣇⠀⢠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠿⣿⠿⢿⣿⡿⠶⠿⠿⠀⠀⣸⣿⠩⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⠀⠀⠨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⢰⡀⠀⠱⣄⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣾⣜⠁⠀⠀⠙⡘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⣼⣿⣿⣿⣿⣿⠀⠀⠀⠐⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⠉⠙⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣦⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠴⣦⣤⣼⣿⣷⡇⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⠛⢿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⠀⠰⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⢈⡿⠻⡿⣿⡇⠀⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢴⣷⣶⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⡎⢻⡿⢿⡏⠀⣿⣿⣿⠱⠤⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣷⡄⠣⣼⡿⡖⣿⣿⣿⢰⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣆⡄⠻⠋⣿⣿⡇⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢻
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⡀⠀⣷⣀⠐⠟⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢰⠀⢼
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣾⣿⡀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣆⠈⡟⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⠉⢻⣿⡇⠀⣶⣦⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠐⢶⣬⣿⣿⠀⠁⠀⣠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠠⠤⠤⢤⣀⡀⠀⠀⠀⠀
⠘⠋⠁⠀⢿⠟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣄⠀⠘⣿⣿⠀⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠏⠀⠀⠈⠍⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠻⣀⠀⠀⠀
⠀⠠⣶⣦⣴⣆⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⠀⠀⠻⠟⠀⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀
⠀⢠⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⢸⣧⣤⣿⡀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣇⠀⢠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠿⣿⠿⢿⣿⡿⠶⠿⠿⠀⠀⢸⣿⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣧⡀⡀⣷⠀⠀⠙⣦⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡿⣿⣿⣿⣿⣿⣜⠀⠀⠀⠸⡈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣾⣽⣿⣾⣿⣿⣿⣿⠀⠀⠀⠐⡁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠛⠛⠻⠿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣣⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠐⢛⣷⣶⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠈⠙⠛⢿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⠛⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣾⡟⢻⣿⣿⣇⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣶⣶⣶⣶
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⢻⠈⢿⠛⣿⣇⣸⣿⣿⣿⠘⢒⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣷⣌⢱⣿⣟⣿⣿⣿⡿⠹⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿⢴⡈⠛⢻⣿⣿⠇⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣅⡀⠘⣿⡇⠙⡟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠘⠇⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠋⠉⣻⣿⣇⠀⣾⣯⣿⣿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣼⣿⣷⠀⠖⠂⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠒⠒⠦⠤⣤⣄⣀⠀⠀⠀⠀
⠘⠋⠁⠀⠻⠟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⡄⠀⠸⣿⣿⢸⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠿⠿⠋⠀⠀⢸⡏⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠻⠧⠀⠀⠀
⠀⠀⣶⣦⣴⣇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⡟⠀⠀⠻⠿⠀⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀
⠀⢠⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⣼⣦⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀
⠀⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣆⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀
⠀⣿⣿⣿⣿⣿⣿⡿⠷⠿⠿⠁⠀⣼⣿⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⢠⠼⡇⠀⠀⠹⡖⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣻⢻⡿⣿⣿⣿⣷⡄⠀⠀⠀⢳⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠱⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢱⠿⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠋⠙⠿⢿⣿⣿⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠘⣻⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠙⠛⢿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣦⣟⠋⣻⣿⣿⣤⠀⠀⠸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣶⣦⣶⣶
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⡇⠙⡟⠛⣿⡀⣿⣿⣿⣿⠙⢏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣦⡘⢿⣿⣛⢻⣿⣿⡇⠻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠷⣷⡛⠓⣺⣿⡿⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⢿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣅⡀⠹⣿⡇⢹⠏⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⢹⠃⡂⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⠉⣻⣿⣇⠀⣾⣧⣿⣿⣿⡿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣿⣿⡇⠸⠂⢠⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠐⠲⠶⠶⣦⣄⣀⠀⠀⠀⠀
⠘⠋⠁⠀⠺⠟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡄⠀⠸⣿⣿⠸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠁⠀⠀⣿⢇⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠉⠹⡦⠀⠀⠀
⠀⠀⣶⣦⣴⣦⠸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⡟⠀⠀⠻⠿⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀
⠀⢠⣿⣿⣿⣿⣧⣿⣿⣿⣿⠇⠀⠀⣼⣦⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣄⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⣿⣿⣿⣿⣿⣿⡿⠷⠿⠿⠀⠀⢸⣿⠫⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣍⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⢦⡀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣀⣄⢿⠀⠀⠈⢻⢵⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣟⣿⢿⣿⣿⣿⣦⠀⠀⠀⠈⡆⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣇⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣻⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⢛⣿⣶⣾⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠙⠛⢿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠉⢿⣿⣿⣿⣿⡟⠀⠀⠀⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣷⣼⡋⠙⣿⣿⣷⡄⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣴⣦⣤⣶
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢻⠈⢿⠛⢻⣧⢰⣿⣿⣿⡇⠻⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣷⣌⠇⣿⣿⡯⣿⣿⣿⠑⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⢺⣇⠉⢙⣿⣿⡏⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣭⣍⡀⠈⣿⣶⠈⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣆⠈⡿⢐⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠋⠉⢿⣿⡇⢀⣾⣧⣿⣿⡿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣼⣿⣿⡄⠶⠀⣴⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠓⠲⠶⣦⣤⣀⠀⠀⠀⠀
⠘⠋⠀⠀⠸⡟⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⣿⢸⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⠟⠀⠀⠈⡿⢡⣾⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠹⠂⠀⠀⠀
⠀⠀⣿⣷⣴⣧⡈⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⡟⠀⠀⠿⠟⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀
⠀⢠⣿⣿⣿⣿⣷⣹⣿⣿⣿⠇⠀⠀⣾⣆⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀
⠀⢻⣿⣿⣿⣿⣿⣧⠻⣿⣿⣆⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⣿⣿⣿⣿⣿⣿⡿⠷⠿⠿⠁⠀⣸⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣭⡋⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠀⠀⠰⣄⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⣶⠹⠇⠀⠀⠙⡏⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢮⣏⣿⣻⣿⣿⣿⣿⠄⠀⠀⠀⠳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢺⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠰⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠙⠟⢿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⣿⣯⣧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⢉⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠙⠛⢿
⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⡀⠉⢻⣿⣿⣿⣿⣿⠀⠀⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣰⣛⠉⣿⣿⣿⣤⢀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣦⣤⣶
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠻⡆⢻⡟⢻⣿⣀⣿⣿⣿⣿⠙⢋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣿⣄⡹⣿⣿⣻⣿⣿⣿⡇⠻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⢿⣟⠙⠇⣻⣿⣿⢁⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡀⠀⢿⣷⡄⢻⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣧⠈⢿⠣⡈⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⠛⠛⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⢸⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠋⠉⢻⣿⡇⢀⣾⣏⣿⡿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⣿⣿⡇⠸⠦⢁⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠙⢻⣿⣶⣄⡀⠀⠀⠀
⠘⠛⠀⠀⠘⠿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⣿⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⣽⡟⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⡀⠀⠀
⠀⠀⢸⣿⣦⣾⡀⢿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⠀⠀⠿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡶⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⣾⣆⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⡹⣿⣿⣄⡀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⣂
⠀⣾⣿⣿⣿⣿⣿⣿⠷⠿⠿⠀⠀⣸⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣛⠁⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠀⠀⠰⣄⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⣶⠹⠇⠀⠀⠙⡏⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢮⣏⣿⣻⣿⣿⣿⣿⠄⠀⠀⠀⠳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢺⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠰⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠿⠿⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⣿⣯⣧⠀⢀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⢉⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠙⠛⢿
⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⠉⠻⣿⣿⣿⣿⣿⠀⠀⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣠⣋⠉⣿⣿⣿⣤⢀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣦⣤⣶
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠻⡆⢹⡟⢻⣿⡀⣿⣿⣿⣿⠘⢋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣄⣹⣿⣿⣻⣿⣿⣿⡇⠻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⠷⣏⠙⠇⣻⣿⣿⢁⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡀⠀⢿⣷⡀⢻⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣧⠈⢿⠣⡘⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⠛⠛⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⢸⣄⡀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠋⠉⣻⣿⡇⢀⣾⣏⣿⡿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⣿⣿⡇⠸⠶⢡⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠿⣿⣶⣄⡀⠀⠀⠀
⠘⠛⠀⠀⠘⠿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⣿⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⢽⡟⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⢣⠂⠀⠀
⠀⠀⢸⣿⣦⣾⡀⢿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⠀⠀⠿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡗⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⣾⣆⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⠹⣿⣿⣄⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⣂
⠀⣾⣿⣿⣿⣿⣿⣿⠷⠿⠿⠀⠀⢸⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣟⣛⠁⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⣀⣶⠀⠀⠈⢷⡤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣾⣷⣼⠀⠀⠀⠀⣇⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢜⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠐⠛⠛⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢼⣿⣿⣿⡀⠀⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠙⠛⠿
⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣀⠉⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⢿⣿⣿⣴⣯⠉⣿⣿⣿⣷⣇⡀⢀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⣶⣶⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⠛⢻⡄⢻⡟⢻⣿⣄⣿⣿⣿⣿⣏⠙⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣄⣿⣿⣿⣻⣿⣿⣿⣿⠘⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⢿⣿⠟⠋⣻⣿⣿⡏⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⠀⠀⢻⣿⡆⠹⡿⠋⢰⣿⣿⣿⣿⣿⣿⣿⣯⣍⣛⠻⠿⣿⣿⣿⣿⣥⣤⣀⡀⠀⠀⠀⠀⠄⠠
⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⠈⢿⡇⡴⠁⢠⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉⠛⠿⣿⣧⣤⣤⡀⠀⠀
⢸⣧⣄⡀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⢿⣿⣇⢀⣾⠇⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣿⣿⣇⢸⣧⠅⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣟⠅⠀⠀
⠈⠋⠉⢀⡀⠙⠟⢿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡄⠀⢘⣿⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⢸⣿⢣⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⠀⠀
⠀⠀⠀⣿⣿⣶⣿⡌⣿⣿⣿⠀⠀⠀⠀⠀⢸⡗⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢹⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣧⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⣾⣦⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢿⡀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣃
⠀⢶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⠁⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣄⢠⡌⣷⠀⠀⠀⠻⡮⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣾⣿⣾⠀⠀⠀⠀⢷⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢉⡹⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⣤⣀⣺⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠂⠀⠀⣼⣷⣄⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠙⠛⠿
⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣄⡀⠹⣿⣿⣿⣿⣿⣇⡀⠀⠀⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣾⣯⠀⣿⣿⣿⣿⡇⣆⡀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢺⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡿⠛⢻⡀⢻⡏⣻⣿⣶⣿⣿⣿⣿⡧⣈⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣦⣿⣿⣿⣽⣿⣿⣿⣿⠀⠻⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠿⢿⣿⣿⣛⣽⣿⣿⡟⣠⣿⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢈⣩⣉⡀⠀⢹⣿⣷⠛⡿⠋⢠⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⡌⠉⠛⠛⠛⠛⠋⠟⠿⣿⣦⣤⣤⣆⠈⠀⢸
⢠⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣧⡀⢻⡟⣴⠃⢠⣾⣿⣿⣿⣿⣿⣿⡆⢘⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀
⠸⡿⠷⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⠋⠉⣻⣿⡇⢠⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣿⣿⣧⢸⣷⡯⣰⣿⢿⣿⣿⣿⣿⣿⣿⡛⢨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀
⠀⠀⠀⢠⣤⣀⣩⠘⣿⣿⣇⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⢸⣿⢧⣾⣿⣿⣿⣯⣿⣿⣷⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀
⠀⠀⢀⣼⣿⣿⣿⣆⢿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⢻⣷⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⣾⣆⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠹⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⣠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣
⠀⢶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⠟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣾⣿⣟⡛⣽⢿⣏⠉⣻⣧⣙⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠉⠈⢹⣟⣿⣿⡉⣽⣿⣿⣿⣿⣿⡿⢿⣣⣿⣿⣿⣿⣿⡄⠀
⣾⣿⣿⣿⣿⣿⣿⠋⠉⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⡶⣼⣿⣿⠟⠛⠛⢿⣿⣿⡟⠻⠿⠀⢤⣽⣿⣿⣿⣿⡿⠀⡀⣀⡀⠀⢘⢿⣿⠛⠀⠉⠉⢻⠙⣿⣿⣿⣿⠉⣏⢽⣿⣿⣿⡗⠀
⢨⠉⠈⠃⠠⢿⣿⠇⠘⡶⣾⠏⣿⠏⠀⠀⠈⢩⠛⠁⠀⠉⠉⠛⢻⢹⣿⣿⡁⠐⠛⠀⢀⡈⡿⠃⠀⠀⡈⠁⠀⣠⢸⡆⢀⢰⣿⢻⡛⣿⡟⠁⠀⢡⡝⠆⡀⠘⠯⣴⠀⢰⠂⠚⠚⢠⡈⢿⡿⠋⠀⠄⠸⡿⣿⣿⡇⠀
⢈⠀⣾⣿⡀⢽⣿⡀⠘⠀⠁⠀⠈⠃⠀⠠⢠⣾⠄⠀⠀⠀⠈⣇⡄⠈⠀⠉⠀⣶⣄⠀⠌⣿⠀⠀⠀⠸⠃⠀⠘⣻⡎⣻⡆⠀⠈⠀⢸⠋⢀⠀⠀⢠⣾⣄⠇⠀⠀⠉⢷⡎⠃⠀⠀⠀⠹⣽⣃⠀⢀⠀⠀⠁⠟⠙⡀⠀
⠀⠸⢋⠈⡇⠀⠸⢳⣠⡄⠀⠀⡀⠀⠀⠀⠉⠟⠀⠀⠀⡀⠾⠊⡷⠀⠀⢀⡀⠀⠃⠀⠀⠿⠀⠀⠀⣠⠀⠀⠹⣼⣿⠛⠻⢶⣄⠀⠈⠀⠀⠀⠀⠀⣿⢿⠙⣦⡀⠁⠙⢡⠄⢐⡄⠀⠀⠀⢻⡈⠸⡆⠀⠘⠀⢀⢃⠉
⢀⡀⠘⢾⣷⣄⡇⠀⢈⣵⠟⠋⠉⠛⢿⣶⠀⠀⣰⡾⠛⠉⠛⢿⡇⠀⠀⢈⣵⠞⠛⠉⣛⠻⣶⡆⡄⠃⠀⠀⠀⠛⠛⠀⠀⠀⢨⣿⡀⠀⠀⣄⠆⠀⣟⣾⢀⣿⡟⠀⠀⠀⠀⡏⢨⠀⠀⠀⢸⣄⠀⠀⣸⡆⠀⠀⠟⠀
⢘⣏⡄⡰⣿⠿⠋⢀⣿⡏⡀⠀⢀⠀⠀⡛⣀⠀⢿⣧⣀⠀⠀⠀⠁⢠⠀⣾⡏⠀⠃⡀⠀⠐⠛⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣆⢸⡇⠈⣄⢹⠈⡎⢸⡇⠀⠀⠀⠈⣽⠘⠀⠀⠀⠈⢈⣷⠈⡻⠁⠀⠀⠀⠀
⠈⢙⣥⣷⣷⠆⡀⢸⣿⡇⠈⠀⠾⠀⢰⡜⢯⡇⠈⠛⠻⠿⣷⣶⣄⠈⠀⣿⡇⠀⠀⠛⠧⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⡇⠙⠦⠈⢷⣶⡇⠸⣿⠀⠀⠐⠀⠸⠃⠀⠀⣀⣠⣾⣿⠀⠁⠀⠀⠀⠀⠀
⠀⠀⢿⣯⣀⠰⠛⠊⣿⣇⠀⠀⠀⠀⢈⣥⠌⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⢀⠀⠀⠀⠀⣤⡄⠀⠀⠈⠖⠠⡄⠀⢰⣾⡟⠋⣉⡅⠉⠀⠖⠀⠀⢹⣷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠈⠩⣄⠻⣿⠆⠀⠆⠀⠀⠀⠀
⢀⠀⠈⠸⣧⠀⠀⢿⣮⠻⢦⣤⣤⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣥⣤⣤⡾⠋⠀⠀⠀⠀⠀⠁⠋⠀⠈⢻⣿⣦⣏⠃⠀⠀⠀⠈⡇⠀⠘⠃⣸⡿⢄⣀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠋⠀⠀⠀⠀⠀⠀⠀
⢼⡇⠀⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠐⠃⢸⠗⠀⠀⠴⠀⠈⠁⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢪⠏⠀⠀⠀⠀⠀⡟⠀⠀⢠⠏⠀⠀⢿⡇⠀⠀⠀⡄⠀⠀⢀⠘⠄⠀⠤⡀⠀⠀⠀⠀
⢸⠃⣴⠁⠀⠀⢠⡿⠀⠀⣾⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠄⠀⠀⠀⠨⠁⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣈⠻⠆⠀⠐⢠
⠀⠀⣿⣄⠀⠀⢼⠃⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⣼⠁⠉⠉⠉⠀⠀⠀⠀⠀⣀⣴⢻⠇⠀⢸⣇⠄⠀⠀⢨⡐⠀⠈⠀⠀⠈⢿⡿⠀⠀⠠⣿
⢨⢿⡿⣻⣧⣄⢆⣤⣤⡾⠋⠀⠀⢰⡶⣼⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣤⣤⠀⠽⣳⠴⣴⣤⣿⣿⠟⣛⣶⣶⣶⢾⣶⡺⠇⠀⡟
⠨⣦⡈⠉⣿⣷⣀⡍⠽⣧⣀⣀⠀⠀⢰⣿⣿⡆⠹⠄⣄⡠⣐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⣦⡄⠛⠟⢠⣬⠿⠃⢶⡀⠀⠀⠀⢼⣬⣴⣺⣿⠇⠀⠐⢢⡛⣎⢑⣿⣿⣤⣿⠛⠿⣟⡄⠀⠀⠀⠀⠀
⢰⣾⣿⣿⣿⣯⣼⣀⣠⡼⣿⣿⣿⣶⣿⣽⣿⣷⣶⣦⣞⡆⠹⣿⣿⣷⣿⣕⣀⡀⣚⢿⣿⣤⠀⢢⣤⣼⣿⣿⣿⣧⡀⣄⣼⣿⣆⡀⢮⠴⣀⣀⣠⠄⠀⢹⣿⣿⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣏⠶⠘⠁⠀⣀⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⢿⣿⣿⣿⣄⣀⣱⠏⠉⠐⠈⠉⣀⠘⡻⠟⠻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡾⣿⣿⣀⠀⣀⣤⣦⣿⣿⣿⣷⣮⣽⣷⣮⣿⣿⣭⣿⣿⣿⣷
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⠟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣾⣿⣟⡛⣽⢿⣏⠉⣻⣧⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢉⠈⢻⣟⣿⣿⡉⣿⣿⣿⣿⣿⣿⡿⢿⣯⣿⣿⣿⣿⣿⡇⠀
⣾⣿⣿⣿⣿⣿⣿⠋⠉⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⡶⣼⣿⣿⠟⠛⠛⢿⣿⣿⡟⠻⡿⠀⢤⣽⣿⣿⣿⣿⡿⠀⡄⣀⡀⠀⢘⣿⣿⠓⠀⠋⠉⢿⠙⣿⣿⣿⣿⠉⣏⢽⣿⣿⣿⡗⠀
⢨⠉⠈⠃⠤⢿⣿⠇⠸⡶⣾⠏⣾⠏⠀⠀⠈⢩⠛⠉⠀⠉⠉⠛⢻⢹⣿⣿⡁⠐⠟⠀⢀⡉⡿⠃⠀⠀⡈⠁⠀⣠⢸⡆⢀⢰⣿⢻⡛⣿⡟⠁⠀⢡⣟⠆⡀⠘⠯⣴⠀⢰⠂⠚⠚⢤⡈⢿⡿⠋⠀⠄⠸⡿⣿⣿⡇⠀
⢈⠀⣾⣿⡀⢽⣿⡀⠘⠀⠃⠀⠈⠃⠀⢀⢠⣾⠄⠀⠀⠀⠈⣇⡄⠈⠀⠉⡀⣶⣄⠀⠌⣿⠀⠀⠀⠸⠃⠀⢘⣻⡞⣿⡆⠀⠉⠀⢹⠋⢀⠀⠀⢠⣾⣄⠇⠀⠀⠉⢷⡎⠃⠀⠀⠀⠹⣽⣃⠀⣀⠀⠀⠁⠟⠙⡀⠀
⠀⠸⢋⢩⡇⠀⢸⢳⣠⡄⠀⠀⡀⠀⠀⠀⠙⠟⠉⠀⠀⣀⠾⠈⡷⠀⠀⢀⡄⡀⠋⠀⠀⠿⠀⠀⠀⣠⠀⠀⠹⣼⣿⠛⠻⢶⣄⠀⠈⠀⠀⠀⠀⠀⣿⢿⠙⣦⡀⠃⠙⢡⠄⢰⡄⠀⠀⠀⢻⡈⠸⡆⠀⠘⠀⢀⢣⠉
⢀⡀⠘⢾⣷⣄⡇⠀⢈⣵⠟⠋⠉⠛⢿⣶⠀⠀⣰⡾⠛⠉⠛⢿⡗⠀⠀⢈⣵⠞⠛⠉⣛⠻⣶⡆⡄⠃⠀⠀⠀⠛⠛⠀⠀⠀⢨⣿⡄⠀⠀⣴⠆⠀⣟⣾⢀⣿⡟⠀⠀⠀⠀⡏⢨⠀⠀⠀⢸⣄⠀⠀⣸⡆⠀⠀⠟⠀
⢘⣏⡄⡰⣿⠿⠋⢀⣿⡏⡀⠀⢀⠀⠀⣛⣀⠀⢿⣧⣀⠀⠀⠀⠁⢠⠀⣾⡏⠀⠇⡄⠀⠐⠛⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣆⢹⡇⠈⣄⣹⠈⡎⢸⡇⠀⠀⠀⠈⣽⠘⠀⠀⠀⠈⢈⣷⠈⡻⠁⠀⠀⠀⠀
⠈⢙⣥⣷⣿⠆⡀⢸⣿⡇⠈⠀⠿⠀⢰⡜⢯⡇⠈⠛⠻⠿⣷⣶⣄⠈⠀⣿⡇⠀⠀⠛⠧⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⡇⠙⠦⠌⢷⣶⡇⠸⣿⠀⠀⠐⠀⠸⠃⠀⢀⣀⣠⣾⣿⠀⠁⠀⠀⠀⠀⠀
⠀⠀⢿⣯⣡⠰⠛⡊⣿⣇⠀⠀⠀⠀⢈⣥⠍⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⢠⠀⠀⠀⠀⣤⡄⠀⠀⠈⠖⢠⡄⠀⢰⣾⡟⠋⣉⡅⠉⠀⠖⢀⠀⢹⣷⡀⢀⣿⠀⠀⠀⠀⠀⠀⠔⠉⠹⣄⠹⣿⠇⠀⠆⠀⠀⠀⠀
⢀⠀⠈⢸⣧⠀⠀⢿⣮⠻⢦⣤⣤⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣥⣤⣤⡾⠋⠀⠀⠀⠀⠀⠃⠋⠀⠈⢻⣿⣦⣏⠇⠀⠀⠀⠈⡇⠄⠘⠃⣸⡿⢄⣀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠋⠀⠀⠀⠀⠀⠀⠀
⢼⡇⠀⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠰⠃⢸⠗⠀⠀⠴⠀⠈⠑⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢪⠏⠀⠀⠀⠀⠀⡟⠀⠀⢠⠏⠀⠀⢿⡇⠀⠀⠀⡄⠀⠀⢀⠘⠄⠀⢤⡀⠀⠀⠀⠀
⢸⠃⣴⠀⠀⠀⢠⡿⠀⠀⣾⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠄⠀⠀⠀⠨⠁⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢈⡄⠀⢀⣈⠻⠆⠀⠐⢠
⠀⠀⣿⣄⠀⠀⢼⠃⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⣾⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⢻⠗⠀⢸⣇⠄⠀⠀⢨⡔⠀⠈⠀⠀⠈⢿⡿⠀⠀⠰⣿
⢨⢿⣿⣿⣧⣄⣆⣤⣤⡾⠏⠀⠀⢰⡶⣼⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣤⣤⠀⠼⡳⡴⣶⣤⣿⣿⠟⣻⣶⣶⣶⣾⣶⡺⠇⠀⡟
⠸⣦⣀⠹⣿⣷⣀⡍⠽⣧⣀⣀⠀⠀⢰⣿⣿⡆⠹⠄⣄⣠⣰⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⣦⡄⠛⠟⢠⣬⠿⠃⢶⡀⠀⠀⠀⢼⣬⣴⣾⣿⠇⠀⠐⢢⡛⣎⢑⣿⣿⣴⣿⠻⠿⣟⡄⠀⠀⠀⠀⠀
⢰⣾⣿⣿⣿⣯⣾⣀⣠⣾⣿⣿⣿⣶⣿⣽⣿⣷⣶⣦⣞⡎⢹⣿⣿⣷⣷⣅⣀⡀⣾⣿⣿⣤⠀⢢⣤⣼⣿⣿⣿⣧⣀⣄⣼⣿⣆⡀⢮⡴⣀⣀⣠⠄⠀⢹⣿⣿⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⡶⠘⠁⠀⣀⡄⢀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢿⣿⣿⣿⣄⣀⣹⠏⠋⡑⠈⠋⣄⠘⡻⠟⠻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡾⣿⣿⣁⠀⣀⣤⣦⣿⣿⣿⣷⣮⣽⣷⣮⣿⣿⣭⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⡾
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣤⣽⣿⡿⠿⣻⣿⡟⠛⢿⣟⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠙⢿⡿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣋⠀
⣼⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣭⣸⣿⣶⡿⠿⢿⣾⠛⠛⠛⢻⣿⠉⢉⣻⣿⣿⣿⣿⣿⠉⠁⠁⠀⠀⠸⣿⣿⠯⠁⠟⠻⣿⠻⣿⣿⣷⣾⠛⡟⣻⣿⣿⣿⡧⠀
⢙⠟⠛⠏⢉⣿⣿⡆⢰⣄⣽⡟⣿⡟⠁⠈⠙⢛⠿⠛⠉⠛⠛⠿⢿⢻⣿⣿⠋⠈⡿⠁⠉⠙⣿⠄⠀⠀⠈⠀⠰⣿⡸⣅⠀⢸⣿⢿⠿⣿⡿⠋⠀⣀⠿⡅⠀⠠⣞⣩⠀⢠⡄⢤⠼⣀⠙⣿⣿⠟⠀⡁⢸⣿⣿⣿⡇⠀
⠘⠀⣤⣶⡀⣺⣿⠀⠰⠁⠋⠁⠙⠄⠀⠀⢀⣼⡀⠀⠀⠀⠐⡆⡈⠘⠉⠛⠁⣤⡀⠀⠈⣿⠁⠀⠀⢐⠯⠀⢶⣽⣇⣿⣌⠈⠛⠈⢳⠟⠃⠀⠀⢈⣷⡁⡇⠀⠀⠛⣦⠜⠆⠀⠀⠈⢳⣾⠇⠀⠀⠀⠀⠋⡿⢿⠁⠀
⠈⢰⡟⠛⡇⠈⢻⢧⢀⠁⠀⠀⡀⠀⠀⠈⠚⡿⠠⠀⠀⠀⠐⠑⠧⠀⠀⠀⠀⠉⠟⠀⠀⠿⠀⠀⠀⠀⠀⠀⠈⢿⢿⠀⠈⠙⠷⣄⠘⠀⠘⠀⠀⠈⣿⣷⢢⣄⠀⠆⠺⢇⡀⢢⡀⠀⠀⠋⢷⡐⢹⡄⠀⠰⠀⠈⠇⠒
⠀⠀⠰⣠⣧⡀⡎⠈⢛⣴⠟⠋⢉⠛⢿⣶⠀⠀⣰⡾⠛⠉⠛⢿⡇⠀⠀⢘⣵⠞⠛⠉⠛⡻⣶⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⡀⡀⠀⡿⣼⠀⣿⡷⠀⠀⠈⠀⡞⢑⠀⠀⠀⢸⡇⠈⠁⢰⡄⠀⠈⡿⠠
⠸⡷⡀⢨⣿⣿⠗⢀⣿⡏⠀⠀⠀⠀⠀⠛⠀⠀⢿⣧⣀⠀⠀⠀⠁⢇⠀⣾⡏⡴⡆⠀⠉⠃⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣦⢸⡏⠰⡀⢻⠙⡜⢹⡇⠀⠀⠀⢰⣣⠸⠀⠀⠀⠘⠉⣦⠐⢿⠃⠀⠀⠀⠀
⠘⠻⣃⣧⣯⠄⠀⢸⣿⡇⠑⠀⣼⠀⢠⡻⣟⡆⠈⠛⠻⠿⣷⣶⣄⠸⠀⣿⡇⠁⠀⢦⢄⠀⠀⠐⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣃⢰⣿⠏⠣⣄⠙⣾⣤⡇⢸⣷⠀⠀⠠⠀⢹⠆⠀⠀⠀⠀⣼⣿⠀⠇⠀⠀⠀⠀⠀
⠀⠈⣿⣟⠋⢠⡷⠎⣿⣇⠀⠀⠈⠀⢈⣥⠜⠃⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠰⠂⣤⠀⣠⣾⠟⢉⣩⡄⠀⠀⡤⠀⠀⢻⣟⠁⠀⣿⠀⠀⠀⠀⠀⠀⡠⠒⢲⡉⢿⣿⡆⠀⡀⠀⠀⠀⠀
⠀⠀⠘⢹⣏⠀⠀⣾⣮⠻⢦⣤⣤⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⡘⠘⠁⠘⢻⡷⣾⡟⠀⠀⠀⠀⠀⡆⠘⠻⠆⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣮⠟⠀⠀⠀⠀⠀⠀⠀
⣰⡆⠀⠈⠉⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠰⠄⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢸⣯⢜⠀⠀⠀⠀⠀⠀⡷⠀⠀⢀⡟⠁⠈⣿⡆⠀⠀⠀⡀⠀⠀⠁⠹⡀⠀⣀⠀⠀⠀⠀⠀
⢸⠇⣠⠁⠀⠀⢀⣿⠁⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠁⠀⠀⣹⠸⣿⡄⠀⠀⠀⢀⠁⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠘⣷⡄⠀⠠⢀
⠈⠀⣿⡀⠀⠀⣸⠇⠀⢠⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣆⡀⠀⠀⡽⠀⠙⠐⠒⠀⠀⠀⠀⠀⠀⣠⢶⡇⠀⢸⡇⠀⠀⠀⢐⠠⠀⠘⠁⠀⠘⣿⣦⠀⠀⢀⣾
⢐⣶⣿⠿⣆⡀⡌⡀⠀⠼⠟⠀⠀⢠⣀⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⡄⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣈⡀⠀⣸⢯⣠⣠⣀⣼⣷⡶⢦⣤⣤⣤⣼⢥⢤⡆⠀⡿
⢘⣈⠑⠻⣿⣇⠈⠛⣲⣆⠀⠀⠀⠈⢡⣿⣷⡄⢲⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣄⠀⠾⡶⢀⣈⣿⠆⣄⠀⠀⠀⠀⣰⣙⣁⣽⣿⡇⠀⠠⢍⢷⡝⢛⣿⣿⣀⣿⢿⣿⡟⠈⠉⠁⠀⠀⠁
⢀⣼⣷⣶⣿⣟⣻⠅⢀⣹⣿⣿⣶⣤⣼⣻⣿⣏⣤⣄⡽⡄⢿⣶⣶⣤⣦⡃⠀⠀⣴⣶⣶⡀⠀⢄⣀⣸⣾⣷⣿⣇⠀⡀⣸⣿⡀⠀⣜⣡⠀⠀⢀⠉⠙⢻⣿⣿⠀⠀⠀⠈⠑⣷⣶⣿⣿⣿⣿⣤⠰⠋⠁⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠋⠻⣿⣿⣿⣾⡁⠉⢪⣟⠿⠠⠘⠟⠉⠻⢿⡿⢿⡗⣿⣿⣿⣿⣷⣬⣯⣷⣾⣽⣅⣠⣼⣿⣿⠀⠀⠀⢀⣄⣿⣿⣿⣯⣽⣿⣧⣴⣶⣦⣿⣷⣶⣶⣦
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣯⡷
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⢒⣛⣛⠻⠻⣛⣛⡛⢿⢛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢟⣛⣛⣛⣛⡻⢿⣿⡿⢛⣋⣛⠻⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⢟⣿⣽⣿⣾⣿⠋⠁
⣼⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡏⣭⡍⣿⣀⢹⣿⢡⣾⣯⢹⡏⠈⢹⣿⢩⡭⠹⠇⢮⢹⡏⣭⡍⢿⡆⢡⣾⠋⠉⠉⢿⣎⠩⠀⠿⠿⣿⢿⣻⣿⣧⣾⠻⡟⢿⣿⣿⣿⡧⠀
⠻⠟⠛⡟⠛⣿⣿⡄⢠⣌⣽⡟⣻⡿⠉⠈⠻⠿⣿⠟⠛⠻⠿⢿⣿⢧⡙⢿⣦⣄⡺⠋⢸⣿⢸⠅⠀⢸⡇⠀⢸⣿⣤⣼⡆⢘⣿⢸⡇⠻⢃⣾⠇⣾⡇⠀⠀⠀⢸⣿⠀⢠⡀⢠⣼⠀⠛⣿⣿⡿⠀⠃⢹⣿⣿⣿⡇⠀
⠘⠀⣠⣤⠉⢸⣿⠁⠠⠁⠟⠁⠻⡄⠀⠀⢀⣸⠀⠀⠀⠀⠀⡄⠈⠘⣯⠓⠈⡙⣿⡄⢸⣿⠈⠀⠀⢸⡇⠀⢸⣿⢠⠘⠃⣈⠛⢸⡟⠉⠉⠁⠀⢻⣧⠀⡆⠀⢸⡿⣀⠘⡄⠀⠀⠈⢦⢼⠏⠀⠀⠀⠈⠋⡿⢿⠃⠀
⠐⢠⡿⠿⡇⠙⢻⣇⢄⠃⠀⠀⡀⠀⠀⠀⠼⣿⠥⠀⠀⠀⠀⠃⠇⠀⠿⠦⣤⠴⠟⠀⠀⠻⠷⠤⠴⠛⠀⠠⠼⠿⠬⠤⠶⠟⠠⠼⠧⠤⠘⠀⠀⠈⡻⠦⣤⠴⠟⠁⠼⢇⠀⢂⠀⠀⠈⠛⣶⡠⢱⡄⠀⠠⠀⠀⠆⠰
⠀⠀⠱⣠⣇⡀⡎⠈⢛⣴⠟⠋⣉⠛⢿⣶⠀⠁⣰⡾⠛⠉⠛⢿⡇⠀⠀⢐⣴⠞⠛⠉⠛⠻⣶⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⡀⠀⣿⣰⠀⣾⣦⠀⠀⠈⠁⠴⠳⠀⠀⠀⠨⡇⠈⠁⢠⡀⠀⠀⡾⠀
⢰⡦⡀⢙⣿⣷⡇⢀⣿⡏⠀⠀⠈⠀⠀⠛⠀⠀⢿⣧⣀⠀⠀⠀⠁⡆⠀⣾⡏⡆⡄⠀⠐⠃⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⣧⢰⡇⠰⡀⢳⠛⡔⢻⡇⠀⠀⠀⠰⣧⢼⠀⠀⠀⠰⠳⣆⠠⢿⠃⠀⠀⠀⠀
⠘⢿⠓⣊⣯⡉⠀⢸⣿⡇⠠⠀⣼⠀⢀⣲⡶⡆⠈⠛⠻⠿⣷⣶⣄⠸⠀⣿⡇⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠸⠿⠘⢧⡀⠹⣞⣀⡇⢸⣷⠀⠀⢠⠀⢻⡄⠀⠀⠀⠀⣰⣿⠀⠆⠀⠀⠀⠀⠀
⠀⠐⣿⣿⠛⢀⣶⡌⣿⣇⠀⠀⠉⠀⢈⣥⠼⡇⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠒⣲⡄⣠⣶⠟⢉⣡⠆⠀⠀⣀⠉⠀⢽⣟⠃⠀⣿⠀⠀⠀⠀⠈⠀⢀⠒⠶⠘⢿⣿⡄⠀⡀⠀⠀⠀⠀
⠀⠀⠙⢫⡎⠀⠀⣾⣮⠻⢦⣤⣤⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⡈⠀⠃⠘⢻⡿⢿⠇⠀⠀⠀⠁⠀⡄⠘⢻⡄⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣬⠟⠀⠀⠀⠀⠀⠀⠀
⢰⡄⠀⠈⠙⠀⠀⢸⡿⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⣶⡄⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠀⠀⠀⢸⣏⢊⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡾⠁⠉⣵⡄⠀⠀⠀⠀⠀⠀⠃⠹⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠇⢠⠃⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡄⠀⠀⠀⢹⠸⣾⡄⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⢹⡇⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠙⣷⡀⠀⠄⢀
⠈⠀⣿⠀⠀⠀⣸⠃⠀⢠⣿⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣻⠀⠽⠥⠤⠀⠀⠈⠀⠀⠀⣠⣴⡆⠀⢸⡇⠀⠀⠀⠠⢀⠀⠰⠁⠀⠘⣷⣦⠀⠀⢀⣾
⠠⣤⣿⣿⡄⠀⡉⠀⠀⠘⠿⠁⠀⢠⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠈⡁⠀⠸⣟⣁⣀⢀⣼⣧⣤⣤⣤⣀⣀⣸⣉⣤⡄⠈⡿
⠸⡘⠛⠻⣿⣗⠒⠂⢠⡄⠀⠀⠀⠘⢋⣿⣯⡀⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⡀⠈⢴⡤⠀⢐⣿⡆⣀⠀⠀⠀⠀⢠⠛⢃⣹⣿⡇⠀⠀⡉⣭⡛⠛⣿⣿⢁⣾⣿⣿⡿⠘⠛⠀⠀⠀⠃
⢈⣹⣶⣤⣿⣟⣲⠃⠉⣻⣶⣶⣤⣠⣼⣻⣿⣏⣌⠁⠀⠀⢶⣦⣤⣄⣤⠆⠀⠀⣤⣤⣤⠀⠀⠀⠀⢰⣴⣷⣿⡇⠀⠁⢸⣿⡀⠀⡜⣂⠀⠀⠀⠙⠛⢿⣿⣿⠁⠀⠀⠈⠲⣷⣶⣿⣿⣿⡯⢀⠩⠗⠃⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡄⠛⠻⣿⣿⣷⣶⠈⠉⢻⣟⠷⢠⠸⠿⠛⢻⣿⣿⣿⡦⣷⣿⣿⣷⣷⣭⣭⣶⣶⣾⣁⣀⣼⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣏⣛⣷⣥⣤⣤⣴⣶⣧⣶⣶⣤
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⠀⠀⢀⣚⣻⠿⠿⣟⣛⡻⣿⢿⣛⣛⢋⣉⣉⣛⣛⣛⣿⢿⣛⣛⣛⣛⠻⢿⣿⡿⢟⣛⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣻⣿⣽⣶⡿⠃
⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣼⡏⣭⡍⣿⠠⢹⣿⢁⣼⣮⢹⡏⠈⢹⣿⠉⡭⠹⠇⣮⢹⡏⣩⡍⢿⡆⢫⣾⠋⠉⠉⢿⣎⠻⠀⣾⣿⣿⣿⣿⣿⣟⣻⣶⡿⣿⣿⣿⣿⣆⠀
⢿⡿⠿⡿⠿⣿⣿⡁⢀⡙⢿⡿⢿⡿⠛⠛⢿⣿⣿⡿⠿⣿⣿⣿⣿⣧⡙⢿⣦⣍⡰⠋⢸⣿⢸⡋⠉⢸⡇⡄⢸⣿⣤⣼⡆⠰⣾⢸⡇⠻⢃⣾⠇⣾⡇⠀⠀⠀⢸⣿⠀⠠⠀⢀⣩⠈⢿⣿⣿⣟⠀⠇⢺⣿⣿⣿⡇⠀
⡰⠀⢀⣁⠒⢹⣿⠓⢈⠛⠿⠇⢿⡁⠀⠀⠀⢰⠈⠀⠀⠀⢀⡙⠙⠸⣿⠲⠌⠙⣿⡄⢸⣿⠘⠁⠀⢸⡇⠀⢸⣿⢰⠘⠃⣙⠻⢸⡟⣉⡉⠁⠀⢻⣧⠀⡄⠈⢸⡿⠀⢸⡁⠘⠉⠰⣄⣹⡟⠁⠀⠀⠘⠟⣿⣿⠇⠀
⠠⠀⣾⣿⡆⠺⢿⡇⠀⠇⠀⠀⡀⠁⠀⠠⣰⣿⡂⠀⠀⠀⠀⠇⠔⠀⠿⠦⣤⠴⠟⠀⠀⠻⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⠠⠀⠀⠈⣻⠦⣥⠴⠟⡁⣻⡄⠁⠀⠀⠀⠘⡾⣤⠀⢢⡀⠀⢀⠋⠈⡄⣠
⠀⠈⢃⠁⡇⠀⡜⠹⢂⣴⠟⠋⣩⠛⢿⣶⠀⠃⣰⡾⠛⢉⠛⢿⡆⠀⠀⢀⣴⠞⠛⠉⠛⠻⣶⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣷⠀⠀⠀⠀⠀⢿⢹⠀⣷⣄⠀⠈⠰⠂⣸⢆⠀⠀⠀⠹⡇⠘⠇⢀⠈⠀⠀⣥⠀
⢠⣄⠀⠻⣿⣦⡇⢀⣿⡏⠀⠀⠛⠀⠀⠛⠀⠀⢿⣧⣀⠀⠀⠀⠁⡄⠀⣾⡏⡤⠄⠀⠲⠗⠛⠃⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣹⡇⢠⡆⢃⠀⣯⠟⢠⢿⡇⠀⠀⠀⢀⡆⣰⠀⠀⠀⢀⡧⡀⠀⣼⡇⠀⠀⠃⠀
⠸⢷⠆⠜⣟⠛⠁⢸⣿⡇⢄⠀⣠⠀⠀⢤⣤⡀⠈⠛⠻⠿⣷⣶⣄⢱⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⢀⡀⠀⠀⠄⠁⡀⠟⠃⠸⡇⠀⢷⡴⠀⡇⢸⣇⠀⠀⠀⠈⢿⡈⠀⠀⠀⠀⢠⣾⠀⡍⠀⠀⠀⠀⠀
⠀⠨⣶⣿⠿⠁⣀⡌⣿⣇⠀⠀⠟⠀⢈⣬⢵⡇⣤⠀⠀⠀⠀⢹⣿⢀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⢀⡀⠀⠁⠎⠷⢀⣤⢆⣥⠘⠃⠀⠀⠈⠓⠀⣿⡿⠇⠈⣿⠀⠀⠈⠀⠘⠁⠀⠀⢤⠤⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⢟⡄⠘⠉⣽⣮⠻⢦⣤⣤⣤⠾⠋⢸⡇⠿⣷⣤⣤⣤⡾⠟⠘⠀⢠⠛⢷⣤⣤⣤⡾⠋⠀⠀⠈⢁⠀⠠⠀⠀⠹⢿⣿⡟⠁⠀⠀⠀⠋⠀⡀⠸⢷⡀⢀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠐⢧⣘⣿⠃⠀⠃⠀⠀⠀⠀
⢠⡀⠀⠘⠧⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⢸⡏⠀⡇⠀⠀⠀⠀⠀⣇⠀⠈⠁⣼⠟⠢⣤⡀⠀⠀⠀⠀⠀⠀⠏⢿⠁⠀⠀⠀⠀⠀⠀⠀
⢸⡇⢀⠆⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⢠⠘⠀⠀⠈⢳⢸⣤⠀⠀⠀⠀⠀⠏⠀⠀⠰⠃⠀⠀⢻⡇⠀⠀⠀⠆⠀⠀⢠⠈⠂⠀⢲⣄⠀⠀⠀⠀
⠘⠀⣾⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⡾⣀⣿⣃⣀⠀⠀⠐⠀⠀⠀⠀⣀⡄⠀⢸⡇⠀⠀⠀⢀⠀⠀⢠⠄⠀⢠⣤⣙⠃⠀⠀⣴
⢀⣀⣿⣦⡀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠂⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠹⠃⠀⢸⡧⠀⠀⠀⣰⣄⣀⣀⠀⠀⠀⢻⠛⢀⡀⠘⣿
⢰⠹⠿⢽⣷⡦⠤⠄⢀⡀⠀⠀⠀⠸⠟⣾⣔⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠘⢡⣀⠀⠠⣦⡄⠀⠀⠀⠀⠀⢀⠾⠟⢿⣶⡆⠀⠘⠽⣞⢾⡶⣿⣿⠋⣭⣿⣿⣿⠻⠽⠝⠃⠀⠏
⠐⢳⣤⣠⣿⣷⢤⠄⠚⢷⣤⣤⣀⠀⣸⢿⣿⡇⠘⠂⠀⠀⣄⣀⡁⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣃⣷⡆⠀⠋⢰⣖⠛⠁⢲⠄⠀⠀⠀⠾⢶⣶⣿⣿⠃⠀⠈⠱⢍⣧⣀⣿⣿⣶⣯⠙⢛⡫⠄⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣴⣤⣆⡘⠛⢿⣿⣿⣦⣤⠒⠚⠻⢿⡦⠀⢰⣶⢾⣿⣿⣿⣧⣄⣤⣾⣿⣦⣄⠳⣖⣄⣤⡴⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⣹⣿⣿⡟⢿⣿⡍⠈⣀⣀⣠⣄⣀⣀⡀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⠀⠀⢀⣚⣻⠿⠿⣟⣛⡻⣿⢿⣛⣛⢋⣉⣉⣛⣛⣛⣿⢿⣛⣛⣛⣛⡻⢿⣿⡿⢟⣛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣽⣶⡿⠉
⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣼⡏⣭⡍⣿⠠⢹⣿⢁⣼⣮⢹⡏⠈⢹⣿⠉⡭⠹⠇⣮⢹⡏⣭⡍⢿⡆⢫⣾⠋⠉⠉⢿⣎⠛⠀⣽⣿⣿⣿⢿⣿⣏⣻⣶⡿⣿⣿⣿⣿⡆⠀
⢿⡿⠿⡿⠿⣿⣿⡁⢀⡙⢿⡿⣿⡿⠛⠛⢿⣿⣿⡿⠿⣿⣿⣿⣿⣧⡙⢿⣦⣍⡰⠋⢸⣿⢸⡋⠉⢸⡇⡄⢸⣿⣤⣼⡆⠰⣾⢸⡇⠻⢃⣾⠇⣾⡇⠀⠀⠀⢸⣿⠀⡠⠀⢀⣩⠈⢿⣿⣿⣿⠀⠇⢺⣿⣿⣿⡏⠀
⡰⠀⠀⣁⠒⢹⣿⠓⢈⠛⠿⠇⢿⡁⠀⠀⠀⢰⠈⠀⠀⠀⢀⡉⠙⠸⣽⠳⠌⠙⣿⡄⢸⣿⠘⠁⠀⢸⡇⠀⢸⣿⢰⠘⠃⣙⠻⢸⡟⣉⠉⠁⠀⢻⣧⠀⡄⠈⢸⡿⠀⢸⡁⠘⠉⠰⣄⣹⡟⠁⠀⠀⠘⠟⣿⣿⠇⠀
⠠⠀⣾⣿⡆⠺⢿⡇⡀⠇⠀⠀⡀⠁⠀⠰⣰⣿⡂⠀⠀⠀⠀⠇⠔⠀⠿⠦⣤⠴⠟⠀⠀⠻⠷⠤⠴⠛⠀⠠⠼⠿⠤⠤⠴⠟⠠⠼⠧⠤⠠⠀⠀⠈⣻⠦⣥⠴⠟⡁⣻⡄⠁⠀⠀⠀⠘⡿⣤⠀⢢⡀⠀⢀⠃⠈⡄⣠
⠀⠈⢃⠁⡇⠀⡜⠹⢂⣴⠟⠋⢩⠛⢿⣶⠀⠃⣰⡾⠛⢉⠛⢿⡆⠀⠀⢀⣴⠞⠛⠉⠛⠻⣶⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣷⠀⠀⠀⠀⠀⣿⢹⠀⣷⣄⠀⠈⠐⠂⢨⢆⠀⠀⠀⠹⡇⠘⠇⢀⠈⠀⠀⣵⠀
⢠⣄⠀⠻⣿⣦⡇⢀⣿⡏⠀⠀⠛⠀⠀⠛⠀⠀⢿⣧⣀⠀⠀⠀⠁⡄⠀⣾⡏⡤⠄⠀⠲⠗⠛⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣹⡇⢠⡆⢃⠀⣯⠟⢠⢿⡇⠀⠀⠀⢀⣆⣰⠀⠀⠀⢀⡧⡀⠀⣼⡇⠀⠀⠃⠀
⠸⢷⡆⡜⣟⠛⠁⢸⣿⡇⢄⠀⣠⠀⠀⢤⣤⡀⠈⠛⠻⠿⣷⣶⣄⢱⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⢀⡀⠀⠀⠀⠁⡠⠟⠃⠸⡇⠀⢷⡼⠀⡇⢸⣇⠀⠀⠀⠈⢿⡈⠀⠀⠀⠀⢠⣾⠀⡍⠀⠀⠀⠀⠀
⠀⠨⣶⣿⠿⠁⣀⡌⣿⣇⠀⠀⠟⠀⢈⣬⢵⡇⣤⠀⠀⠀⠀⢹⣿⢀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⢀⡀⠀⠁⠎⠷⢀⣴⢎⣥⠘⠃⠀⠀⠈⠓⠀⣿⡿⠇⠈⣿⠀⠀⠈⠀⠘⠁⠀⠄⣄⠤⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠻⢟⡄⠘⠉⣽⣮⠻⢦⣤⣤⣤⠾⠋⢸⡇⠿⣷⣤⣤⣤⡾⠟⠘⠀⢠⠛⢷⣤⣤⣤⡾⠋⠀⠀⠈⢁⠀⠠⠀⠀⠹⢿⣿⡟⠁⠀⠀⠀⠋⠀⡀⢸⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠐⢧⣘⣿⠃⠀⠃⠀⠀⠀⠀
⢠⡀⠀⠘⠧⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⢸⡏⠀⡇⠀⠀⠀⠀⠀⣇⠀⠈⠁⣼⠟⠢⣤⡀⠀⠀⠀⠀⠀⠀⠏⢿⠁⠀⠀⠀⠀⠀⠀⠀
⢸⡇⢀⠆⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⢠⠘⠀⠀⠈⢳⢸⣤⠀⠀⠀⠀⠀⠏⠀⠀⡰⠃⠀⠀⢻⡇⠀⠀⠀⠆⠀⠀⢠⠈⠂⠀⢲⣄⠀⠀⠀⠀
⠘⠀⣾⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⡼⣈⢿⣃⣀⠀⠀⠐⠀⠀⠀⠀⣀⡄⠀⢸⡇⠀⠀⠀⢀⠀⠀⢠⠆⠀⢠⣤⣙⠃⠀⠈⣴
⢀⣀⣿⣦⡀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠂⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠹⠃⠀⢸⡧⠀⠀⠀⣰⣌⣀⣀⠀⠀⠀⢻⠛⢀⡀⠘⣿
⢰⠹⠿⢽⣷⡦⠤⠄⢀⡀⠀⠀⠀⠸⠟⣾⣔⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠘⢡⣀⠀⠠⣦⡄⠀⠀⠀⠀⠀⢀⠾⠟⢻⣶⡆⠀⠘⠽⣞⢾⡶⣿⣿⠋⣭⣿⣿⣿⠻⠽⠝⠃⠀⠏
⠐⢳⣤⣠⣿⣷⢤⠄⠚⢷⣤⣤⣀⠀⣸⢿⣿⡇⠘⠂⠀⠀⣄⣀⡁⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣁⣶⡆⠀⠋⢰⣶⠛⠁⢲⠄⠀⠀⠀⠾⢶⣶⣿⣿⠃⠀⠈⠱⢍⣧⣀⣿⣿⣶⣯⠉⢛⡣⠄⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣴⣤⣄⡘⠻⢿⣿⣿⣦⣤⠚⠛⠻⢿⣦⠀⢰⣶⠾⣿⣿⣿⣧⣄⣤⣾⣿⣦⣄⠳⡖⣄⣤⡴⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⣹⣿⣿⡟⢿⣧⡍⢈⣀⢀⣠⣄⣀⣀⡀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠀⠀⢀⣙⣻⠿⣿⣟⣛⣿⣿⣿⣛⣻⢀⣀⣛⣘⣛⣻⣿⣿⣟⣛⣛⣛⡿⢿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⡟
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣼⡏⣭⡍⣿⢠⢹⣿⠁⣻⣮⢹⡏⡌⢹⣿⢉⡭⠹⠇⣮⢹⡏⣩⡍⢿⡎⢫⣾⠋⠉⠉⢿⣎⠻⠋⣽⣿⣿⣿⣿⣿⡿⢿⣧⣷⣿⣿⣿⣯⡥⠀
⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣦⣍⡲⠂⢸⣿⢸⠟⠛⢸⡇⠁⢸⣿⣬⣼⡇⠲⣽⢸⡇⠻⢃⣾⠇⣾⡇⠀⠀⠀⢸⣿⠀⢀⠉⠉⠻⠙⣿⣿⣿⣿⠙⡏⢽⣿⣿⣿⡗⠀
⢨⠁⠀⠃⠤⢻⣿⡧⠘⠷⢾⡏⣿⠁⠀⠀⠈⢉⠛⠋⠀⠉⠉⠻⠻⠙⣯⢳⡈⠙⣿⡄⢸⣿⠸⠃⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢉⡩⠁⠀⢻⣧⠀⡀⠐⢸⡿⠀⢲⠆⠺⠛⢤⡉⢿⡿⠋⠐⠁⠸⡿⣿⣿⡇⠀
⢁⠀⣴⣿⡄⢼⣿⡇⠀⡆⠈⠀⡈⠂⠀⠀⢢⣶⠄⠀⠀⠀⠈⠇⠠⠀⠿⠦⣤⠴⠟⡀⠀⠻⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⢁⠀⠀⢈⣻⠦⣥⠴⠟⠁⢷⡈⠃⠀⠀⠀⠹⣽⡁⠀⢄⠀⠀⠀⠟⢙⡀⠀
⠀⠐⠏⠋⡇⠀⠸⠳⢀⣴⠟⠋⢉⠛⢿⣶⠈⠏⣰⡾⠛⠉⠛⢿⡇⠀⠀⢀⣴⠞⠛⠉⠛⠻⣶⡆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⡀⠈⠀⠀⠀⣿⢿⠳⣦⡀⠁⠙⢣⠄⠱⡄⠀⠀⠁⢻⡆⠸⣇⠀⠘⠀⠀⣃⠉
⢀⡀⠈⢶⣷⣄⡇⢀⣿⡏⠀⠀⠿⠀⠀⠛⠀⠀⢿⣧⣀⠈⠀⠀⠡⡄⠀⣾⡏⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠟⠃⣾⠇⠀⡀⠆⠀⣿⡼⢀⣿⡟⠀⠀⠀⠀⡊⢨⠀⠀⠀⠀⣇⠀⠀⣸⡆⠀⠀⠟⠀
⢺⣏⡄⡰⣿⠿⠃⢸⣿⡇⡀⠀⢀⠀⠀⣀⣀⠀⠈⠛⠻⠿⣷⣶⣄⢣⠀⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠋⡼⣦⠀⠀⠀⠀⢰⠋⠀⢸⡇⠈⣄⢩⠁⡎⢸⡇⠀⠀⠀⠘⣵⠘⠀⠀⠀⠈⢑⣵⠀⡻⠁⠀⠀⠀⠀
⠀⢙⣥⣷⣿⠂⠀⡈⣿⣇⠈⠀⡿⠀⢀⣬⢯⡇⣤⠀⠀⠀⠀⢹⣿⢈⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⢀⡀⠀⢀⠀⠀⠀⣀⣤⣴⠉⠀⠀⠀⠑⠤⠈⣿⣦⡇⠘⣿⠀⠀⠐⠀⠸⠂⠀⠀⠀⣀⣼⣿⡀⠁⠀⠀⠀⠀⠀
⠀⠀⢿⡯⡀⠰⠛⣻⣎⠻⢦⣤⣤⣤⠾⠋⣼⡇⠿⣷⣤⣤⣤⡾⠟⢸⠀⣦⠛⢷⣤⣤⣤⡾⠋⠀⠀⠘⠁⠀⠸⠀⠀⠨⡿⣿⠃⢰⠀⠀⠀⠖⠀⠀⢹⣯⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠉⠹⣆⠹⣿⠇⠀⠄⠀⠀⠀⠀
⢀⠀⠈⠸⣇⠀⠀⢿⣿⠀⢀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠒⠀⠀⠀⠀⡈⠀⢹⡇⠀⠀⠀⣀⠀⠘⡆⠀⠀⠈⠀⠀⢢⠀⠀⢱⡇⠀⡄⠀⠀⠀⠀⠈⣇⠈⠙⠃⢰⡿⢀⣀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠋⠀⠀⠀⠀⠀⠀⠀
⢼⡇⠀⡄⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⡟⠀⠀⠀⠀⢶⠀⠀⠀⠘⡄⠀⠘⢧⢰⣃⠀⠀⠀⠀⠀⡟⠀⠀⢠⠏⠀⠀⢾⡇⠀⠀⠀⡄⠀⠀⢀⠘⠄⠀⢤⡀⠀⠀⠀⠀
⠸⠁⣼⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠃⠀⠀⠀⣼⠘⣿⡆⠀⠀⠀⠠⠁⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣈⠻⠆⠀⠐⢠
⠀⠀⣿⣄⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠆⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⡟⠂⠘⠈⠓⠂⠀⠀⠀⠀⢀⣴⢻⡟⠀⢸⣇⠀⠀⠀⠀⡂⠀⠈⠀⠀⠈⢿⡿⠀⠀⠰⣿
⢠⢻⣿⣻⣧⡄⢀⡀⠀⠀⠀⠀⠀⢸⡷⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⢣⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⡤⠀⠸⣣⡤⣤⣤⣶⣷⠟⣶⣶⣶⣶⣾⣲⡲⠇⠀⡟
⠨⢦⡈⠙⣿⣧⣀⡁⠼⣇⣀⣀⠀⠀⢰⣿⣿⣆⠹⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⡀⠈⠛⢠⣾⠿⠃⢤⡀⠀⠀⠀⣴⣨⣥⣾⣿⠏⠀⠐⢤⡻⡎⠉⣿⣿⣤⣿⠻⢿⣟⡀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣴⣿⣽⣿⣧⣦⣀⣀⡀⢰⣶⣷⣶⣷⣥⠀⢰⡄⠶⢾⡄⠀⢠⣤⣼⣾⣿⣿⣇⡀⣀⣸⣷⣄⣀⣎⣤⡀⠀⢀⡀⠉⠙⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠂⠘⠉⠀⢀⠀⠀⠀⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢾⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠋⠋⢉⣛⣻⠿⣿⣟⣛⣿⣿⣿⣟⣻⣆⣘⣚⣃⣘⣻⣿⣿⣟⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⠾
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣼⡏⣭⡍⣿⠸⢹⣿⠙⢿⣏⢹⡏⠉⢹⣿⢩⠍⠹⢏⣏⢹⡏⢩⡍⢿⡎⢫⣾⠋⠉⠉⢿⣎⢻⠟⣻⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣛⠁
⣾⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣦⣍⡂⠀⢸⣿⢰⣿⡿⢸⡇⠀⢸⣿⣬⣼⡆⠀⠉⢸⡇⠺⢃⣾⠇⣾⡇⠀⠀⠀⢸⣿⠀⠀⠟⠻⣿⠿⣿⣿⣧⣿⠻⡟⣿⣿⣿⣿⡧⠀
⢙⠛⠛⠏⢉⢻⣿⣇⠠⣦⣽⡟⣿⠋⠁⠉⠻⠟⢿⠟⠛⠛⠟⢿⣿⠛⣭⢲⠎⠙⣿⡄⢸⣿⢸⠅⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢉⣭⠅⠀⢻⣧⠀⠀⠀⢸⡿⠀⢤⡄⢴⠴⡀⠛⣿⣿⠗⠠⠃⢹⣿⣿⣿⡇⠀
⠚⠀⣠⣶⡀⣸⣿⡇⠀⡅⠘⠁⡋⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠆⠀⠀⠿⠦⣥⠴⠟⠀⠀⠻⠷⢤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⠉⠀⠀⠈⡻⠦⣤⠴⠟⠑⣆⠜⠆⠀⠀⠈⢷⣼⠇⠀⠀⠀⠀⠋⡿⠿⡃⠀
⠈⠠⡟⠟⡇⠈⢻⣧⢀⣴⠟⠋⠉⠛⢿⣶⢘⡟⣰⡾⠛⠉⣛⢿⡆⠀⠀⢀⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⣿⠀⠘⠀⠀⠈⣿⣷⢦⣀⠀⠀⠾⢇⡀⢢⡀⠀⠀⠋⢶⡄⢹⡆⠀⠠⠀⠀⠇⠖
⠀⠀⠐⣤⣧⡀⡆⢀⣿⡏⠀⠀⡟⠀⠀⠛⠀⠀⢿⣧⣀⠐⠉⠈⢡⠀⠀⣾⡏⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠐⠖⣴⡄⠀⠀⠎⠉⢠⡟⠀⠀⠀⡀⠀⣿⣸⠀⣿⡷⠀⠀⠈⠀⠴⢳⠀⠀⠀⠈⡇⠈⠉⢰⡄⠀⠀⡾⠀
⢸⡗⡄⢈⣿⣿⠇⢸⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣶⣄⢇⠀⣿⡇⠀⠀⠀⠀⢠⡄⠀⠀⠰⠂⠀⡀⠃⠃⠀⠀⠘⠀⣾⠀⠀⢰⡇⠰⡀⢛⠃⡜⢻⡇⠀⠀⠀⠰⣧⠸⠀⠀⠀⠀⠟⣦⠀⢿⠃⠀⠀⠀⠀
⠘⠻⣃⣧⣯⡉⠀⠈⣿⣇⠰⢀⡶⠀⢀⣤⠟⡆⣤⠀⠀⠀⠀⢹⣿⠸⠀⢿⣧⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠠⢱⠀⠀⠀⢀⣤⡿⠁⠀⠀⠘⠣⣀⠹⣾⣄⡇⢸⣷⠀⠀⠠⠀⢻⠄⠀⠀⠀⠀⣰⣿⠀⠇⠀⠀⠀⠀⠀
⠀⠈⣿⣿⠋⢠⡶⢿⡎⠻⢦⣤⣥⣤⠾⠋⣼⡇⠿⣷⣤⣤⣤⡾⠟⢰⠀⣦⠛⢷⣤⣤⣤⡾⠋⠀⠀⢸⠃⠀⠸⠀⠀⠀⣿⣿⠁⢸⠀⠀⠀⣀⠀⠀⢻⣟⠃⠀⣿⠀⠀⠀⠀⠀⠀⢀⠒⢲⡝⢿⣿⡆⠀⡀⠀⠀⠀⠀
⠀⠀⠘⢹⡇⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠐⠆⠠⠀⠀⠀⠈⠀⢻⡆⠀⠀⢀⠀⠀⠰⡆⠀⠀⠀⠀⠀⢎⠀⠀⢨⡇⠀⡈⠀⠀⠀⠁⠐⡆⠘⢻⠆⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣮⠟⠀⠀⠀⠀⠀⠀⠀
⣰⡆⠀⠈⠁⠀⠀⣿⡏⠀⠘⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣇⠀⠀⠀⣿⠀⠀⡇⠀⣀⠀⠀⠀⠸⠀⠀⠘⣧⢠⠇⠀⠀⠀⠀⠀⢽⠀⠀⢀⡾⠁⠈⣽⡆⠀⠀⠀⡀⠀⠀⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀
⢸⠇⣠⠁⠀⠀⠀⠉⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠋⠀⠀⠀⠀⠈⣧⠀⠀⠀⠁⠀⠁⣼⠸⣿⡄⠀⠀⠀⢀⠃⠀⠀⠚⠀⠀⠀⢹⡇⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠘⣷⡄⠀⠀⢀
⠈⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⡿⠀⠹⠡⠦⠀⠀⠈⠀⠀⠀⣠⢴⡶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⣿⣦⠀⠀⢀⣾
⠀⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣰⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡆⠀⠀⢄⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣈⡁⠀⠸⣟⣁⣀⢂⣬⣧⣤⣤⣤⣤⣠⣸⡍⢤⡆⠈⣿
⢸⣈⠓⢻⣿⣇⠐⠛⣿⡷⠆⠀⠀⠈⢫⣿⣿⡄⢤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠘⡤⢀⣼⣿⡆⢀⠀⠀⠀⠀⢀⠛⢛⣹⣿⡗⠀⠀⡉⣧⡟⠛⣿⣿⣁⣷⣿⣿⡿⠙⠉⠀⠀⠀⠁
⢠⣿⣷⣾⣿⣿⣿⠿⠿⣿⣷⣷⣤⣠⣾⣻⣿⣏⡌⠀⠐⠀⢦⣤⣶⣦⣦⣂⠀⢀⣀⣤⣤⠀⠀⠀⢀⣰⣤⣷⣿⡇⠀⠀⢸⣿⡀⠀⡸⣁⠀⠀⠀⠙⠛⠿⣿⣿⠀⠀⠀⠈⠐⣷⣶⣿⣿⣿⣿⠀⠰⠟⠁⠀⠀⠀⠀⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢀⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⣹⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢛⣛⣻⠿⣿⣟⣛⣿⣿⣿⣟⣻⣇⣘⣛⣛⣘⣻⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣵
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⣼⡏⣭⡍⣿⠘⢹⣿⠹⣿⡟⢹⡏⠉⢹⣿⢩⠍⠹⠏⠯⢹⡏⢩⡍⢿⡎⢫⣾⠋⠉⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣾⣿⠟⠀
⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣦⣅⡂⠀⢸⣿⢠⣾⡟⢸⡇⠀⢸⣿⣤⣼⡆⠀⠀⢸⡇⠺⢃⣾⠇⣾⡇⠀⠀⠰⢸⣿⠈⠀⡿⠿⣿⣿⣿⣿⣯⣿⢾⡿⢿⣿⣿⣿⣏⠀
⠻⠟⠛⡟⠛⢿⣿⡇⢀⣌⣻⡿⣿⠟⠋⠛⢿⡿⣿⡿⠛⠿⠿⣿⣿⠟⣭⢲⠌⠙⣿⡄⢸⣿⢸⡅⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢉⣭⡵⠀⢻⣧⠀⠀⠀⢸⡿⠀⢐⡀⣠⣭⠀⠿⣿⣿⡯⢀⡇⢹⣿⣿⣿⡇⠀
⠜⠀⢠⣤⠈⢸⣿⡏⠀⡍⠹⠃⡋⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠌⠉⠀⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⠙⠀⠀⠈⡻⠦⣤⠴⠟⠵⡄⡸⡅⠈⠀⠙⢦⣽⠏⠀⠀⠀⠈⠏⣿⢿⡃⠀
⠐⠠⡟⡿⡇⠙⢻⣇⢀⣴⠟⠋⠉⠛⢿⣶⠸⡟⣱⡾⠛⠉⠛⢿⡆⠀⠀⢀⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⣿⠀⠰⠀⠀⠘⣿⣦⣄⡀⠀⠀⣽⡆⠀⢄⠀⠀⠈⠟⣤⡀⢱⡄⠀⠠⠁⠀⡇⠴
⠀⠀⠡⣀⣇⡀⡌⢀⣿⡏⠀⠀⡶⠀⠀⠛⠈⠁⢿⣧⣀⠠⠋⠀⣅⠀⠀⣾⡏⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠁⡿⡆⠀⠀⠉⠍⢠⡟⠀⠀⠀⡀⠀⣿⢹⠈⣿⣦⠀⠀⠘⠁⡨⢣⠀⠀⠀⠘⡇⠘⠓⢠⡀⠀⠀⣴⢀
⢰⡧⡀⢈⣿⣷⡇⢸⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣶⣌⠇⠀⣿⡇⠀⠀⠀⠀⢠⡆⠀⠀⠸⠆⠀⡄⠁⠀⠀⠀⠘⢀⣾⠀⠀⢠⡆⠡⠀⠿⠇⡰⢻⡇⠀⠀⠀⢠⢆⢸⠀⠀⠀⠀⠷⢄⠀⣾⠇⠀⠀⠁⠀
⠘⢿⠇⣎⣟⠉⠀⠀⢿⣇⠢⠀⣤⠀⢀⣤⠴⡄⣤⠀⠀⠀⠀⢹⣿⠠⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠠⣼⠀⠀⠀⢀⣤⡏⠁⠀⠀⠸⢇⠀⠳⣼⡀⡇⢸⣷⠀⠀⢀⠀⢿⡀⠀⠀⠀⠀⢰⣿⠀⠎⠀⠀⠀⠀⠀
⠀⠐⣿⡿⠛⢁⣤⣶⣮⠻⢦⣬⣥⣤⠾⠋⣼⡇⠿⣷⣤⣤⣤⡾⠟⢴⠀⣦⠛⢷⣤⣤⣤⡾⠋⠀⠀⢲⠆⠀⠹⠀⠀⠀⢸⣿⠁⢹⠀⠀⠀⣀⠉⠀⢿⡿⠃⠈⣿⠀⠀⠀⠀⠈⠀⠀⠤⢤⡲⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠹⢫⡆⠉⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠐⠄⠀⠀⠀⠀⠈⠀⢻⠀⠀⠀⢀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡜⠂⠀⢇⡏⠀⠘⠀⠀⠀⠃⠠⡄⠸⢿⡄⢀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠈⣳⣌⡿⠁⠀⠁⠀⠀⠀⠀
⢰⡄⠀⠈⠓⠀⠀⣿⡏⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣦⡀⠀⠈⣿⠀⠀⡇⠀⣀⠀⠀⠀⢸⠀⠀⠘⣇⢀⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⣼⠋⠐⣲⡄⠀⠀⠀⠀⠀⠀⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀
⢹⠇⢠⠂⠀⠀⠀⠀⠁⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣧⠀⠀⢙⠀⠀⠁⠀⠙⣧⠀⠀⠀⠂⠀⠀⣸⢸⣶⡀⠀⠀⡀⠐⠇⠀⠀⠼⠁⠀⠀⢻⡇⠀⠀⠀⠃⠀⠀⠰⠀⠁⠀⠹⣦⡀⠀⢀⠀
⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⣿⠀⢹⢣⣀⠀⠀⠘⠀⠀⠀⢀⣠⣤⠀⢸⡇⠀⠀⠀⠀⡀⠀⠠⠂⠀⠰⣷⣬⠁⠀⢀⣼
⠠⣤⣿⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣄⢠⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠘⠃⠀⢸⡷⠂⠀⠀⣀⣆⣤⣀⣀⣀⣀⣹⡛⣀⡄⠈⣿
⠸⠙⠫⢿⣿⡆⠐⢶⣿⣧⠀⠀⠀⠘⢏⣿⣶⡀⣤⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠘⠀⠀⡀⠀⠀⠰⣠⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠿⠟⣻⣿⡯⠀⠀⠛⣏⡻⠷⢿⣯⠁⣿⣿⣿⣿⠛⠒⠊⠁⠀⠋
⢈⣿⣶⣾⣿⣿⢶⡶⠿⢷⣶⣶⣀⣀⣼⣿⣿⡗⡘⠁⠀⠀⣤⣤⣤⣇⣄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⣠⣤⣿⡆⠀⠁⢸⣿⠉⠁⢸⠂⠀⠀⠀⠺⠶⣾⣿⣿⠁⠀⠀⠑⠨⣧⣤⣿⣿⣿⣿⠈⢉⡵⠂⠀⠀⠀⠀⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢀⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣹⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢛⣛⣻⠿⣿⣟⣛⣿⣿⣿⣟⣻⣇⣈⣛⣛⣘⣻⣿⣿⣟⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣵
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⣼⡏⣭⡍⣿⠘⢹⣿⠹⣿⡟⢹⡏⠉⢹⣿⢩⠍⠹⠏⠯⢹⡏⢩⡍⢿⡎⢫⣾⠋⠉⡉⢿⣎⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣾⣿⠟⠀
⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣦⣅⡂⠀⢸⣿⢠⣾⡟⢸⡇⠀⢸⣿⣤⣼⡆⠀⠀⢸⡇⠺⢃⣾⠇⣾⡇⠀⠀⠰⢸⣿⠈⠀⠿⢿⣿⣿⣿⣿⣯⣿⢿⡿⢿⣿⣿⣿⣏⠀
⠻⠟⠛⡟⠛⢿⣿⣇⢀⣌⣻⡿⣿⠟⠋⠛⢿⡿⣿⡿⠛⠿⡿⣿⣿⠟⣭⢲⠌⠙⣿⡄⢸⣿⢸⡅⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢉⣭⡵⠀⢻⣧⠀⠀⠀⢸⡿⠀⢐⡀⣠⣭⠀⠿⣿⣿⡯⢀⡇⢹⣿⣿⣿⡇⠀
⠜⠀⢠⣤⠈⢸⣿⡏⠀⡍⠹⠃⡋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠌⠉⠀⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⠙⠀⠀⠈⡻⠦⣤⠴⠟⠵⡄⠸⡅⠈⠀⠙⢦⣽⡏⠀⠀⠀⠈⠋⣿⢿⡃⠀
⠐⢀⡟⡿⡇⠙⢻⣇⢀⣴⠟⠋⠉⠛⢿⣶⠸⡟⣱⡾⠛⠉⠛⢿⡆⠀⠀⢀⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⣿⠀⠰⠀⠀⠘⣿⣦⣄⡀⠀⠀⣽⡆⠀⢄⠀⠀⠈⠟⢤⡀⢱⡄⠀⠠⠁⠀⡇⠴
⠀⠀⠡⣀⣇⠀⡌⢀⣿⡏⠀⠀⡶⠀⠀⠛⠈⠁⢿⣧⣀⠠⠋⠀⣅⠀⠀⣾⡏⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠃⠿⡆⠀⠀⠉⠅⢠⡟⠀⠀⠀⡀⠀⣿⢹⠈⣿⣦⠀⠀⠘⠁⣨⠣⠀⠀⠀⠘⡇⠈⠓⢠⡀⠀⠀⣴⢀
⢰⡧⡀⢈⣿⣷⡇⢸⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣶⣌⠇⠀⣿⡇⠀⠀⠀⠀⢠⠆⠀⠀⠸⠆⠀⡄⠁⠀⠀⠀⠘⠀⣼⠀⠀⢠⡆⠡⠀⠿⠇⡰⢻⡇⠀⠀⠀⢠⢆⢸⠀⠀⠀⠀⠷⢄⠀⣾⠇⠀⠀⠁⠀
⠘⢻⠗⣎⣟⠉⠀⠀⢿⣇⠠⠀⣤⠀⢀⣤⠴⡄⣤⠀⠀⠀⠀⢹⣿⠨⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠠⣼⠀⠀⠀⢀⣤⡏⠁⠀⠀⠸⢇⠀⠳⣼⡀⡇⢸⣷⠀⠀⢀⠀⢿⡀⠀⠀⠀⠀⢰⣿⠀⠎⠀⠀⠀⠀⠀
⠀⠐⣿⡿⠛⢁⣤⣶⣮⠻⢦⣬⣥⣤⠾⠋⣼⡇⠿⣷⣤⣤⣤⡾⠟⢴⠀⣦⠛⢷⣤⣤⣤⡾⠋⠀⠀⢲⠆⠀⠹⠀⠀⠀⠸⣿⠁⢹⠀⠀⠀⣀⠉⠀⢿⡿⠃⠈⣿⠀⠀⠀⠀⠈⠀⢀⠤⢤⡲⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣫⡆⠉⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠐⠄⠀⠀⠀⠀⠈⠀⢻⠀⠀⠀⢀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡼⠂⠀⢇⡏⠀⠘⠀⠀⠀⠃⠠⡄⠸⢿⡄⢀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠈⣳⣌⡿⠁⠀⠁⠀⠀⠀⠀
⢰⡄⠀⠈⠓⠀⠀⣿⡏⠀⠐⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣦⡀⠀⠈⣿⠀⠀⡇⠀⣀⠀⠀⠀⢸⠀⠀⠘⣇⢀⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⣼⠋⠐⣲⡄⠀⠀⠀⠀⠀⠀⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀
⢹⠇⢠⠂⠀⠀⠀⠀⠁⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⠀⢛⠀⠀⠁⠀⠙⣧⠀⠀⠀⠂⠀⠀⣸⢸⣶⡀⠀⠀⡀⠐⠇⠀⠀⠼⠁⠀⠀⢻⡇⠀⠀⠀⠃⠀⠀⠰⠀⠁⠀⠹⣦⡀⠀⢀⠀
⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣿⠀⢹⢣⣀⠀⠀⠘⠀⠀⠀⢀⣠⣤⠀⠸⡇⠀⠀⠀⠀⡀⠀⠠⠂⠀⠰⣷⣬⠁⠀⢀⣼
⠠⣤⣿⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣄⢠⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣰⡇⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠘⠃⠀⢸⣷⠂⠀⠀⣐⣆⣤⣀⣀⣀⣀⣹⡛⣀⡄⠈⣿
⠸⠙⠫⢿⣿⡆⠐⠶⣿⣧⠀⠀⠀⠘⢋⣿⣶⡀⢤⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠘⠀⠀⡀⠀⠀⠰⣠⠀⣲⣶⡄⠀⠀⠀⠀⠀⠀⠿⠟⢻⣿⡯⠀⠈⠛⣏⡻⠷⢿⣯⠁⣯⣿⣿⣿⠛⠒⠊⠁⠀⠃
⢈⣿⣶⣾⣿⣿⢶⡶⠿⢷⣶⣶⣀⣀⣼⣿⣿⡗⡘⠁⠀⠀⣤⣤⣤⣇⣄⠄⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⣠⣤⣿⡆⠀⠁⢸⣟⠉⠁⢸⠂⠀⠀⠀⠺⠶⢾⣿⣿⠁⠀⠀⠑⠩⣧⣤⣿⣿⣿⣿⠉⢉⡵⠂⠀⠀⠀⠀⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⠿⣛⣛⣿⣿⣿⣟⣻⢟⣀⣛⣛⣛⣛⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡿⠀⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⡿⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⡍⢿⡎⢫⣾⢫⣭⡉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣫⣵⣿⠋
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡙⢿⣮⣍⡁⠀⢸⣿⠈⣻⣧⢸⡇⠀⢸⣿⣤⣼⡆⠀⠀⢸⡇⠸⢃⣾⠇⣾⡇⠈⠀⢳⢸⣿⠘⠋⣽⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⣿⣿⣯⡇⠀
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠹⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⢳⣬⠙⣿⡄⢸⣿⠸⢿⠛⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⣩⣭⣵⠂⢻⣧⠀⠀⠈⢸⡿⠀⢀⠉⠉⠻⠛⣽⣿⣿⡿⠙⡏⢽⣿⣿⣿⡇⠀
⢸⠁⠀⠃⠠⢹⣿⠷⠀⠷⠾⠇⡎⠁⠀⠀⢙⠉⡝⠋⠀⠉⠉⠻⠛⠁⠿⠦⣥⠴⠟⠀⠀⠛⠷⠤⠴⠛⢠⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⢹⠋⠀⢈⡻⠦⣤⠴⠟⣵⠀⢰⠂⠺⠛⢠⡈⢻⡿⠋⠀⠀⠸⡿⣿⣿⡇⠀
⢁⠀⣾⣿⡆⠺⣿⡇⢀⣴⠟⠋⠉⠛⢿⣶⢸⡗⣰⡾⠛⠉⠛⢿⡆⠀⠁⢁⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠈⠠⠆⣤⡀⠀⠀⢰⣿⠀⣾⠃⢁⠀⠀⢠⣾⡀⠆⠀⠀⠉⢧⡈⠃⠀⠀⠀⠹⣿⡁⠀⢄⠀⠐⠀⠞⠉⡆⢀
⠀⠀⠇⠉⡇⠀⠸⢃⣿⡏⠀⠀⣀⠀⠀⠛⠨⠃⢿⣧⣀⠀⠴⢄⣥⠀⠀⣾⡏⠀⠀⠀⠀⠀⠛⠃⠀⢠⠀⠀⠘⠉⠃⠀⠀⠩⡞⢀⡟⠀⠈⠀⠀⠀⣿⢿⠳⣦⡀⠀⠛⢣⠄⢱⡄⠀⠀⠁⢸⡇⠸⣇⠀⠀⠀⠀⠃⠉
⢠⡄⠀⠳⣷⣆⡇⢸⣿⡇⠀⠀⡏⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣶⣝⠀⠀⣿⡇⠀⠀⠀⠀⠀⠃⣀⠀⠈⡄⠀⠂⠀⠀⠘⠀⠸⠀⣾⠀⠀⠀⡀⢆⠀⣿⡞⢀⣿⡏⠀⠀⠀⠀⡎⢨⠀⠀⠀⠀⣇⠀⠀⣸⡆⠀⠀⠋⠀
⢸⣯⣆⡰⡿⠿⠃⠈⢿⣇⠀⠀⡀⠀⢀⣤⠄⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡅⠀⠄⠁⢀⣥⠀⠀⠀⠀⣠⣾⢁⠀⠀⢸⡇⠈⣆⣩⠁⡎⢸⣇⠀⠀⠀⠘⣵⠘⠀⠀⠀⠀⢁⣵⠀⡻⠁⠀⠀⠀⠀
⠀⢘⣥⣶⣿⠂⢀⣠⣬⡻⢦⣤⣭⣤⠾⠋⣮⡇⠿⣷⣤⣤⣤⡾⠟⢘⠀⢤⠛⢷⣤⣤⣤⡾⠋⠀⠣⢄⡀⠀⠻⠡⡀⠀⠀⢸⠿⢾⠀⠀⠀⠑⠤⠈⣿⣶⡗⠘⣿⠀⠀⠐⠀⠹⠂⠀⠀⠀⣀⣾⣿⡀⠁⠀⠀⠀⠀⠀
⠀⠀⢿⡯⡀⠐⠛⣻⣏⠁⠀⠀⠀⠀⠈⠁⠿⡇⠀⠠⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢠⡀⠀⢠⡄⠀⠘⠁⠀⠀⢰⠑⠀⢰⡌⠀⢸⠀⠀⠀⠖⠀⠀⢹⣯⠀⠀⣿⠂⠀⠀⠀⠀⠀⠐⠉⠹⣄⠻⣿⠇⠀⠆⠀⠀⠀⠀
⢀⠀⠀⠺⢇⠀⠀⠉⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢼⡆⠀⠘⣷⠀⠘⡇⠀⠀⠀⠀⠀⢣⠀⠀⠸⣇⠀⡄⠀⠀⠀⠀⠈⣇⠀⠘⠃⢰⡿⢀⣀⠀⠀⠀⠀⠀⠀⠀⡞⣷⠋⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠹⠀⠀⠇⠀⢶⣦⠀⠀⠘⡀⠀⠀⢻⢰⣃⠀⠀⠀⣀⢄⡟⠀⠀⣤⠟⠀⠀⢾⡇⠀⠀⠀⡄⠀⠀⢀⠘⠄⠀⠤⡀⠀⠀⠀⠀
⠸⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣺⠘⢿⡗⠈⠀⠀⠠⠀⠀⠀⠈⠀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡻⠆⠀⠐⢠
⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠐⠓⠀⠀⡀⠀⠀⠛⠀⠘⠐⠓⠀⠀⠀⠀⠀⢀⣴⢻⡟⠀⢈⣇⡀⠀⠀⠀⡂⠀⠈⠀⠀⠈⢿⡿⠀⠀⠰⣿
⢨⢻⡿⣯⣧⡀⢀⣤⣴⡀⠀⠀⠀⢸⡷⣼⣀⠀⠙⠸⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠛⠃⠀⠀⢢⠀⠀⠀⠀⠀⢣⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣤⠀⠸⣿⡤⣤⣤⣶⣷⠟⣒⣶⣶⣶⣾⣂⡲⠇⠀⡿
⠸⣶⣶⣿⣿⣷⣤⡽⠿⣷⣆⣀⠀⠀⠰⣿⣿⣄⠹⠄⠀⠀⢐⠀⠤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣤⡀⠀⠟⢠⣾⠿⠇⢤⠀⠀⠀⠀⣠⢩⣡⣾⣿⡏⠀⠀⠄⠲⡎⠁⣽⣿⣤⣟⠻⠿⠟⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣦⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠏⠀⣀⣂⣻⣿⣿⣟⣛⢋⣁⣀⣋⣛⣋⠛⢛⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣼⡏⢭⡍⣿⠀⢹⣿⢹⣿⣏⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣯⡿
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⣀⡙⢿⣮⣝⡻⠃⢸⣿⠸⣿⡟⢸⡇⠀⢸⣿⣤⣼⡆⠀⠀⢸⡇⠻⢋⣾⠇⣾⡇⠻⠛⣽⢸⣿⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣽⣿⣿⣿⣟⠁
⣼⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⢳⠈⠙⣿⡄⢸⣿⠈⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⣩⣭⣵⡆⢻⣧⠀⠀⠈⢸⡿⠀⠀⠿⢿⣿⣿⣻⣿⣯⣿⢻⡟⢿⣿⣿⣿⡯⠀
⢙⡟⠛⠟⠛⢻⣿⣧⠠⣌⠹⠛⡛⠛⠉⠛⠿⡿⡿⠿⠛⠛⠿⠿⢿⠇⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⢰⡠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⢹⡿⠁⢈⠻⠦⣤⠴⡟⢁⠀⢔⡀⣠⡤⠀⠻⣿⣿⡧⠀⡇⢹⣿⣿⣿⡇⠀
⠞⠀⢠⣴⡈⣸⣿⡏⢀⣴⠟⠋⠉⠛⢿⣶⢰⡆⣰⡾⠛⠉⠛⢿⡇⠀⠛⢃⣴⠞⠛⠉⠛⠻⣶⡆⠀⢀⠀⠘⢠⢻⠆⠀⠀⢠⣿⠃⢸⡿⠟⠀⠀⠘⣳⠂⡆⠀⠉⢿⡆⡸⡄⠈⠀⠘⢦⣼⠏⠀⠀⠁⢈⠏⣿⠿⡃⠀
⠘⠀⡟⡿⡧⠈⢻⢃⣿⡏⠀⠀⠀⠀⠀⠛⢸⠇⢿⣧⣀⠀⠀⠇⣅⠀⠀⣾⡏⠀⠀⠀⠀⠀⡛⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⢩⣿⠀⣾⠀⠰⠀⠀⠘⣿⣧⣅⡀⠀⠀⣿⠄⠀⢀⠀⠀⠈⠟⢲⡤⢱⡄⠀⠀⠁⠀⡇⢴
⠀⠀⠡⣄⣇⡀⡌⢸⣿⡇⠀⢀⡶⠀⠀⠀⠈⠀⠈⠛⠻⠿⣷⣶⣍⠀⠀⣿⡇⠂⠀⠀⠀⠀⠀⠘⠀⣠⠀⠀⢈⠀⠀⠘⠀⢨⡟⢠⠃⠀⠀⢀⡀⠀⣿⢹⠈⣿⡦⠀⠀⠘⠁⠼⠣⠀⠀⠀⠘⡇⠈⠃⢠⡀⠀⠀⡤⠀
⢸⡧⡀⢈⣿⣷⡇⠈⢿⣇⠀⠀⠃⠀⢀⣤⠄⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠻⠇⠀⠈⡄⠀⠀⠀⢈⠡⣿⠀⠀⢠⡆⠱⡀⠿⠇⡔⢻⡇⠀⠀⠀⠠⢇⢸⠀⠀⠀⠀⠗⢄⠀⣾⠇⠀⠀⠀⠀
⠘⢿⠗⣊⣯⡉⠀⠀⠈⠻⢦⣤⣤⣤⠾⢫⡶⡄⠿⣷⣤⣤⣤⡾⠟⠈⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠄⠁⠀⠀⠹⠐⡀⠀⠀⠈⡄⣿⠀⠀⠸⣇⡀⠹⣾⣀⣇⠸⣿⠀⠀⢀⠀⢻⡀⠀⠀⠀⠀⣰⣿⠀⠞⠀⠀⠀⠀⠀
⠀⠐⣿⡿⠛⠀⠴⠞⠿⠇⠀⠀⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⣄⠀⢰⡄⠀⣰⡄⠈⢳⡆⠀⠀⢠⠘⠄⢰⣶⠁⢹⠀⠀⠀⠀⠉⠀⣿⡟⠋⠀⣹⡆⠀⠀⠀⠈⠀⠀⠤⢤⠒⣿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠙⠋⠂⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣯⠀⠹⡇⠀⠈⠁⠀⠀⡜⠀⠀⠸⣿⠀⠸⠀⠀⠀⠁⠰⡄⠘⢻⡆⢀⣿⠃⠀⠀⠀⠀⠀⠈⠀⠈⣳⣌⡿⠁⠀⠁⠀⠀⠀⠀
⣰⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⡇⠀⣀⡀⠀⠀⢸⠀⠀⠀⣿⠀⠇⠀⢀⠀⠀⠀⣷⠀⠀⣠⣾⠋⠐⣲⡄⠀⠀⠀⠀⠀⠀⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠹⣿⡄⠀⠀⠂⠀⠀⢸⢸⣶⡄⠀⠀⠀⠐⠃⠀⠀⠛⠁⠀⠀⢹⡇⠀⠀⠀⠁⠀⠀⠘⠀⠁⠀⠉⣧⡀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣙⣧⠀⠀⠀⠀⠀⠘⠀⠹⢃⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠸⡇⠀⠀⠀⠀⡀⠀⠠⠆⠀⠐⣷⣮⠁⠀⢠⣼
⠰⣤⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠀⠀⢿⠀⠀⠀⠀⠀⠀⠃⠀⠀⡄⠀⠀⢸⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠘⠋⠀⢰⣷⠂⠀⠀⣀⣧⣤⣀⣀⣀⣀⣸⡏⣀⣤⠈⣿
⠸⠿⠷⣿⣿⣷⠶⠿⣿⡶⠖⠀⠀⠘⠋⣷⣶⠀⣤⠀⠀⠀⢀⠀⡀⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠀⠀⡀⠀⠀⠀⣤⠀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠗⠟⣻⣿⡿⠀⠈⠛⣋⡿⠿⢿⣿⡁⣷⢿⣿⣿⠓⠒⠂⠁⠀⠋
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣗⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⡝⣿⣿⣿⣿⣿⣿⡆⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠧⠀⣀⣁⣿⣿⣿⣟⣋⢁⣀⣀⣛⣛⣉⠙⢛⣛⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⡏⢭⡍⣿⡄⢹⣿⢹⣿⣏⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⠀⠙⢿⣮⣝⡁⠀⢸⣿⠨⠛⠛⢸⡇⠀⢸⣿⣤⣼⡆⠀⠀⢸⡇⠻⢋⣾⠇⣾⡇⠿⢿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⡿⠃
⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢳⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⣩⣭⣵⡇⢻⣧⠐⠀⠍⢸⡿⠈⠀⣿⣿⣿⣿⣿⣿⣟⣿⢾⡿⣿⣿⣿⣿⣏⠀
⠻⡿⠻⡟⠻⢿⣿⣧⢀⡜⠻⠛⡛⠛⠛⠿⣿⣿⣿⠿⠟⣛⠻⠿⢿⣇⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠰⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⢹⣿⡁⢨⠻⠦⣤⠴⡟⠡⠈⡠⠀⢀⣉⠈⢿⣿⣿⣏⠈⡇⢻⣿⣿⣿⡇⠀
⡼⠀⢀⣤⠘⢸⣿⡟⢀⣴⠟⠋⠍⠛⢿⣶⢠⡅⣰⡾⠛⠉⠛⢿⡇⠀⠿⢇⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⣀⡈⠰⠹⠀⠀⠀⢠⣿⠏⢰⣿⡿⠁⠀⠨⢷⡅⡄⠀⠉⣾⡄⢸⡅⠘⠈⠰⣄⣹⡟⠁⠀⠁⠘⠟⢿⣿⡇⠀
⠐⢀⣿⡿⣧⠙⢿⢃⣿⡏⠀⠀⠀⠀⠀⢛⣼⡇⣿⣧⣀⠀⠀⢇⡁⠀⠀⣾⡏⠀⠀⠀⠀⠀⠛⢃⠀⠀⠉⠃⢆⠀⠀⠀⠀⣹⣿⡀⢸⠁⢠⠀⠀⠐⣿⣆⡃⠀⠀⠈⣻⡁⠁⢄⠀⠀⠘⡟⢤⣀⢢⡄⠈⠀⠉⠀⡇⡤
⠀⠈⠣⣀⣇⠀⡜⢸⣿⡇⠀⠀⢦⠀⠀⠀⠙⠀⠈⠛⠻⠿⣷⣶⣄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⠀⣴⠄⠀⠸⠀⠀⠀⠀⢹⣿⢃⡎⠀⠀⠀⠀⠀⣿⢻⠘⣷⣄⠀⠉⠰⠂⣸⢆⠀⠀⠀⠘⡇⠘⠇⢀⡀⠀⠀⣀⠈
⢰⣦⡀⠙⣿⣧⡇⠈⢿⣇⠀⠈⠇⠀⢀⣤⠄⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⢿⠆⠀⠀⢂⠀⠀⠀⠈⡏⢼⡇⠀⢀⡆⢡⠀⡿⡇⡠⢻⡇⠀⠀⠀⢀⡆⢰⠀⠀⠀⠀⡧⣄⠀⣼⡇⠀⠀⠁⠀
⠘⣷⡧⠜⣟⠛⠁⠀⢈⠻⢦⣤⣤⣤⠾⠋⣤⡀⠿⣷⣤⣤⣤⡾⠟⠘⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠂⠀⠀⠰⠈⢆⠀⠀⠀⡇⣘⠃⠀⠸⡇⠀⢳⣴⠀⡇⠻⣷⠀⠀⠀⠀⢿⡈⠀⠀⠀⠀⠠⣾⠀⡽⠀⠀⠀⠀⠀
⠀⠠⣶⣿⠿⠁⠀⠈⢲⡆⠀⠐⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣷⠀⣴⡆⠀⣰⡄⠐⢦⡄⠀⠀⢀⠈⠀⢰⣷⠀⢹⠀⠀⠀⠉⠓⠀⣿⡿⠟⠀⢻⡄⠀⠈⠀⠘⠁⠀⣀⣠⠴⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠋⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⢹⡇⠀⠈⠁⠀⠀⠸⠀⠀⠸⣿⠀⢸⠀⠀⠀⠁⢠⡀⠹⢿⡄⠀⣿⠇⠀⠀⠀⠀⠀⠈⠀⠘⢦⣘⣿⠁⠀⠃⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⢿⠀⡆⠀⠀⠀⢀⠀⣧⠂⠀⣀⣼⠟⠂⢤⡀⠀⠀⠀⠀⠀⠀⠏⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠺⣿⡄⠀⠈⠆⠀⠀⢸⣷⣥⡄⠀⠀⠀⢀⠋⠀⠀⠻⠃⠀⠀⢻⡇⠀⠀⠀⠃⠀⠀⠰⠈⠂⠀⠒⣆⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢈⠁⢻⢏⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⣤⣌⠃⠀⢀⣰
⢠⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠈⠈⠀⠀⠀⠀⠀⣠⣾⠹⠟⠀⢰⣧⠀⢀⠀⠀⣇⣀⡀⠀⠀⠀⢹⡟⠁⣀⠘⢿
⢰⡿⠿⣿⣿⣶⠴⣶⣾⠶⠆⠀⠀⠼⢟⣮⣤⠀⣠⠀⠀⠀⠀⠀⣀⡄⠀⠀⠁⠀⠀⠘⠙⠃⠀⠀⠱⠀⠀⠀⠀⠀⠈⣀⡀⣷⣤⠀⠀⠀⠀⠀⠀⠀⡦⡿⢿⣶⣶⠀⠘⠽⢖⠷⣶⣿⣿⠋⣩⣿⣿⣿⠿⠷⠍⠋⠀⠏
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣖⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢷⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⡝⣿⣿⣿⣿⣿⣿⡆⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠧⠀⣀⣁⣿⣿⣿⣟⣋⢁⣀⣀⣛⣛⣉⠙⢛⣛⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⡏⢭⡍⣿⡄⢹⣿⢹⣿⣏⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡏⠀⠙⢿⣮⣝⡁⠀⢸⣿⠨⠛⠛⢸⡇⠀⢸⣿⣤⣼⡆⠀⠀⢸⡇⠻⢋⣾⠇⣾⡇⠿⠿⣽⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⡿⠃
⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢳⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⣩⣭⣵⡇⢻⣧⠐⠀⠈⢸⡿⠈⠀⣿⣿⣿⣿⣿⣿⣟⣿⢾⡿⣿⣿⣿⣿⣏⠀
⠻⡿⠻⡟⠻⢿⣿⣧⢀⡜⠻⠛⡛⠛⠛⠿⣿⣿⣿⠿⠟⣛⠻⠿⢿⣇⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠰⠠⠼⠿⠤⠤⠶⠟⠠⠼⠧⠬⢹⣿⡁⢨⠻⠦⣤⠴⡟⠡⠈⡠⠀⢀⣉⠈⢿⣿⣿⣏⢈⡇⣺⣿⣿⣿⡇⠀
⡼⠁⢀⣤⠘⢸⣿⡟⢀⣴⠟⠋⠍⠛⢿⣶⢠⡅⣰⡾⠛⠉⠛⢿⡇⠀⠿⢇⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⣀⡈⠰⠹⠀⠀⠀⢠⣿⠏⢰⣿⡿⠁⠀⢨⢷⡅⡄⠀⠉⣾⡄⢸⡁⠘⠈⠰⣄⣹⡟⠁⠀⠁⠘⠟⢿⣿⡇⠀
⠐⠀⣿⣿⣇⠙⢿⢃⣿⡏⠀⠀⠀⠀⠀⢛⣼⡇⣿⣧⣀⠀⠀⢇⡁⠀⠀⣾⡏⠀⠀⠀⠀⠀⠛⢃⠀⠀⠉⠃⢆⠀⠀⠀⠀⣹⣿⡀⢸⠁⢰⠀⠀⠐⣿⣆⡃⠀⠀⠈⣳⡁⠁⢄⠀⠀⠘⡟⢤⣀⢢⡄⠈⠀⠉⠀⡇⢤
⠀⠀⠣⣀⣇⠀⡜⢸⣿⡇⠀⠀⣦⠀⠀⠀⠙⠀⠈⠛⠻⠿⣷⣶⣄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⠀⣴⠄⠀⠸⠀⠀⠀⠀⢹⣿⢃⡏⠀⠀⠀⠀⠀⣿⢻⠘⣷⣄⠀⠉⠰⠂⣸⢆⠀⠀⠀⠘⡇⠘⠇⢀⡀⠀⠀⣀⠈
⢸⣦⡀⠙⣿⣧⡇⠈⢿⣇⠀⠈⠇⠀⢀⣤⠄⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⢿⠆⠀⠀⢂⠀⠀⠀⠈⡏⢼⡇⠀⢠⡎⢡⠀⡿⡇⡠⢻⡇⠀⠀⠀⢀⡆⢰⠀⠀⠀⠀⡧⣄⠀⣼⡇⠀⠀⠁⠀
⠘⣷⡧⠞⣟⠛⠀⠀⢈⠻⢦⣤⣤⣤⠾⠋⣤⡀⠿⣷⣤⣤⣤⡾⠟⠘⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠂⠀⠀⠰⠈⢆⠀⠀⠀⡇⣘⠃⠀⠸⡇⠀⢳⣴⠀⡇⠻⣷⠀⠀⠀⠀⢿⡈⠀⠀⠀⠀⢠⣾⠀⡽⠀⠀⠀⠀⠀
⠀⠰⣶⣿⠿⠁⠀⠈⢲⡆⠀⠐⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣷⠀⢶⡆⠀⣰⡄⠐⢦⡄⠀⠀⢀⠈⠀⢰⣷⠀⢹⠀⠀⠀⠉⠓⠀⣿⡿⠟⠀⢻⡄⠀⠈⠀⠘⠁⠀⣀⣠⠴⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠋⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⢹⡇⠀⠈⠁⡀⠀⡸⠀⠀⠸⣿⠀⢸⠀⠀⠀⠁⢠⡀⠹⢿⡄⠀⣿⠇⠀⠀⠀⠀⠀⠈⠀⠘⢦⣘⣿⠁⠀⠃⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⢿⠀⡆⠀⠀⠀⢀⠀⣧⠂⠀⣀⣼⠟⠠⢤⡀⠀⠀⠀⠀⠀⠀⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠺⣿⡄⠀⠈⠆⠀⠀⢸⣷⣥⡄⠀⠀⠀⢀⠋⠀⠀⠻⠃⠀⠀⢻⡇⠀⠀⠀⠃⠀⠀⠰⠈⠂⠀⠒⣆⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢈⠁⢻⢏⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⣤⣌⠃⠀⢀⣰
⢠⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⣾⠹⠟⠀⢠⣧⠀⢀⠀⠀⣇⣀⡀⠀⠀⠀⢹⡛⠁⣀⠘⢿
⠸⠿⠿⣿⣿⣶⠴⣶⣾⠶⠆⠀⠀⠼⠞⣮⣤⠀⣠⠀⠀⠀⠀⠀⣀⣄⠀⠀⠁⠀⠀⠘⠙⠃⠀⠀⠱⠀⠀⠀⠀⠀⠈⣀⡀⣿⣤⠀⠀⠀⠀⠀⠀⠀⡦⡿⢿⣶⣶⠀⠘⠽⢖⠷⣶⣿⣿⠋⣩⣿⣿⡿⠿⠿⠍⠋⠀⠏
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠁⣌⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⡌⢿⣿⣿⣿⣿⣿⡄⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⠻⣾⣿⣿⣿⣿⣿⠷⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⡇⣀⣀⣿⣿⣿⣟⣁⢀⣀⣀⣈⣉⣀⠀⢉⣉⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⡍⠉⣿⠀⢹⣿⠁⠙⠋⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠁⠙⢿⣦⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⡄⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⠟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣤⢲⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⣩⣭⣵⣦⢻⣧⠉⠉⠟⢸⡿⢸⠛⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⡷⠀
⣿⣿⣿⣿⣿⣿⣿⣟⢁⠙⠿⠟⡛⠿⠿⢿⣿⣿⣿⠿⠿⣛⠿⠿⢿⣇⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠴⠟⠠⠼⠧⠬⣹⣿⠏⠈⡻⠦⣤⠴⠟⣡⠖⠉⠋⠙⠿⠻⣿⣿⣿⡿⠙⡏⢽⣿⣿⣿⡇⠀
⣸⠃⠀⠁⠠⢹⣿⡿⢋⣵⢟⡋⡍⠛⢿⣶⠈⠋⣱⡾⠛⠉⠛⢿⡇⠙⣿⢃⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⢠⡄⡀⠘⠀⠀⠀⠀⣿⣿⡆⣾⣿⠟⠐⣇⣿⡗⡀⠀⠿⣽⠀⢰⠄⠲⠋⢤⡉⢿⡿⠃⠀⠇⢸⡿⣿⣿⡇⠀
⢩⠀⣼⣿⡆⠺⣿⢃⣿⡏⠈⠀⠁⠀⠀⠛⣸⡇⣿⣧⣀⠀⠀⡆⠁⠀⠁⣾⡏⠀⠀⠀⠀⠀⠛⢃⠀⢰⠿⡇⢱⠀⠀⠀⠀⠀⣿⠁⠁⡟⢉⠀⠀⠉⣿⡁⠇⠀⠀⠹⣧⠚⠃⠀⠀⠀⠻⣿⠃⠀⣀⠀⠐⠁⠟⠉⡇⢀
⠀⠀⠏⠋⡏⠀⠸⢸⣿⡇⠀⠀⣀⠀⠀⠙⠿⠉⠈⠛⠻⠿⣷⣶⣄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠄⠀⠀⠀⠀⢽⡇⢠⡇⠈⠀⠀⠀⣿⣿⠲⣤⡀⠀⠾⢢⠄⠱⡄⠀⠀⠁⠸⣷⠸⣇⠀⠀⠀⠀⠃⠙
⢠⡄⠈⢦⣷⣄⡇⠈⢿⣇⠀⠐⡏⠀⢀⣤⠄⠀⣤⠀⠀⠀⠀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⣿⡅⠀⠄⠘⡀⠀⠀⠀⠸⣧⠸⣿⠀⡠⢆⠀⣾⡜⣀⢻⡟⠀⠀⠀⠀⡚⢹⠀⠀⠀⠰⣏⠀⠀⣸⡆⠀⠀⠒⠀
⠸⣏⡆⡰⣿⠿⠃⠀⠈⡻⢦⣤⣤⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠰⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⡜⠁⠀⠀⠀⠑⠀⠀⣠⡀⢩⠀⠁⣸⡇⠈⢆⢉⠃⡏⣾⣧⠀⠀⠀⠘⣧⠘⠀⠈⠀⠈⠉⣳⡄⢻⠁⠀⠀⠀⠀
⠀⢙⣥⣷⣷⠆⠀⠐⢨⡅⠀⠠⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⠀⣾⡇⠣⡀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢿⠀⠀⠈⠣⠤⠈⣿⣶⣷⠀⢿⡄⠀⠀⠂⠹⠆⠀⠀⠀⣀⣴⣿⡇⠉⠀⠀⠀⠀⠀
⠀⠀⠉⠫⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢻⡇⠀⢿⡇⠀⠸⠓⠀⠂⢠⠁⠀⠸⢿⠀⢸⠀⠀⠀⠀⠀⠈⢻⣯⠉⠀⣼⡇⠀⠀⠀⠀⠀⠠⠉⠛⣎⠻⣿⠇⠀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠃⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠘⣆⠄⠘⣁⣼⡿⢁⣀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠛⠀⠀⠀⠀⠀⠀⠀
⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⣤⣤⡄⠀⠸⡀⠀⠀⠹⣇⠇⠀⠀⠁⠀⢀⠛⠀⠀⠻⠏⠀⠀⣾⡇⠀⠀⠀⠆⠀⠀⢠⠘⠄⠀⢄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠈⢿⣷⠀⠀⠁⠀⠀⢠⠘⣿⡧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⣄⠻⠆⠀⠐⢠
⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢰⡄⠀⠀⢀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠜⠿⠀⠀⠀⠀⠀⢸⠂⠚⠐⠒⠀⠀⠀⠀⠀⠀⣰⢺⡿⠀⠘⣧⣀⠀⠀⠀⡄⠄⠀⠃⠀⠈⢻⣿⠆⠀⠰⣾
⢸⢿⢿⣿⣿⢶⠄⣰⡶⠶⠆⠀⠀⣰⣷⡼⡀⠀⠙⠄⠀⠀⠀⠀⡀⣍⠀⠀⠐⠀⠀⢸⠿⡇⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣀⣁⠀⢸⣿⣀⣔⣄⣤⣿⡶⠶⣶⣦⣤⣴⠧⠶⠶⠀⠸
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⡙⢻⣿⣿⣿⣿⣿⡇⢰⣼⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣷⣼⣿⣿⣿⣿⣿⣇⠈⣿⣗⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠛⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⠿⠋⣀⣀⡻⠻⢿⣟⣉⢀⣀⣀⣀⣁⣀⠀⢉⣉⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⡍⠉⣿⠀⢹⣿⠁⠀⠈⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣦⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⠆⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⡿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⣤⠀⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢩⣭⣵⣧⢻⣧⠻⠛⡟⢸⡿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣾⣿⣻⠀
⣾⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⡿⠿⠿⢿⣿⣿⣿⠿⠿⡻⠿⠿⢿⣇⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣹⣿⡿⠊⠻⠦⣤⠴⠟⣡⣟⠥⠿⢿⣿⣿⣿⣿⣯⣿⢿⡿⢿⣿⣿⣿⡇⠀
⢙⡟⠛⠿⠛⢿⣿⡿⢀⣴⠟⡋⣉⠛⢿⣶⠹⡟⣱⡾⠛⠉⡛⢿⡇⢻⣿⢃⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⢰⡤⡀⠈⠀⠀⠀⠀⢸⣿⡷⢸⣿⣿⠁⡌⣿⣶⠀⠀⢮⢛⠁⣄⡀⣠⣭⠈⠿⣿⣿⡇⢀⡇⣽⣿⣿⣿⡇⠀
⠞⠀⣠⣴⡈⢸⣿⢁⣿⡏⠸⠃⠋⠀⠀⠛⢰⡄⣿⣧⣀⠀⠀⡌⠁⠀⠋⣾⡏⠀⠀⠀⠀⠀⠛⢃⡄⢐⣾⡇⢹⠀⠀⠀⠀⠀⠸⠏⠇⢸⠟⠁⠀⠷⣿⠏⡆⠀⠈⢿⡄⡸⡅⠈⠀⠙⢦⣽⠏⠀⠀⠁⢈⠏⣿⠿⡇⠀
⠘⠀⡿⠿⡇⠈⢻⢸⣿⡇⠀⠀⠀⠀⠀⢤⣿⡿⠈⠛⠻⠿⣷⣶⣌⠀⠀⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⢾⠀⠃⠈⠆⠀⠒⠢⠀⠀⡆⠀⢸⡴⠀⠀⠀⣿⣦⣁⡀⠀⠈⣿⠀⠀⢄⠀⠀⠈⠟⢠⣤⢱⡆⠀⠀⠁⠀⡇⢴
⢀⠀⠱⣠⣇⡀⡌⠈⢿⣇⠀⢐⡲⠀⢀⣤⠍⠀⣤⠀⠀⠠⠆⢹⣿⠀⠀⢿⣧⠉⠀⠀⠀⠀⣤⡄⠀⣼⠇⠀⠂⠀⡄⠀⠀⢰⡀⠇⠀⠻⡇⠀⡀⠀⣿⠹⠈⣿⣦⠀⠀⠘⠁⢼⢣⠀⠀⠀⢠⣿⠈⠓⢠⡄⠀⠀⡤⠀
⢸⡧⡀⢈⣿⣷⡇⠀⠈⡻⢦⣬⣤⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⢀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠻⠗⠰⠀⠀⠘⡄⠀⢩⡇⢸⠀⠀⣤⡎⠰⡀⠟⡇⡧⣹⡇⠀⠀⠀⢠⢇⢸⠀⠀⠀⠨⠿⢤⠀⣾⠇⠀⠀⠀⠀
⠈⢿⡗⣇⣯⡉⠀⢀⠠⠓⠢⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣶⣴⠀⣰⡄⡄⠃⠀⠀⠀⠀⠀⠁⠀⣾⡇⣼⠀⠀⠻⣇⠀⠹⡾⣀⣇⠋⣿⠀⠀⠀⡀⢿⡀⠀⠀⠀⠀⢀⣾⡇⠞⠀⠀⠀⠀⠀
⠀⠁⠙⡿⠛⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢿⠉⠀⢿⡇⠈⢒⣄⠀⠀⠀⠀⠀⠘⢿⠃⢹⠀⠀⠀⠈⠉⠐⣷⣟⠻⠠⢸⡇⠀⠀⠀⠈⠁⠀⠤⢤⠲⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⢠⠀⢸⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⢰⡀⠸⠹⢆⣠⣿⠇⠀⠀⠀⠀⠀⠈⠀⠈⣷⣌⣿⠁⠀⠁⠀⠀⠀⠀
⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠸⡆⡆⠀⠀⠀⠀⠀⠷⠁⠀⠻⠟⠁⠐⣲⡄⠀⠀⠀⡀⠀⠀⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠻⣿⣿⠀⠀⠆⠀⠀⢸⣸⣶⡄⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢁⠀⠀⠘⠀⠁⠀⠉⣦⡄⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣈⣀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⢸⡇⣻⢛⣀⡀⠀⠐⠀⠀⠀⢀⣠⣤⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⡖⠀⠐⣷⣮⡡⠀⢠⣼
⠰⣶⣿⣷⠿⢶⠄⠰⠶⠶⠖⠀⠀⢠⣄⢠⠀⠀⣻⢀⡀⠀⠀⠀⢺⣧⠀⠀⠐⠀⠀⢿⣿⣿⠀⠀⢀⠀⠁⠀⠀⠀⢐⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠘⠏⠀⠀⡿⠂⢀⠀⠀⣧⡀⣀⣀⣀⡀⢘⡟⣁⣤⠈⢻
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡜⢻⣿⣿⣿⣿⣿⡏⢰⣼⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣾⣬⣿⣿⣿⣿⣿⣧⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⠛⣿⣿⣿⣿⣿⣿⣿⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⠛⠋⣀⣀⡹⠻⢿⣟⣋⢁⣀⣀⣀⣁⣀⠀⢉⣉⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⡍⠉⣿⠀⢹⣿⠁⠀⠈⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠝⢿⣦⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⠇⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⣤⠀⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢹⣭⣵⣷⢻⣧⠻⡿⡿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣵⣾⢿⠃
⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡿⠿⠿⣿⣿⣿⣿⡿⠿⡿⠿⠿⢷⣆⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠛⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⠮⠻⠦⣤⠴⢟⣱⣿⠉⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⡏⠀
⠻⡿⠿⣿⠿⣿⣿⡿⢀⣴⠟⡋⣉⡛⢿⣶⢹⡟⣱⡾⠛⢉⣛⢿⡇⢻⣿⢃⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⢲⣄⡀⠀⠀⠀⠀⠊⢸⣾⣿⠀⣿⣿⠃⡐⣶⣤⠀⠀⣸⢻⠋⡈⠁⢈⣋⠙⣿⣿⣿⡏⠈⡇⣺⣿⣿⣿⡇⠀
⡼⠁⢀⣄⠐⢸⣿⢃⣿⡏⢸⠇⠟⠀⠀⠛⢠⡁⣿⣧⣀⠀⠀⡈⠉⠈⠏⣾⡏⠀⠀⠀⠀⠀⠛⢃⡄⠠⣼⡏⢱⠀⠀⠀⡀⠀⠘⡟⣏⢀⡿⠋⠀⣯⣿⡟⡄⠀⠘⣾⡄⢸⡃⠙⠁⠲⣄⣻⡟⠁⠀⠁⢘⠟⣿⣿⡇⠀
⠰⠀⣿⣿⡇⠘⢿⢸⣿⡇⠀⠀⠀⠀⠀⣄⣾⣷⠎⠛⠻⠿⣷⣶⣄⠀⠀⣿⡇⣄⠀⠀⠀⠀⠀⠈⠀⣼⠉⠇⠈⠄⠀⠲⡶⠀⠀⡇⠈⢸⣧⠀⠀⠀⣿⣄⠃⠀⠀⠘⣷⠁⠁⡀⠀⠀⠘⡿⢀⣀⢢⡄⠈⠀⠋⠀⡇⣤
⠀⠀⢡⢀⡇⠀⡘⠈⢿⣇⠀⠠⣤⠀⢀⣬⠝⠀⣤⠀⠀⢀⡶⢹⣿⠀⠀⢿⣧⠉⠀⠀⠀⠀⣤⡄⠀⢰⡆⠀⠀⠀⡀⠀⠄⢸⡆⠇⠀⠘⣿⠀⠀⠀⣿⢻⠙⣶⣄⠀⠋⠐⠂⢘⢆⠀⠀⠀⢈⣿⠘⠧⢀⡀⠀⠀⣀⠈
⢸⡆⠀⠙⣿⣧⡇⠀⢈⡻⢦⣬⣥⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠄⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⢶⡦⠀⠀⠀⠐⡀⠀⠘⡇⢰⠀⠀⣀⡔⢡⠀⡿⡎⣆⢽⡏⠀⠀⠀⢀⡌⢸⠀⠀⠀⢘⣿⣀⠀⣼⡇⠀⠀⠁⠀
⠛⣷⡇⠎⣟⠛⠁⠀⢀⠧⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⣦⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⣼⡇⣸⠀⠀⢿⡆⠀⠳⡴⠁⡇⡟⣷⠀⠀⠀⠠⣿⠈⠀⠀⠀⠀⠀⣼⡆⡽⠀⠀⠀⠀⠀
⠀⠊⠁⢿⠿⠁⠀⠈⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡿⠘⠂⢴⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⢿⠃⢻⠀⠀⠀⠙⠂⠠⣧⡿⢿⢀⢹⡇⠀⠈⠁⠘⠃⠀⣀⣀⢤⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗⢀⠀⢨⠀⠀⠘⠋⠂⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⢠⠀⢹⢻⢄⣠⣾⡇⠀⠀⠀⠀⠀⠐⠀⠈⣧⡙⣿⠃⠀⠂⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡌⠀⠀⠀⠀⠈⢧⠀⠀⠺⡟⠉⠠⢤⡀⠀⠀⠀⠀⠀⠀⠋⢿⠉⠀⠀⠀⠀⠀⠀⠀
⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢲⣶⣶⠀⠀⡆⠀⠀⠸⣷⣃⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠃⠀⠀⠰⠈⠂⠀⠂⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⢨⡏⢿⠷⠀⠀⠀⠨⠀⠀⠀⠀⢀⣀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⡤⠀⠠⣦⣝⠃⠀⢈⣰
⢠⣶⣶⣶⠯⢶⠆⠰⠶⠶⠖⠀⠀⢀⡀⢀⠀⠀⣿⠀⣀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⠃⠈⠈⠉⠀⠀⠀⠀⠀⢀⣼⠹⠟⠀⠈⣧⠄⠀⠀⠀⣇⠀⠀⠁⠀⠀⠹⡿⠃⢀⠘⢿
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣜⢻⣿⣿⣿⣿⣿⡏⢰⣼⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣿⣬⣿⣿⣿⣿⣿⣧⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⠛⣿⣿⣿⣿⣿⣿⣿⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⠛⠋⣀⣀⡹⠻⢿⣟⣋⢁⣀⣀⣀⣁⣀⠀⢉⣉⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⡍⠉⣿⠀⢹⣿⠁⠀⠈⢹⡏⠈⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠝⢿⣦⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⠇⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⣤⠀⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢹⣭⣵⣷⢻⣧⠻⡿⡿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣵⣾⢿⠃
⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡿⠿⠿⣿⣿⣿⣿⡿⠿⡿⠿⠿⢷⣆⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠛⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⠮⠻⠦⣤⠴⢟⣱⡿⠉⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⡏⠀
⠻⡿⠿⣿⠿⣿⣿⣿⢁⣴⠟⡋⣉⡛⢿⣶⠹⡟⣱⡾⠛⣉⣛⢿⡇⢻⣿⢃⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⢲⣄⡀⠀⠀⠀⠀⠊⢸⣾⣿⠐⣿⣿⠃⡐⣶⣤⠀⠀⣸⢿⠋⠀⠁⢈⣋⠙⣿⣿⣿⡏⠈⡇⣻⣿⣿⣿⡇⠀
⡼⠁⢀⣄⠐⢸⣿⢃⣿⡏⢸⠇⠟⠀⠀⠛⢠⡁⣿⣧⣀⠀⠁⡈⠉⠈⠏⣾⡏⠀⠀⠀⠀⠀⠛⢃⡄⠠⣼⡏⢱⠀⠀⢀⡀⠀⠘⡟⣏⢀⡿⠉⠀⣯⣿⡟⡄⠀⠘⣾⡄⢸⡃⠙⠁⠲⣄⣻⡟⠁⠀⠁⢘⡟⣿⣿⡇⠀
⠰⠀⣿⣿⡇⠘⢿⢸⣿⡇⠀⠀⠀⠀⠀⣄⣾⣷⠎⠛⠻⠿⣷⣶⣄⠀⠀⣿⡇⣄⠀⠀⠀⠀⠀⠈⠀⡼⠉⠇⠈⠄⠀⠲⡶⠀⠀⡇⠈⢸⣧⠀⠀⠀⣿⣄⠃⠀⠀⠘⣷⠁⠁⡀⠀⠀⠘⡿⢀⣀⢢⡄⠈⠀⠋⠀⡇⣤
⠀⠀⢡⢀⡇⠀⡜⠈⢿⣇⠀⠠⣤⠀⢀⣬⠝⠀⣤⠀⠀⢀⡶⢹⣿⠀⠀⢿⣧⠉⠀⠀⠀⠀⣤⡄⠀⢰⠆⠀⠀⠀⡀⠀⠀⢸⡆⠇⠀⠘⣿⠀⠀⠀⣿⢻⠙⣶⣄⠀⠋⠐⠂⢘⢆⠀⠀⠀⢈⣿⠘⠧⢀⡀⠀⠀⣀⠈
⢸⣆⠀⠛⣿⣧⡇⠀⢈⡻⢦⣬⣥⣤⠾⠋⠀⠀⠿⣷⣤⣤⣤⡾⠟⠄⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⢶⡦⠀⠀⠀⠐⡀⠀⠘⡇⢰⠀⠀⣀⡔⢡⠀⡿⡎⣆⢽⡏⠀⠀⠀⢀⡄⢸⠀⠀⠀⢘⣿⣀⠀⣼⡇⠀⠀⠁⠀
⠛⢳⡇⠎⣟⠛⠁⠀⢀⠧⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣦⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⣼⡇⣸⠀⠀⢿⡆⠀⠳⡴⠁⡇⡟⣷⠀⠀⠀⠠⣿⠈⠀⠀⠀⠀⠀⣼⡆⡽⠀⠀⠀⠀⠀
⠀⠀⠁⢿⠿⠁⠀⠈⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡿⠘⠂⢴⠀⠑⢠⡀⠀⠀⠀⠀⠀⠘⢾⠃⢻⠀⠀⠀⠙⠂⠠⣧⡿⢿⢀⢹⡇⠀⠈⠁⠈⠃⠀⣀⣀⢤⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗⢀⠀⢨⠀⠀⠘⠋⠂⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⢠⠀⢹⢻⢄⣠⣾⡇⠀⠀⠀⠀⠀⠐⠀⠈⣧⡙⣿⠃⠀⠂⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡌⠀⠀⠀⠀⠈⢧⠂⠀⠺⡟⠉⠠⢤⡀⠀⠀⠀⠀⠀⠀⠋⢿⠉⠀⠀⠀⠀⠀⠀⠀
⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢲⣶⣶⠀⠀⡆⠀⠀⠸⣷⣃⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠃⠀⠀⠰⠈⠂⠀⠂⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⢨⡏⢿⠷⠀⠀⠀⠨⠀⠀⠀⠀⢀⣀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⡤⠀⠠⣦⣝⠃⠀⢈⣰
⢠⣶⣶⣶⡯⢶⠆⠰⠶⠶⠖⠀⠀⢀⡀⢀⠀⠀⣿⠀⣀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⢸⠃⠈⠈⠉⠀⠀⠀⠀⠀⢀⣼⠹⠟⠀⠈⣧⠄⠀⠀⠀⣆⠀⠀⠁⠀⠀⠹⡿⠃⣀⠘⢿
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢨⠛⣿⣿⣿⣿⣿⣿⠁⣌⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠰⣾⣦⣿⣿⣿⣿⣿⣿⠀⢹⣿⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⠛⠛⣁⣀⡘⠛⢿⣛⣛⢛⣉⣁⣀⣈⣉⠉⢙⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⠉⣿⠀⢹⣿⠁⠀⠈⢹⡏⠈⢹⣿⠉⠉⠹⠇⡈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⠇⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠋⣭⠀⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠀⢸⡟⢩⣭⣵⣷⢻⣧⢿⣿⠿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⠟
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⢧⣄⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣮⡻⠦⣤⠴⠟⣵⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⡧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢏⣵⠟⣋⣉⣛⢿⣶⢹⡟⣱⡾⢛⣉⣛⢿⡆⢻⣿⢇⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⢠⡀⠀⠇⠀⠀⠒⠚⢡⣽⣿⠀⣿⣿⡟⢉⣅⡀⠀⠰⢚⣿⡯⠁⠛⠻⡿⢿⣿⣿⣷⡿⠹⡏⣿⣿⣿⣿⡇⠀
⣨⠏⠀⠛⢉⢻⣿⢁⣿⡏⣼⡟⣿⠋⠀⠛⢘⠇⣿⣧⣉⠙⠛⢮⠥⠟⠋⣾⡏⠀⠀⠀⠀⠀⠛⠃⠀⠀⢸⡟⢣⠀⠀⠀⣠⡁⠘⡿⡿⠃⣿⠟⠀⣦⣿⣿⠀⠀⠸⣾⠀⢢⠄⢴⠶⢀⠙⢿⣿⠇⠀⠃⢺⣿⣿⣿⡇⠀
⢉⠀⣼⣿⡆⢨⣿⢸⣿⡇⠘⠁⠁⠀⠀⠀⣸⣧⡌⠛⠻⠿⣷⣶⣄⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠰⠀⣺⠿⡇⠐⠀⢠⠈⣿⣷⡀⠃⠳⠆⣟⠀⠀⠛⣿⠃⡇⠀⠀⠸⣇⠜⠆⠀⠀⠈⢳⣿⠃⠀⡀⠀⠰⠁⠿⠛⡇⢀
⠀⠀⢛⢹⡇⠀⢸⠊⣿⣇⠀⠀⠀⠀⢀⣥⢝⠛⣤⠀⠀⠀⣠⢹⣿⠀⠀⢿⣧⠁⠀⠀⠀⠀⣤⡄⠀⢙⡀⠀⠀⠠⠈⢠⠀⢹⣧⠃⠀⠀⣿⠀⠀⠀⣿⣷⢦⣄⠀⠀⠿⠆⡀⠢⡀⠀⠀⠃⠸⣷⢸⡇⠀⠀⠀⠀⠃⠹
⣤⡀⠸⢼⣧⡄⡇⠀⣈⡻⢦⣤⣭⣤⠾⠋⠀⠀⠿⣷⣤⣤⣥⡾⠟⡀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⣼⡃⠀⠀⠀⠠⠀⠀⠸⡟⠀⠀⠀⠘⠃⡄⠀⣿⡘⡀⣿⡷⠀⠀⠀⠁⠀⢙⠀⠀⠀⢰⣿⠀⠁⢰⡆⠀⠀⠖⠀
⠼⣇⡀⡸⣿⣿⠃⠀⠘⢇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⡀⡄⠀⠀⠀⠀⡙⠉⠀⠀⠀⠀⠀⠀⢠⡇⢸⠂⠀⣶⠈⠘⣄⢃⠃⡗⡼⣧⠀⠀⠀⢂⣦⠸⠀⠀⠀⠐⠛⢳⡄⢻⠃⠀⠀⠀⠀
⠀⠘⠇⣥⣷⠄⠀⠰⠀⠉⠑⢀⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠰⡀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢾⠀⠀⠙⠤⠀⢀⡏⣶⣧⠃⠻⡆⠀⠠⠌⠹⡆⠀⠀⠀⠀⣠⣿⡇⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡦⡄⠀⠀⠀⠀⠀⡌⠂⢸⠀⠀⠀⠀⠀⠀⢿⢿⣉⣑⣰⣿⠀⠀⠀⠀⠀⢀⠒⠲⡍⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⠀⠸⠀⠀⠀⠀⠘⠄⠈⠀⠙⠟⢋⣁⠀⠀⠀⠀⠀⠀⠀⠀⡿⣦⠿⠀⠀⠀⠀⠀⠀⠀
⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀⠀⠀⡇⠀⠀⢸⡇⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠄⠀⠀⢠⠹⡀⠀⣀⡀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠄⠀⠐⠀⠙⣿⣿⡇⠀⠰⠀⠀⠀⡿⣷⣆⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀⢳⡆⠀⠠⢀
⠀⠖⡶⣶⠇⢶⠄⠰⠶⠶⠖⠀⠀⠈⠀⠀⠀⢠⣧⠀⠀⡀⠀⢀⣠⡄⠀⠀⠀⠀⠠⣤⣤⣤⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⢰⡇⠼⠩⠤⠄⠀⠈⠀⠀⠀⢠⢴⡶⠀⠸⡇⠀⠀⠀⠀⡀⠀⠀⠋⠀⠈⢻⣷⡄⠀⠰⣾
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⣿⣿⣿⣿⣿⣿⡏⠀⢶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣆⣿⣿⣿⣿⣿⣿⡅⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⠿⣃⣀⡹⢿⣿⣟⣻⣿⣛⣛⣀⣘⣛⡛⢛⣛⣛⣛⣻⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⠍⣿⠀⢹⣿⠁⠀⠈⢹⡏⠈⢹⣿⠉⠉⠹⠇⡈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⡀⠇⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠓⠎⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣁⠀⢸⡟⢩⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⡿
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣾⡿⠿⣿⠿⠿⡏⠀⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣹⣿⣿⣯⡻⠦⣭⠴⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣿⣿⠁
⣾⣿⣿⣿⣿⣿⣿⣿⢟⣵⠟⣫⣭⣛⢿⣶⢹⡿⣱⡾⢛⣉⣛⢿⡇⢻⣿⢏⣴⠞⠛⠉⠛⠻⣶⡆⢀⠀⠀⠀⢳⠂⠀⠀⠒⠺⢃⢻⣿⠀⣿⣿⡿⠿⠏⠀⠀⢰⠿⣿⣿⠇⡿⣿⣿⣿⣿⣿⣯⣿⢿⡿⢿⣿⣿⣿⡏⠀
⢙⡟⠛⠿⠛⢿⣿⢃⣿⡏⣜⡿⣿⠟⠃⠛⢸⡇⣿⣧⣙⠻⠿⣮⣥⣿⡏⣾⡏⠘⠀⠀⠀⠀⠛⠃⠈⠀⢸⣦⡌⠀⠀⠀⢐⡆⠸⣿⣿⡆⣿⣿⠁⡔⣿⣦⠀⠸⢰⣹⠉⠆⠀⣀⡭⠈⠿⣿⣿⡇⠈⡇⣹⣿⣿⣿⡇⠀
⠞⠀⣰⣤⡐⢸⣿⢸⣿⡇⠻⠃⠏⠀⠀⠀⢸⡄⠎⠛⠻⠿⣷⣶⣍⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢐⣼⡗⠀⠀⢀⠸⣿⣿⠀⡏⢯⡃⡿⠁⠀⢿⣿⡏⣄⠀⠀⠹⡆⡸⡅⠘⠀⠑⣆⣽⠏⠀⠀⠀⢘⠏⣿⠿⡇⠀
⠘⠠⠿⢻⡇⠈⢻⡆⢿⣇⠀⠀⠀⠀⢀⣤⠽⡟⣥⠀⠀⢠⡀⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠁⢻⠉⠃⠈⠀⠘⢀⠈⢻⣧⠀⠀⠀⣷⠀⠀⠀⣿⣦⣁⠀⠀⠀⣻⡅⠁⢄⠀⠀⠈⠟⢠⣤⢲⡄⠀⠀⠁⠀⡏⢴
⠀⠀⢀⢰⣇⡀⡌⠙⢮⡻⢦⣤⣤⣤⠾⠋⠈⠀⠿⣷⣤⣤⣥⡾⠟⠀⠀⢀⡛⢷⣤⣤⣤⡾⠋⠀⠀⣰⠆⠀⠀⠈⠀⠈⠀⢸⠟⠆⠀⠀⠹⠄⡀⠀⣿⢹⡌⣿⣦⠀⠈⠀⠂⠌⢣⠀⠀⠀⢀⣻⠈⠓⢠⡀⠀⠀⡠⠀
⣿⡆⠀⢹⣿⣷⡇⠀⢻⡇⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⡀⠗⠰⠀⠀⠀⠀⠀⠀⢸⡀⣠⠄⠀⣤⠰⠱⡀⡏⡷⡧⡝⣿⡀⠀⠀⢠⣄⢸⠀⠀⠀⠈⠿⣄⠀⣾⠇⠀⠀⠀⠀
⠈⠿⡇⢇⣟⡉⠀⢀⠠⠓⠢⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⣸⠀⠀⠻⠀⠀⢙⡘⣤⣇⠇⠘⢿⡄⠀⡚⢿⡀⠀⠀⠀⠀⠀⣼⡇⠸⠀⠀⠀⠀⠀
⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠸⠈⠁⠀⠀⠐⢢⡄⠀⠀⠀⠀⠀⠀⠸⡃⢹⠀⠀⠀⠀⠀⠀⢻⢿⢿⣶⣴⣿⡿⠀⠁⠀⠁⠀⠀⣀⡠⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠉⠇⠀⠀⠀⠀⠀⣧⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣄⠀⠀⠀⠀⠈⠀⠀⣧⣈⣿⠃⠀⠃⠀⠀⠀⠀
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⡌⠀⠀⠀⢠⣾⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⢁⢻⡄⠀⠀⠀⠀⠀⠀⠀
⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠠⠀⢺⣿⣶⡆⠀⠸⠀⠂⠘⣷⣥⡄⠀⠀⠀⠽⠉⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢁⠀⠀⠈⠀⠃⠀⠐⣦⡀⠀⢀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⠀⠀⠀⠀⠹⣿⡷⠀⠀⠀⠀⢠⡏⢻⠿⠀⠀⠀⠀⠀⠀⠀⣀⣠⡆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⣶⣬⡁⠀⠀⣰
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⢤⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⡄⣿⣿⣿⣿⣿⣿⡇⠸⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣇⣈⣻⣿⣿⣟⣻⣿⣟⣛⣀⣙⣛⡻⢿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠀⢹⣿⠁⠈⠉⢹⡏⠉⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⡇⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠳⡮⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣁⠈⢸⡟⣹⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣽⡿⠿⣿⠿⠿⡟⠀⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠟⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣯⡻⠦⣭⠵⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⠃
⣼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣛⣭⣛⢿⡇⢺⣿⢟⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠀⠐⣤⠀⠀⠀⠒⠾⠧⢿⣷⢸⣿⣿⣿⣿⡟⠀⠀⢲⣯⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⠀
⠻⡿⠛⣿⠿⣿⣿⢃⣿⡏⣸⣿⣿⡿⠃⠛⣸⡇⣿⣧⣙⠿⢿⣦⣥⣿⡏⣾⡏⠸⠀⠀⠀⠀⠛⠃⠈⠀⢰⡀⡃⠀⠀⠀⢐⡆⢸⣿⣿⠀⣿⣿⠃⡰⣶⣄⠀⢸⢀⣻⠋⡆⠁⢈⣛⠙⣿⣿⣿⡏⠈⡇⣺⣿⣿⣿⡇⠀
⡾⠁⣠⣀⠠⢸⣿⢸⣿⡇⠿⠇⡟⠀⠀⠀⢹⡁⠌⠛⠻⠿⣷⣶⣍⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⡆⠀⢀⠸⣿⣧⠀⡟⣟⢸⡿⠃⠀⢹⣿⡟⡀⠀⠀⢻⡄⢸⡂⠙⠁⠲⣄⣹⡟⠁⠀⠁⢘⠟⣿⣿⡇⠀
⠰⠠⠿⢿⡇⠘⢻⡎⢿⣇⠀⠀⠀⠀⢀⣤⢼⡟⣤⠀⠀⢠⡄⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠂⢸⠛⠃⠀⠀⠸⠀⠙⣿⡆⠀⠈⢸⣧⠀⠀⠈⣿⣇⡋⠀⠀⠀⣷⡃⠁⡀⠀⠀⠘⡿⢀⣄⢢⡄⠈⠀⠉⠀⡇⡠
⠀⠀⡆⣘⡆⠀⡜⠳⣬⡻⢦⣤⣤⣤⠾⠋⠘⠁⠿⣷⣤⣬⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⢸⡄⠀⠀⠀⠀⠁⠀⣽⡿⠀⠀⠈⠛⠄⡀⠀⣿⢻⡉⢷⣄⠀⠉⠁⠆⡈⢆⠀⠀⠀⢈⣿⠘⠧⢀⡀⠀⠀⢀⠈
⣶⡄⠉⢻⣿⣧⡇⠀⢿⡇⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠈⠀⢠⡀⠀⣤⢲⠱⡀⡟⣾⣧⡾⢿⣆⠀⠀⣀⡄⢸⠀⠀⠀⢘⣿⣄⠀⣼⡇⠀⠀⠀⠀
⠈⣷⡆⡎⣟⠛⠁⠀⢈⠧⢄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⠀⠐⠻⠀⠀⠱⣴⣡⣿⡇⠀⠙⣷⡀⡾⣿⡈⠀⠀⠀⠀⠀⣽⡇⢹⠀⠀⠀⠀⠀
⠀⠁⠁⠘⠿⠁⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⢸⠘⠂⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⢸⠃⢻⠀⠀⠀⠀⠀⠀⠹⡻⠻⢾⣷⠿⠟⠃⠁⠈⠃⠀⣀⡀⢠⣴⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠠⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠓⡆⠀⠀⠀⠀⠀⣆⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠐⠀⠈⣧⡙⣿⠃⠀⠂⠀⠀⠀⠀
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⡌⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡘⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠉⢿⡍⠀⠀⠀⠀⠀⠀⠀
⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢶⣶⣦⡄⠀⠸⠀⠀⠘⣧⣃⡀⠀⠀⠈⡹⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢁⠀⠀⠘⠀⠃⠀⠀⣄⡀⠀⠀⠀
⠀⠖⠶⣶⠇⢶⠄⠰⠶⠶⠖⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⢀⡏⢿⡷⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⢀⡟⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⣦⣜⠓⠀⠈⢠
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⢤⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⡄⣿⣿⣿⣿⣿⣿⡇⠸⣾⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣇⣈⣻⣿⣿⣟⣻⣿⣟⣛⣀⣙⣛⠻⢿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⠍⣿⠀⢹⣿⠁⠈⠉⢹⡏⠉⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠀⡇⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠳⡮⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣁⠈⢸⡟⢹⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣽⡿⠿⣿⠿⠿⡟⠀⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⠛⠀⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣯⡻⠦⣭⠵⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣷⣿⣿⠃
⣼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣛⣩⣛⢿⡇⢺⣿⢏⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠀⠰⣤⠀⠀⠀⠒⠾⠧⢿⣶⢸⣿⣿⣿⢿⡟⠠⠀⢶⣯⣿⣿⢋⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣏⠀
⠻⡿⠛⣿⠿⣿⣿⢃⣿⡏⣸⣿⣿⡿⠃⠛⣸⡇⣿⣧⣙⠿⠿⣦⣥⣿⡏⣾⡏⠘⠀⠀⠀⠀⠛⠃⠈⠀⢰⡀⡃⠀⠀⠀⢐⡆⢸⣿⣿⠀⣿⣿⠃⡰⣶⣄⠀⢸⢀⣻⠛⡂⠁⢈⣛⠙⣿⣿⣿⡏⠈⡇⣺⣿⣿⣿⡇⠀
⡼⠁⣠⣄⠠⢸⣿⢸⣿⡇⠿⠇⡟⠀⠀⠀⢹⡁⠌⠛⠻⠿⣷⣶⣍⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⡆⠀⢀⠸⣿⣧⠀⡟⣟⢸⡿⠃⠀⢹⣿⡟⡀⠀⠀⢻⡄⢸⡂⠙⠁⠲⣄⣹⡟⠁⠀⠁⢘⠟⣿⣿⡇⠀
⠰⠀⠿⢿⡇⠘⢻⡎⢿⣇⠀⠀⠀⠀⢀⣤⢼⡟⣤⠀⠀⢠⡄⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠂⢸⠛⠃⠀⠀⠸⠀⠉⢿⡄⠀⠈⢸⣧⠀⠀⠈⣿⣇⡋⠀⠀⠀⣷⡁⠁⡀⠀⠀⠘⡿⢠⣄⢢⡄⠈⠀⠉⠀⡇⡠
⠀⠀⡆⣘⡆⠀⡜⠳⣬⡻⢦⣤⣤⣤⠾⠋⠘⠁⠿⣷⣤⣬⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⢰⠄⠀⠀⠀⠀⠁⠀⣿⡿⠀⠀⠈⠛⠀⡀⠀⣿⢹⡈⢳⣄⠀⠉⠁⠆⡈⢆⠀⠀⠀⢈⢿⠘⠧⢀⡀⠀⠀⢀⠈
⣲⡄⠈⢻⣿⣧⡇⠀⢿⡇⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠈⠀⢠⡀⠀⣤⠲⠱⡀⡟⣾⣧⡾⢿⣆⠀⠀⣀⡄⢸⠀⠀⠀⢘⡿⣄⠀⣼⡇⠀⠀⠀⠀
⠈⣷⡆⡎⣟⠛⠁⠀⢈⠧⢄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⠀⠐⠻⠀⠀⠱⣴⣡⣿⡇⠀⠙⣷⡀⡼⣿⡈⠀⠀⠀⠀⠀⣽⡇⢹⠀⠀⠀⠀⠀
⠀⠁⠁⠘⠿⠁⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⢸⠘⠂⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⢸⠃⢻⠀⠀⠀⠀⠀⠀⠹⡿⠻⢾⣷⠿⠟⠃⠁⠈⠃⠀⣀⡀⢠⣶⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠠⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠓⡆⠀⠀⠀⠀⠀⣆⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠐⠀⠈⣧⡙⣿⠃⠀⠂⠀⠀⠀⠀
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⡌⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡘⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠉⢿⡍⠀⠀⠀⠀⠀⠀⠀
⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢶⣶⣦⡄⠀⠸⠀⠀⠘⣧⣃⡀⠀⠀⠈⡹⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢁⠀⠀⠘⠀⠃⠀⠀⣄⡀⠀⠀⠀
⠀⠆⠶⣶⠇⢶⠄⠰⠶⠶⠖⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⢀⡏⢿⡷⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⢀⡟⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⣦⣜⠓⠀⠈⢠
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⠛⣿⣿⣿⣿⣿⣿⡟⢰⣼⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣧⣿⣿⣿⣿⣿⣿⣷⠀⢿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣀⣙⣻⣿⣿⣟⣻⣿⣟⣛⣀⣘⣛⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠈⢹⣿⠙⠻⠿⢹⡏⠟⢹⣿⠉⠉⠹⠇⠈⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⠈⡆⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⠀⠘⠃⣀⠃⢸⡟⣹⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⡿⠁⠿⠦⣥⠴⠟⠀⠀⠛⠷⠤⠴⠟⠘⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣯⣻⠦⣭⠵⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣵⣿⡏
⣸⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣛⢿⡇⢠⣶⢖⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⢇⣿⡆⢸⣿⣿⣿⣿⣿⠃⠀⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⢿⣿⣿⣿⣿⣿⣿⢇⣿⡏⡘⣿⣿⣿⡧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣭⣿⡏⣾⡏⢸⠀⠀⠀⠀⠛⠃⠴⠀⠀⢰⠢⠀⠀⠀⢠⡄⢰⣼⣿⢸⣿⣿⠏⢉⣅⠀⠀⢸⠋⣿⠿⡍⠋⠛⠿⠻⣿⣿⣿⡿⠙⡏⢽⣿⣿⣿⡇⠀
⣰⠃⠀⠙⢀⢻⣿⢸⣿⡇⣿⡏⣿⠋⠀⠀⢻⠋⡌⠛⠻⠿⣷⣶⣝⠟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠁⠀⠀⢴⣾⡇⠘⡿⡿⣸⣿⠟⠀⢦⣿⡿⠀⠈⠀⢯⡀⢡⠀⢲⠛⢄⡉⢿⡿⠋⠐⠇⠸⡿⣿⣿⡇⠀
⢡⠀⣿⣿⡆⠸⣿⡆⢿⣇⠁⠀⠁⠀⢀⣤⢼⡇⣤⠀⠀⠸⣤⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⢀⡿⠟⠀⠀⡆⠈⠻⡇⢀⠃⠁⣿⢋⠀⠀⠚⣿⡇⠗⠀⠀⠀⣧⡎⠇⠀⠀⠀⠳⣿⠃⠀⢀⡀⠐⠁⠛⠉⡧⢀
⠀⠈⡅⢹⡁⠀⠸⢷⣈⠻⢦⣤⣤⣤⠾⠋⢸⠇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⢘⡀⠀⠀⠀⠁⠃⠀⣇⠈⠀⠀⢿⠋⠀⠀⠀⣿⢻⠙⢶⣦⡀⠺⠃⢀⠱⡄⠀⠀⠑⠘⣿⠸⣇⠀⠀⠀⠀⠁⠙
⣠⠀⠳⣿⣷⣄⡇⠀⣿⡗⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⠀⠀⠀⠈⠋⠀⢀⠀⠈⣄⠈⢣⠀⣿⣼⣇⡜⠛⠿⠦⣄⠀⡇⢸⠀⠀⠀⠰⣿⠀⠀⢸⡆⠀⠀⠘⠀
⠙⣧⡐⡜⣿⣿⠃⠀⠘⣇⡀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠃⠁⠈⠀⠀⠀⠀⠀⠀⢀⡀⢺⠀⠈⠻⠀⠀⢡⢣⣿⣿⣇⣀⣀⣴⣿⣿⣷⠘⠀⠀⠀⠀⠁⢻⡄⢻⠁⠀⠀⠀⠀
⠀⠉⠃⠁⣶⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠⠸⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢾⠀⠀⠀⠀⠀⠀⠈⢻⠏⠛⠿⣟⠁⠘⠇⠙⠇⠀⠀⠀⢀⣠⣿⡇⠈⠀⠀⠀⠀⠀
⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢹⡧⡄⠀⠀⠀⠀⠀⡘⠃⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⠀⠐⡊⠻⣿⡇⠀⡄⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⡴⡘⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢷⠀⠸⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠛⣶⡛⠀⠀⠀⠀⠀⠀⠀
⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀⠀⠀⠸⠀⠀⢸⣇⡇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠂⠀⠀⠰⠈⡇⠀⢀⡀⠀⠀⠀⠀
⠘⠖⠶⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠄⠀⠈⠀⠘⢿⣿⣿⠀⠀⠂⠀⠀⡟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠻⠦⠀⠐⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣙⠿⣿⣿⣿⣿⣿⣿⡿⢠⣹⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣽⣄⣿⣿⣿⣿⣿⣿⣧⠀⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣧⣘⣛⣻⣿⣿⣟⣻⣿⣟⣛⣂⣀⣛⣾⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠻⢹⣿⠹⢿⣿⢹⡏⡿⢹⣿⠉⠉⠹⢇⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⣿⣤⣼⡆⡘⡄⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣀⠃⢸⡟⣩⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⠟⣾⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣯⣻⠦⣭⠵⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⡟
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⣀⣤⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠋⠀⠀⠀⠀⠠⣶⣾⡇⣿⡄⣿⣿⣿⣿⣿⣿⠟⠂⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⡿⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠘⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣭⣿⡏⣾⡏⠰⠀⠀⠀⠀⠛⠃⡤⠀⠀⠀⡆⠀⠀⠀⣀⡉⢨⣽⡇⣿⣿⣿⠟⢛⡃⠈⠁⢸⠛⣿⣿⡳⠟⠻⣿⢿⣿⣿⣿⣿⠻⡟⢻⣿⣿⣿⡗⠀
⣨⠏⠀⠛⠉⢿⣿⢸⣿⡇⣷⡟⣿⠏⠁⠉⢛⠟⡪⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠇⠀⠀⣤⣾⠀⢨⣿⡇⣿⣿⡿⠀⣎⣿⡇⠀⠘⠀⣟⠀⢃⠀⢤⠾⣀⠛⣿⣿⠟⠀⡇⢸⣿⣿⣿⡇⠀
⢋⢠⣾⣷⡌⠸⣿⡌⢿⣇⠋⠁⢻⠀⢀⣤⢌⡇⣥⠁⠀⢺⣄⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⣦⠈⠀⠀⡆⠘⠿⠀⢸⠋⢹⡟⠋⠀⠀⠿⣿⡇⡧⠀⠀⠈⣇⡜⡆⠀⠀⠈⢳⣾⠇⠀⡀⠀⠠⠃⠿⠛⣇⠀
⠈⠈⠁⢻⡀⠀⢹⣧⣈⠻⢦⣤⣤⣤⠾⠋⢾⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠐⠀⠁⠀⠀⠀⠀⠂⠀⠀⠸⠀⢸⡇⠈⠀⠀⠀⡿⢏⠓⢶⣶⣄⣽⡇⢀⠢⡀⠀⠀⠻⠐⣶⢸⡇⠀⠀⠀⠀⠃⠨
⢀⠀⢦⣾⣧⡄⡇⠈⣿⡇⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁⣤⡐⠆⠀⡿⢸⡄⡘⠉⠛⠁⣹⣿⡆⢱⠀⠀⠀⢂⣿⠀⠉⢰⡆⠀⠀⠰⠀
⠸⣆⡰⡹⣿⣿⠇⠀⠹⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠉⠘⠀⠀⠀⠀⠀⠀⢀⡄⢼⠂⠈⠛⠀⠀⠀⠛⢿⣿⣇⢦⣠⣴⠿⣷⣷⠸⠀⠀⠀⠀⠋⢶⡄⢾⠃⠀⠀⠀⠀
⠀⠋⠇⠃⣧⠄⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠⢱⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⣙⠋⠁⠀⠏⠻⡦⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⢱⣆⡀⠀⠀⠀⠀⠀⢘⠃⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⡜⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠄⠠⠀⢀⡤⠸⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠈⠀⠀⠟⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⠀⠀⢸⡆⡆⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠙⠇⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡄⠀⠘⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⡿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⢳⣆⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡹⢿⣿⣿⣿⣿⣿⣿⡿⢀⣸⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢠⣷⣸⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣛⣂⣈⣛⣼⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⠃⢹⣿⠹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠁⢸⣿⣤⣼⡆⠘⡄⢸⡇⠿⢏⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣀⠣⢸⡟⣹⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⠟⣾⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣯⣻⠦⣭⠵⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⡟
⢺⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⢀⣤⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠏⠀⠀⠀⠀⠀⣠⣾⡇⣿⠀⣿⣿⣿⣿⣿⣿⠟⠒⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠙⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡄⠀⠀⠀⡄⠀⠀⠀⣀⠌⢨⣹⡇⣿⣿⣿⠛⢛⡃⠈⠁⢹⠟⣿⣿⡷⠟⠻⣿⢿⣿⣿⣿⣿⠻⡟⢻⣿⣿⣿⡗⠀
⣨⠏⠀⠛⠉⢿⣿⢸⣿⡇⣷⡟⣿⠟⠁⠈⢻⠟⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⠇⠀⠀⣤⣾⠀⢨⣿⢳⣿⣿⡏⠀⣎⣿⡇⠀⠘⠀⣟⠀⢃⠀⢤⠾⣀⠛⣿⣿⠗⠠⠇⢸⣿⣿⣿⡇⠀
⢋⢠⣾⣷⡄⠸⣿⡄⢿⣇⠋⠁⠻⡀⢀⣤⢄⡆⣥⠁⠀⢺⣄⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⣄⠁⠀⠀⡆⠘⠇⠀⢸⠏⣼⠿⠋⠀⠀⠿⣿⡇⡦⠀⠀⠈⣇⡜⡆⠀⠀⠈⢣⣾⠇⠀⠀⠀⠨⠃⠿⠛⣇⠀
⠈⠈⠀⢻⡀⠀⢹⣧⣈⠻⢦⣤⣤⣤⠾⠋⢺⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠈⠀⠀⠐⡟⠏⠉⢿⣷⣤⡼⣇⣀⢢⡀⠀⠀⠫⠐⣶⢸⡇⠀⠀⠀⠀⠃⠨
⢀⠀⢤⣾⣧⡄⡇⠈⣿⡧⡀⢰⡄⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⢀⣤⠀⠆⠈⣾⣸⡀⠈⡉⠉⠀⣼⡿⡆⢱⠀⠀⠀⢂⣿⠀⠉⢰⡄⠀⠀⠰⠀
⠸⣆⡰⡹⣿⣿⠇⠀⠹⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠙⠑⠀⠀⠀⠀⠀⠀⢠⡄⢼⠀⠈⠙⠀⠀⠀⠉⠻⣿⣃⢥⣤⡼⠻⢧⢧⠸⠀⠀⠀⠀⠋⢶⡀⢾⠃⠀⠀⠀⠀
⠀⠊⠇⠃⣦⠄⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢠⢱⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠉⠀⠠⡏⠻⡆⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⢱⣆⡀⠀⠀⠀⠀⠀⣈⠃⢸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⣶⠀⠀⠀⠀⠀⠀⠀⠄⠠⡐⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⡄⠠⠀⢀⡤⠸⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠘⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⡿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡹⢿⣿⣿⣿⣿⣿⣿⡿⢀⣸⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢠⣷⣸⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣛⣂⣀⣛⣼⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⠃⢹⣿⠹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠀⢸⡇⠁⢸⣿⣤⣼⡆⠘⡄⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣀⠣⢸⡟⣩⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⠟⣾⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠬⣻⣿⣿⣯⣻⠦⣭⠵⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⠟
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡆⢀⣤⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠏⠀⠀⠀⠀⠀⣰⣾⡇⣿⡀⣿⣿⣿⣿⣿⣿⠟⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠄
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠙⣿⣿⣿⣧⣛⣸⡇⢿⣧⣙⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡄⠀⠀⠀⡄⠀⠀⠀⣀⡈⢨⣹⡇⣿⣿⣿⠛⢛⡃⠈⠀⢺⠗⢿⣿⡻⠟⠻⣿⢿⣿⣿⣿⣿⠻⡟⢻⣿⣿⣿⡗⠀
⢨⠏⠀⠛⠉⢿⣿⢸⣿⡇⣷⡟⣿⠟⠁⠈⢻⠟⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠇⠀⠀⣤⣾⠀⢨⣿⢳⣿⣿⡟⠀⣎⣿⡇⠀⠘⠀⣏⠀⢃⠀⢤⠾⣀⠛⣿⣿⠗⠀⠇⢸⣿⣿⣿⡇⠀
⢋⢠⣾⣷⡄⠸⣿⡌⢿⣇⠋⠁⠻⡀⢀⣤⢄⡆⣥⠁⠀⢺⣄⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⣄⠁⠀⠀⠆⠘⠇⠀⢸⠏⣼⠿⠋⠀⠀⠿⣿⡇⡦⠀⠀⠈⣇⡜⡆⠀⠀⠈⢣⣾⠇⠀⡀⠀⠨⠃⠿⠛⣇⠀
⠈⠈⠀⢻⡀⠀⢹⣧⣈⠻⢦⣤⣤⣤⠾⠋⢾⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠈⠀⠀⠐⡟⠏⠉⢿⣷⣤⡼⣇⣀⢢⡀⠀⠀⠫⠐⣶⢸⡇⠀⠀⠀⠀⠃⠪
⢀⠀⢤⣾⣧⡄⡇⠈⣿⡧⡀⢰⡄⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⢀⣤⠀⠆⠈⣽⣸⡀⠈⡉⠉⠀⣼⡿⡆⢱⠀⠀⠀⢂⣿⠀⠉⢰⡄⠀⠀⠰⠀
⢸⣆⡰⡹⣿⣿⠇⠀⠹⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠉⠑⠀⠀⠀⠀⠀⠀⢠⡄⢼⠀⠈⠙⠀⠀⠀⠈⠻⣿⣃⢥⣤⡼⠻⢧⢧⠸⠀⠀⠀⠀⠋⢶⡀⢾⠃⠀⠀⠀⠀
⠀⠉⠇⠃⣥⠄⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢠⢱⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠉⠀⠠⡏⠻⡄⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⢱⣆⡀⠀⠀⠀⠀⠀⣈⠃⢸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⣶⠀⠀⠀⠀⠀⠀⠀⠄⠠⡐⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⡄⠠⠀⢀⡤⠸⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⡸⠀⢸⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠙⠇⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠘⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⡿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⠿⣿⣿⣿⣿⣿⣿⣿⡿⢀⢸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣇⣻⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⠀⣛⣛⣿⣿⣿⣟⣻⣿⣟⣛⣀⣈⣛⣼⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣽⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⢏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⠈⢸⡇⠁⢸⣿⣤⣼⡆⠘⡄⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣀⠃⢸⡟⣹⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣤⠴⠟⠀⠀⠻⠷⠤⠴⢟⣾⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⣻⣿⣿⣯⣻⠦⣭⠵⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⠟
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢆⣴⠞⠛⠉⠛⠻⣶⡆⠀⢸⠟⠀⠀⠀⠀⠀⣶⣿⢇⣷⢠⣿⣿⣿⣿⣿⣿⠟⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠙⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣭⣿⡏⣾⡏⠄⠀⠀⠀⠀⠛⢣⡀⠀⠀⠀⡄⠀⠀⠀⣈⠍⢨⣝⢸⣿⣿⡟⠉⣙⡅⠈⠀⢹⠟⣿⣿⡿⠟⠻⣿⢿⣿⣿⣷⣿⠻⡟⣻⣿⣿⣿⡗⠀
⢨⠏⠉⠻⠉⢿⣿⢸⣿⡇⣷⡟⣿⡟⠉⠉⢛⠟⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⣤⡶⠀⢨⣿⣸⣿⣿⡇⠰⣬⣿⡇⠀⠘⠀⣟⠀⢃⠄⢴⠾⣘⠛⣿⣿⠗⠠⡇⢸⣿⣿⣿⡇⠀
⢋⢠⣿⣷⠐⢸⣿⡌⢿⣇⠋⠁⠻⠁⢀⣤⠄⡆⣥⠁⠀⢲⣆⢹⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠸⡹⠀⠀⠀⠙⠁⠀⠘⢧⡿⠿⠋⠀⠀⠿⣿⣄⣦⣀⡀⠉⣧⡜⡆⠀⠀⠈⢣⣾⠇⠀⡀⠀⠀⠃⠽⠛⣇⠀
⠈⠘⠈⣻⠀⠀⢹⣧⢈⡻⢦⣤⣤⣤⠾⠋⢾⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡇⠀⠈⠀⠀⢸⠟⡃⠉⣻⣿⣿⠛⢳⣦⢠⡀⠀⠀⠻⢐⣶⢸⡇⠀⠀⠀⠀⠇⠪
⢀⠐⢤⣿⣧⡀⡇⠈⣿⡧⡀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⢠⣦⠁⠀⠈⢄⣷⡀⠉⡀⠀⠀⣾⡿⡄⢱⠀⠀⠀⢊⡟⠀⠉⢰⡄⠀⠀⠰⠀
⢸⣆⡴⡹⣿⣿⠇⠀⠹⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠙⠃⠀⠀⠀⠀⠀⠀⢠⡄⢼⠀⠀⠉⠀⠀⠀⠀⠻⣿⡡⢥⣤⡞⠹⣦⢷⠸⠀⠀⠀⠀⠋⢶⡀⢾⠃⠀⠀⠀⠀
⠀⠉⠇⠃⣤⠅⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠉⠁⠀⠰⡏⠻⡄⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀⠀⠀⣘⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣷⠀⠀⠀⠀⠀⠀⠀⠄⠠⡐⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠈⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠣⡄⠠⡀⢀⡤⠸⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡌⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠙⣿⣿⣶⠀⠀⠀⠀⠈⡿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢀⢻⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣀⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠇⠀⣛⣛⣿⣿⣿⣟⣻⣿⣟⣛⣀⣉⣓⣾⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⢹⢸⡇⠁⢸⣿⣤⣼⡆⡸⡄⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⠈⠙⣿⡄⢸⣿⠀⠀⠘⢸⣇⡀⢸⣿⠀⠘⠃⣀⠃⢸⡟⣩⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⠀⠀⠛⠷⠤⠴⣟⣾⠠⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⣻⣿⣿⣯⣻⠦⣭⠵⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⡟
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⢀⣠⢀⣴⠞⠛⠉⠛⠻⣶⡆⠀⢻⡟⠀⠀⠀⠀⢠⣴⣿⢇⣧⢸⣿⣿⣿⠿⢿⣿⠟⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠙⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡏⣾⡏⠀⠠⠀⠀⠀⠛⣣⠀⢰⠂⠀⡄⠀⠀⠀⣀⠍⢨⣍⢸⣿⣿⡏⢀⠲⣧⡈⠀⢻⠿⣿⣿⣻⠟⠛⣿⢿⣿⣿⣿⣿⠻⡟⢻⣿⣿⣿⡗⠀
⢸⠏⠉⠻⠉⢿⣿⢸⣿⡇⣷⡟⣿⡿⠉⠉⠙⠟⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠁⠀⠠⣤⡎⠀⢠⡇⣿⣿⣿⡇⠈⣿⣿⡇⠀⠘⠐⣟⠀⢃⠄⢶⠾⢈⠛⣿⣿⠟⠰⡇⢸⣿⣿⣿⡇⠀
⢛⢰⣿⣷⠐⢸⣿⡌⢿⣇⠋⠁⠻⠇⢀⣤⢄⡆⣥⠁⠀⠰⣆⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⢰⠀⠀⠀⠀⠙⠀⠀⡈⣹⡿⠿⠛⠀⠀⢩⣿⡧⢦⣤⣄⡈⣧⡜⡆⠀⠀⠈⢳⣶⠇⠀⠀⠀⠀⠃⢽⠟⣇⠀
⠈⠈⠈⣿⠀⠀⢹⣧⢨⡻⢦⣤⣤⣤⠾⠋⢸⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠇⣿⠇⠀⠀⡀⠀⡸⠃⡄⠀⡹⠿⠿⠋⢻⣧⠠⡀⠀⠀⠻⠐⣶⢸⡇⠀⠀⠀⠀⠇⠨
⢀⠐⢤⣿⣧⡀⡇⠈⣿⡇⡀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢰⣦⠁⠀⠀⣇⣿⣀⡀⡀⠀⠀⣼⡿⡄⢱⠀⠀⠀⢈⡟⠀⠉⢰⡄⠀⠀⠰⠀
⠸⣄⡼⡹⣿⣿⠇⠀⠹⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠨⡄⠀⠀⠀⠆⠙⠃⠀⠀⠀⠀⠀⠀⢤⡄⢽⠀⠉⠁⠀⠀⠀⠉⢻⣿⡁⢥⣤⡾⠹⣦⢷⠸⠀⠀⠀⠀⠋⢶⡀⢾⠃⠀⠀⠀⠀
⠀⠈⠇⢃⣤⡅⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡐⠀⠀⠀⠀⢢⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠘⠁⠀⠰⡏⠻⡆⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⡘⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠢⡀⠠⠀⣀⡤⠢⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⢸⣦⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⡌⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠙⣿⣿⣶⡀⠀⢀⠀⠈⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡻⢿⣿⣿⣿⣿⣿⣿⣿⡿⢀⢲⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⣷⣸⣿⣿⣿⣿⣿⣿⣿⣧⢘⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠇⠸⣛⣛⣿⣿⣿⣟⣻⣿⣟⣛⣀⣉⣓⣾⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⢹⢸⡇⠁⢸⣿⣤⣼⡆⠺⡆⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠈⠙⣿⡄⢸⣿⠀⠀⢸⢸⣇⡀⢸⣿⠀⠘⠃⣀⢃⢸⡟⣭⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⠤⠴⣟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⢻⣿⣿⡏⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢸⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡆⢀⣤⢀⣴⠞⠛⠉⡛⠻⣶⡆⠀⢿⡟⠀⠀⠀⠀⠀⣶⣿⢇⣇⢸⣿⡇⢸⡇⢚⢸⡇⠐⣾⡿⢱⡟⢰⣦⠹⣷⢹⠏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠙⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⣃⠀⢰⠂⠀⡀⠀⠀⠀⣈⠈⢨⡍⢸⣿⣧⢸⡇⣽⢸⡇⠀⠹⢃⢺⡇⢸⠟⢀⣿⠀⣸⣃⣀⣿⡌⡗⢻⢸⣿⢸⡗⠀
⢸⠏⠉⠻⠉⣿⣿⢸⣿⡇⣶⡟⣿⣿⠋⠉⠙⠟⡮⠛⠻⠿⣷⣶⣝⠿⠅⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠠⠁⠀⠠⣤⠆⠀⢠⣅⣿⣿⢋⣼⣇⡛⣸⣧⣤⣤⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣦⣸⣷⡁⢘⣼⣿⣌⠃⠀
⢛⢰⣿⣷⠐⢸⣿⡌⢿⣇⠋⠁⢻⠇⢀⣤⢄⡆⣥⠁⠀⠰⣆⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⡤⠀⠀⠀⠀⠙⠀⠀⡈⣼⠷⡿⠃⠀⠀⢰⡶⠖⠲⣶⣦⣈⣧⡄⡆⠀⠀⠀⢲⣶⠇⠀⡀⠀⠀⠂⢴⠖⣇⠀
⠈⠈⠈⣿⠀⠀⢹⣧⢨⡻⢦⣤⣤⣤⠾⠋⢸⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠄⠀⠘⡁⣆⠀⠼⠿⠿⠋⢻⣧⠢⡀⠀⠀⠻⢐⣦⢸⡇⠀⠀⠀⠀⠇⠨
⢀⠐⢴⣿⣧⡀⡇⠈⣿⡇⡀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡃⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⣰⡖⠀⠀⠀⢃⣿⣤⡄⡀⠀⠀⣼⣿⡄⢱⠀⠀⠀⢈⡟⠀⠉⢰⡄⠀⠀⠰⠀
⢸⣄⡼⡹⣿⣷⠇⠀⠹⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠆⠙⠑⠀⠀⠀⠀⠀⠀⢦⡄⢼⠀⠉⠁⠀⠀⠈⠙⣿⣟⣃⢥⣤⡼⠹⣤⢷⠸⠀⠀⠀⠀⠋⢦⡀⢾⠃⠀⠀⠀⠀
⠀⠈⠇⢣⣬⡅⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⢦⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠘⠃⠀⠰⡏⠻⡄⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⡘⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠣⡀⠠⠀⣀⡤⠠⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⢺⣦⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡌⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠙⣿⣿⣶⡀⠀⢀⠀⠐⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡻⢿⣿⣿⣿⣿⣿⣿⣿⡿⢀⢳⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⣷⣸⣿⣿⣿⣿⣿⣿⣿⣧⢘⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠇⠸⣛⣛⣿⣿⣿⣛⣻⣿⣟⣛⣀⣉⣓⣾⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⢹⢸⡇⠁⢸⣿⣤⣼⡆⠸⡆⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠈⠙⣿⡄⢸⣿⠀⠀⢸⢸⣇⡀⢸⣿⠀⠘⠃⣀⠃⢸⡟⣭⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⠤⠴⣟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⢻⣿⣿⡏⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⢀⣠⢀⣴⠞⠛⠉⡛⠻⣶⡆⠀⢿⡟⠀⠀⠀⠀⢐⣶⣿⢇⣧⢸⣿⡇⢸⡇⢚⢸⡇⠐⣾⡿⢱⡟⢰⣦⠹⣷⢹⠏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠙⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⣃⠀⢰⠂⠀⡀⠀⠀⢀⣈⠈⢨⡍⢸⣿⣷⢸⡇⣽⢸⡇⠀⠻⢃⢺⡇⢸⠟⢀⣿⠀⣸⣇⣀⣿⡜⡗⢻⢸⣿⢸⡗⠀
⢸⠏⠉⠻⠉⢿⣿⢸⣿⡇⣷⡟⣿⣿⠋⠉⠙⠟⡮⡛⠻⠿⣷⣶⣝⠿⠅⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠠⠁⠀⠠⣤⠇⠀⢠⣇⣿⣿⢋⣼⣇⡛⣸⣧⣤⣤⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⡦⣸⣷⡁⢘⣼⣿⣌⠃⠀
⢛⢰⣿⣷⠐⢨⣿⡌⢿⣇⠋⠁⢻⠇⢀⣤⢄⡆⣥⠁⠀⠰⣆⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⡄⠀⠀⠀⠀⠙⠀⠀⡈⣼⠷⡿⠃⠀⠀⢰⡶⠖⠲⣶⣦⣈⣧⡄⡆⠀⠀⠀⢢⣶⠇⠀⠀⠀⠀⠂⢴⠖⣇⠀
⠈⠈⠈⣿⠀⠀⢹⣧⢨⡻⢦⣤⣤⣤⠾⠋⢸⡇⠿⣷⣤⣤⣭⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠚⡁⣆⠀⠼⠿⠿⠋⢻⣧⠢⡀⠀⠀⠻⢐⣦⢸⡇⠀⠀⠀⠀⠇⠢
⢀⠐⢴⣿⣧⡀⡇⠈⣿⡇⡀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⣰⡖⠀⠀⠀⢃⣿⣤⡄⡀⠀⠀⣼⣿⡄⢱⠀⠀⠀⢈⡟⠀⠉⢰⡄⠀⠀⠰⠀
⢸⣄⡼⡹⣿⣷⠇⠀⠹⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠆⠙⠑⠀⠀⠀⠀⠀⠀⢦⡄⢼⠀⠉⠁⠀⠀⠀⠙⣿⣟⡃⢥⣤⡼⠹⣤⢷⠸⠀⠀⠀⠈⠋⢦⡀⢾⠃⠀⠀⠀⠀
⠀⠈⠇⢣⣬⠅⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⢦⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠃⠀⠰⡏⠻⡄⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⡘⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢿⣿⡇⠀⡀⠀⠀⠀⠀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠣⡀⠠⠀⣀⡤⠠⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⢺⣦⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡌⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠙⣿⣿⣶⡀⠀⢀⠀⠀⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⢻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣇⣺⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠀⠟⣛⣛⣿⣿⣿⣟⣻⣿⣟⣛⣀⣙⣛⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⣿⢸⡇⠁⢸⣿⣤⣼⡆⢠⡆⢸⡇⠿⢏⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠈⠙⣿⡄⢸⣿⠀⠀⢻⢸⣇⡀⢸⣿⠀⠘⠃⣀⠃⢸⡟⣭⣭⣵⣷⢻⣧⢿⣿⣿⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⢤⠴⣟⣾⠣⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⢻⣿⣯⡉⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣤⢀⣴⠞⠛⠉⡛⠻⣶⡆⠈⢛⠿⠀⠀⠀⠀⠀⣴⣿⢃⣇⢸⣿⡷⢸⡇⣌⢸⡇⠰⣾⡿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⠹⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡇⣾⡏⠀⠀⠀⠀⠀⠛⡃⠀⢰⠆⠀⠀⠀⠀⢀⣠⠀⠨⡍⣸⣿⣷⢸⡇⣿⢸⡇⠀⠿⢃⢺⡇⢸⠟⢀⣿⠀⣸⣇⣀⣿⡜⡗⣻⢸⣿⢸⡗⠀
⢨⠏⠉⠛⠉⣿⣿⢸⣿⡇⣶⡟⣿⣿⠋⠉⠙⠟⡮⡛⠻⠿⣷⣶⣝⠿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠠⠀⠀⠀⣴⠇⠀⠀⢅⣿⡿⢋⣼⣇⡐⣸⣧⣤⣤⣿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣦⣸⣷⡁⢘⣼⣿⣜⠃⠀
⢛⢰⣿⣷⠐⠸⣿⡌⢿⣇⠋⠁⢻⠧⢀⣤⢦⡆⣤⠁⠀⠰⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠀⠙⠀⠀⡀⣼⠇⠀⠀⠀⠀⠰⡀⣄⠀⢰⣾⣿⣧⡔⡆⠀⠀⠀⢲⣶⠇⠀⠀⠀⠠⠂⢴⠶⡇⠀
⠈⠀⢨⣿⠀⠀⢹⣧⣨⡻⢦⣤⣤⣤⠾⠋⠸⡇⠿⣷⣤⣤⣭⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⢀⠀⠀⠀⠀⠃⣿⣀⡀⠈⠛⠛⣿⡆⠢⡀⠀⠀⠻⢐⣦⢹⡇⠀⠀⠀⠀⠇⠂
⠀⠀⣾⣿⣧⡀⡇⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⢣⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⣾⡇⠀⠀⠀⠐⢻⣟⠇⡀⠀⢀⣿⢿⡄⢳⠀⠀⠀⢨⡟⠀⠉⢰⡄⠀⠀⠰⠀
⢸⣠⡾⡝⣿⣷⠇⠀⠹⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠸⡀⠀⠀⡈⠆⠙⠃⠀⠀⠀⠀⠀⠀⢦⠄⠜⠀⠀⠀⠀⠀⠀⣷⣿⡟⢀⣥⣀⡜⠰⣤⣷⠸⠀⠀⠀⠈⠛⢦⡀⢾⠃⠀⠀⠀⠀
⠀⠉⠇⢣⣬⡅⠀⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢇⠁⠀⠀⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠈⠉⠈⡀⠘⡟⠁⠰⡏⠻⡆⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⡄⠀⡘⠇⢸⠀⠀⠀⣀⡀⠀⠀⠀⣤⣽⣶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠣⡀⠀⠀⢠⡴⠂⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⣾⣧⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡌⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠙⣿⣿⣶⡀⠀⢀⠀⢈⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⡄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⣼⣆⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠀⠟⣛⣛⣿⣿⣿⣟⣻⣿⣟⣓⣈⣙⣓⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⣿⢸⡇⠁⢸⣿⣤⣼⡆⢢⡆⢸⡇⠿⢏⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠁⠈⠙⣿⡄⢸⣿⠀⠀⢿⢸⣇⡀⢸⣿⠀⠘⠃⣈⠃⢸⡟⣭⣭⣵⠃⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⢤⠴⣟⣾⠣⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⢻⣯⣤⡎⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⣀⣠⢀⣴⠞⠛⠉⡛⠻⣶⡆⠘⢟⠿⠀⠀⠀⠀⢠⣰⣿⢃⡇⢸⣿⣧⢸⡇⠶⢸⡇⠰⣾⡿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡇⣾⡏⠀⠀⠀⠀⠀⠛⡃⠀⢲⠂⠀⠀⠀⠀⠀⣠⠀⠎⡅⣼⡿⠏⢸⡇⠰⢸⡇⢰⣿⢃⢺⡇⢸⠟⢁⣿⠈⣸⣇⣀⣿⡜⡗⣻⢸⣿⢸⡗⠀
⣨⠏⠉⠛⠙⣿⣿⢸⣿⡇⣾⡟⣿⣿⠋⠉⠉⠟⡮⡛⠻⠿⣷⣶⣝⠿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⣤⠇⠀⠀⣇⡿⠀⢀⣼⣇⡘⣸⣧⣤⣤⣿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣦⣸⣷⡁⢘⣼⣿⣜⠃⠀
⢛⠰⣿⣷⠐⢨⣿⡄⢿⣇⠋⠁⠻⠿⢀⣤⢷⡆⣤⠁⠀⠴⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠊⠀⠀⠀⢠⠀⠛⠀⠀⡄⣸⡇⠀⠀⠀⠀⠀⠂⣶⣄⠀⠸⣿⣷⡔⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⢴⠶⡇⠀
⠈⠀⢸⣿⠀⠀⢹⣥⢨⡻⢦⣤⣤⣤⠾⠋⠜⡇⠿⣷⣤⣤⣭⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⣿⠃⣼⠀⠀⠀⠀⠘⢻⡟⢧⠀⠀⢸⣿⡄⠢⡀⠀⠀⠻⢰⣦⢸⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⡇⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠉⢳⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠙⢠⠀⠀⠀⠀⢿⣿⠎⡀⠀⣸⠏⢻⡄⢱⠀⠀⠀⢸⡟⠀⠉⢰⡄⠘⠀⠰⠠
⢸⣠⡾⡝⣿⣷⠃⠀⠹⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠸⡀⠀⠀⡈⠆⠙⠃⠀⠀⠀⠀⠀⠀⢤⠄⡽⠀⠀⠀⠀⠀⢹⣶⡄⠁⣤⣡⣴⡏⠗⣢⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠇⠀⠀⠀⠀
⠀⠈⠇⣣⣬⠅⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢇⠁⠀⠀⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠙⡿⠀⠸⡏⠻⡆⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⡄⠀⣘⠇⢸⠀⠀⠀⣶⡄⠀⠀⠀⣶⣬⠶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⢩⠀⠸⠀⠀⠀⣿⡇⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⡌⠀⠀⠀⠙⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠙⣿⣿⣶⡀⠀⢀⠀⢈⡷⣷⣆⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣾⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣆⣿⣿⣿⣿⣿⣿⣿⣿⡇⢫⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠀⠝⣛⣛⣿⣿⣿⣟⣻⣿⣟⣓⣈⣙⣓⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣽⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⣿⢸⡇⠁⢸⣿⣤⣼⡆⢣⡄⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠈⠙⣿⡄⢸⣿⠀⠀⢻⢸⣇⡀⢸⣿⠀⠘⠃⣈⠃⢸⡟⣭⣭⣵⠀⢻⣧⢹⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⠤⠴⣟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⢻⣯⣤⡉⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢀⣴⠞⠛⠉⡛⠻⣶⡆⠈⢟⠿⠀⠀⠀⠀⠀⣴⣿⢃⡇⢸⣿⡷⢸⡇⠀⢸⡇⢐⣾⡿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡇⣾⡏⠀⠀⠀⠀⠀⠛⡃⠀⢲⠂⠀⠀⠀⠀⢀⣠⠀⡎⡅⣸⠏⠀⢸⡇⢠⢸⡇⠘⢿⣇⢺⡇⢸⠟⢁⣿⠈⣸⣇⣀⣿⡜⡗⣻⢸⣿⢸⡗⠀
⢨⠏⠉⠛⠙⣿⣿⢸⣿⡇⣾⡟⣿⣿⠋⠉⠉⠟⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⡤⠇⠀⠀⡇⣿⠀⢀⣼⣇⡀⣸⣧⣤⣤⣿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢘⣼⣿⣜⠃⠀
⢛⠰⣿⣶⠔⢨⣿⡌⢿⣇⠋⠁⠻⠿⢀⣤⢷⡆⣤⠁⠀⠴⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠊⠀⠁⠀⢠⠀⠛⠀⠀⡄⣸⡇⠀⠀⠀⠀⠀⠠⢲⣦⣄⠘⢿⣧⣴⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⢴⠶⡇⠀
⠈⠀⢸⣿⠀⠀⢹⣥⢨⡻⢦⣤⣤⣤⠾⠋⠞⡇⠿⣷⣤⣤⣭⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⣿⡇⣿⠀⠀⠀⠀⠂⣾⣧⡹⠀⠀⢹⡿⡄⠢⡀⠀⠀⠻⢰⣦⢸⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⡇⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⢻⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠱⠀⠀⡀⠀⠙⠟⠁⡀⠀⣾⠁⢻⡄⢱⠀⠀⠀⢸⡟⠀⠉⢰⡄⠘⠀⠸⠠
⢹⣠⡾⡙⣿⣧⠃⠀⠹⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡄⠀⠀⡈⠇⠙⠃⠀⠀⠀⠀⠀⠀⣠⠄⢽⠀⠀⠀⠀⠀⢸⣶⣀⠀⢻⣥⣼⠏⠒⣢⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠇⠀⠀⠀⠀
⠀⠈⠇⢷⣬⠅⠀⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢇⠁⠀⠀⡝⠆⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⣼⠀⠀⠀⠀⠀⢈⠀⠁⠁⠘⠼⡟⠀⠸⡏⠻⡆⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⡄⠀⣘⠇⢸⠀⠀⠀⢶⡆⠀⠀⢠⣿⡆⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠃⠀⢩⠀⠸⠀⠀⠀⣿⡇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⡌⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠙⣿⣿⣶⡀⠀⢀⠀⢘⡷⣷⣆⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣶⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣆⣿⣿⣿⣿⣿⣿⣿⣿⡇⢫⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠀⠽⣛⣛⣿⣿⣿⣟⣻⣿⣟⣓⣈⣙⣓⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢫⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⣿⢸⡇⠁⢸⣿⣤⣼⡆⢢⡆⢸⡇⠿⢟⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠈⠙⣿⡄⢸⣿⠀⠀⢻⢸⣇⡀⢸⣿⠀⠘⠃⣈⠃⢸⡟⣭⣭⣵⠀⢻⣧⢹⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⢤⠴⣟⣾⠡⠼⠿⠤⠤⠴⠿⠠⠼⠧⠭⢻⣯⣤⡉⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢀⣴⠞⠛⠉⡛⠻⣶⡆⠈⢟⡿⠀⠀⠀⠀⠠⣴⣿⢃⡇⢸⣿⡷⢸⡇⠀⢸⡇⢐⣾⡿⢱⡟⠰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡇⣾⡏⠀⠀⠀⠀⠀⠛⡃⠀⢲⠂⠀⠀⠀⠀⢀⣠⠀⡎⡅⣸⠏⠀⢸⡇⢠⢸⡇⠘⢿⣇⢺⡇⢸⠟⢁⣿⠈⣸⣇⣀⣿⡜⡗⣻⢸⣿⢸⡗⠀
⢸⠏⠉⠛⠙⣿⣿⢸⣿⡇⣾⡟⣿⣿⠋⠉⠉⠟⠮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⡴⠆⠀⠀⡇⣿⠀⢀⣼⣇⡀⣸⣧⣤⣤⣿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢘⣼⣿⣜⠃⠀
⢛⠰⣿⣷⠔⢸⣿⡌⢿⣇⠋⠁⠻⠿⢀⣤⢷⡎⣤⠁⠀⠴⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠈⠀⠁⠀⢠⠀⠛⠀⠀⡄⣸⡇⠀⠀⠀⠀⠀⠠⢲⣦⣄⠘⢿⣧⣔⡆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣴⠶⡇⠀
⠈⠀⢨⣿⠀⠀⢹⣥⢨⡻⢦⣤⣤⣤⠾⠋⠞⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡇⣿⠀⠀⠀⠀⠂⣾⣧⡹⠀⠀⢹⡿⡄⠢⡀⠀⠀⠻⢰⣦⢸⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⡇⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⢳⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠱⠀⠀⡀⠀⠙⠟⠁⡀⠀⣾⠁⢻⡄⢱⠀⠀⠀⢸⡟⠀⠉⢰⡄⠐⠀⠰⠠
⢹⣠⡾⡙⣿⣧⠃⠀⠹⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠸⡄⠀⠀⡈⠇⠙⠃⠀⠀⠀⠀⠀⠀⣠⠄⠽⠀⠀⠀⠀⠀⠸⣶⣀⠀⢻⣥⣼⠋⠒⣢⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠃⠀⠀⠀⠀
⠀⠈⠇⢷⣬⡅⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢇⠁⠀⠀⡝⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⢈⠀⠁⠁⠘⠼⡟⠀⢸⡏⠻⡆⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⡄⠀⣘⠇⢸⠀⠀⠀⢶⡆⠀⠀⢠⣿⡆⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠃⠀⢩⠀⠸⠀⠀⠀⣿⡇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⡌⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠹⣿⣿⣶⡀⠀⢀⠀⢸⡷⣷⣆⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣷⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⡧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠇⠨⣛⣛⣿⣿⣿⣟⣻⣿⣟⣃⣀⣀⣃⣿⣿⣛⣛⣛⣛⡿⣿⣿⡿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢡⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⢽⢸⡇⠁⢸⣿⣤⣼⡇⢢⡄⢸⡇⠿⢟⣾⠇⣾⡇⣾⣿⣿⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⠈⠙⣿⡄⢸⣿⠀⠀⠸⢸⣇⡀⢸⣿⠀⠘⠃⣈⠆⢸⡟⣩⣭⣵⡆⢻⣧⢹⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠦⣤⠴⠟⢀⠀⠻⠷⠤⠴⣟⣾⠡⠼⠿⠤⠤⠴⠿⠠⠼⠧⠭⢻⣭⣤⡈⣿⣦⡭⠵⣟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢀⣴⠞⠛⠉⡛⠻⣶⡆⠀⢟⡿⠀⠀⠀⠀⠀⣴⣿⢀⡇⢸⡄⠀⢸⡇⠀⢸⡇⠀⠘⣿⢱⡟⢰⣦⠹⣷⢹⠏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⣣⠀⢰⠂⠀⠀⠀⠀⢀⣠⠁⡏⠥⢸⡇⠀⢸⡇⠀⢸⡇⢠⠀⣛⢺⡇⢸⠟⢁⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡗⠀
⢨⠏⡉⠋⠙⣿⣿⢸⣿⡇⣾⡟⣿⣿⠁⠀⣈⠛⠮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⢀⠤⠇⠀⠇⠆⣿⠀⢀⣼⣇⡀⣸⣧⣬⣤⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢘⣸⣿⣌⠃⠀
⢛⠰⣿⣶⠜⢩⣿⡌⢿⣇⠋⠁⠻⠿⢀⣤⢿⡎⣤⠁⠀⠔⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠁⠀⠠⠀⠛⠀⠀⡆⢰⡏⠀⣀⠀⠀⠀⠀⢰⡰⠖⠀⢹⡧⣴⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣴⠶⡇⠀
⠈⠀⢨⣿⠀⠀⢹⣥⣨⡻⢦⣤⣤⣤⠾⠋⠸⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⢸⡇⠀⠘⠦⡀⠀⠀⠀⠇⠀⠀⢸⡗⠻⡆⠢⡀⠀⠀⠹⢰⣦⢹⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⠃⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠐⠀⠀⠀⠘⠃⠀⠀⠀⠈⢲⣄⣤⣥⠁⡀⣼⠀⠀⠿⣄⢳⠀⠀⠀⢸⡟⠀⠉⢰⡄⠘⠈⠰⠠
⢹⣠⡾⡝⣿⡧⠂⠀⠹⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠇⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⢼⠄⠀⠀⠀⠀⠈⠉⢿⣿⣸⣷⡏⠈⠰⢢⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠇⠀⠀⠀⠀
⠀⠘⠇⢳⣬⠅⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⢠⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⠀⠀⠀⣀⠀⠈⠀⢈⣤⠈⢿⠃⠀⠸⡏⠻⡇⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠰⣆⡀⠀⠀⠀⡄⠀⣸⠃⢸⠀⠀⠀⣿⡇⠀⠀⢸⣿⠇⠺⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠀⣔⠀⢰⠀⠀⠀⣿⠃⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⠆⠀⢸⡷⣷⣆⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣹⣄⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⠈⣛⣛⣿⣿⣿⣟⣻⣿⣟⣀⣀⣈⣃⣿⣿⣛⣛⣛⣛⡿⣿⠟⠿⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡆⢠⣾⢋⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⣄⡀⠀⢸⣿⠀⠀⠘⢸⡇⠁⢸⣿⣤⣼⡆⢣⡄⢸⡇⠿⢏⣾⠇⣾⡇⢿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⠈⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⣭⣭⡵⠃⢻⣧⢻⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣤⠴⠟⠀⠀⠛⠷⠤⠴⢟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠭⢠⣤⣤⡈⣿⣦⡭⠵⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⡛⠻⣶⡆⠀⢛⡿⠀⠀⠀⠀⠀⣰⣿⢠⡇⢸⡄⠀⢸⡇⠀⢸⡇⢀⠀⣿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⢣⠀⠰⠆⠀⠀⠀⠀⢀⡠⠁⡏⠅⢸⡇⠀⢸⡇⠀⢸⡇⢸⡤⢟⢺⡇⢸⠟⢀⣿⠘⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡗⠀
⢸⠏⡉⠋⠹⣿⣿⢸⣿⡇⣾⡟⣿⣿⠁⠀⣈⠛⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠴⠇⠀⡇⠂⣿⠀⢀⣼⣇⡀⣸⣧⣤⣥⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢙⣼⣿⣌⠃⠀
⢛⠰⣿⣶⠟⢩⣿⡌⢿⣇⠉⠁⠻⠿⢀⣤⠽⡎⣤⠁⠀⠔⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠁⠀⠐⠀⠛⠀⠀⡇⢰⡟⠀⠰⡄⠀⠀⠀⠐⣆⠒⠀⢹⠇⣶⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣴⠶⡇⠀
⠈⠀⢸⣿⠀⠀⢹⣥⣨⠻⢦⣤⣤⣤⠾⠋⠸⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⢸⡇⠀⠀⠛⢀⡀⠀⠁⡅⠀⠀⣺⠀⠺⡆⠢⡀⠀⠀⠹⢰⣦⢹⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⠃⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠐⠀⠀⠀⠘⠇⠀⠀⠀⠀⢹⣶⣾⣿⠀⢀⡟⠀⠀⡿⣄⢳⠀⠀⠀⢸⡟⠀⠉⢰⡄⠘⠈⠸⠠
⢹⣠⡾⡝⣿⡇⠂⠀⠹⡆⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠇⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⢼⠄⠀⠀⠀⠀⢀⠀⠹⠿⢸⣿⡇⠀⠀⢢⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠇⠀⠀⠀⠀
⠀⠙⠇⢻⣬⡅⠀⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⠡⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⠀⠀⠀⣠⠀⠀⠀⢠⣿⡀⠻⠁⠀⠸⡏⠻⡇⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⡄⠀⢸⠇⢸⠀⠀⠀⣿⡇⠀⠀⢸⣿⠃⠻⠀⠀⠀⠀⠀⠀⠀⠄⠠⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠀⣤⠀⢸⠀⠀⠀⡿⠁⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠷⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⠇⠀⢸⡷⣷⣆⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣸⣆⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⠀⣙⣛⣿⣿⣿⣟⣻⣿⣟⣀⣀⣘⣂⣿⣿⣛⣛⣛⣛⡿⡿⠉⠩⢙⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⡉⢹⡏⣭⣍⢿⡆⢠⣾⢋⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠈⢸⡇⠁⢸⣿⣤⣼⡇⢣⡄⢸⡇⠿⢟⣾⠇⣾⡇⣼⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⠌⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡭⠉⠁⠀⢻⣧⢿⣿⣿⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣤⠴⠟⢀⠂⠛⠷⠤⠴⢟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⢘⡿⠀⠀⠀⠀⠀⣼⣿⢠⡇⢸⡄⠀⢸⡇⠀⢸⡇⢰⣀⣽⢱⡟⠰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⡀⠀⠀⠀⠀⠛⢣⠀⠐⠂⠀⠀⠀⠀⢀⡀⠁⡏⠅⢸⡇⠀⢸⡇⠀⢸⡇⣼⡿⢛⢺⡇⢸⠟⢁⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡗⠀
⢘⠏⡉⠋⠙⣿⣿⢸⣿⡇⣾⡟⣿⣿⠁⠀⣈⠛⠮⡛⠻⠿⣷⣶⣝⠿⠅⣿⡇⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠴⠇⠀⡇⠀⣿⠁⢀⣼⣇⡀⣸⣧⣬⣥⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣌⠃⠀
⢛⠰⣿⣶⠗⢹⣿⡌⢿⣇⠉⠁⠻⠿⢀⣤⠝⡏⣤⠁⠀⠔⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠁⠀⠐⠈⠛⠀⠀⡇⢰⡿⠀⠀⣦⠀⠀⠀⠄⠔⠐⠀⣿⠃⣶⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣴⠶⡇⠀
⠈⠀⢸⣿⠀⠀⢹⣥⣈⠻⢦⣤⣤⣤⠾⠋⠸⡇⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠑⢄⢀⣢⣦⡀⠀⣿⠀⡺⡇⠢⡀⠀⠀⠹⢰⣦⢸⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⠃⠈⣿⡇⡀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠐⠀⠀⠀⠘⠇⠀⠀⡀⠀⠘⠿⣿⣿⠃⣠⡇⠀⠀⡿⣄⢳⠀⠀⠀⢸⡟⠀⠉⢰⡄⠘⠈⠸⠠
⢹⣠⡾⡍⣿⡇⠂⠀⠹⡆⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠇⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠸⢛⠸⣿⡇⠀⠐⢢⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠇⠀⠀⠀⠀
⠀⠘⠇⢛⣬⡅⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⢡⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⣴⠀⠀⠀⢸⣿⡀⠙⠀⠀⠸⡏⠻⡇⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠈⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⡄⠀⠹⠂⢸⠀⠀⠀⣿⡇⠰⠀⢸⣿⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠇⠀⣦⠀⢸⠀⠀⠀⠿⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡷⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢿⡄⡎⠀⠀⠀⠀⠀⠄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⡆⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⠇⠀⢸⡷⣷⣆⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣸⣆⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⠀⣙⣛⣿⣿⣿⣟⣻⣿⣟⣀⣀⣘⣂⣿⣿⣛⣛⣛⣛⡿⡿⠉⠩⢝⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⠀⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⡉⢹⡏⣭⣍⢿⡆⢠⣾⢋⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣄⡀⠀⢸⣿⠀⠀⠈⢸⡇⠁⢸⣿⣤⣼⡇⢣⡄⢸⡇⠿⢏⣾⠇⣾⡇⣼⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⠌⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡭⠉⠁⠀⢻⣧⢿⣿⣿⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣤⠴⠟⢀⠂⠛⠷⠤⠴⢟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⢘⡿⠀⠀⠀⠀⠀⣸⣿⢠⡇⢸⡄⠀⢸⡇⠀⢸⡇⢰⣀⣽⢱⡟⠰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⡀⠀⠀⠀⠀⠛⢣⠀⠐⠆⠀⠀⠀⠀⢀⡀⠁⡏⠅⢸⡇⠀⢸⡇⠀⢸⡇⣼⡿⢛⢺⡇⢸⠟⢀⣿⠘⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡗⠀
⢘⠏⡉⠋⠹⣿⣿⢸⣿⡇⣾⡟⣿⣿⠁⠀⣈⠛⡮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠴⠇⠀⡇⠀⣿⠁⢀⣼⣇⡀⣸⣧⣬⣥⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣿⣶⠟⢹⣿⡌⢿⣇⠉⠁⠻⠿⢀⣤⠝⡏⣤⠁⠀⠔⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠁⠀⠀⠈⠛⠀⠀⡇⢰⡿⠀⠀⣦⠀⠀⠀⠄⠔⠐⠀⣿⠃⣶⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣴⠶⡇⠀
⠈⠀⢸⣿⠀⠀⢹⣥⣨⠻⢦⣤⣤⣤⠾⠋⠸⡇⠿⣷⣤⣤⣬⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⢸⡇⠀⠀⠀⠑⣄⢀⣢⣦⡀⠀⣿⠀⡺⡇⠢⡀⠀⠀⠹⢰⣦⢸⡇⠀⠀⠀⠀⠇⠀
⠀⠀⣾⣿⣧⡀⠃⠈⣿⡇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠐⠀⠀⠀⠘⠇⠀⠀⡀⠀⠘⠿⣿⣿⠃⣠⡇⠀⠀⡿⣄⢳⠀⠀⠀⢸⡟⠀⠉⢰⡄⠘⠈⠸⠠
⢹⣠⡾⡍⣿⡇⠂⠀⠹⡆⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠇⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠸⢛⠸⣿⡇⠀⠐⢠⣿⠸⠀⠀⠀⠈⠛⢦⡀⢾⠇⠀⠀⠀⠀
⠀⠘⠏⢛⣬⡅⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⢡⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⣴⠀⠀⠀⢸⣿⡀⠙⠀⠀⠸⡏⠻⡇⠀⠀⠀⠀⢀⣾⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠈⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⡄⠀⠹⠂⢸⠀⠀⠀⣿⡇⠰⠀⢸⣿⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠇⠀⣦⠀⢸⠀⠀⠀⠿⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠷⣤⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢿⡄⡎⠀⠀⠀⠀⠀⠆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⠇⠀⢸⡷⣷⣆⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣷⣈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⡨⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣀⣀⣐⣀⣿⣿⣛⣛⣛⣛⡿⣿⠀⠷⢟⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡏⣭⡍⣿⡶⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢠⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠀⠈⠉⢸⡇⠁⢸⣿⣤⣼⡇⢷⡀⢸⡇⠿⢋⣾⠇⣾⡇⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⠉⠉⠁⠀⢻⣧⠈⣾⡈⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠻⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣸⡿⢰⡇⢸⡀⠀⢸⡇⠀⢸⡇⢰⣾⣿⢱⡟⠰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣙⠿⢿⣮⣭⣿⡏⣾⡏⢠⠀⠀⠀⠀⠛⠃⡄⠀⠂⠀⠀⠀⠀⢀⡀⠁⡟⠅⣼⡇⠀⢸⡇⠀⢸⡇⢸⠹⢛⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡗⠀
⢘⠏⡉⠋⡙⣿⣿⢸⣿⡗⣾⡟⣿⣿⠁⠀⣬⠙⠮⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⡇⠀⣿⣧⢀⣼⣇⡀⣸⣧⣬⣥⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣿⣶⠗⢩⣿⡆⢿⣇⠈⠁⠻⠿⢀⣤⢝⡏⣤⠁⠀⠄⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠃⠀⠀⠈⠛⠀⠀⡇⢸⡟⠟⠀⠀⠢⣀⣠⢤⣶⡔⠀⣿⠇⣤⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣴⠖⢧⠀
⠈⠀⢹⣿⠀⠀⢹⣥⣨⠻⢦⣤⣤⣤⠾⠋⠘⡇⠿⣷⣤⣤⣤⡾⠟⠀⢠⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⡇⠀⠀⠀⠀⢹⣾⣾⣿⡇⢰⡇⠀⢺⡇⠢⡀⠀⠀⠹⢰⣦⢸⡇⠀⠀⢀⠀⠃⠸
⠀⠀⣾⣿⣧⡀⠃⠈⣿⡇⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠀⠀⠀⠀⠐⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⡉⠻⣿⢣⢻⡇⠀⠈⠿⣄⢱⠀⠀⠀⢈⡟⠀⠉⢰⡄⠐⠀⠰⠠
⢹⣠⡾⡏⣿⡇⠀⠀⠹⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠻⠁⠀⠐⢠⣿⡸⠀⠀⠂⠀⠋⢶⡄⢾⠃⠀⠀⠀⠀
⠈⠘⠏⠛⣬⡅⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⢀⢱⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⢴⡄⡐⠀⢸⣿⢇⠀⠀⠀⠸⠏⠻⡇⠀⠀⠀⠀⣀⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⡄⠀⠫⠃⢸⠀⠀⠀⣺⠁⢸⠀⠘⣿⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠠⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡅⠈⣦⠀⢸⠀⠀⠀⠉⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⠧⠀⢨⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠈⢳⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣹⣔⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠁⡔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣷⣈⣛⣻⣿⣿⣟⣻⣿⣟⣀⣀⣀⣀⣿⣿⣛⣛⣛⣛⡿⣿⠀⠻⢟⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢠⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠀⠈⠉⢸⡇⠁⢸⣿⣤⣼⡇⢳⡀⢸⡇⠟⢉⣾⠇⣾⡇⢿⢿⣿⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⠈⣾⡏⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⠀⠀⠻⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣤⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣴⡿⢰⡇⣸⡇⠀⢸⡇⠀⢸⡇⢰⣾⣿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⣸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⢠⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⡀⠁⡿⠁⣿⡇⠀⢸⡇⠀⢸⡇⢸⡹⢉⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⢸⠏⡉⠋⡹⣿⣿⢸⣿⡗⣾⡟⣿⣿⠁⠀⣤⡙⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⡇⠀⣿⣷⢀⣼⣇⡀⣸⣧⣬⣥⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣿⣶⠇⢹⣿⡌⢿⣇⠉⠁⠻⠿⢀⣤⢽⡏⣤⠁⠀⠄⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠃⠀⠈⠈⢛⠀⠀⡇⢸⡟⠏⠀⠀⠰⡀⣴⢲⣶⣖⠀⣿⠇⣶⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣶⠖⢧⠀
⠈⠀⢹⣿⠀⠀⢽⣥⣨⡻⢦⣤⣤⣤⠾⠋⠘⡇⠿⣷⣤⣤⣤⡾⠟⠀⢠⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡇⠀⠀⠀⠀⢿⣷⣿⣿⡇⢠⡇⠀⢺⡇⢠⡀⠀⠀⠹⠐⣦⢺⡇⠀⠀⢈⠀⠁⠰
⠀⠀⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠀⠀⠀⠀⠸⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠌⠙⢿⠣⢻⡇⠀⠘⠿⣄⢱⠀⠀⠀⢀⣟⠀⠉⢰⡄⠘⠀⠰⠠
⢻⣠⡾⡏⢿⡇⠀⠀⠹⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⠼⠀⠀⠀⠀⠀⡀⠀⠀⣾⡀⠙⠁⠀⠐⢠⣿⡼⠀⠀⠂⠀⠋⢶⡄⢾⠃⠀⠀⠀⠀
⠈⠙⠏⠛⣬⡅⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⢱⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⢰⡄⡘⠀⢸⣿⠇⡀⠀⠀⠸⠏⠻⡧⠀⠀⠀⠀⣀⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⡄⠀⢫⠃⢸⠀⠀⠀⣼⠃⢸⠀⠈⣿⠀⠻⠄⠀⠀⠀⠀⠁⠀⠂⠠⠙⢿⣿⡧⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⡅⠈⣧⠀⢸⠀⠀⠀⠉⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣌⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡎⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠎⢶⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣸⡄⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣀⣛⣻⣿⣿⣟⣻⣿⣇⣀⣀⣀⣀⣿⣿⣛⣛⣛⣛⡿⣿⠀⠸⢛⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢡⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠈⠉⢸⡇⠁⢸⣿⣤⣼⡇⢳⠀⢸⡇⠋⢁⣾⠇⣾⡇⢻⢻⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⠁⣿⡇⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⠀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡬⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣤⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣴⡿⢰⡇⣻⡇⢀⢸⡇⠀⢸⡇⢰⣾⣿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢏⣿⡏⢻⣿⣿⣿⣧⡛⣸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⡀⠁⡿⠁⣿⡇⠀⢸⡇⠀⢸⡇⢸⡜⢀⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡘⡟⣿⢸⣿⢸⡷⠀
⢸⠏⡉⠋⡹⣿⣿⢸⣿⡗⣾⡟⣿⣿⠁⠀⣤⠙⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⡇⢀⣿⣿⢀⣼⣇⡀⣸⣧⣤⣤⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣿⣶⠇⢹⣿⡄⢿⣇⠈⠁⠻⠿⢀⣤⠽⡏⣤⠁⠀⠄⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠃⠀⠀⠈⠛⠀⠀⡇⢸⡟⠇⠀⠀⠰⡔⡶⢰⣶⣶⠀⣿⠇⣴⡆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣶⠖⢣⠀
⠈⠀⢹⣏⠀⠀⢽⣥⣨⡻⢦⣤⣤⣤⠾⠋⠈⡇⠿⣷⣤⣤⣤⡾⠟⠀⠠⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⠀⠀⠀⢿⣿⢿⣿⡿⣠⡇⠀⢺⡇⢢⡀⠀⠀⠹⠐⣶⣹⡇⠀⠀⢨⠀⠁⠸
⠀⠀⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠂⠙⢿⠳⢻⡇⠀⠘⠿⣄⢱⠀⠀⠀⠀⣟⠁⠉⢰⡄⠘⠀⠰⠠
⢹⣠⡾⡟⣿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⠼⠀⠀⠀⠀⠀⡀⠀⠀⣿⡤⠈⠀⠀⠐⢰⣿⡼⠀⠀⠂⠀⠋⢶⡄⢾⠃⠀⠀⠀⠀
⠈⠙⠏⠛⣬⡅⠀⠀⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢱⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⢠⡄⡜⠀⢸⣿⠃⡀⠀⠀⠸⠏⠻⡇⠀⠀⠀⠀⣀⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⡄⠀⢫⠃⢹⠀⠀⠀⣼⠁⢹⠀⠈⢿⠀⠻⠄⠀⠀⠀⠀⠁⠀⠂⠠⠙⢿⣿⡧⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡄⠈⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡎⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢁⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠎⢶⠤⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡇⠀⢸⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠈⢷⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣸⣄⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣈⣛⣻⣿⣿⣟⣻⣿⣇⣀⣀⣀⣀⣿⣿⣛⣛⣛⣛⡿⣿⠀⠸⢛⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⣍⢿⡎⢡⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠈⠉⢸⡇⠁⢸⣿⣤⣼⡇⢳⠀⢸⡇⠋⢁⣾⠇⣾⡇⢻⢿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⠁⣿⡇⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⠀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡬⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣤⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣼⡿⢰⡇⣻⡇⢀⢸⡇⠀⢸⡇⢰⣾⣿⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⣸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⡀⠁⡿⠁⣿⡇⠀⢸⡇⠀⢸⡇⢸⡜⢀⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⢸⠏⡉⠋⡙⣿⣿⢸⣿⡗⣾⡟⣿⣿⠁⠀⣤⠙⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⡇⢀⣿⣿⢀⣼⣇⡀⣸⣧⣤⣤⡿⣘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣿⣶⠇⢹⣿⡄⢿⣇⠈⠁⠻⠿⢀⣤⠽⡏⣤⠁⠀⠄⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠃⠀⠀⠈⠓⠀⠀⡇⢸⡟⠇⠀⠀⠰⡔⡲⢰⣶⣶⠀⣿⠇⣶⠆⠀⠀⠀⠰⣶⠇⠀⠀⠀⠠⠂⣶⠖⢣⠀
⠈⠀⢹⣏⠀⠀⢽⣥⣨⡻⢦⣤⣤⣤⠾⠋⠈⡇⠿⣷⣤⣤⣤⡾⠟⠀⠠⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⠀⠀⠀⢿⣿⢿⣿⡿⣠⡇⠀⢺⡇⢠⡀⠀⠀⠹⠐⣶⣹⡇⠀⠀⢨⠀⠁⠸
⠀⠀⣾⣿⣧⡀⠃⠈⣿⡇⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠂⠙⢿⠳⢻⡇⠀⠘⠿⣄⢱⠀⠀⠀⠀⣟⠁⠉⢰⡄⠘⠀⠰⠠
⢹⣠⡾⣏⣿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢠⠀⠼⠀⠀⠀⠀⠀⡀⠀⠀⣿⡤⠈⠀⠀⠐⢰⣿⡼⠀⠀⠀⠀⠋⢶⡄⢾⠃⠀⠀⠀⠀
⠈⠘⠏⠛⣬⡅⠀⠀⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢱⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⢠⡄⡜⠀⢸⣿⠇⡀⠀⠀⢸⠏⠻⡇⠀⠀⠀⠀⣀⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⡄⠀⢫⠃⢹⠀⠀⠀⣸⠁⢹⠀⠈⣿⠀⠻⠄⠀⠀⠀⠀⠁⠀⠂⠠⠙⢿⣿⡧⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡄⠈⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣌⠿⠁⠀⠁⠀⠀⠀⠀
⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢁⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠇⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠈⢷⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢺⣿⣿⣿⣿⡇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣀⣛⣛⣿⣿⣟⣻⣿⣇⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⡄⠰⢛⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣾⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⣭⠍⢿⡎⢡⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡆⢿⠀⢸⡇⠀⢀⣾⠇⣾⡇⠸⣽⡿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⢰⣿⡟⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠻⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠥⢠⣤⣤⡈⣿⣦⡬⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣴⡿⢰⡆⣿⡇⠀⢸⡇⠀⢸⡇⢰⢳⠛⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⠛⢸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⢀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠁⣿⣧⠀⢸⡇⠀⢸⡇⠘⠟⢀⢺⡇⢹⠟⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡗⠀
⢘⠏⡉⠋⡹⣿⣿⢸⣿⡗⣾⡟⣿⣿⠁⠀⣤⡙⡮⡛⠻⠿⣷⣶⣝⢿⠅⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⡿⢠⣿⣿⢀⣼⣇⡀⣸⣧⣤⣤⡿⢘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠟⢹⣿⡌⢿⣇⠉⠁⠹⠿⢀⣤⠼⡇⣤⠁⠀⢆⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠃⠀⠀⠈⠃⠀⠀⡇⣼⠏⠇⠀⠀⢰⣄⣦⣶⣶⣶⠀⢸⡇⣶⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣶⠖⢣⡀
⠈⠀⢹⣏⠀⠀⢽⣥⣈⡻⢦⣤⣤⣤⠾⠋⠈⡇⠿⣷⣤⣤⣤⡾⠟⠀⠀⠄⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠈⠛⣿⣻⣿⣿⠀⣾⠀⢺⡇⢢⡀⠀⠀⢸⠀⣶⣽⡇⠀⠀⢸⠀⠈⠘
⠀⠠⣾⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠂⠿⠀⠘⢳⣄⢱⠀⠀⠈⠀⣿⠃⠉⢰⡄⠸⠀⠐⠀
⢻⣠⡿⡏⢿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠀⠀⠀⠀⠀⢥⠀⠀⣿⡾⠀⠀⠀⠐⣸⣿⡼⠀⠀⠀⠀⠋⠶⡄⢾⠃⠀⠀⠀⠀
⠈⠙⠏⠙⣬⡅⠀⠀⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⢀⡄⡘⠀⠀⣿⠁⡀⠀⠀⢸⠋⠻⡇⠀⠀⠀⠀⣀⣾⣧⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⠀⠀⢫⠃⢸⠀⠀⠀⠸⠁⢸⠀⠀⢿⠀⠛⠀⠀⠀⠀⠀⠃⠀⠀⢐⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣯⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣌⢿⠁⠀⠀⠀⠀⠀⠀
⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣇⠀⢸⡷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢸⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣂⣙⣛⣿⣿⣟⣿⣿⣇⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⡆⠰⢛⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⡭⠍⢿⡆⢠⣾⢫⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡆⢾⠀⢸⡇⠀⢀⣾⠇⣾⡇⠘⣾⣟⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⢸⣿⡟⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠻⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠥⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣼⡿⢰⡆⣿⡇⠀⢸⡇⠀⢸⡇⢰⣸⠛⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⠛⢸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⢀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠁⣿⣷⠀⢸⡇⠀⢸⡇⠘⡛⢀⢺⡇⢸⠟⢀⣿⠀⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡗⠀
⢸⠏⡉⠋⡙⣿⣿⢸⣿⡗⣾⣿⣿⣿⠁⠀⣤⡙⡮⡛⠻⠿⣷⣶⣝⢿⠅⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⡿⢰⣿⣿⢀⣼⣇⡀⣸⣧⣤⣤⡿⢘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣌⠃⠀
⢛⠴⣷⣶⠟⢹⣿⡌⢿⣇⠉⠁⠹⠿⢀⣤⠼⡏⣤⠁⠀⢆⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠃⠀⠀⡇⣾⠏⠇⠀⠀⢰⣄⣶⣶⣶⣶⠀⢸⡇⣶⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣶⠖⢡⡀
⠈⠀⢙⣏⠀⠀⢽⣥⣈⡻⢦⣤⣤⣤⠾⠋⠀⡇⠿⣷⣤⣤⣤⡾⠟⠀⠀⠄⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠈⠻⠼⣱⣿⣿⠀⢾⣇⢺⡇⢠⡀⠀⠀⢸⠀⣶⣼⡇⠀⠀⢸⠀⠘⠘
⠀⠠⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⡘⠸⠃⠸⠳⣄⢱⠀⠀⠘⠀⣿⠃⠉⢰⡄⠸⠀⠀⠀
⢻⣠⡿⡏⣿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⣠⠀⠽⠀⠀⠀⠀⠀⠥⠀⠀⣿⡾⠁⠀⠀⠐⣰⣿⡼⠀⠀⠀⠀⠙⠷⡄⢾⠃⠀⠀⠀⠀
⠘⠘⠏⠙⣬⡅⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⢀⡄⠘⠀⠀⣿⠁⣀⠀⠀⢸⠋⠻⡇⠀⠀⠀⠀⣀⣾⣿⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⡀⠀⢫⠃⢸⠀⠀⠀⠸⠁⢸⠀⠀⢻⠀⠙⠀⠀⠀⠀⠀⠇⠀⠀⢐⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣌⠿⠁⠀⠀⠀⠀⠀⠀
⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡷⣷⣆⠀⠑⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⡐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢸⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣂⣛⣛⣿⣿⣟⣿⣿⣇⣀⣀⣀⣘⣿⣿⣟⣛⣛⣛⡿⣿⡆⠸⢛⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⡭⠉⢿⡆⢠⣾⢋⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠀⠉⢸⡇⠁⢸⣿⣤⣼⡆⢾⠀⢸⡇⠀⢀⣾⠇⣾⡇⠈⣿⣟⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⢸⣿⡏⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠥⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⣼⡿⢰⡆⣿⡇⠀⢸⡇⠀⢸⡇⢰⣸⠉⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⠛⢸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠄⢀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠁⣿⣷⠀⢸⡇⠀⢸⡇⠀⡹⢀⢺⡇⢸⠟⢁⣿⠀⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢸⠏⡉⠋⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⠁⠀⣴⡘⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⡿⢰⣿⣿⢀⣼⣇⡀⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠛⢹⣿⡌⢿⣇⠉⠁⠹⠻⢀⣤⠼⡇⣤⠁⠀⢦⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⡇⣾⠏⠇⠀⠀⢰⣤⣴⡶⣶⣶⠀⠈⡇⢴⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣶⠖⢡⡄
⠈⠀⢙⣏⠀⠀⢹⣥⣈⡻⢦⣤⣤⣤⠾⠋⠀⡇⠿⣷⣤⣤⣬⡾⠟⠀⠀⠄⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠈⠻⠘⣑⣿⣿⠀⢸⣇⢺⡇⢠⡀⠀⠀⢸⠀⣶⣼⡇⠀⠀⢸⠀⠘⠘
⠀⠠⣾⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡐⠸⠇⠘⢳⣄⢱⠀⠀⠘⠀⣿⠃⠉⢰⡄⠸⠀⠀⠀
⢻⣠⡿⡏⣿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⣠⠀⠽⠀⠀⠀⠀⠀⠓⠀⠀⣿⡾⠁⠀⠀⠐⣸⣿⡼⠀⠀⠀⠀⠙⠷⣄⢾⠃⠀⠀⠀⠀
⠈⠘⠏⠙⣬⡅⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⡄⠘⠀⠀⣿⠁⣀⠀⠀⢸⠋⠻⡇⠀⠀⠀⠀⣀⣾⣿⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⡀⠀⢫⠃⢸⠀⠀⠀⠸⠁⢰⠀⠀⢻⠀⠙⠀⠀⠀⠀⠀⡏⠀⠀⢐⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣮⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣬⢿⠁⠀⠀⠀⠀⠀⠀
⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡷⣷⣆⠀⠐⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠋⡐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢺⣿⣿⣿⣿⡇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣂⣛⡛⣿⣿⣟⣻⣿⣇⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⡆⠸⢛⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣭⣍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠀⠉⢸⡇⠁⢸⣿⣤⣼⡆⢾⠀⢸⡇⠀⢀⣾⠇⣾⡇⠈⣿⣟⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⡉⠉⠁⠀⢻⣧⢸⣿⡟⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠥⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠽⠀⠀⠀⠀⠀⣸⡿⢰⡆⣿⡇⠀⢸⡇⠀⢸⡇⢰⣸⠉⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⠛⢸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠄⠀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠁⣿⣷⠀⢸⡇⠀⢸⡇⠈⡻⢀⢺⡇⢸⠟⢀⣿⠀⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡷⠀
⢸⠏⡉⠋⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⠁⠀⣴⡘⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⡿⢰⣿⣿⢀⣼⣇⡀⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠛⢹⣿⡌⢿⣇⠉⠁⠹⠻⢀⣤⠼⡇⣤⠁⠀⢦⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⡇⣾⠏⠇⠀⠀⢰⣄⣴⡶⣶⣶⠀⠈⡇⢴⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣶⠖⢡⡄
⠈⠀⢙⣏⠀⠀⢹⣥⣈⡻⢦⣤⣤⣤⠾⠋⠀⡇⠿⣷⣤⣤⣬⡾⠟⠀⠀⠄⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠈⠻⠘⣑⣿⣿⠀⢸⣇⢺⡇⢠⡀⠀⠀⢸⠀⣶⣼⡇⠀⠀⢸⠀⠘⠘
⠀⠠⣾⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡐⠸⠇⠘⢳⣄⢱⠀⠀⠘⠀⣿⠏⠉⢰⡄⠸⠀⠀⠀
⢹⣠⡿⡏⣿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠀⠀⠀⠀⠀⠓⠀⠀⣿⡾⠁⠀⠀⠐⣸⣿⡼⠀⠀⠀⠀⠙⠷⣄⢾⠃⠀⠀⠀⠀
⠈⠘⠏⠙⣬⡅⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⡄⠘⠀⠀⣿⠉⣀⠀⠀⢸⠋⠻⡇⠀⠀⠀⠀⣀⣾⣿⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡀⠀⢫⠃⢸⠀⠀⠀⠸⠁⢰⠀⠀⢻⠀⠙⠀⠀⠀⠀⠀⡏⠀⠀⢐⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣮⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣬⢿⠁⠀⠀⠀⠀⠀⠀
⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠗⠲⣶⠎⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡇⠀⢸⡷⣷⣆⠀⠐⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⡔⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢸⣿⣿⣿⣿⡇⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣂⣛⡛⣿⣿⣿⣿⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⣿⠀⠈⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠍⠉⢿⡆⢠⣾⠋⣭⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡆⣶⠀⢸⡇⠀⢀⣾⠇⣾⡇⢠⣿⣧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⡟⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠽⠀⠀⠀⠀⠀⣸⡷⢰⡆⣿⡆⠀⢸⡇⠀⢸⡇⠰⣾⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⠛⢸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠄⢀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠁⣿⣇⠀⢸⡇⠀⢸⡇⢀⡿⢂⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⢸⠏⡉⠋⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⠃⠀⣴⡜⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡿⢰⣿⡿⢀⣼⣇⡁⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠛⢹⣿⡌⢿⣇⠁⠉⠸⠻⢀⣤⠌⡇⣥⠁⠀⠰⣤⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⠀⣴⡀⢐⠖⣶⣶⠀⠀⣷⢰⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣶⠖⢡⣄
⠈⠀⣙⣏⠀⠀⢹⣥⣈⡻⢦⣤⣤⣤⠾⠋⠀⡇⠿⣷⣤⣤⣥⡾⠟⠀⠀⠆⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠈⠑⠈⠘⣿⣿⠀⠀⢿⣺⡇⢠⡀⠀⠀⢸⠀⣶⣽⡇⠀⠀⢸⠀⠘⠈
⠀⠠⣿⣿⣧⡀⠃⠈⣿⡇⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠠⠀⠀⢀⡄⠀⠀⡸⣏⡐⡀⠸⠹⢳⣄⢱⠀⠀⠘⠀⣽⠋⠉⢰⡄⠘⠀⠀⠀
⢹⣠⡿⡏⣿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⣠⠀⠽⠄⠀⠀⠀⠀⡓⠀⠀⣿⠘⠁⠀⠀⠐⣸⣿⡾⠀⠀⠀⠀⠙⠷⣄⢾⠃⠀⠀⠀⠀
⠈⠘⠏⠙⣬⡅⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣾⠀⠀⠀⠀⡄⠘⠀⠀⣿⠂⡀⠀⠀⢸⠋⠻⡇⠀⠀⠀⢀⣀⣾⣿⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡀⢀⢡⠃⢸⠀⠀⠀⠀⠃⠰⠀⠀⢿⠀⠹⠀⠀⠀⠀⠀⡟⠀⠁⢐⠈⢿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣬⢿⠃⠀⠀⠀⠀⠀⠀
⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹⠀⠀⢀⠀⠀⠀⠀⠀
⠻⠖⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡇⠀⢸⡷⣷⣆⠀⠑⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⡔⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢸⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣀⣛⡛⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⠀⠘⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠍⠉⢿⡆⢠⣾⠋⣭⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡇⣶⠀⢸⡇⠀⢀⣾⠇⣾⡇⢰⣿⣧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⡟⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢾⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⡸⡷⢰⡆⣿⡀⠀⢸⡇⠀⢸⡇⠰⣾⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠄⢀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠁⣿⡇⠀⢸⡇⠀⢸⡇⢀⡾⢂⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⢘⠏⡉⠋⣙⣿⣿⢸⣿⡇⣾⣿⣿⣿⠃⠀⢴⡜⡮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡿⢰⣿⡿⢀⣼⣇⡀⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠛⢩⣿⡌⢿⣇⠁⠁⠸⠻⢀⣤⠌⡇⣥⠁⠀⠰⣦⢹⣿⠀⠂⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⠀⣦⡀⢐⠖⣶⣶⠀⠀⣲⢰⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣴⡖⢁⡄
⠈⠀⣙⣟⠀⠀⢹⣥⣈⡻⢦⣤⣤⣤⠾⠋⠀⡅⠿⣷⣤⣤⣥⡾⠟⠀⠀⠆⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠈⠃⠈⠘⣿⣿⠀⠀⢿⣺⡇⢠⡀⠀⠀⢸⠀⣶⣼⡇⠀⠀⢸⠄⠘⠀
⠀⠠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠠⠀⠀⠀⡀⠀⠀⠸⣏⡰⡀⠸⠹⢳⣄⢱⠀⠀⠘⠀⣾⠋⠉⢰⡄⠸⠀⠀⠀
⢹⣠⡿⡏⢿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⣠⠀⠽⠄⠀⠀⠀⠀⡓⠀⠀⣿⠘⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠀⠙⠶⣄⢾⠃⠀⠀⠀⠀
⠘⠙⠏⠙⣬⡅⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣾⠀⠀⠀⠀⡄⠘⠀⠀⣿⠀⡀⠀⠀⢸⠋⠻⡇⠀⠀⠀⢀⣀⣾⣿⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡀⢀⣡⠃⢸⠀⠀⠀⠀⠇⠰⠀⠀⢿⠀⠹⠀⠀⠀⠀⠀⡟⠀⠁⢀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣬⢿⠃⠀⠀⠀⠀⠀⠀
⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡷⣷⣆⠀⠑⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⡞⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢸⣿⣿⣿⣿⠃⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣇⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣀⣛⡛⣿⣿⣿⣿⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⠀⠨⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠍⠉⢿⡆⢠⣾⠋⣭⡉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡆⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⣧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⡟⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢴⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢐⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⡸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⠰⣾⠀⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⢀⠀⠀⠛⠃⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡇⠀⢸⡇⠀⢸⡇⢀⡽⢂⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡷⠀
⢘⠏⡉⠋⣙⣿⣿⢸⣿⡇⣾⣿⢿⣿⠃⠀⢠⡜⣮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡿⢰⣿⡿⢀⣼⣇⡀⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠛⢩⣿⡌⢿⣇⠁⠉⠸⠻⢀⣤⠌⡇⣥⠃⠀⠰⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⠀⣦⠀⢰⠖⣶⣶⠀⠁⣳⢰⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠠⠂⣶⡖⢁⡄
⠈⠀⣹⣟⠀⠀⢹⣥⣈⡻⢦⣤⣤⣤⠾⠋⠀⡅⠿⣷⣤⣤⣭⡾⠟⠀⠀⠂⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠉⠇⠀⢈⣿⣿⠀⠀⢿⣲⡇⢠⡀⠀⠀⢸⠀⣶⣼⡆⠀⠀⢸⠅⠈⠀
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⢀⠀⠀⢀⠀⠀⠀⠸⡇⡠⡀⠘⠹⢳⣄⢳⠀⠀⠘⠀⣼⠋⠉⢰⡄⠸⠂⠀⠄
⢠⣠⡿⡍⢿⡇⠀⠀⠹⡇⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⣠⠀⠽⠄⠀⠀⠀⠀⡒⠀⠀⣿⠘⠅⠀⠀⠀⣸⣿⡾⠀⠀⠀⠀⠙⠗⡄⢾⠃⠀⠀⠀⠀
⠘⠚⠏⠙⣬⡅⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢱⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣿⡀⣶⠀⠀⠀⠀⡄⠘⠀⠀⣿⠀⡀⠀⠀⢸⠋⢻⡇⠀⠀⠀⣀⣠⣾⣧⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⡀⢀⢡⠃⢸⠀⠀⠀⠀⠇⠰⠀⠀⣿⠀⠹⠀⠀⠀⠀⠀⡟⠀⠀⢀⡈⢿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣬⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹⠀⠀⢀⠀⠀⠀⠀⠀
⠙⠆⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡧⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⡞⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⣇⢸⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣀⣛⡛⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⠀⠠⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⠋⣭⠍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡆⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⣇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⡟⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠻⠷⠤⠴⠟⣼⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⢸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⠰⣾⠀⢱⡟⢰⣶⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⡇⣿⣧⣛⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⢀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡇⠀⢸⡇⠀⢸⡇⢀⡼⢂⢺⡇⢰⠟⢀⣿⠈⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠏⣙⣿⣿⢸⣿⡇⣾⣿⣿⣿⠃⠀⢠⡜⣮⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢰⣿⡿⢀⣼⣇⡀⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠴⣷⣶⠛⢩⣿⡌⢿⣇⠁⠉⠸⠻⢀⣤⠌⡏⣥⠃⠀⠰⣆⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⠀⣤⠀⢐⢖⣶⣶⠀⠁⣷⢰⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠰⠂⣶⡖⢁⡄
⠈⠀⣙⣟⠀⠀⢹⣤⣈⡻⢦⣤⣤⣤⠾⠋⠀⡅⠿⣷⣤⣤⣭⡾⠟⠀⠀⠂⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠉⠇⠈⢈⣿⣿⠀⠀⢿⣺⡇⢠⡀⠀⠀⢸⠀⣶⣼⡇⠀⠀⢸⠂⠈⠀
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⢀⠀⠀⢀⠀⠀⠀⠸⡇⡠⡀⠘⠹⢳⣄⢱⠀⠀⠘⠀⣽⠋⠉⢰⡄⠘⠆⠀⠄
⢠⣠⡿⣇⢿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠄⠀⠀⠀⠀⡐⠀⠀⣾⠘⠅⠀⠀⠀⣸⣿⡾⠀⠀⠀⠀⠙⠗⡄⢾⠃⠀⠀⠀⠀
⠀⠘⡏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢱⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣿⡀⣴⠀⠀⠀⠀⡄⠘⠀⠀⣿⢀⡀⠀⠀⢸⠋⢻⡇⠀⠀⠀⣀⣠⣾⣇⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⡀⢀⢡⠃⢸⠀⠀⠀⠀⠇⠰⠀⠀⣿⠀⠹⠀⠀⠀⠀⠀⡟⠀⠀⢀⡈⢿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣦⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢻⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠆⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠠⠀
⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡆⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣀⣛⣛⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣟⣛⣛⣻⡿⣿⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⢋⣭⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡇⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⢧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠈⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⠿⠀⠀⠀⠀⠀⠸⡗⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⠠⣺⠈⢱⡟⢰⣦⠹⣷⢹⠏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⡇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡄⠀⢸⡇⠀⢸⡇⢀⡼⢂⢺⡇⢰⠟⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠟⢙⣿⣿⢸⣿⡗⣿⣿⢿⣿⡏⠀⢠⣌⣪⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢰⣿⡇⢀⣼⣇⡘⣸⣧⣬⣥⡿⠘⠷⣌⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣷⣷⠚⢩⣿⡌⢿⣇⠉⠉⠸⡻⢁⣤⠔⠙⣥⠃⠀⠀⣦⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⠀⣄⠀⢠⢲⣶⣶⠀⢀⡇⢰⡆⠀⠀⠀⠰⣶⠇⠀⡀⠀⠰⠂⣶⡖⢁⡄
⠈⠀⣝⣟⠀⠈⢹⣤⣈⡻⢦⣤⣤⣤⠾⠋⠀⡀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠂⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠙⠀⠀⢈⣿⡿⠀⠘⣷⢰⡇⢠⡀⠀⠀⢸⠀⣶⣽⡇⠀⠀⢸⠃⠈⠀
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡠⡀⠃⠸⢳⣄⢱⠀⠀⠀⢁⣿⠃⠉⢰⡄⠸⠂⠀⠄
⢠⣰⡿⣏⢿⡇⠀⠀⠹⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣠⠀⢽⠄⠀⠀⠀⠀⡒⠀⠀⣀⠸⠁⠀⠀⠐⣸⣿⡾⠀⠀⠀⠀⠋⢶⡄⢾⠃⠀⠀⠀⠀
⠀⠘⠏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢱⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⣀⣠⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠆⢰⠀⠀⣿⠀⠹⠀⠀⠀⠀⠀⡟⠀⠀⢀⡈⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠻⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡆⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣀⣛⣛⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣼⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠍⠉⢿⡆⢠⣾⢋⣭⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡇⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢼⣿⢧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⢿⠀⠀⠀⠀⠀⠸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⠠⣺⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡄⠀⢸⡇⠀⢸⡇⢀⡼⢀⢺⡇⢸⠟⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠟⣙⣿⣿⢸⣿⡗⣿⣿⢿⣿⡋⠀⢠⣄⡪⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡿⢰⣿⡇⢀⣼⣇⡘⣸⣧⣬⣥⡿⠘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣶⣷⠚⢭⣿⡌⢿⣇⠉⠉⠸⡻⢁⣤⠴⠙⣥⠃⠀⠀⣶⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⢀⣄⠀⢠⢲⣶⣶⠀⢸⡇⢰⡆⠀⠀⠀⠐⣶⠇⠀⡀⠀⠰⠂⣶⡖⢁⡄
⠈⠀⣽⣿⠀⠈⢻⣤⣈⡻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠂⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⠀⠀⠙⠀⠀⢘⣿⡿⠀⢸⡇⣲⡇⢠⡀⠀⠀⠸⠀⣶⣹⡇⠀⠀⢸⠂⠈⠀
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡠⡈⠁⠸⢳⣄⢱⠀⠀⠀⢣⣿⠂⠉⢰⡄⠸⠂⠀⠄
⢡⣴⡿⣏⢿⡇⠀⠀⠹⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠤⠀⠀⠀⠀⠒⠀⠀⣀⠸⠁⠀⠀⠐⣸⣿⡾⠀⠀⠀⠀⠋⢦⡄⢾⠃⠀⠀⠀⠀
⠀⠘⠏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⣀⣠⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠆⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡗⠄⠀⢀⡈⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠻⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡆⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣀⣛⣛⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⣿⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣼⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠍⠉⢿⡆⢠⣾⢋⣭⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡇⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢼⣿⠧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⡿⠀⠀⠀⠀⠀⠸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⠠⣺⠀⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⢀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡄⠀⢸⡇⠀⢸⡇⢀⠹⢀⢺⡇⢱⠟⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠏⣙⣿⣿⢸⣿⡇⣿⣿⢿⣿⡏⠀⠠⣤⡪⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡿⢰⣿⡇⢀⣼⣇⡘⣸⣧⣬⣥⡿⢘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣶⣷⠚⣭⣿⡌⢿⣇⠉⠉⠸⡻⢁⣤⠴⠙⣥⠃⠀⠀⣶⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⠠⣄⠀⢠⢲⣶⣶⠀⣸⡇⢰⡆⠀⠀⠀⠐⣶⠇⠀⡀⠀⠰⠂⣶⡖⢁⡄
⠈⠀⣽⣿⠀⠈⢻⣤⣈⡻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠂⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠙⠀⠀⢘⣿⠏⠀⢹⡇⢲⡗⢠⡀⠀⠀⠸⠰⣶⣹⡇⠀⠀⢸⠂⠈⠀
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡠⡈⠁⠸⢷⣄⢱⠀⠀⠀⢣⣿⠈⠉⢰⡄⠘⠂⠀⠅
⢠⣰⡾⡏⢿⡇⠀⠀⠹⡆⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠤⠀⠀⠀⠀⠒⠀⠀⣠⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠀⠋⢦⡀⢾⠃⠀⠀⠀⠀
⠀⠘⠏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⣀⣠⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡗⠈⠀⢀⡈⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠻⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣸⡆⣿⣿⣿⣿⣿⠃⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⣿⣀⣛⣛⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⣿⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⢋⣭⡉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣍⡀⠀⢸⣿⠀⠁⠉⢸⡇⠁⢸⣿⣤⣼⡇⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢼⣿⠧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢄⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⡿⠀⠀⠀⠀⠀⢸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⠠⣺⠈⢱⡟⢰⣦⠹⣷⢹⠏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⢀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡄⠀⢸⡇⠀⢸⡇⢀⠽⢀⢺⡇⢹⠟⢁⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠟⢙⣿⣿⢸⣿⡇⣾⣿⢿⣿⡏⠀⠀⣤⡪⡛⠻⠿⣷⣶⣝⢿⠁⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡿⢰⣿⡇⢀⣼⣇⡐⣸⣧⣬⣥⡿⢘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢋⠰⣶⣷⠚⣹⣿⡌⢿⣇⠉⠉⠸⡻⢁⣤⠴⠙⣥⠃⠀⠀⣶⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⢀⣄⠀⢠⢲⣶⣶⠀⣸⡇⢰⡆⠀⠀⠀⠐⣶⠇⠀⡀⠀⠰⠂⣶⡖⢁⡄
⠈⠀⣽⣿⠀⠈⢻⣤⣈⡻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠂⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠙⠀⠀⢘⣿⠏⠀⢹⡇⢲⡗⢠⡀⠀⠀⠸⠰⣶⣹⡇⠀⠀⢸⡆⠈⠀
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡠⡈⠀⠹⢳⣄⢱⠀⠀⠀⢣⣿⠈⠉⢰⡄⠘⠂⠀⠍
⢠⣴⡾⡏⢿⡇⠀⠀⠹⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠤⠂⠀⠀⠀⠒⠀⠀⣠⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠀⠋⢦⡀⢾⠃⠀⠀⠀⠀
⠨⠘⠏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⣀⣠⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠹⠀⠀⠀⠀⠀⡗⠈⠀⢀⡈⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠻⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣹⡔⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢨⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣿⣈⣛⣻⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⡷⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⢋⣭⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠉⠉⢸⡇⠁⢸⣿⣤⣼⡆⣤⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣛⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⡿⠀⠀⠀⠀⠀⠸⡷⢸⡆⣿⠀⠀⢸⡇⠀⢸⡇⢠⡋⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⢠⠀⠀⠀⠀⠛⠃⡀⠀⠆⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢠⠸⢀⢺⡇⢰⠿⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠏⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⡛⠀⠀⣤⡪⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢰⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣌⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣶⣷⠚⣽⣿⡌⢿⣇⠉⠁⠸⡻⢁⣤⠴⠙⣥⠃⠀⠀⢶⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⢀⣄⠀⢠⢲⣶⠀⢠⣿⠇⢰⡆⠀⠀⠀⠀⢶⠇⠀⡀⠀⠠⠂⣶⡖⢁⡄
⠈⠀⣽⣿⠀⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⠀⠀⠙⠀⠀⢘⠋⠀⢸⡿⠀⢲⡗⢠⡀⠀⠀⠘⢲⣆⢹⡇⠀⠀⢸⠀⠈⠈
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⡠⡁⠀⠹⢳⣄⢱⠀⠀⠀⢾⡟⠈⠉⢰⡄⠘⠃⠀⠅
⢠⣴⡾⡏⢿⡇⠀⠀⠹⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⢽⠄⠄⠀⠀⠀⠀⠀⠀⣠⠸⡀⠀⠀⠀⣸⣿⡾⠀⠀⠀⠘⠑⣢⡀⢿⠃⠀⠀⠀⠀
⠐⠘⠏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⢀⣴⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢡⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡗⡀⠀⢐⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣾⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠻⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠆⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣹⡀⣿⣿⣿⣿⣿⠃⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣷⣈⣛⣻⣿⣿⣟⣿⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⡗⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⢋⣍⡍⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠁⢸⣿⣤⣼⡆⣤⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣮⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣱⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⡿⠀⠀⠀⠀⠀⠸⡷⢰⡆⣿⠀⠀⢸⡇⢀⢸⡇⢠⡋⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣥⣿⡏⣾⡏⢠⠀⠀⠀⠀⠛⠃⡄⠀⠆⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢠⠱⢀⢺⡇⢰⠿⢀⣿⠀⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠏⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⡛⠀⠀⣤⡪⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢠⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⣘⠷⣄⣨⡼⠋⣠⣿⣰⣦⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠰⣾⣷⠞⣽⣿⡄⢿⣇⠈⠁⠹⡻⢁⣤⠴⠙⣥⠃⠀⠀⢶⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⢐⣄⠀⢠⢲⣶⠀⢠⡏⠇⢰⡆⠀⠀⠀⠀⠲⠇⠀⡀⠀⠰⠂⣶⡖⢁⡄
⠈⠀⣜⣿⠀⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⡀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠹⠀⠀⠘⠋⢀⢸⡇⠀⢲⡗⢠⡀⠀⠀⠘⢲⡆⢹⡇⠀⠀⢸⠀⠈⠈
⠀⠠⣿⣿⣧⡀⠃⠈⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⡠⡁⠀⠸⢳⣄⢱⠀⠀⠀⣾⡇⠀⠉⢰⡄⠘⠂⠀⠅
⢠⣴⡾⡍⢿⡇⠀⠀⠻⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠄⠄⠀⠀⠀⠀⠀⠀⣤⠸⡀⠀⠀⠀⣸⣿⡾⠀⠀⠀⠘⠱⣢⠀⢿⠃⠀⠀⠀⠀
⠀⠘⡏⠙⣼⡅⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⢀⣼⣿⡇⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡗⡀⠀⢐⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣾⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠸⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⡧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣻⡀⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣗⣘⣛⣻⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⡇⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠁⢸⣿⣤⣼⡇⣤⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣎⠙⣿⡄⢸⣿⠀⠀⠈⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣭⠴⠟⢀⠀⠛⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⡿⠀⠀⠀⠀⠀⢸⡷⢰⡆⣿⠀⠀⢸⡇⢀⢸⡇⢠⡃⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠠⠀⡀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢠⠱⢀⢺⡇⢱⠿⢀⣿⠈⣸⣇⣀⣿⡘⡟⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠟⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⡟⠀⠀⣤⡪⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢰⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣌⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢋⠰⣶⣷⠞⣭⣿⡌⢿⣇⠈⠁⠹⡻⢁⣤⠴⠙⣥⠃⠀⠀⢴⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⢐⣄⠀⢰⢲⡶⠀⣰⡏⠇⢰⡆⠀⠀⠀⠀⠲⠇⠀⡀⠀⠰⠂⣶⠖⢁⠄
⠈⠀⣜⣿⠀⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⡀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠻⠀⠀⠘⠃⢀⢼⡇⢀⢲⡗⢠⡀⠀⠀⠘⢶⡄⢹⡇⠀⠀⢸⠀⠘⠈
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡨⡀⠀⠸⢳⣄⢱⠀⠀⠈⣾⡇⠀⠉⢰⡄⠸⠂⠀⠌
⠠⣴⡾⡍⢿⡇⠀⠀⠻⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⢽⠄⠀⠀⠀⠀⠀⠀⠀⣶⠹⠀⠀⠀⠀⣸⣿⡾⠀⠀⠀⠘⠱⣢⠀⢿⠃⠀⠀⠀⠀
⠀⠘⠏⠙⣼⡅⠀⠀⠚⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣴⣿⡄⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡗⡀⠀⢒⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡆⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣾⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠹⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣻⡀⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⣗⣘⣛⣻⣿⣿⣟⣻⣿⣃⣀⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⡇⠀⠹⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠋⢹⡏⠍⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠁⢸⣿⣤⣼⡇⣤⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣎⠙⣿⡄⢸⣿⠀⠀⠈⢸⣇⠀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⢀⠀⠻⠷⠤⠴⠟⣾⠡⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⢀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠀⡿⠀⠀⠀⠀⠀⢸⡷⢸⡆⣿⠀⠀⢸⡇⢀⢸⡇⢠⡃⠈⢱⡟⢰⣦⠹⣷⢹⠏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠠⠀⡀⠀⠀⠛⠃⡀⠀⠆⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢠⠱⢀⢺⡇⢲⠿⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠟⣙⣿⣿⢸⣿⡗⣾⣿⣿⣿⡛⠀⠀⣤⡪⡛⠻⠿⣷⣶⣝⠿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢰⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣌⠃⠀
⢋⠰⣶⣷⠞⣭⣿⡄⢿⣇⠈⠁⠹⡻⢁⣤⠴⠙⣥⠃⠀⠀⢴⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠇⠇⠀⢐⣄⠀⢰⢲⡶⠀⣰⡏⠇⢰⡆⠀⠀⠀⠀⠲⠇⠀⡀⠀⠰⠂⣶⠖⢁⠄
⠈⠀⣜⣿⠀⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⣀⠿⣷⣤⣤⣤⡾⠟⡀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠹⠀⠀⠘⠃⢀⢼⡇⠀⢰⡗⢠⡀⠀⠀⠘⢶⡄⢻⡇⠀⠀⢸⠀⠘⠈
⠀⢠⣿⣿⣧⡀⠃⠈⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡨⡀⠀⠸⢳⣄⢱⠀⠀⠈⣾⡇⠈⠉⢰⡄⠸⠂⠀⠌
⢠⣴⡾⡍⢿⡇⠀⠀⠻⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⠽⠄⠀⠀⠀⠀⠀⠀⠀⣶⠸⠀⠀⠀⠀⣸⣿⡾⠀⠀⠀⠘⠱⣢⠀⢿⠃⠀⠀⠀⠀
⠀⠘⠏⠙⣼⡅⠀⠀⠚⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢻⡇⠀⠀⠀⢀⣴⣿⡀⠘⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⠄⢀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡗⡐⠀⢒⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡆⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠹⠀⠀⢀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠰⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣷⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣇⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⡇⠀⠸⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠍⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⣴⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠈⢸⣇⡀⢸⣿⠀⠘⠃⣙⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⢟⣾⠣⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠈⣿⠀⠀⠀⠀⠀⢸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⢠⡋⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⡀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⢀⠀⠀⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢠⠁⢀⢺⡇⢰⠿⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⢈⠏⡉⡟⣙⣿⣿⢸⣿⡗⣾⡿⣿⣿⡛⠀⠀⣤⡪⡛⠻⠿⣷⣶⣝⠿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢰⣿⡇⢀⣼⣇⡀⣸⣧⣬⣤⡿⣘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣸⣿⣜⠃⠀
⢛⢰⣾⣷⡞⣬⣿⡌⢿⣇⠘⠁⠹⡿⢉⣤⠴⠙⣥⠃⠀⠀⢤⢹⣿⠀⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⢐⣄⠀⢰⢲⡶⠀⣰⡏⡆⢰⡆⠀⠀⠀⠀⠰⠇⠀⡀⠀⠠⠂⣶⠖⢡⠀
⠈⠀⣘⣿⠀⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠻⠀⠀⠘⠃⠀⣿⡇⢀⢰⡷⢠⡀⠀⠀⠘⣶⡀⢹⡇⠀⠀⢸⠀⠘⠘
⠀⠠⣿⣿⣧⡀⠂⢩⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡨⡀⠀⠹⢳⣄⢱⠀⠀⠘⣾⡃⠈⠉⢰⡄⠸⠀⠈⠄
⢡⣴⡾⡙⣿⣧⠄⠀⠻⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⢽⠄⠀⠀⠀⠀⠀⠀⠀⣦⠹⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠙⠱⣦⠀⢿⠃⠀⠀⠀⠀
⠀⠙⡏⠙⣼⡅⠀⠀⠚⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠠⣿⠀⣀⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠄⠀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡇⡐⠀⢒⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⣾⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣷⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⠸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣇⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⡗⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠇⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⡉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⣤⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠈⢸⣇⡀⢸⣿⠀⠘⠃⣘⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⢟⣾⠧⠼⠿⠤⠤⠶⠟⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢖⣴⠞⠛⠉⠛⠻⣶⡆⠀⠘⣿⠀⠀⠀⠀⠀⢸⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⢠⡋⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⡀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⠀⡀⠀⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢠⠑⢀⢺⡇⢰⠿⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⣈⠏⡉⠟⢉⢿⣿⢸⣿⡗⣾⡟⣿⣿⡛⠀⠀⣤⡨⡛⠻⠿⣷⣶⣝⢿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢠⣿⡇⢀⣼⣇⡀⣸⣧⣬⣤⣿⣘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠠⣾⣷⡞⣬⣿⡎⢿⣇⠉⠁⠹⠿⢉⣤⠤⠘⣥⠃⠀⠀⠤⢹⣿⠐⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡇⣾⠏⠇⠀⢐⣄⠀⢰⢲⡶⠀⣰⡏⡇⢰⡆⠀⠀⠀⠀⠰⠇⠀⡀⠀⠠⠂⣶⠖⢡⠀
⠈⠀⢘⣿⠃⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠹⠀⠀⠘⠃⠀⣿⡇⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⠀⠀⣿⣿⣧⡀⠃⢩⣿⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡨⡀⠀⠹⢳⣄⢱⠀⠀⠘⣾⠃⠀⠉⢰⡄⠸⠀⠈⠄
⢸⣴⡶⡙⣿⣷⠀⠀⠻⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠙⠋⠀⠀⠀⠀⠀⠀⣠⠀⣽⠄⠌⠀⠀⠀⠀⠀⠀⣦⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠙⠑⣦⠀⢿⠃⠀⠀⠀⠀
⠀⠘⡇⠓⣼⡅⠀⠀⠞⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣼⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠄⠀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡇⡐⠂⢒⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⡇⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣮⢻⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⣿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣷⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠨⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣇⣀⣀⣀⣘⣿⣿⣛⣛⣛⣻⡿⡗⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⣿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡇⣦⠀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠀⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠻⠷⠤⠴⢟⣾⠧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠘⣿⠀⠀⠀⠀⠀⢰⡷⢰⡆⣿⠀⠀⢸⡇⠀⢸⡇⢠⡋⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⡛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⡀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⠀⡀⠁⣿⠁⣿⡀⠀⢸⡇⠀⢸⡇⢀⠐⢀⢺⡇⢱⠿⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡈⠛⢉⢿⣿⢸⣿⡗⣾⡿⣿⣿⡛⠀⠀⣤⡨⡛⠻⠿⣷⣶⣝⢿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⢠⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⣘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠠⣾⣷⡞⣬⣿⡌⢿⣇⠉⠁⠹⡿⢉⣤⠄⠘⣥⠃⠀⠀⠀⢹⣿⠐⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡇⣼⠇⠇⠀⢐⣄⠀⢰⢲⡶⠀⣰⡏⡆⢰⡆⠀⠀⠀⠀⠐⠇⠀⡀⠀⠠⠂⣴⠖⢡⠀
⠈⠀⢈⣿⠃⠈⢻⣤⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠹⠀⠀⠘⠋⠀⣻⡇⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢹⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣿⣿⣧⡀⠀⢹⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡩⡀⠀⠸⢳⣄⢱⠀⠀⠘⣾⠃⠀⠉⢰⡄⠸⠀⠈⠄
⢸⣴⡶⡙⣿⣷⠀⠀⠻⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠙⠃⠀⠀⠀⠀⠀⠀⣠⠀⣽⠄⠌⠀⠀⠀⠀⠀⠀⣦⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠙⠱⣦⠀⢿⠃⠀⠀⠀⠀
⠀⠘⡇⠓⣼⡅⠀⠀⠚⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣀⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠄⠀⢫⠇⢸⠀⠀⠀⠀⠄⢰⠀⠀⣿⠀⠙⠀⠀⠀⠀⠀⡇⡀⠀⢒⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡆⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣮⢻⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣷⢸⣿⣿⣿⣿⣿⣿⠀⠠⡄⠀⣿⣿⣿⣿⣿⣿⣿⡄⠸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣀⣀⣑⣃⣿⣿⣛⣛⣛⣻⡿⡷⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠇⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⢃⡀⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠄⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠄⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠻⠷⠤⠴⢟⣾⡧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⠛⠻⣶⡆⠀⠸⣿⠀⠀⠀⠀⠀⢰⣿⢀⡇⢸⡄⠀⢸⡇⠀⢸⡇⠠⡋⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⠀⡀⠀⣾⠁⣾⡇⠀⢸⡇⠀⢸⡇⢀⠰⢀⢺⡇⢱⠿⢀⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⢈⠏⡈⠛⢉⢿⣿⢸⣿⡗⣿⡿⣿⣿⣻⠁⠀⣠⡨⡛⠻⠿⣷⣶⣝⢿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⣘⠷⣌⣨⡼⠋⣠⣿⣰⣶⣸⣷⡁⢛⣼⣿⣜⠃⠀
⢛⠠⣾⣷⡞⣼⣿⡌⢿⣇⠉⠁⠹⠿⢉⣤⠄⡜⣥⠃⠀⠀⠀⢹⣿⠘⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⠠⠀⠃⠀⠀⡆⢸⡏⠇⠀⢐⣄⠀⢰⢲⣶⡀⢀⡏⡇⢰⡆⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠂⣴⠖⢡⠀
⠈⠀⢨⣿⠃⠈⢻⣄⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡄⠀⠀⠀⠙⠀⠀⠘⡟⠀⢸⡇⢀⢰⡷⢠⡀⠀⠀⠐⣷⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣿⣿⣧⡀⠀⢙⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⡁⠀⠸⢳⣄⢱⠀⠀⠐⣿⠃⠀⠉⢰⡄⠸⠀⠈⠄
⢸⣤⡶⡙⣿⣷⠀⠀⠳⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠙⠋⠀⠀⠀⠀⠀⠀⢀⠀⣼⠄⠌⠀⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠑⣦⠀⢿⠃⠀⠀⠀⠀
⠀⠘⠅⠣⣼⡁⠀⠀⠞⠉⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢱⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⣄⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣼⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡄⠀⢫⠃⢸⠀⠀⠀⠀⠄⢰⠀⠀⢿⠀⠉⠀⠀⠀⠀⠀⡇⡀⠂⢲⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡆⠈⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣦⢻⠃⠀⠀⠀⠀⠀⠀
⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⡆⠈⣿⣿⣿⣿⣿⣿⣿⠃⢨⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⣷⢸⣿⣿⣿⣿⣿⣿⡔⠂⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣿⣿⣟⣃⣀⣉⣃⣿⣿⣟⣛⣛⣛⡿⡿⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣭⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⢢⡄⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣘⠅⢸⡟⠉⠉⠁⠀⢻⣧⢰⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠻⠷⠤⠴⢟⣾⡧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡥⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⢛⠻⣶⡆⠀⠸⣿⠀⠀⠀⠀⠀⢐⣿⢂⡇⢸⡆⠀⢸⡇⠀⢸⡇⠠⡊⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⠸⠇⣿⣧⣛⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⡀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⠀⡀⠀⣾⠁⣼⡇⠀⢸⡇⠀⢸⡇⢀⠸⢀⢺⡇⢰⠿⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡈⠛⢉⢿⣿⢸⣿⡇⣿⡟⣿⣿⣻⠁⠀⣠⡨⡛⠻⠿⣷⣶⣝⢿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢹⠀⣿⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣌⣨⡼⠋⣠⣿⣰⣶⣸⣷⡉⢛⣼⣿⣜⠃⠀
⢛⠀⣾⣷⡞⣨⣿⡎⢿⣇⠉⠁⠹⡻⢉⣤⠄⡜⣥⠃⠀⠀⠀⢹⣿⠘⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠂⠀⢀⠀⠓⠀⠀⠀⢸⡏⠇⠀⢐⣄⠀⢰⢲⣶⡂⢀⡟⡆⢰⡆⠀⠀⠀⠀⠘⠇⠀⡀⠀⠠⠂⢴⠖⢡⠀
⠈⠀⢨⣿⠃⠈⢻⣄⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⡇⠀⠀⠀⠹⠀⠀⠘⡟⠁⢸⣷⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣾⣿⣧⡀⠀⢹⣿⡇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⡃⠀⠹⢳⣄⢱⠀⠀⠰⣿⠃⠀⠉⢰⡄⠸⠀⠐⠄
⢸⣤⡶⡙⣿⣷⠀⠀⠳⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠻⠋⠀⠀⠀⠀⠀⠀⢀⠀⣼⠄⠈⠀⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠑⣦⠀⢾⠃⠀⠀⠀⠀
⠀⠘⡄⠓⣬⡁⠀⠀⠞⠉⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡄⠀⢋⠃⢹⠀⠀⠀⠀⠄⢰⠀⠀⢿⠀⠉⠀⠀⠀⠀⠀⠇⠀⠀⢢⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡄⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⣦⢻⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⢶⠈⣿⣿⣿⣿⣿⣿⣿⠃⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⣷⢸⣿⣿⣿⣿⣿⣿⡇⢺⣼⡇⣿⣿⣿⣿⣿⣿⣿⡇⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣃⣀⣉⣛⣿⣿⣛⣛⣛⣻⡿⡿⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⢮⡄⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠄⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣈⢇⢸⡟⠉⠉⠁⠀⢻⣧⢰⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠻⠷⠤⠴⢟⣾⡧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡇⣀⣠⢔⣴⠞⠛⠉⢛⠻⣶⡆⠀⢸⢿⠀⠀⠀⠀⠀⠀⣿⠆⡇⢸⡇⠀⢸⡇⠀⢸⡇⠠⡊⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⠸⠇⣿⣧⣛⠿⢿⣮⣥⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⠀⣀⠀⣼⠁⢸⡇⠀⢸⡇⠀⢸⡇⢀⠸⢀⢺⡇⢱⠿⢀⣿⠈⣸⣇⣀⣿⡜⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡉⠛⢉⢿⣿⢸⣿⡇⣿⡟⣿⣿⡻⠁⠀⣠⡨⡛⠻⠿⣷⣶⣝⢿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⡠⠄⠀⢹⠀⣼⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡉⢛⣼⣿⣜⠃⠀
⢛⠀⣾⣷⡞⣼⣿⡎⢿⣇⠉⠁⠹⠿⢉⣤⠄⡜⣥⠃⠀⠀⠀⢹⣿⠘⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠈⢰⡟⠇⠀⢐⣄⠀⢰⢶⣶⡂⠀⣿⡇⢰⡆⠀⠀⠀⠀⠘⠃⠀⡀⠀⠠⠂⣴⠖⢡⠀
⠈⠀⢨⣿⠃⠈⢻⣄⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣼⡇⠀⠀⠀⠹⠀⠀⠘⣿⠁⢸⣿⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣾⣿⣧⡀⠀⢹⣿⠇⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠆⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⡃⠀⠹⢳⣄⢱⠀⠀⠰⣿⠃⠀⠉⢰⡄⠸⠀⠘⠄
⢸⣤⡶⡙⣿⣷⠀⠈⢿⡅⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠹⠋⠀⠀⠀⠀⠀⠀⢀⠄⣸⠄⠈⠀⠀⠀⠀⠀⠀⣤⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠑⣦⠀⢾⠃⠀⠀⠀⠀
⠀⠘⡅⠧⣬⡁⠀⠀⠞⠉⠠⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢳⡇⠀⠀⠀⢀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡄⠀⢊⠇⢹⠀⠀⠀⠀⠄⢰⠀⠀⢿⠀⠉⠂⠀⠀⠀⠀⠃⠀⠀⢢⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡄⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡽⣦⢻⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠲⡆⣿⣿⣿⣿⣿⣿⣿⠃⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣷⢸⣿⣿⣿⣿⣿⣿⡇⠀⣷⣿⣸⣿⣿⣿⣿⣿⣿⡇⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣿⣀⣛⣛⣿⣿⣟⣛⣛⣻⡿⡿⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⠉⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⢸⡄⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠄⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡀⢸⣿⠀⠘⠃⣀⢇⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⢟⣾⡧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡆⢀⣠⢔⣴⠞⠛⠉⢛⠻⣶⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠇⣧⢸⡇⠀⢸⡇⠀⢸⡇⠠⡊⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢃⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⠃⡀⠀⡆⠀⠀⠀⠀⠀⣀⠈⢼⠩⢸⡇⠀⢸⡇⠀⢸⡇⢀⠸⢀⢺⡇⢱⠿⢃⣿⠈⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡷⠀
⢈⠏⡈⠛⢉⢿⣿⢸⣿⡇⣿⡿⣿⣿⣻⠁⠀⣠⡨⡛⠻⠿⣷⣶⣝⢿⡁⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⡀⣤⠀⢸⠀⣼⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡉⢛⣼⣿⣜⠃⠀
⢛⠀⣾⣷⡞⢸⣿⡄⢿⣇⠉⠁⠹⠿⢉⣤⠄⡜⣥⠃⠀⠀⠀⢹⣿⠘⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⢈⢠⣿⠇⠀⢐⣄⠀⢰⢶⣶⡆⠀⣿⡆⢰⡆⠀⠀⠀⠀⠘⠃⠀⡀⠀⠠⠂⣴⠖⢡⠀
⠈⠀⢨⣿⠃⠈⢻⣄⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⠀⠀⠹⠀⠀⢘⣿⠁⢸⣿⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣾⣿⣧⡀⠀⢹⣿⠇⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠆⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⡋⠀⠹⢳⣄⢱⠀⠀⠰⣿⠃⠀⠉⢰⡄⠸⠀⠘⠄
⢸⣤⡶⡙⣿⣷⠀⠈⢾⡄⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡆⠙⠟⠀⠀⠀⠀⠀⠀⢀⡄⣼⠄⠈⠀⠀⠀⠂⠀⠀⣤⢸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠑⣦⠀⢾⠃⠀⠀⠀⠀
⠀⠘⡄⠳⣨⡁⠀⠀⠞⠉⠠⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢳⡇⠀⠀⠀⠀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⡄⠀⢊⠇⢹⠀⠀⠀⠀⠄⢰⠀⠀⢿⠀⠉⠂⠀⠀⠀⠀⠃⠀⠀⢢⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡄⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡵⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢿⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀
⠙⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⡟⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⠇⢨⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢄⣷⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⡇⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣛⣀⣀⣛⣿⣿⣛⣛⣛⣻⡿⡿⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣽⡍⣿⠿⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⢏⠏⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⠙⡄⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡄⢸⣿⠀⠘⠃⣀⠣⢸⡟⠉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⣿⢿⡿⠿⣿⠿⠿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⢟⣾⡧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⠈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⢟⣵⢟⣫⣭⣟⢿⣶⢹⡿⣰⡾⣻⣭⣟⢿⡆⣀⣠⢔⣴⠞⠛⠉⢛⠻⣶⡆⠀⢸⠿⠀⠀⠀⠀⠀⠀⣾⡗⣼⢘⡇⠀⢸⡇⠀⢸⡇⠠⡊⠈⢱⡟⢰⣶⠹⣷⢹⠏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⢇⣿⡏⢻⣿⣿⣿⣧⣛⠸⠇⣿⣧⣛⠿⢿⣮⣭⣿⡏⣾⡏⠀⠀⠀⠀⠀⠛⢃⠀⠀⡆⠀⡀⠀⠀⠀⣀⡉⢸⠩⢸⡿⠀⢸⡇⠀⢸⡇⠀⠸⢀⢺⡇⢰⠿⢂⣿⠈⣸⣇⣀⣿⡜⡟⣿⢸⣿⢸⡷⠀
⣈⠏⣈⠛⢉⢿⣿⢸⣿⡇⣿⡿⣿⣿⣻⠁⠀⣠⡨⡛⠻⠿⣷⣶⣝⢿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢼⡅⠘⠰⢸⡇⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣄⣨⡼⠋⣠⣿⣰⣶⣸⣷⡉⢛⣼⣿⣌⠃⠀
⢛⠀⣶⣷⡞⢼⣿⡄⢿⣇⠉⠁⠹⠿⢉⣤⠄⡜⣥⠃⠀⠀⠀⢹⣿⠘⠃⢿⣧⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠄⠘⢻⡇⠀⠀⣾⠇⠀⢐⣄⠀⢰⢲⣶⡆⠀⣿⡆⢰⡆⠀⠀⠀⠀⠘⠃⠀⡀⠀⠠⠂⣴⠖⢡⡀
⠈⠀⢨⣿⠃⠈⢻⣄⣨⠻⢦⣤⣤⣤⠾⠋⠀⢀⠿⣷⣤⣤⣤⡾⠟⠀⠀⠀⠛⢷⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⢰⣿⠀⠀⠀⠹⠀⠀⢘⣿⠅⠰⣿⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣾⣿⣧⡀⠀⠽⣿⠇⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠾⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⡛⠀⠹⢳⣄⢱⠀⠀⠰⣿⠃⠀⠉⢰⡄⠸⠀⠐⠀
⢹⣤⡶⡙⣿⣷⠀⠈⣿⡄⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠹⠏⠀⠀⠀⠀⠀⠀⢀⡀⡰⠄⡈⠀⠀⠀⠂⠀⠀⣠⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠱⣢⠀⢾⠃⠀⠀⠀⠀
⠀⠘⠀⢳⣈⠁⠀⠀⠚⠉⠠⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⣜⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢳⡇⠀⠀⠀⠀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠀⠀⢈⠃⢹⠀⠀⠀⠀⠀⢰⠀⠀⢿⠀⠉⠂⠀⠀⠀⠀⠃⠀⠀⢢⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡄⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣮⢿⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢻⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢨⡇⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⢱⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠶⡾⣿⣿⣿⣿⣿⣿⠇⢨⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢄⣷⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢐⣷⣿⣿⣿⣿⣿⣿⡇⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⠿⡇⣘⣛⣻⣿⣿⣟⣻⣿⣟⣻⣀⣀⣘⣿⣿⣛⣛⣛⣛⡿⡿⠀⠼⢿⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡏⣭⡍⣿⠷⢹⣿⢹⣿⣿⢹⡏⣿⢹⣿⠉⠉⠹⠏⡏⢹⡏⠭⠉⢿⡆⢠⣾⢋⣍⠉⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣮⣅⡀⠀⢸⣿⠈⠈⠉⢸⡇⠋⢸⣿⣤⣼⡆⢸⡇⢸⡇⠀⢀⣾⠇⣾⡇⢸⣿⠎⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⡎⠙⣿⡄⢸⣿⠀⠀⠀⢸⣇⡄⢸⣿⠀⠘⠃⣈⠰⢸⡟⡉⠉⠁⠀⢻⣧⢸⣿⠀⢸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠿⠮⣥⠴⠟⠀⠀⠛⠷⠤⠴⢟⣾⠧⠼⠿⠤⠤⠶⠿⠠⠼⠧⠤⢠⣤⣤⡈⣿⣦⡭⠴⢟⣵⢟⣻⣿⣛⢿⣿⣿⢟⣿⢿⣿⢿⣿⣿⣿⣭⣭⠛
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣴⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⣸⡿⣸⠀⣧⠀⢸⡇⠀⢸⡇⢠⠊⠈⢱⡟⢰⣦⠹⣷⢹⡏⣾⢹⣆⢋⢸⢣⢸⣿⢀⢹⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⡀⠀⠀⠀⢀⣉⢱⢩⢤⣿⠀⢸⡇⠀⢸⡇⠀⠸⢀⢺⡇⢰⠿⢀⣿⠈⣸⣇⣀⣿⡘⡗⣿⢸⣿⢸⡷⠀
⢈⠏⣉⠛⢉⢿⣿⣿⠷⢸⣿⡿⣿⣿⡻⠃⠀⣀⡹⡿⠋⠉⠹⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢬⡇⠘⢰⢸⡏⢀⣼⣇⡐⣸⣧⣬⣤⡿⢘⠷⣄⣠⡼⠋⣠⣿⣰⣶⣸⣷⡉⢛⣼⣿⣜⠃⠀
⢛⠀⣶⣷⡞⣼⣿⡇⠀⣾⠉⠁⠹⠿⠩⠀⠀⡜⡇⠃⠀⠀⠀⡎⠁⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢻⡟⠀⠀⣼⠇⠀⢐⣄⠀⢰⢲⣶⡆⠀⣿⡆⢰⡆⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠂⣴⠖⢡⠀
⠈⠀⢨⣿⠃⠈⢻⣄⣰⡈⠀⠀⠀⠀⠀⠀⠀⢐⠧⢀⠀⠀⠀⠡⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⡇⠰⢀⣿⠀⠀⠀⠹⠀⠀⢘⣿⠇⠐⣿⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⠀⠀⣾⣿⣧⡀⠀⠿⣿⠇⠀⠨⡕⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠼⠃⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡛⠀⠹⢳⣄⢱⠀⠀⠰⣿⠃⠀⠉⢰⡄⠸⠀⠐⠀
⢹⣤⡶⡙⣿⣷⠀⠀⣿⡄⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠹⠏⠀⠀⠀⠀⠀⠀⠀⡀⡴⠄⡈⠀⠀⠀⠂⠀⠀⣠⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠑⣢⠀⢾⠃⠀⠀⠀⠀
⠀⠘⠀⠧⣈⠁⠀⠀⠚⠉⠠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢻⡇⠀⠀⠀⠀⣸⣿⡀⠚⠀⠀⠀⠀⠀
⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢱⣆⡀⠀⠀⠀⠀⠀⠘⠃⢹⠀⠀⠀⠀⠀⢰⠀⠀⢿⠀⠉⠂⠀⠀⠀⠀⠃⠀⠀⠢⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⡄⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⣬⢻⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀
⠙⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⣧⠀⢸⡧⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⢱⣄⠀⠠⠀
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⢶⣿⣿⣿⣿⣿⣿⠇⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣷⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠒⣺⣿⣿⣿⣿⣿⣿⡇⠸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠘⢹⡿⢿⣿⡿⠛⠉⠀⠀⢹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠈⠉⣿⣿⠏⠀⠀⠀⠀⠀⢺⢇⡈⢠⠀⠀⠀⠀⠀⠈⣾⣿⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠸⠸⡁⣿⡇⠀⠀⠀⠀⣈⣷⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⣄⠁⢻⡇⠀⠀⠀⠀⠘⡿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⡿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣶⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⢸⡿⣸⠈⣿⠀⠀⠀⠀⠇⠿⡧⡋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⡀⠀⠀⠀⢀⣨⢱⢩⡄⣿⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⣳⠿⡏⠀⡹⣿⣿⣿⣿⠻⡟⣿⣿⣿⣿⡿⠀
⢈⠋⣈⠛⢉⢿⣿⣿⠷⢸⣿⡟⣿⣿⡛⠃⠀⣀⡹⡿⠋⠉⠹⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢤⣿⠈⠰⢀⡿⠀⡄⠀⠰⢏⣿⣽⣤⠀⣿⠀⢫⢸⡷⠀⠃⠛⣿⣿⠗⠠⡇⢿⣿⣿⣿⡇⠀
⢙⠀⣶⣷⡞⢸⣿⡇⠀⢾⠉⠁⠹⠿⠩⠀⠀⡜⡇⠃⠀⠀⠀⡎⠁⠹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⢸⡇⠀⢙⣄⠀⢘⢻⣿⡏⠁⣿⡇⢸⡆⠀⠀⠀⠀⠘⠋⠀⡀⠀⠠⠃⢽⠟⢡⠀
⠈⠀⢨⣿⠃⠈⢻⢄⣰⡈⠀⠀⠀⠀⠀⠀⠀⢐⠣⠀⠀⠀⠀⠣⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⡿⠀⠀⣿⠀⠀⠀⠹⠀⠀⠘⣿⠇⠐⣿⠀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢀⠀⣾⣿⣧⡀⠀⠹⣿⠇⠀⠨⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆⠀⠀⠀⠀⠀⠸⠇⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡛⠀⠸⢳⣄⢱⠀⠀⠰⣿⠃⠀⠉⢰⡄⠸⠀⠐⠀
⠹⣤⡶⡙⣿⣿⠀⠀⣿⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⠹⠋⠀⠀⠀⠀⠀⠀⠀⡀⡼⠄⡀⠀⠀⠀⠂⠀⠀⣠⠸⠁⠀⠀⠀⣸⣿⡾⠀⠀⠀⠛⠱⣢⠀⢾⠃⠀⠀⠀⠀
⠀⠘⠀⠇⣈⠁⠀⠀⠛⠉⠢⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢻⡇⠀⠀⠀⠀⣸⣿⡀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⠀⠀⠘⠃⢹⠀⠀⠀⠀⠀⢰⠀⠀⢿⠀⠉⠃⠀⠀⠀⠀⠃⠀⠀⠠⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣬⢻⠃⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀
⠙⠆⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⡀⠀⢧⠀⢨⡷⣷⣆⠀⠑⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢱⣄⠀⠠⠀
⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢶⣿⣿⣿⣿⣿⣿⠇⢠⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⢖⣿⣿⣿⣿⣿⣿⡇⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐⢛⡿⢿⣿⡿⠛⠉⠀⠀⢹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠈⢉⣿⣿⠇⠀⠀⠀⠀⠀⢜⣇⡄⢀⡀⠀⠀⠀⠀⠀⣾⣿⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠠⠉⡇⣾⡇⠀⠀⠀⠀⣈⣷⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠋⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣄⠈⢹⣇⠀⠀⠀⠀⠸⠿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⡟
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣼⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⢸⣿⢸⡀⣿⠀⠀⠀⠀⠆⠿⣧⠏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠄
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⡀⠀⠀⠀⢀⣈⠩⠩⡅⣿⠀⠀⠀⠀⠀⠀⠄⢸⠀⣿⣿⣳⠿⡏⠀⡙⣿⣿⣿⣿⠻⡟⣿⣿⣿⣿⡿⠀
⢈⠏⡉⠛⢉⢿⣿⣿⠷⢸⣿⡿⣿⣿⡻⠃⠀⣀⡸⡿⠋⠉⠹⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢤⣿⡀⠰⡇⣿⠀⡄⠀⠰⢏⣿⣽⣤⠀⣿⠁⢯⢸⡷⠀⠃⠛⣿⣿⠗⠠⡏⢻⣿⣿⣿⡇⠀
⢉⠀⣶⣷⡞⢸⣿⡇⠀⢾⠉⠁⠹⡿⠉⠀⠀⡜⡇⠃⠀⠀⠀⡎⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⢳⡇⠀⢙⣄⠀⢘⢿⣿⡏⠁⣿⡇⢸⡆⠀⠀⠀⠀⠈⠋⠀⡀⠀⠈⠃⢽⠟⢣⠀
⠈⠀⢨⣿⠃⠈⢻⣄⣰⡈⠀⠀⠀⠀⠀⠀⠀⢐⠣⠀⠀⠀⠀⠣⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢿⠁⠀⣾⡇⠀⠀⠹⠀⠀⢘⣻⠇⠐⣿⢀⢰⡷⢠⡀⠀⠀⠐⣶⡀⢸⡇⠀⠀⢸⠀⠘⠘
⢠⠀⣾⣿⣧⡄⠈⢹⣿⠅⠀⠨⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠰⠟⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⡛⠀⠸⢳⣄⢱⠀⠀⠰⣿⡃⠀⠉⢰⡄⠸⠀⠐⠀
⢸⣠⡶⡻⡿⣿⠀⠈⣿⡄⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⡀⠀⠀⠀⠀⠀⠀⣠⢸⠁⠀⠀⠀⢸⣿⡾⠀⠀⠀⠛⠱⣢⠀⢾⠃⠀⠀⠀⠀
⠀⠘⠀⢧⣈⠁⠀⠀⠛⠉⠢⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⣄⠀⠀⢸⠋⢻⡇⠀⠀⠀⠀⣰⣿⡀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢰⣆⡀⠀⠀⠀⠀⠀⠘⠁⢹⠀⠀⠀⠀⠀⢰⠀⠀⢿⠀⠉⠃⠀⠀⠀⠀⠃⠀⠀⠠⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⣬⢿⠁⠀⠀⠀⠀⠀⠀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀
⠙⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠹⣿⣿⣶⠀⠀⢇⠀⢨⡗⣷⣆⠀⠱⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠠⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠄⡤⢤⡴⣶⣤⣴⣶⢴⣄⠀⠄⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠘⠀⠀⠈⠁⠀⠲⠦⠙⢿⣾⣿⣷⡤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣡⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⣬⣿⣿⣿⣿⣿⣿⣯⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣏⣹⣿⣿
⢸⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⢹⣿⣿⣿⣿⡿
⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣿⣿⣿⣿⠀⠘⠿⠿⣿⣿⣿⡏⠉⠹⣿⣿⣿⣿⠁⠀⢨⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⡏⠉⢻⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡆⠀⠀⢠⣶⣿⣿⠀⠀⠀⠹⣿⣿⣿⡆⠀⠻⢿
⢸⣿⣿⡟⠉⠹⣿⣿⣿⣿⡄⢿⣿⡇⠀⠀⢻⣿⣿⣿⡄⠀⢿⣿⣿⠛⣿⣿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⡿⠀⣾⣿⣿⣿⣿⣧⣄⠀⢸⣿⣿⣿⣿⣧⠀⠀⠈⠉⢻⣿⠀⠀⠀
⢸⣿⣿⠁⠀⣴⣿⣿⣿⣿⣿⡆⠁⠀⠀⣰⣿⣿⣿⣿⠇⠀⠈⠛⠁⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠙⠛⠛⢹⣧⣯⣠⣴⠿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡄⠀⣠⣦⣾⣿⡄⠀⠀
⠸⠿⠏⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⣀⣀⣿⣿⣿⣿⣏⠀⠀⢀⣤⣄⠀⣿⣿⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣀⣀⡀⠘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⡄⠀
⢠⣤⡄⠀⠀⠻⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⢿⠟⠻⣿⣇⠀
⢸⣿⣇⠀⠀⠀⣿⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠈⣿⣼
⢸⣿⢗⣤⣶⣾⣿⡿⢻⡎⠡⣤⣿⡿⠋⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡏⢻⡮⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⠀⠀⠈⠉⠛⠟⠁⣿⣿⠀⣰⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⣸⣿⣿⣿⡇⢸⣧⠀⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠁⠀⠀⠀⣽⣿⣿⣿⣷⣿⣿⣿⣿⣆⠀⠀⣤⡀⠀⢰⣿⣿⣷⣿⡇⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⡱⠛⠻⣿⣇⢸⣿⣷⣤⡀⠀⠀⣿⢿⣿⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⣀⣴⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⡄⠀⢿⡇⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠸⠿⠸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⣿⣿⣿⡛⠿⠿⢿⣟⣻⣿⣿⡇⠘⢿⣿⠏⢻⣷⡀⠈⣿⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿
⢰⡄⠀⠀⠀⠀⢻⣿⣿⣿⡟⠉⠻⠏⠀⠀⠀⠙⠁⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠹⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⠁⠀⠸⠋⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢹⣿⣿
⢿⣿⣦⡀⣠⣄⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠰⠀⠀⠀⠀⢻⣿⣿⡋⠉⠉⠹⡛⠛⢿⣿⣿⣀⠀⠀⠀⣹⣿
⢸⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡇⠀⠀⣸⣿⣧⣤⡀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⡄⢠⡖⠁⠀⠀⠈⠙⢿⣿⣶⣾⣿⣿
⠈⣿⢿⣿⣿⣿⡇⣸⣿⣿⡟⠋⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠘⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⢿⣿⣿⣿⣿⣶⣤⣀⠀⢻⣿⣿⣿⠁⠈⠀⠀⢰⣾⣷⡄⠀⢿⣿⣿⣿⣿
⢸⣿⣴⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢋⡀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⢿⣿⣿⡟
⠸⠿⠿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣷⣄⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣄⠀⢸⣿⣿⣿⣧⣤⣿⣿⣿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⢠⣤⣤⣶⣦⣤⣴⣦⣤⡄⠀⠄⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠃⠀⠀⠙⠀⠐⠶⢌⠙⢿⣾⣷⣦⢄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣠⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢳⣶⣼⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣿⣻⣿⣿
⢸⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⢹⣿⣿⣿⣿⣿
⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⣿⠀⠘⠿⢿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⠁⠀⢹⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⡏⠉⢻⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⣧⡀⠀⠀⠀⠀⠀⢹⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⢰⣶⣿⣟⠀⠀⠀⠻⣿⣿⣿⡆⠀⠿⣿
⢸⣿⣿⡟⠉⠹⣿⣿⣿⣿⡄⢿⣿⡇⠀⠀⣻⣿⣿⣿⡄⠀⢻⣿⣿⠟⣿⣿⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⣿⣿⣿⣿⣧⣄⠀⢸⣿⣿⣿⣿⣧⠀⠀⠈⠉⢻⣿⠀⠀⠈
⢸⣿⣿⠁⠀⣴⣿⣿⣿⣿⣿⡆⠉⠀⠀⢰⣿⣿⣿⣿⠇⠀⠀⠟⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠛⠛⠛⠛⢻⣧⣏⣠⡴⠿⣇⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡀⠀⢰⣦⣾⣿⡄⠀⠀
⠸⠿⠏⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⣀⣀⣿⣿⣿⣿⣏⠀⠀⢀⣤⣄⠀⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣀⡀⠸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡄⠀
⢠⣤⡄⠀⠀⠻⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣀⣄⣺⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⢿⡿⠿⣿⣧⠀
⢸⣿⣇⠀⠀⠀⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠘⣿⣼
⢸⣿⢗⣤⣶⣾⣿⡿⢻⡏⠁⣤⣿⡿⠛⢿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡏⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠻⡿⠁⣿⣿⠁⣰⡀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⣸⣿⣿⣿⡇⢸⣧⠀⠋⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣤⡀⠀⢰⣿⣿⣶⣿⡇⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⡟⠛⠻⣿⡇⢸⣿⣷⣤⡀⠀⠀⣿⢿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⣿⣿⣶⣀⣤⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⡄⠀⣿⡇⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠸⠿⠸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⡿⠿⠿⠿⡿⣻⣿⣿⠈⢿⣿⠏⢻⣷⡀⠈⣿⣄⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣿⣿⣿
⢰⡄⠀⠀⠀⠀⢻⣿⣿⣿⡟⠉⠻⠇⠀⠀⠀⠙⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢻⣿⣯⣤⣶⣿⣿⣿⣿⣿⡟⠀⠸⠋⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿
⢿⣿⣦⡀⣠⣄⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠀⠀⠀⠀⢿⣿⣿⠋⠉⠉⠹⡟⠛⢿⣿⣷⣀⠀⠀⠀⢹⣿
⢸⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⠇⠀⠀⣸⣿⣧⣤⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢠⡞⠀⠀⠀⠀⠙⢿⣿⣶⣶⣿⣿
⠈⣿⢿⣿⣿⣿⡇⣸⣿⣿⡟⠋⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠘⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⢿⣿⣿⣷⣦⣄⡀⠀⢺⣿⣿⣿⠃⠈⠀⠀⢰⣶⣷⡄⠈⢻⣿⣿⣿⣿
⢸⣿⣨⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⢻⣿⣿⣿⣿⣷⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⢋⡀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⣿⣿⣿⡟
⠸⠿⠿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣄⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢸⣿⣿⣿⣧⣤⣿⣿⣿⡇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⢤⣤⣴⣶⣤⣤⣶⣤⣤⡀⠠⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠀⠀⠉⠛⠈⠱⠮⡌⠻⣷⣿⣷⡤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣂⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣶⣶⣴⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣏⢻⣿⣿
⢸⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣻⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⢹⣿⣿⣿⣿⡿
⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⠀⠘⠿⢻⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⠁⠀⢹⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⡏⠉⢻⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢶⣄⡠⠂⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡆⠀⠀⢠⣶⣿⣟⠀⠀⠀⠻⣿⣿⣿⡆⠀⠿⣿
⢸⣿⣿⡟⠉⠹⣿⣿⣿⣿⡄⢿⣿⠇⠀⠀⢻⣿⣿⣿⡄⠀⠹⣿⣿⠛⣿⣿⡿⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠐⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣧⣄⠀⢸⣿⣿⣿⣿⣧⠀⠀⠈⠉⢻⣿⠀⠀⠈
⢸⣿⣿⠁⠀⣴⣿⣿⣿⣿⣿⡆⠁⠀⠀⢰⣿⣿⣿⣿⠇⠀⠀⠙⠁⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠿⠛⠛⠻⠟⣿⣼⣇⣠⠼⣷⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡄⠀⣰⣦⣾⣿⡄⠀⠀
⠸⠿⠏⠀⠸⣿⣿⣿⣿⣿⣿⠇⢀⣀⣀⣿⣿⣿⣿⣏⠀⠀⢀⣤⣄⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣀⠀⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡄⠀
⢠⣤⡄⠀⠀⠻⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣾⣿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⣿⠿⠿⣿⣧⠀
⢸⣿⣇⠀⠀⠀⣿⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠊⠀⠀⠈⣿⣼
⢸⣿⣗⣤⣴⣾⣿⡿⢿⡏⠁⣤⣿⡿⠛⢿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠻⠿⠁⣿⣿⠁⣰⡀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⢸⣿⣿⣿⡇⢸⣧⠈⠋⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣤⡀⠀⢰⣿⣿⣷⣿⡇⠀⠀⠀⢰⣿⣿⣯
⠀⠀⠀⡽⠛⠻⣿⡇⢸⣿⣷⣤⣀⠀⠀⣿⢿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⣿⣿⣿⣦⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⡇⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠸⠟⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⢿⣿⠿⢿⠿⣿⣿⡏⢿⣿⠏⢻⣷⡀⠈⣿⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿
⣰⡄⠀⠀⠀⠀⢻⣿⣿⣿⡿⠉⠻⠇⠀⠀⠀⠙⠁⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠙⣿⣿⣯⣤⣾⣿⣿⣿⣿⣿⠀⠘⠋⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹⣿⣿
⢿⣿⣦⡀⣠⣄⠀⢿⣿⣿⣿⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⠋⠉⠉⠹⡛⠛⢿⣿⣷⡀⠀⠀⠀⢹⣿
⢸⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⠇⠀⠀⣼⣿⣦⣤⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢠⡞⠀⠀⠀⠈⠙⢿⣿⣶⣶⣿⣿
⠈⣿⢿⣿⣿⣿⡷⣸⣿⣿⡟⠋⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠘⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⣿⡿⣿⣿⣿⣦⣄⣀⠀⢺⣿⣿⣿⠀⠈⠀⠀⢠⣶⣷⡄⠀⢻⣿⣿⣿⣿
⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⢻⣿⣿⣿⣿⣷⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣾⣝⢋⡀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⣿⣿⣿⡟
⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣄⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢸⣿⣿⣿⣧⣄⣿⣿⣿⡇

                    ䷩ 𝚕𝚒𝚗𝚎 6652

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/13/reaking-laws-to-uphold-laws/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/13/reaking-laws-to-uphold-laws/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_“There_is_No_Crueler_Tyranny_Than_That_Which_is_Perpetuated_Under_the
Shield_of_Law_and_in_the_Name_of_Justice.”⠀✐


Posted in Europe, Patents at 2:35 am by Dr. Roy Schestowitz


              🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tyranny_in_the_name_of_justice⦈_
                        Breaking laws to ‘uphold’ laws?


Summary: The EPO says it is there to cushion patent law; but the EPO itself is
constantly breaking laws, not to mention its endless violations of treaties and
constitutions


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

                    ䷩ 𝚕𝚒𝚗𝚎 6892

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/07/2022:_Debian_11.4.0_Tour_and_More⠀✐


Posted in News_Roundup at 6:40 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
    * Leftovers
          o Security
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ Make Use Of ☛ Linux_PC_Maker_System76_Teases_Hackable_Launch_Lite
            Keyboard⠀⇛


                 System76 is using the tagline on its website, “A new keeb
                 is coming,” to promote the product. The company also took
                 to Twitter to tease the upcoming keyboard, touting its
                 configurability, small size, and comfort:


                 The company has not yet announced a price point for the
                 new keyboard, but the current version is priced at
                 $285.00


          o § Server⠀➾


                # ⚓ Kubernetes Blog ☛ Kubernetes_Gateway_API_Graduates_to
                  Beta⠀⇛


                       We are excited to announce the v0.5.0 release of
                       Gateway API. For the first time, several of our
                       most important Gateway API resources are graduating
                       to beta. Additional, we are starting a new
                       initiative to explore how Gateway API can be used
                       for mesh and introducing new experimental concepts
                       such as URL rewrites. We’ll cover all of this and
                       more below.


          o § Audiocasts/Shows⠀➾


                # ⚓ FLOSS_Weekly_689:_Record_Discord_with_Craig_–_New
                  Maintainers_of_Craig_for_Discord_Recording⠀⇛


                       Doc Searls and Aaron Newcomb revisit Craig, the
                       open source way to make live multitrack recordings
                       of Discord sessions, with its new and already-
                       seasoned maintainers, @Snazzah and @DJCoolguy. The
                       new maintainers share their experience with
                       transitioning from the previous developers as well
                       as other updates in version 2 of Craig.chat.


                # ⚓ Video ☛ We_Have_Too_Many_Linux_Distros!!_Or_Do_We??_–
                  Invidious⠀⇛


                       We have an absolutely insane number of distros out
                       there and it seems like we’re only ever getting
                       more but how many of those distros are actually
                       active and is more than it used to be.


                # ⚓ Video ☛ Debian_11.4.0_“Bullseye”_overview_|_The_universal
                  operating_system._–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       Debian 11.4.0 “Bullseye” and some of the
                       applications pre-installed.


          o § Instructionals/Technical⠀➾


                # ⚓ RoseHosting ☛ How_to_Install_Magento_2.4.4_on_Ubuntu_22.04
                  –_RoseHosting⠀⇛


                       Magento is an open-source e-commerce platform
                       written in PHP that uses multiple PHP frameworks
                       such as Symfony and Laminas. The platform is
                       flexible and has a large variety of features to
                       build an online store.


                       Magento offers a community and enterprise edition.
                       The community edition is available free of charge
                       and is designed primarily for individuals and/or
                       small businesses.
                       The enterprise edition is the paid version of
                       Magento. Compared to the community edition, the
                       enterprise edition has advanced custom features and
                       functionalities and is mainly aimed at medium to
                       large businesses.


                       In this tutorial, we will show you how to install
                       the Magento 2.4.4 community edition on Ubuntu 22.04
                       server, which can be done easily if you follow it
                       step by step.


                # ⚓ Pragmatic Linux ☛ Enable_compiler_warnings_with_CMake_–
                  PragmaticLinux⠀⇛


                       C and C++ compiler toolchains make it possible for
                       us software geeks to build amazing things. Did you
                       know that both GCC and Clang offer build-in
                       functionality that aids us in becoming better
                       developers and creating higher quality software?
                       I’m talking about compiler warnings. This article
                       explains how you can enable compiler warnings, when
                       using CMake to generate the build environment.


                # ⚓ Make Use Of ☛ How_to_Set_Up_a_TFTP_Server_on_Linux⠀⇛


                       TFTP (Trivial File Transfer Protocol) was first
                       described in 1980. It is a fairly old protocol
                       published in June 1981 as TFTP Protocol revision 2
                       in RFC 783 (Request For Comments) by Karen R.
                       Sollins.


                       In the early days, the main goal of TFTP was to
                       send and receive files over a network. In
                       particular, it was used to transfer the files
                       needed during boot to enable systems to boot over a
                       network.


                       Here’s how you can set up a TFTP server on a Linux
                       machine.


                # ⚓ Linux Made Simple ☛ How_to_install_Darktable_4.0_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Darktable
                       4.0 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.


                # ⚓ Video ☛ How_to_install_Godot_game_engine_on_Pop!_OS_22.04_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       Godot game engine on Pop!_OS 22.04.


                # ⚓ LinuxOpSys ☛ Bash_Command_Line_Chain_Operators_in_Linux
                  with_Examples⠀⇛


                       Here learn about chain operators in Linux with
                       examples. Linux command chaining is very useful if
                       you want to execute multiple commands at one goal.


                # ⚓ LinuxOpSys ☛ Download_RPM_Package_Using_DNF_without
                  Installing_it⠀⇛


                # ⚓ LinuxOpSys ☛ How_to_Delete_History_in_Linux_Easily⠀⇛


                # ⚓ Linux Journal ☛ The_Echo_Command_|_Linux_Journal⠀⇛


                       In this article, we’re going to look at the echo
                       command, which is useful for showing text on the
                       terminal, as well as the contents of variables.
                       Let’s get started!


                # ⚓ MakeTech Easier ☛ How_to_Use_Rm_Command_in_Linux_–_Make
                  Tech_Easier⠀⇛


                       There are times when you need to delete files in
                       the Linux terminal. The rm command lets you delete
                       directories, files, symbolic links, and more. This
                       in-depth guide shows you how to use the rm command
                       effortlessly.


                # ⚓ Make Use Of ☛ How_to_Install_QEMU_on_Ubuntu_to_Set_Up_a
                  Virtual_Machine⠀⇛


                       Virtualization is a neat way to use both Linux and
                       Windows at once, getting the best of both worlds
                       without having to tackle dual booting and all the
                       issues that come with it.


                       VirtualBox and VMware are household names when it
                       comes to the best virtualization solutions. But did
                       you know that there are alternatives as well? QEMU
                       is one such free and open-source alternative for
                       you to try, should you wish to explore.


                # ⚓ ID Root ☛ How_To_Install_PrestaShop_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       PrestaShop on Ubuntu 22.04 LTS. For those of you
                       who didn’t know, PrestaShop is an e-commerce
                       solution that allows you to create your own online
                       shop easily. It is written in PHP, is highly
                       customizable, supports all the major payment
                       services, is translated into many languages and
                       localized for many countries, has a fully
                       responsive design (both front and back-office),
                       etc.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the PrestaShop e-commerce platform
                       on Ubuntu 22.04 (Jammy Jellyfish). You can follow
                       the same instructions for Ubuntu 22.04 and any
                       other Debian-based distribution like Linux Mint,
                       Elementary OS, Pop!_OS, and more as well.


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ SUSECON_2022_Fujitsu_Presentations
                  Available_Now⠀⇛


                # ⚓ SUSE’s Corporate Blog ☛ Harvesting_the_Benefits_of_Cloud-
                  Native_Hyperconvergence⠀⇛


          o § Fedora Family / IBM⠀➾


                # ⚓ Matt_Hicks_Is_Red_Hat’s_New_CEO⠀⇛


                       Red Hat has appointed Matt Hicks as its president
                       and chief executive officer. Hicks, who previously
                       served as Red Hat’s executive vice president of
                       Products and Technologies, succeeds Paul Cormier,
                       who will serve as chairman of Red Hat.


                # ⚓ IT Pro Today ☛ Cormier_Steps_Down,_Hicks_Steps_Up_as_Red
                  Hat_CEO [Ed: How Red Hat-funded "publishers" cover this
                  news]⠀⇛


                       Less than two-and-a-half years after becoming Red
                       Hat CEO, Paul Cormier has resigned from the role.
                       Cormier will remain onboard as the company’s
                       Chairman.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ghacks ☛ Linux_Mint_21_Beta_is_now_available_for_testing_–
                  gHacks_Tech_News⠀⇛


                       Linux Mint 21 is almost ready. If you are
                       interested in trying the next version of the
                       popular Linux distribution early, you may download
                       official beta ISO images to do so. All three Linux
                       Mint desktop environments can be downloaded and
                       tested.


                       Linux Mint 21 is powered by Linux Kernel 5.15 and
                       Ubuntu 22.04 LTs, which means that the Linux
                       distribution will be supported until 2027 with
                       security patches.


                       Once the stable version of Linux Mint 21 released,
                       Linux Mint 20.3 systems can be upgraded with the
                       help of the new Linux Mint upgrade tool. It removes
                       the need to run commands from a terminal window,
                       and streamlines the upgrade process for most users
                       because of that.


                # ⚓ OMG Ubuntu ☛ Linux_Mint_21_Beta_is_Available_to_Download_–
                  OMG!_Ubuntu!⠀⇛


                       The milestone is here to help intrepid bug hunters
                       stress-test the next version of the hugely popular
                       Linux distro, which is based on the latest Ubuntu
                       22.04 LTS release.


                       Linux Mint 21 includes a swathe of refreshed
                       components throughout its stack (mostly inherited
                       from Ubuntu) including the Linux kernel 5.15 point
                       release, refreshed graphics drivers, and lower-
                       level tooling and developer library updates.


                # ⚓ Ubuntu ☛ Introducing_Ubuntu_for_Google_Cloud’s_Arm-based
                  T2A_virtual_machines⠀⇛


                       Canonical and Google Cloud today announce an
                       optimised Ubuntu image for the preview of Tau T2A
                       virtual machines (VMs) on Compute Engine. Google
                       Cloud users will benefit from running Ubuntu, a
                       popular cloud operating system, on a secure,
                       scalable, and highly cost-effective cloud
                       infrastructure. The Ampere® Altra® Arm-based T2A
                       VMs are ideal for computing workloads including
                       microservices, application servers, machine
                       learning (ML), open source databases, and in-memory
                       caches.


                       Canonical has had a long-term strategy for Arm
                       architecture for a decade. At Computex 2012, MiTAC
                       demonstrated their first Arm Server, running
                       Ubuntu. Ubuntu 14.04 LTS was also the pioneer in
                       supporting Armv7-A Cortex-A15 chip and Armv8 SoCs.
                       Since the start of our Arm journey, Canonical has
                       been focused on solving challenges such as: mixed
                       x86 and Arm environments; multiple SoCs;
                       provisioning large deployments; and mixed public
                       and private cloud deployments. Continuing this
                       strategy, Canonical and Ampere have collaborated to
                       bring SOC certified Ubuntu images to the market at
                       launch. Today, the availability of optimised Ubuntu
                       for T2A VMs enables developers to better address
                       these challenges.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ New_Android_Games:_Best_New_Android_Games_This_Week_–_Droid
                  Gamers⠀⇛


                # ⚓ Android Authority ☛ Wallpaper_Wednesday:_Android_wallpapers
                  2022-07-13_–_Android_Authority⠀⇛


                # ⚓ Computer World ☛ Drop,_crack,_d’oh!_My_broken_Android_phone
                  epiphany_|_Computerworld⠀⇛


                # ⚓ Android Central ☛ I_used_all_Android_flagships_of_2022_—
                  this_is_the_phone_you_should_buy_|_Android_Central⠀⇛


                # ⚓ Android Police ☛ Want_a_compact_flagship_Android_phone?
                  Asus_shows_off_its_next_Zenfone_on_July_28⠀⇛


                # ⚓ Notebook Check ☛ Nubia_Z40S_Pro_is_teased_as_an_upcoming
                  Android_flagship_smartphone_with_an_updated_processor_and_a
                  sliding_hardware_toggle_–_NotebookCheck.net_News⠀⇛


                # ⚓ 9to5Google ☛ Bluetooth_debuts_a_new_set_of_incredible
                  features_called_Bluetooth_LE_Audio⠀⇛


                # ⚓ Android Police ☛ Android_13_Beta_4_is_here_to_convince_you
                  it’s_ready_to_be_your_daily_driver⠀⇛


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


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Mozilla ☛ Reworking_our_Visual_Metrics_Processing
                        System_–_Mozilla_Performance⠀⇛


                             Our visual metrics processing system used to
                             use two separate machines to produce visual
                             metrics from our pageload tests. In this
                             post, I’ll describe how we moved to a single-
                             machine system that also brought about many
                             other benefits for us.


                             Note: If you’ve never heard of visual metrics
                             before, they can be summed up as performance
                             metrics processed from a video recording of a
                             pageload. You can find more information about
                             these from this article titled Improving
                             Firefox Page Load, by Bas Schouten.


                      # ⚓ Mozilla ☛ Migrating_to_Browsertime_for_Performance
                        Testing_–_Mozilla_Performance⠀⇛


                             Originally, we used a Web Extension for doing
                             performance testing on Firefox in our Raptor
                             test harness. But, we needed to add new
                             features such as visual metrics, so in this
                             post, I’ll briefly describe the steps we took
                             to migrate Raptor to Browsertime.


                             We now have enabled Browsertime by default in
                             our Raptor harness both locally, and in
                             Continuous Integration (CI) but for some
                             time, we needed to use the flag
                             `–browsertime` to enable it. This work
                             started with Nick Alexander, Rob Wood, and
                             Barret Rennie adding the flag in bug 1566171.
                             From there, others on the Performance team
                             (myself included), began testing Browsertime,
                             preparing the Raptor harness, and building up
                             the infrastructure required for running
                             Browsertime tests in CI.


                             Our primary motivation for all of this work
                             was obtaining visual metrics. If you’ve never
                             heard of visual metrics before, they can be
                             summed up as performance metrics processed
                             from a video recording of a pageload. You can
                             find more information about these from this
                             article titled Improving Firefox Page Load,
                             by Bas Schouten. Initially, our visual
                             metrics processing system used a two-machine
                             system where one machine would run the test
                             and the other would process the video
                             recordings to obtain the metrics. This worked
                             well for some time until we found some issues
                             with it that were a large point of friction
                             when it came to using our tooling. In
                             Reworking our Visual Metrics Processing
                             System, I describe these issues and how we
                             overcame them. It suffices to say that we now
                             use a single machine in CI, and that those
                             issues were resolved.


    * § Leftovers⠀➾


          o § Security⠀➾


                # ⚓ Unix Men ☛ 5_Data_Security_Issues_on_Linux⠀⇛


                       Every tech enthusiast knows that Linux comes with
                       the freedom that hardly any other OS can offer. We
                       don’t even have to get into the benefits that come
                       with a large community and open source philosophy.


                       However, some people (especially Linux newbies)
                       tend to think that Linux can’t be harmed by
                       cyberthreats at all.


                       Hackers and scammers are getting ever more
                       creative, so let’s talk about the security issues
                       on Linux that can get you and your data in trouble.


                # ⚓ The Register UK ☛ X.org_servers_updated,_among_many_other
                  X11_bits_•_The_Register⠀⇛


                       X.org has released a bunch of updates, which
                       includes closing two security holes and, yes, this
                       affects Wayland users too.


                       A batch of updates to X.org’s suite of X11 servers
                       and components just appeared. Among the new
                       features, there were also fixes for two security
                       holes mentioned in an X.org Foundation security
                       advisory, which covers CVE-2022-2319 and CVE-2022-
                       2320.


                       Although the X window system is pretty old, it’s
                       still everywhere, including on almost every xNix
                       operating system that has a graphical desktop.
                       Wayland users don’t get to be smug: they too rely
                       upon XWayland, which is what lets them run most
                       older apps. Together, these mean that X.org version
                       21.1.4 will be a necessary update for a lot of
                       people, alongside XWayland version 22.1.3.


                # ⚓ LinuxSecurity ☛ Hacker’s_Corner:_Complete_Guide_to_Anti-
                  Debugging_in_Linux_–_Part_2⠀⇛


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ of_*course*_we’re_time_traveler⠀⇛


                # ⚓ The_June_Archive_and_Restoration_Project⠀⇛


                       I recently have come across the most impressive
                       horror series I’ve seen in a long time.


                       It’s best to go into this series as blind as
                       possible, but some context and history will really
                       improve what you get out of it. It’s based on the
                       culture around Flipnote Hatena (Flipnote Studio in
                       the US). It was a program for the DSi that allowed
                       anyone to create and share animations with each
                       other. A very unique culture of highly talented
                       people developed there until the service shut down
                       on May 31, 2013 despite being popular.


          o § Technical⠀➾


                # ⚓ tmux_notes⠀⇛


                # ⚓ I_think_Mac_OS-X_is_wrong_in_this_case,_and_Linux_is
                  right⠀⇛


                       There was apparently a frantic bug-hunt involving
                       “Project: Lumbergh [1]” yesterday that I was not
                       involved in. From the description of the bug, it
                       certainly sounded like it was a manifestation of
                       “undefined behavior” as “Project: Lumbergh” was
                       actinging differently between Linux and Mac OS-X
                       (our testing and development platforms).


                # § Programming⠀➾


                      # ⚓ The_Snail_Layout⠀⇛


                             It started as a thought experiment, but I’m
                             slowly translating it into C.


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



                    ䷩ 𝚕𝚒𝚗𝚎 7518

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/07/2022:_Free_Software_in_DoD⠀✐


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Licensing_/_Legal
          o Programming/Development
                # Python
                # Shell/Bash/Zsh/Ksh
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
    * Gemini*_and_Gopher
          o Personal
          o Politics
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Instructionals/Technical⠀➾


                # ⚓ Trend Oceans ☛ How_to_install_a_Graphical_Desktop
                  Environment_on_Ubuntu_or_Debian_server⠀⇛


                       
                       As you know, the Ubuntu Desktop variant ships with
                       the default GNOME desktop environment for users, so
                       why do we need to install a graphical desktop
                       environment on Ubuntu?


                       Yes, it is shipped with the GNOME desktop
                       environment to use, but it is not always like that.
                       If you have installed the Ubuntu server or Debian
                       minimal, then you won’t find the regular desktop
                       setup to use your favourite application
                       graphically.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ 43_of_the_Top_50_most_highly-reviewed_Steam
                  games_are_Steam_Deck_Playable⠀⇛


                       Recently I went over the top 100 most-played games
                       on Steam by player count but what about the most
                       highly rated games on Steam? Here’s how the top 50
                       most positively reviewed Steam games work on Steam
                       Deck.


                # ⚓ GamingOnLinux ☛ Valve_gives_the_Discovery_Queue_a_makeover
                  to_help_you_find_your_next_game⠀⇛


                       The Discovery Queue is a feature that many people
                       probably miss or just don’t use. I use it from time
                       to time but it was a little basic. Valve has put
                       live the next Steam Labs experiment to overhaul
                       Discovery Queue.


                # ⚓ GamingOnLinux ☛ Veil_of_Dust:_A_Homesteading_Game_arrives
                  for_Linux⠀⇛


                       Veil of Dust: A Homesteading Game is a story-driven
                       historically-grounded homesteading game about
                       finding your way after loss inspired by games like
                       Don’t Starve and Stardew Valley with a healthy
                       sprinkle of fantasy elements too. Just recently
                       they had a Native Linux version released on Steam.


                # ⚓ GamingOnLinux ☛ Season_of_Pride_2022_Steam_Event_is_live
                  now⠀⇛


                       Season of Pride is going live for 2022, with the
                       event and sale hosted by MidBoss. Not only is there
                       a big Steam sale along with upcoming games features
                       but there will also be a ton of livestreams.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ Silicon Angle ☛ Red_Hat_announces_Matt_Hicks_as_its_new
                  leader⠀⇛


                       Red Hat is a subsidiary of IBM Corp. and seen as
                       one of the pioneers of open-source software. Its
                       flagship product is the Red Hat Enterprise Linux
                       operating system, which is widely used to power
                       thousands of enterprise data centers around the
                       world. The company also sells tools around
                       virtualization, software containers, middleware and
                       various other applications. It was acquired by IBM
                       in 2019.


                # ⚓ IT Wire ☛ Red_Hat_names_Matt_Hicks_president_and_chief
                  executive_officer⠀⇛


                       Hicks – who joined the company in 2006 as a
                       developer on the IT team- previously served as Red
                       Hat’s executive vice president of products and
                       technologies.


                # ⚓ CRN ☛ IBM’s_Red_Hat_Names_Matt_Hicks_As_New_CEO,_Hints_At
                  Future_Acquisitions⠀⇛


                       IBM subsidiary Red Hat has named a new president
                       and CEO effective immediately: Matt Hicks, the
                       company’s executive vice president of products and
                       technologies.


                       Paul Cormier, the current CEO and president of the
                       open source software tools provider, will continue
                       on as Red Hat’s chairman, according to a company
                       statement Tuesday.


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ FireBeetle_2,_another_ESP32_based_MCU
                  alternative⠀⇛


                       Just as the Banana Pi Leaf-S3 and XIAO ESP32C3
                       covered a few days ago, the FireBeetle 2 shares a
                       similar form factor, I/O peripherals including Wi-
                       Fi/BLE, external battery support and an onboard
                       charging circuit.


                       The FireBeetle 2 was designed around the ESP-WROOM-
                       32E from Expressif Systems and contains a dual core
                       Tensilica LX6 with maximum frequency of 240MHz. On
                       the other hand, the XIAO ESP32C3 features a single
                       RISC-V core (up to 160MHz) while the Banana Pi
                       Leaf-S3 integrates the newer dual core Tensilica
                       LX7 (up to 240MHz).


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ SlashGear ☛ The_Best_Feature_Of_Android_Phones,_According
                  To_44%_Of_People_We_Polled⠀⇛


                # ⚓ Android Central ☛ Pixel_7_Pro_leak_shows_off_live_images_of
                  Google’s_next_flagship_Android_phone_|_Android_Central⠀⇛


                # ⚓ The Verge ☛ How_to_enable_Android’s_TalkBack_screen_reader
                  –_The_Verge⠀⇛


                # ⚓ CNX Software ☛ Mekotronics_R58_review_–_Part_2:_Android_12
                  on_Rockchip_RK3588_CPU_–_CNX_Software⠀⇛


                # ⚓ Android Headlines ☛ Review_Of_The_Overlyzer_Android_App⠀⇛


                # ⚓ SlashGear ☛ Why_You_Should_Be_Using_An_Antivirus_App_On
                  Your_Android_Phone⠀⇛


                # ⚓ Hindustan Times ☛ These_Popular_Android_apps_have_been
                  BANNED_by_Google;_Delete_them_now!_They_can_steal_your_money
                  |_Tech_News⠀⇛


                # ⚓ Sportskeeda ☛ PUBG_Mobile_2.1_update_APK_download_link_and
                  file_size_for_Android_phones_(2022)⠀⇛


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


          o § Licensing / Legal⠀➾


                # ⚓ USDOD ☛ DoD_Open_Source_Software_FAQ⠀⇛


                       This page is an educational resource for government
                       employees and government contractors to understand
                       the policies and legal issues relating to the use
                       of open source software (OSS) in the United States
                       Department of Defense (DoD). The information on
                       this page does not constitute legal advice and any
                       legal questions relating to specific situations
                       should be referred to legal counsel. References to
                       specific products or organizations are for
                       information only, and do not constitute an
                       endorsement of the product/company.


          o § Programming/Development⠀➾


                # § Python⠀➾


                      # ⚓ Yes,_I_have_opinions_on_your_open_source
                        contributions⠀⇛


                             There are other things people are talking
                             about — like the perma-thread arguing that
                             PGP solves every security problem and PyPI
                             should just PGP all the things (it doesn’t
                             solve every security problem and wouldn’t for
                             PyPI, and PyPI actually already lets you PGP-
                             sign packages, which should be a hint about
                             how little signing actually solves on an
                             index like PyPI) — but the big focus has been
                             on this idea that open source equals no
                             responsibility, and that 2FA is too much to
                             ask of package maintainers. Hopefully I’ve
                             convinced you, one way or another, that this
                             doesn’t hold up to even pretty light
                             scrutiny; that we most certainly can ask
                             people to accept a certain amount of
                             responsibility — such as securing their
                             package-index accounts — as the price of
                             entry to a large community like PyPI/Python;
                             and that participation in such communities
                             has both benefits and responsibilities,
                             neither of which can be had without the
                             other.


                             If you still can’t stand the idea that PyPI
                             can ask you to do things as a condition of
                             getting to publish your packages there, I
                             don’t know what to tell you. If that’s enough
                             to make you angrily flame out of Python or of
                             open source altogether, then probably that’s
                             the best outcome for both you and everyone
                             else, since it’s unlikely that things were
                             going to go well in the long term.


                      # ⚓ Congratulations:_We_Now_Have_Opinions_on_Your_Open
                        Source_Contributions⠀⇛


                             Maybe we can find a future for package
                             indexes where maintainers of packages are not
                             burdened further because the [Internet]
                             started depending on it. It’s not the fault
                             of the creator that their creation became
                             popular.


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ Linux Handbook ☛ Convert_Hex_to_ASCII_Characters_in
                        Linux_Command_Line⠀⇛


                             Got a bunch of hexadecimal characters and
                             want to convert them to a readable decimal
                             system (ASCII)?


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ NBC ☛ Photos:_How_pictures_from_the_Webb_telescope_compare
                  to_Hubble’s⠀⇛


                       The first images from the James Webb Space
                       Telescope are just a preview of the impressive
                       capabilities of NASA’s $10-billion, next-generation
                       observatory. Billed as the successor to the iconic
                       Hubble Space Telescope, which launched into orbit
                       in 1990, Webb was designed to peer deeper into
                       space than ever before, with powerful instruments
                       that can capture previously undetectable details in
                       the cosmos.


                       Here’s how the Webb telescope stacks up to its
                       famous predecessor.


                # ⚓ The Verge ☛ Marvel_at_the_first_batch_of_full-color_images
                  from_NASA’s_James_Webb_Space_Telescope⠀⇛


                       The images join the very first picture from the
                       James Webb Space Telescope, or JWST, that NASA and
                       President Joe Biden released yesterday during a
                       special briefing at the White House. That first
                       picture — a portion of the night sky called SMACS
                       0723 — showcased a dizzying array of thousands of
                       distant galaxies, all bundled into just a tiny dot
                       in the sky about the size of a grain of sand when
                       held out an arm’s distance. NASA hailed the image
                       as the deepest infrared image of the Universe ever
                       taken. In fact, the light from some of the galaxies
                       in the picture has traveled roughly 13 billion
                       years to reach JWST.


          o § Hardware⠀➾


                # ⚓ DaemonFC (Ryan Farmer) ☛ [Repost]_Matthew_Garrett_makes
                  noise_about_Lenovo_attacking_GNU/Linux_six_years_after
                  accusing_me_of_“spewing_nonsense”_for_taking_action_against
                  Lenovo.⠀⇛


                       As part of this “upgrade”, Lenovo also refreshed
                       their UEFI firmware, and in the process they put
                       the disk storage controller into a secret
                       undocumented mode that Linux couldn’t use, making
                       it appear as though there was no Solid State Drive
                       in the laptop.


                       The code to enable AHCI mode was there, but Lenovo
                       also wrote new code to reset it to the secret
                       storage controller mode on every reboot even if you
                       reset it from UEFI shell.


                # ⚓ Nikkei ☛ Nikon_to_stop_making_SLR_cameras_and_focus_on
                  mirrorless_models⠀⇛


                       Nikon’s SLR cameras have been widely used by
                       professional photographers for more than 60 years.


                # ⚓ India Times ☛ Computer_chips_face_toilet_paper_hoarding
                  moment_as_shortage_turns_to_glut⠀⇛


                       Chip shortages turned into a glut in some sectors,
                       taking Wall Street by surprise. By late June,
                       memory chip firm Micron Technology Inc said it
                       would reduce production. The market reversal caught
                       Micron off guard, admitted Chief Business Officer
                       Sumit Sadana.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Teen Vogue ☛ COVID_Is_Still_Happening,_Whether_or_Not
                  You’ve_Moved_On⠀⇛


                       A recent pre-print study led by a clinical
                       epidemiologist at Washington University in St.
                       Louis, which has yet to be peer-reviewed, found
                       that, compared with those infected by COVID once,
                       those with two or more documented infections were
                       more than twice as likely to die and three times as
                       likely to be hospitalized within six months of the
                       last infection.


                       The study was based on VA Health System records
                       from nearly 6 million veterans. According to the
                       findings, another COVID infection also put them at
                       higher risk for “lung and heart problems, fatigue,
                       digestive and kidney disorders, diabetes and
                       neurologic problems,” as reported by CNN. The Daily
                       Beast summarized the study simply: “Every time you
                       catch COVID, your chance of getting really sick
                       with something — likely COVID-related — seems to go
                       up.”


                # ⚓ NBC ☛ Covid_hospitalizations_double_since_May,_driven_by
                  BA.5⠀⇛


                       Nationwide, hospitalizations have doubled since
                       May, Centers for Disease Control and Prevention
                       Director Dr. Rochelle Walensky said during a media
                       briefing Tuesday. An NBC News analysis found that
                       Covid-related hospitalizations are up in all but
                       four states, with the biggest recent jumps in the
                       South.


                       The increase is driven by BA.5 and another closely
                       related subvariant, BA.4, Walenksy said. BA.5
                       accounted for 65% of new cases for the week ending
                       July 9, according to the CDC. BA.4 accounted for
                       16.3%.


          o § Proprietary⠀➾


                # ⚓ The Verge ☛ Google_already_broke_its_new_YouTube_UI_on_old
                  Chromecasts⠀⇛


                       While you can technically still browse through
                       YouTube using your phone as a remote, you’ll have
                       to do so as a logged-out guest — no personalized
                       recommendations, playlists, or viewing history from
                       the rest of your devices directly on the
                       Chromecast. For YouTube Premium subscribers, it’s
                       even worse; currently, if they use the YouTube
                       interface on the Chromecast, it’ll include the ads
                       they pay not to see on the rest of their devices.


                # ⚓ The Verge ☛ Read_the_memo_Google’s_CEO_sent_employees_about
                  a_hiring_slowdown⠀⇛


                       Google isn’t the only company that’s had to
                       recently pump the brakes on hiring people: Uber has
                       said it’ll have to be “hardcore about costs,” Meta
                       sent a memo to employees warning of “serious times”
                       and fierce headwinds after implementing hiring
                       freezes for some teams, and Spotify and Snap have
                       also announced plans to slow hiring. Other
                       companies, like Twitter, Netflix, and GameStop,
                       have recently decided to lay off employees.


                # ⚓ The Verge ☛ Apple_and_Jony_Ive_are_no_longer_working
                  together⠀⇛


                       Moving forward, Apple COO Jeff Williams will
                       continue to manage Apple’s design teams, though the
                       product marketing team has “assumed a central role
                       in product choices,” The New York Times says.
                       LoveFrom will keep working with Airbnb and Ferrari.
                       Apple and LoveFrom didn’t immediately reply to a
                       request for comment.


                       Ive, who joined Apple in 1992, was the visionary
                       behind many of Apple’s most iconic hardware
                       designs, including the iMac and the iPod’s white
                       headphones. After Scott Forstall’s ouster, Ive was
                       put in charge of software design, too, resulting in
                       the radically different look for iOS 7.


                # ⚓ New York Times ☛ Apple_Ends_Consulting_Agreement_With_Jony
                  Ive,_Its_Former_Design_Leader⠀⇛


                       Mr. Ive and Apple have agreed to stop working
                       together, according to two people with knowledge of
                       their contractual agreement, ending a three-decade
                       run during which the designer helped define every
                       rounded corner of an iPhone and guided development
                       of its only new product category in recent years,
                       the Apple Watch.


                       When Mr. Ive left Apple in 2019 to start his own
                       design firm, LoveFrom, the iPhone maker signed a
                       multiyear contract with him valued at more than
                       $100 million. That made Apple his firm’s primary
                       client, people with knowledge of the agreement
                       said.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Hill ☛ Experts_say_US_must_not_let_EU_lead_on
                        cybersecurity⠀⇛


                             Cybersecurity experts argued on Tuesday that
                             the U.S. is falling behind the European Union
                             when it comes to being a leader in the realm
                             of cyber security.


                             Experts called the bloc’s General Data
                             Protection Regulation, a law governing data
                             privacy and security rules, the global
                             standard. The law, adopted in 2018, renewed
                             how businesses handle personal data in
                             Europe, with large fines for companies that
                             fail to comply.


                      # ⚓ The Hindu ☛ TikTok_delays_changes_to_privacy_policy
                        over_Europe_data_concerns⠀⇛


                             TikTok suspended changes to its privacy
                             policy for targeted advertising on Tuesday, a
                             day before they took effect, while the lead
                             European Union regulator studies whether they
                             comply with the bloc’s data protection rules.


                      # ⚓ Reuters ☛ TikTok_delays_changes_to_privacy_policy
                        over_Europe_data_concerns⠀⇛


                             TikTok, which has achieved rapid growth,
                             particularly among younger people, confirmed
                             it was pausing the changes to its privacy
                             policy in Europe but defended its plans for
                             targeted advertising.


          o § Defence/Aggression⠀➾


                # ⚓ Rolling Stone ☛ 5_Key_Revelations_From_Tuesday’s_Jan._6
                  Hearing⠀⇛


                       Trump drafted but didn’t send a tweet that a march
                       to the Capitol was going to be part of the much-
                       hyped Jan. 6 protest, the committee revealed. The
                       panel also laid out the extent to which rally
                       organizers and those close to Trump knew of plans
                       to have the president direct protestors to the
                       Capitol. The committee continued to draw
                       connections between Trump and his allies, the
                       organizers of his rally at the Ellipse, and the
                       extremist groups present the day of the
                       [insurrection].


                # ⚓ NPR ☛ Live_updates:_Jan._6_rioter,_former_Oath_Keepers
                  spokesman_sit_for_live_testimony⠀⇛


                       The committee investigating the Jan. 6 Capitol
                       attack holds its seventh public hearing Tuesday,
                       focusing on the role right-wing extremist groups –
                       such as the Proud Boys and the Oath Keepers –
                       played in planning the deadly siege.


                       Expect the committee to try to connect the dots
                       between these groups and the effort to overturn the
                       2020 election – and also to show how a tweet from
                       former President Donald Trump spurred some in those
                       groups to organize around Jan.6, 2021.


                # ⚓ Jerusalem Post ☛ ‘This_is_Biden’s_last_chance_to_stop_Iran
                  from_getting_the_bomb’_–_Steinitz⠀⇛


                       Steinitz, who as strategic affairs and intelligence
                       minister coordinated Israel’s talks with the P5+1
                       (the five permanent UN Security Council members:
                       China, France, Russia, the UK and the US, plus
                       Germany) as they engaged in nuclear negotiations
                       with Iran in 2013-2015, expressed concerns that
                       Tehran advanced its nuclear program significantly
                       farther than ever before in the past year because
                       it no longer felt threatened by the US, and that
                       Washington-backed air defense coordination between
                       Israel and Gulf States is no replacement.


                # ⚓ NBC ☛ Takeaways_from_Day_7_of_the_Jan._6_panel:_Trump_can’t
                  be_‘willfully_blind’_in_defending_assembling_the_mob⠀⇛


                       Twitter suspended Trump’s account two days after
                       the attack on the Capitol. But a surprise witness —
                       an ex-Twitter employee — testified that if Trump
                       were anyone else, he would have been banned much
                       earlier.


                # ⚓ Ghana ☛ 2023:_Nigerians_react_to_Tinubu’s_Muslim-Muslim
                  ticket⠀⇛


                       In a series of tweets, Nigerians are raising
                       concerns about the decision to run on a Muslim-
                       Muslim ticket for the 2023 election.


                # ⚓ The Washington Post ☛ ISIS_planned_chemical_attacks_in
                  Europe,_new_details_on_weapons_program_reveal⠀⇛


                       U.S. officials learned through electronic
                       surveillance in 2014 that Sabawi was working to
                       produce powerful new weapons using highly lethal
                       botulinum toxin and ricin, while also pursuing
                       plans to make weaponized anthrax. Botulinum toxin,
                       a neurotoxin derived from same bacteria that causes
                       botulism, was explored as potential weapon by both
                       the United States and the Soviet Union during the
                       Cold War. Ricin, a toxin extracted from castor
                       beans, was weaponized by the Soviets and used in
                       political assassinations.


                       Sabawi’s intention, current and former U.S.
                       officials said, was to create a large stockpile
                       consisting of multiple types of chemical and
                       biological agents to be used in military campaigns
                       as well as in terrorist attacks against the major
                       cities of Europe.


          o § Environment⠀➾


                # ⚓ Eesti Rahvusringhääling ☛ High_winds_bring_spectacular
                  waterspouts_on_both_sides_of_Finnish_gulf⠀⇛


                       While not unheard of in the region – a single
                       waterspout was spotted off the Finnish coast in
                       2019 – an agglomeration of spouts is highly
                       unusual.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Verge ☛ Twitter_sues_Elon_Musk_for_attempting_to
                  abandon_$44_billion_acquisition⠀⇛


                       The lawsuit paints a picture of Musk going out of
                       his way to make an unexpected and unusually
                       generous offer to Twitter, only to almost
                       immediately turn around and start toying with the
                       company and the idea of abandoning their agreement.
                       After the market turned and tech stocks began
                       sinking, Twitter alleges that Musk looked for an
                       escape from the deal, which required a “material
                       adverse effect” or breach of contract. “Musk had to
                       try to conjure one of those,” the lawsuit states.


                       That’s where Musk’s argument about Twitter having a
                       spam bot problem came in, according to the lawsuit.
                       Despite his concerns, the lawsuit alleges that Musk
                       didn’t ask Twitter about its spam estimates before
                       the agreement was in place. “He even sweetened his
                       offer,” the lawsuit says, by removing a diligence
                       condition from the agreement that would have given
                       him access to non-public information about the
                       company.


                # ⚓ VOA News ☛ Twitter_Sues_to_Force_Musk_to_Complete_His_$44B
                  Acquisition⠀⇛


                       Twitter filed its lawsuit in the Delaware Court of
                       Chancery, which frequently handles business
                       disputes among the many corporations, including
                       Twitter, that are incorporated there.


                       As part of the April deal, Musk and Twitter had
                       agreed to pay each other a $1 billion breakup fee
                       if either was responsible for the deal falling
                       through. The company could have pushed Musk to pay
                       the hefty fee but is going further than that,
                       trying to force him to complete the full $44
                       billion purchase approved by the company’s board.


                # ⚓ Variety ☛ Twitter_Sues_Elon_Musk,_Seeking_to_Force_Him_to
                  Complete_$44_Billion_Takeover⠀⇛


                       As promised, Twitter sued Elon Musk, swinging a
                       legal cudgel at the tech mogul in hopes of making
                       him comply with his original $44 billion offer for
                       the company.


                       The 241-page lawsuit was filed Tuesday in the
                       Delaware Court of Chancery, which specializes in
                       hearing business disputes, including M&A battles,
                       that involve corporations incorporated in Delaware
                       (as Twitter is). In the suit, Twitter outlined “a
                       long list of material contractual breaches by Musk
                       that have cast a pall over Twitter and its
                       business.”


                # ⚓ IT Wire ☛ Twitter_sues_Musk_for_terminating_$64_billion
                  acquisition_deal⠀⇛


                       Twitter co-CEO Bret Taylor has responded on the
                       social media platform and said Twitter will pursue
                       legal action to ensure the deal goes ahead,
                       according to ABC Australia.


                # ⚓ Gatestone Institute ☛ Brussels:_Capital_of_Europe_or
                  Eurabia?⠀⇛


                       “Almost a third of the population of Brussels
                       already is Muslim”, stated Olivier Servais, a
                       sociologist at the University of Louvain.
                       “Practitioners of Islam, due to their high birth
                       rate, should be the majority ‘in fifteen-twenty
                       years’. Since 2001, Mohamed has been the most
                       popular name among babies in Brussels”.


                       Verstraete had told the truth — but, as is said, in
                       the time of universal deception, telling the truth
                       is a revolutionary act.


                # ⚓ RAIR Foundation ☛ Dutch_Intelligence_Investigates
                  Politician_Filip_Dewinter_for_Mentioning_the_‘Great
                  Replacement’⠀⇛


                       During his interview, the author and politician
                       spoke about the drastic demographic changes in
                       Flanders and Europe. He used the word
                       “repopulation,” in which the native population is
                       replaced, and the immigrants’ way of life takes on
                       a leading role. The decision to investigate
                       Dewinter by the Dutch government came at the
                       request of the left-wing parties and politicians
                       controlling Parliament, D66, VVD, PvdA, Green-Left,
                       PvdD, Christian Union, Denk, Volt, and Gundogen
                       List.


                       “With this so-called investigation, the impression
                       is created that I, directly or indirectly, would
                       incite violence and terrorism,” explained Dewinter.
                       “This is not only totally laughable, but it also
                       prevents the NCTV from doing what it was created to
                       do, namely, preventing and combating real terror.
                       According to the Dutch government, legitimate
                       statements from a democratically elected politician
                       are more dangerous than the permanent threat of
                       Islamic terror.”


                # ⚓ Broadband Breakfast ☛ Should_the_Federal_Government
                  Regulate_Artificial_Intelligence?⠀⇛


                       Representatives from academia and a nonprofit
                       diverged at a Bipartisan Policy Center event
                       Tuesday about whether the government should step in
                       and minimize problems associated with artificial
                       intelligence, including bias and discrimination in
                       algorithms.


          o § Censorship/Free Speech⠀➾


                # ⚓ VOA News ☛ Iran_Arrests_Third_Outspoken_Filmmaker_in
                  Escalating_Crackdown⠀⇛


                       Iran has arrested an internationally renowned
                       filmmaker, several newspapers reported Tuesday, the
                       third Iranian director to be locked up in less than
                       a week as the government escalates a crackdown on
                       the country’s celebrated cinema industry.


                       The arrest of award-winning director Jafar Panahi
                       and wider pressure on filmmakers follows a wave of
                       recent arrests as tensions escalate between Iran’s
                       hardline government and the West. Security forces
                       have detained several foreigners and a prominent
                       reformist politician as talks to revive Tehran’s
                       nuclear accord with world powers hit a deadlock and
                       fears grow over the country’s economic crisis.


                # ⚓ NBC ☛ Exile,_silence_or_arrest:_Russian_celebrities_against
                  Ukraine_war_have_no_good_choices⠀⇛


                       They faced the stark choice that many Russians
                       opposing the war have confronted amid an
                       unprecedented crackdown on free speech by President
                       Vladimir Putin’s government. For most Russians who
                       don’t agree with the war, new draconian legislation
                       threatening jail time for any criticism of the
                       armed forces has meant a choice between speaking
                       out and leaving their homeland, or staying put and
                       facing probable arrest and imprisonment.


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


                # ⚓ VOA News ☛ Ten_Years_Without_Answers_for_Family_of
                  Journalist_Austin_Tice⠀⇛


                       In 2012, VOA reporter Sirwan Kajjo met the American
                       freelance journalist Austin Tice, who was planning
                       a reporting trip to Syria. A few months later, Tice
                       went missing at a Syrian checkpoint. His family
                       believes he is alive and in captivity and have
                       spent the past decade advocating for his return.
                       Here, Kajjo reflects on Tice and interviews the
                       journalist’s family about the case.


                       Sitting at a table at a Dupont Circle bar in
                       Washington, Austin Tice was impassioned as he spoke
                       about the war in Syria.


          o § Civil Rights/Policing⠀➾


                # ⚓ CBC ☛ Uber_deliberately_dodged_authorities,_ignored_rules
                  in_early_years,_leaked_documents_show⠀⇛


                       What happened in Montreal was far from an isolated
                       incident, but a tactic Uber used to try to thwart
                       authorities in cities where it was trying to
                       establish its business, according to documents
                       found in the Uber Files, a large new leak of
                       internal records from the gig-economy company.


                       The leaked records show how the company that
                       launched itself as a luxury ride service in San
                       Francisco in 2010 tried to surmount legal and
                       political obstacles through a complex choreography
                       of lobbying, cultivating influential allies,
                       dodging authorities and ignoring the rules when
                       they appeared inconvenient.


                # ⚓ Christian Post ☛ 4_Christians_arrested_under_annulled
                  apostasy_law_in_Sudan;_Bibles_confiscated⠀⇛


                       Police in Darfur Region, Sudan have arrested four
                       Christians under a law against apostasy that was
                       annulled two years ago, according to local sources.


                       Police on June 28 arrested the Christians from the
                       Sudanese Baptist Church in Zalingei, in western
                       Sudan’s Central Darfur state, on charges of
                       apostasy, detaining them until their release on
                       bail on Tuesday, according to local media outlet
                       Sudania 24.


                       The Christian converts from Islam – Bader el Dean
                       Haroon Abdel Jabaar, his brother Mohammad Haroon
                       Abdel Jabaar, Tariq Adam Abdalla and Morthada
                       Ismail – had also been arrested on June 22 and
                       released the same day.


                # ⚓ Medforth ☛ Forced_marriage_in_Germany:_“That’s_the_way
                  things_are_in_Islam”⠀⇛


                       The last nationwide study on forced marriages was
                       commissioned by the Federal Ministry for Family
                       Affairs in 2008. It surveyed counselling centres:
                       3443 people, mainly young women, had asked for help
                       there in the course of a year because of a
                       threatened (60 percent) or already enforced (40
                       percent) forced marriage. “We assume that the
                       number of unreported cases is much, much higher,”
                       says Böhmecke. Especially minors do not dare to
                       seek help in counselling. “There is the extreme
                       relationship of dependence on the parents.”


                # ⚓ HRW ☛ Indonesian_Islamic_College_Bans_Magazine_Reporting
                  Sexual_Abuse⠀⇛


                       One would hope that an educational institution that
                       learned of sexual assaults on campus would focus on
                       holding perpetrators accountable and preventing
                       further incidents rather than targeting the
                       messenger. Not so the State Islamic Institute in
                       Ambon (Institut Agama Islam Negeri Ambon, IAIN
                       Ambon) in Indonesia’s Maluku province, which
                       instead of recognizing and valuing a student
                       magazine’s groundbreaking and thorough
                       investigation, ordered its shutdown.


                       On March 14, when Lintas magazine reported on
                       dozens of incidents of sexual violence on campus
                       taking place between 2015 and 2021, the story
                       unsurprisingly created an uproar. Lintas had spent
                       5 years investigating the story, interviewing 32
                       sexual violence survivors (27 female and 5 male
                       students) as well as campus officials, including
                       Zainal Abidin Rahawarin, the IAIN Ambon rector. The
                       magazine identified 14 alleged perpetrators. Some
                       of the victims, who were not named, detailed sexual
                       assaults that took place during field research
                       trips, on campus, or in lecturers’ offices and
                       houses.


                # ⚓ Christian Post ☛ Christian_woman_strangled,_nearly_beheaded
                  in_ambush_attack_in_Egypt⠀⇛


                       Egyptian media have claimed that the attacker was
                       mentally ill, “but unprovoked attacks against
                       Christians overall are becoming increasingly
                       common, betraying the undercurrent of anti-
                       Christian sentiment that is likely behind this and
                       other violent incidents,” ICC added.


                # ⚓ ICC ☛ Christian_Woman_Assaulted_with_a_Sickle_in_Egypt⠀⇛


                       While the attacker’s motives have not been
                       concretely identified, the Muslim radical likely
                       targeted Mona because of her Christian faith. The
                       day before this attack, he had burglarized the home
                       of another local Coptic Christian. Egyptian media
                       have portrayed the perpetrator as mentally ill, but
                       unprovoked attacks against Christians overall are
                       becoming increasingly common, betraying the
                       undercurrent of anti-Christian sentiment that is
                       likely behind this and other violent incidents.


                # ⚓ Teen Vogue ☛ The_Red_Hill_Leak:_How_the_U.S._Navy_Has
                  Poisoned_Hawai’i’s_Waters_for_Decades⠀⇛


                       The Red Hill Underground Bulk Fuel Storage Facility
                       was built in secret during World War II, 100-feet
                       above O’ahu’s principal drinking water source: the
                       Moanalua-Waimalu aquifer, which has some of the
                       purest, most abundant water. The Red Hill facility
                       was declassified five decades later, and the public
                       subsequently learned that there were 20 underground
                       fuel-storage tanks, each 250-feet high, sitting
                       right above O’ahu’s aquifer, which spans the whole
                       south-central island plain. Currently, the facility
                       stores over 100 million gallons of fuel, including
                       two types of jet fuel — JP-5 and JP-8 — and marine
                       diesel.


                       Here is where the issue stands: As we now know, for
                       the past eight decades, the facility has been
                       leaking fuel into the porous lava rock below it.
                       Due to the complex hydrogeology and location of
                       O’ahu’s groundwater aquifer, the fuel that has
                       infiltrated the porous lava rock can leak at any
                       given time, speed, and direction.


                # ⚓ ABC ☛ Michigan_state_court_agrees_to_limit_use_of_cash_bail
                  in_class_action_suit_settlement⠀⇛


                       “People will not be detained unless, after
                       reviewing evidence presented, a judge determines
                       that releasing a person would create an
                       unmanageable flight risk or danger to the public,”
                       according to the ACLU.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Variety ☛ YouTube_TV_Now_Has_More_Than_5_Million_Users,
                  Topping_Hulu’s_Live_TV_Service⠀⇛


                       Meanwhile, Google nearly decided to call the
                       internet TV service “YouTube Air,” because an early
                       version used an over-the-air TV antenna, according
                       to Christian Oestlien, VP of product management for
                       YouTube TV and Connected TV, who revealed that
                       engineers climbed onto the roof of YouTube’s
                       headquarters while holding an antenna to build the
                       prototype. The pre-launch code name for YouTube TV
                       was “Unplugged” (i.e., users don’t need a cable
                       box).


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Low-Hanging_Fruit⠀⇛


                       A lot of the time, I’ll have something original for
                       y’all on here, but this one I’m sure is on a lot of
                       Swedish people’s minds if they saw the same
                       documentary on peatlands.


                       It sounds weird but a wet peatland sequesters
                       carbon while a dry one releases it.


                       Turns out that 20% of Swedish CO2e emissions are
                       from our diked-out peatlands, and we’ve been
                       promising to fix this since 1971. That’s the same
                       amount as private cars (which we also need to fix).
                       Other countries have similar issues with their own
                       peatlands.


                       They’re asking for 120 000 kkr, and the gov’t has
                       been promising and reneging and promising and
                       reneging this over and over again.


                # ⚓ Parenting,_Loneliness,_and_Why_New_Parents_“Disappear”⠀⇛


                       I have three children and have experienced this
                       over the years. We were pretty young when we had
                       our first child and most of our friends were either
                       single or in relationships that just weren’t in
                       that place yet.


          o § Politics⠀➾


                # ⚓ “Desert”:_on_the_future_of_human_civilisation⠀⇛


                       Over the last few decades, my leftist politics has
                       gradually drifted from strongly statist to strongly
                       anti-statist[a], but a common theme i’ve
                       encountered is a lack of realism regarding the
                       likelihood of certain political outcomes.


                # ⚓ The_quaint_wealth_gaps_of_history⠀⇛


                       I was at National Museum of Fine Arts the other
                       week and one thing that struck me was the wealth
                       gaps on display. Palaces and kings on some
                       paintings, people dying in the streets on others.


                       “How quaint”, I thought, as I was thinking that the
                       ultra-rich of today could buy and sell such palaces
                       as if they were peanuts, and it’s still built on
                       the backs of the worker class.


                       We’re living in the time of the biggest wealth gaps
                       of all time. This has gotten way worse within the
                       last few decades, too.


                       [...]


                       We have the most messed up environment of all time,
                       too. We have a lot of work to do towards saving the
                       Earth.


          o § Technical⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ Automatic_Gemlog_Discovery⠀⇛


                             Discovery in geminispace is hard. I’ve
                             thought a lot about it, running Antenna and
                             all, and blippy and masqq had also have some
                             thoughts…


                             But all hope is not lost! Some sort of
                             automatic discovery is still possible. I
                             should know, because Antenna sort of in a way
                             does it.


                             No, Antenna doesn’t find gemlogs, but
                             whenever a URL is submitted it does verify
                             whether it’s a gemsub feed, an atom feed, a
                             twtxt file, or none of it. Whatever the page
                             it checks all of them, because I’ve noticed
                             that the MIME type isn’t always correct.


                             I believe that’s the way to do it. A search
                             crawler (which must respect robots.txt of
                             course) can check the pages it finds to suss
                             out if they’re feeds or twtxt and add them to
                             an index of gemlogs/micro-blogs if they are.


                             The big problem is all those mini-blogs/mini-
                             gemlogs where the entire thing is in one file
                             with a totally arbitrary format. I tried to
                             build a parser for it, but it’s just not
                             possible because they’re so different.


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



                    ䷩ 𝚕𝚒𝚗𝚎 8724

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/07/2022:_Linux_Mint_21_Beta_and_Red_Hat_Changes_CEO⠀✐


Posted in News_Roundup at 12:21 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o BSD
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o FSF
          o Programming/Development
                # Rust
    * Leftovers
          o Hardware
          o Linux_Foundation
          o Security
    * Gemini*_and_Gopher
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Microsoft_Store_Might_Not_Ban_Commercial_FOSS_Apps
                  –_Invidious⠀⇛


                       Microsoft made a move that get a lot of people
                       angry, recently they updated the TOS for the
                       Microsoft Windows Store with a really controversial
                       that made it look like they were banning free and
                       open source software from making money on the
                       Windows Store.


          o § Graphics Stack⠀➾


                # ⚓ What_is_NGG_and_shader_culling_on_AMD_RDNA_GPUs?_|_Timur’s
                  blog⠀⇛


                       NGG (Next Generation Geometry) is the technology
                       that is responsible for any vertex and geometry
                       processing in AMD RDNA GPUs. I decided to do a
                       write-up about my experience implementing it in
                       RADV, which is the Vulkan driver used by many Linux
                       systems, including the Steam Deck. I will also talk
                       about shader culling on RDNA GPUs.


                # ⚓ xwayland_22.1.3⠀⇛


          o § Applications⠀➾


                # ⚓ OMG Ubuntu ☛ Gotop_is_a_Cool_CLI_System_Monitor_Tool_for
                  Linux_–_OMG!_Ubuntu!⠀⇛


                       I’m a ‘fessed up fan of btop, a colossally cool
                       looking and comprehensive system monitoring utility
                       accessed from the command line.


                       I included it in my list of the best command line
                       tools because I genuinely think it’s one of the
                       best command line tools available. It’s flashy,
                       it’s fast, it’s interactive, you can customise the
                       appearance, disable sections, filter processes
                       speedily, and so on.


                       Thing is this: while all of those bells and
                       whistles are music to my ears they are a bit ‘too
                       much’ for other.


                       So I want(ed an excuse) to highlight another
                       command line system monitor that I dig using. I
                       only discovered it recently — spying on Alan Pope
                       has many advantages 👀 — but the second I saw it, I
                       was smitten. It’s definitely one of those “too cool
                       to not shoehorn into a post” apps.


                       It’s sort of like the midway point between the raw
                       simplicity provided by the likes of top and htop
                       and the visual flair™ put forward by btop++ (or any
                       of its incarnations, e.g., bashtop, bpytop, etc).


                # ⚓ PostgreSQL ☛ PostgreSQL:_Release:_check_pgactivity_2.6⠀⇛


                       check_pgactivity is a PostgreSQL plugin for Nagios.
                       This plugin is written with a focus on a rich
                       perfdata set. Every new features of PostgreSQL can
                       be easily monitored with check_pgactivity.


          o § Instructionals/Technical⠀➾


                # ⚓ Make Use Of ☛ How_to_Extract_Text_From_PDFs_and_Images_on
                  Linux_Using_gImageReader⠀⇛


                       If you’re a student or your work involves working
                       with lots of images and PDFs, you’d have, at some
                       point, felt the need to extract text from an image
                       or a document.


                       Luckily, text extraction makes this possible. And
                       there are several tools that you can use to do
                       this. gImageReader is one of the many tools. It’s
                       free to use and works with both image files and PDF
                       documents.


                # ⚓ Video ☛ How_to_install_Notepadqq_on_Pop!_OS_22.04_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       Notepadqq on Pop!_OS 22.04.


                # ⚓ Linux Made Simple ☛ How_to_install_Sonic_Smash_Flash_V3_on
                  a_Chromebook⠀⇛


                       Today we are looking at how to install Sonic Smash
                       Flash V3 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.


                # ⚓ UNIX Cop ☛ Ansible_Server_Provisioning⠀⇛


                       From bare metal through function-as-a-service,
                       automating with ansible server provisioning of
                       infrastructure is the first step in automating the
                       operation of your applications. Ansible can
                       provision from cloud platforms and virtualized
                       hosts to hypervisors, network devices, and bare-
                       metal servers.


                # ⚓ UNIX Cop ☛ Getting_Started_with_OpenBSD_httpd⠀⇛


                       In this article, I’m going to go through the basics
                       of configuring the httpdweb server which comes by
                       default in the recent versions of OpenBSD (7.1, in
                       this case). OpenBSD is well-known in the industry
                       for being a great operating system when it comes to
                       simplicity, code quality, and security. They’re
                       also well-known for creating tons of good software,
                       all free and open-source; among which some even
                       come pre-installed on other operating systems. With
                       the release of OpenBSD 5.6, they’ve started to
                       include their own web server simply named httpd.


                       httpd is a web-server built to provide the most
                       common web functions. OpenBSD is a great choice for
                       hosting static web sites while also fulfilling
                       basic website needs like handling PHP scripts, load
                       balancing, etc. Furthermore, all of the software in
                       its web stack will be built with the better, more
                       secure LibreSSL library. Please have a look at the
                       talk by Bob Beck on LibreSSL (Invidious / YouTube )
                       to learn why that project exists and why you should
                       care about it. This much should give me enough
                       reason to use httpd on its native operating system
                       – OpenBSD.


                # ⚓ UNIX Cop ☛ How_to_install_WhatsApp_on_Debian_/_Ubuntu?⠀⇛


                       Hello, friends. WhatsApp is one of the most popular
                       mobile messaging applications in the world. It is
                       incredible how many people use it, and we can also
                       install it on Linux, but with an unofficial client.
                       So, in this post, you will learn how to install
                       WhatsApp on Debian / Ubuntu.


                # ⚓ UNIX Cop ☛ How_to_install_FluxBB_on_Ubuntu_&_Debian
                  Servers⠀⇛


                       This post is about How to install FluxBB on Ubuntu
                       & Debian Servers


                       FluxBB is a free, open-source CMS based on phpBB.
                       It is a flat-forum bulletin board based on PHP.
                       It allows individuals and companies to instantly
                       setup a bulletin board for users or customers or
                       according to their needs for interactions or
                       sharing information. FluxBB is highly customizable
                       and fully scalable which comes with code
                       integrations and many modifications which adds
                       flexibility to whole forum. It comes with
                       customizations which were originally developed for
                       phpBB XS Projects which are not included in the
                       phpBB Platform


                # ⚓ UNIX Cop ☛ Using_Nginx_As_A_Load_Balancer⠀⇛


                       The following is a tutorial for setting up Nginx to
                       act as a load balancer between our servers. This is
                       also the final part of my Nginx series. Throughout
                       this series, I’ve mentioned that Nginx is really
                       just a reverse proxy.


                # ⚓ Linux Shell Tips ☛ How_to_Install_AWS_CLI_on_Linux
                  Systems⠀⇛


                       AWS (Amazon Web Services) is becoming a popular and
                       growing trend in the Linux community. It is the
                       perfect cloud infrastructure for any Linux user
                       that wants to scale the productivity potential of
                       their acquired Linux administration skills.


                       Whether you are looking for technological solutions
                       related to Analytics & Data Lakes, Machine
                       Learning, Serverless Computing, Storage, or Linux-
                       centered products related to Analytics, Databases,
                       Containers, and Front-End Web & Mobile, AWS has
                       enough piece of the pie for all users.


                # ⚓ LinuxBuz ☛ How_to_Push_and_Pull_Images_To_Docker_Hub⠀⇛


                       The Docker pull command is used for downloading
                       Docker images from the Docker Hub or private
                       registry. By default, it will download the images
                       from the Docker Hub. You will need to specify the
                       name of the private registry if you want to pull
                       from it.


                       The Docker push command is used to upload or share
                       images to the Docker Hub registry. Before pushing
                       an image to the Docker Hub. You will need to create
                       an account on Docker Hub.


                       In this tutorial, we will show you how to use
                       Docker pull and Docker push commands to upload and
                       download Docker Images to Docker Hub.


                       If you want to host Docker on Cloud and don’t know
                       how to choose the best Cloud hosting provider. You
                       can read my guide on The 8 Best Docker Hosting
                       Platforms in 2022.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ TSDgeos’_blog:_KDE_Gear_22.08_branches_created⠀⇛


                             Make sure you commit anything you want to end
                             up in the KDE Gear 22.08


    * § Distributions and Operating Systems⠀➾


          o § BSD⠀➾


                # ⚓ DragonFly BSD Digest ☛ New_committer:_Sergey_Zigachev⠀⇛


                       Welcome Sergey Zigachev, new DragonFly committer
                       who has already committed an amdgpu fix.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ SUSE_is_a_Showcase_Sponsor_at
                  Microsoft_Inspire [Ed: SUSE reminds us it is a slave of the
                  company that's attacking Linux]⠀⇛


          o § Fedora Family / IBM⠀➾


                # ⚓ Red Hat Official ☛ Taking_the_next_step_in_Red_Hat’s
                  journey⠀⇛


                       Editor’s note: Today, we announced that Matt Hicks
                       will assume the role of president and chief
                       executive officer of Red Hat, succeeding Paul
                       Cormier who will serve as chairman of Red Hat, Inc.
                       Paul shared the following email with Red Hatters.


                # ⚓ Red Hat Official ☛ Ready_to_earn_our_success⠀⇛


                       Editor’s note: Today, we announced that Matt Hicks
                       will assume the role of president and chief
                       executive officer of Red Hat, succeeding Paul
                       Cormier who will serve as chairman of Red Hat, Inc.
                       Matt shared the following email with Red Hatters.


                       [...]


                       As I’ve prepared to step into the CEO role, I’ve
                       spent a lot of time reflecting on what makes Red
                       Hat unique. There are three values that I want to
                       see us embrace, or in some cases recommit to, as
                       Red Hatters.


                # ⚓ ZDNet ☛ Red_Hat_names_new_CEO_|_ZDNet⠀⇛


                       In a move many will find surprising, Red Hat
                       announced that Paul Cormier, the company’s CEO and
                       president since 2020, is stepping over to become
                       chairman of the board. Matt Hicks, a Red Hat
                       veteran and the company’s head of products and
                       technologies, will replace Cormier as president and
                       CEO.


                # ⚓ Exploring_Security_Applications_for_IBM_i_OLAP⠀⇛


                # ⚓ Give_Me_A_Fulcrum_And_A_Lever_Long_Enough,_And_I_Can_Move
                  Your_Data⠀⇛


                # ⚓ More_IBM_i_Security_Flaws_Revealed⠀⇛


                # ⚓ Four_Hundred_Monitor,_July_13⠀⇛


                # ⚓ IBM_i_PTF_Guide,_Volume_24,_Number_28⠀⇛


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ Lubuntu_Devs_Announce_the_Lubuntu_Backports_PPA
                  with_Latest_LXQt_Desktop_Releases_–_9to5Linux⠀⇛


                       Lubuntu developer Simon Quigley exclusively informs
                       9to5linux.com today about the launch of the Lubuntu
                       Backports PPA to provide Lubuntu users with the
                       latest and greatest LXQt desktop environment
                       releases.


                       Inspired by Kubuntu’s Backports PPA, the Lubuntu
                       Backports PPA repository was created due to the
                       request of many Lubuntu users to make it a lot
                       easier to enjoy the most recent LXQt desktop
                       environment on top of the latest stable Lubuntu
                       release.


                # ⚓ Beta News ☛ Download_Linux_Mint_21_‘Vanessa’_Beta_now⠀⇛


                       Back in April, we learned that Linux Mint 21 would
                       be named “Vanessa.” Not much was revealed about the
                       operating system at the time, but the developers
                       did share a small bit of information. For instance,
                       we now know that version 21 of Linux Mint will be
                       based on Ubuntu 22.04, and as expected, the same
                       three desktop environments will once again be
                       offered — Cinnamon, MATE, and Xfce.


                       Earlier this month, we also learned that the
                       controversial systemd-oom will thankfully not be
                       included in Linux Mint 21, while the Blueman
                       Bluetooth manager will replace Blueberry. And now,
                       the developers have shared something much more
                       exciting than tidbits of information — actual ISO
                       files! Yes, the Beta of Linux Mint 21 “Vanessa” is
                       now available to download.


                # ⚓ Linux_Mint_21_Beta_(Cinnamon)⠀⇛


                # ⚓ Linux_Mint_21_Beta_(MATE)⠀⇛


                # ⚓ Linux_Mint_21_Beta_(Xfce)⠀⇛


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_small_device_helps_test_thousands_of_old_PS/
                  2_keyboards_|_Arduino_Blog⠀⇛


                       Some vintage computer keyboards, especially units
                       like the IBM Model M, are still quite desirable.
                       Usually they’re popular among mechanical keyboard
                       or retro computing enthusiasts who want period-
                       correct hardware. YouTuber Midwest Cyberpunk had
                       thousands of these old keyboards and needed a way
                       to test them. So he built this small Arduino-based
                       device that displays the text input from PS/
                       2 keyboards.


                       IBM developed the PS/2 port standard in the ’80s
                       for the IBM Personal System/2 series of computers.
                       By the ’90s, it was the standard for connecting
                       keyboards and mice to PCs. USB made the PS/2 port
                       almost obsolete in the ‘00s, which means that there
                       aren’t many modern computers that still have PS/
                       2 ports. Midwest Cyberkpunk could have used a
                       vintage computer for testing his keyboards, but
                       wanted a more portable option. This PS/2 Keyboard
                       Tester device is easy to carry and provides instant
                       results.


                # ⚓ Tom’s Hardware ☛ Best_Raspberry_Pi_Accessories_of_2022_|
                  Tom’s_Hardware⠀⇛


                       Raspberry Pis are still in short supply, but you
                       can still purchase a Raspberry Pi for as little as
                       $5 (for the Raspberry Pi Zero) or more likely from
                       $35 (for the Raspberry Pi 4 1GB), but you’ll need a
                       few extra products to make it run. There’s a whole
                       world of accessories that help you make the most of
                       the Raspberry Pi’s GPIO. These accessories have
                       been around since the Raspberry Pi was released,
                       when it had just 26 GPIO pins. Using special addon
                       boards we can take advantage of the more modern
                       Raspberry Pi’s 40 pin GPIO to control and interact
                       with electronic components and create diverse
                       projects such as robotics, machine learning and IoT
                       and even our own home server.


                # ⚓ Tom’s Hardware ☛ Best_Amazon_Prime_Day_Raspberry_Pi_Deals
                  2022⠀⇛


                # ⚓ Tom’s Hardware ☛ Intel-Based_Raspberry_Pi_Alternative_UP
                  4000_Available_For_Pre_Order [Ed: 3-5 times more expensive
                  than Raspberry Pi and a lot less efficient, full of security
                  holes]⠀⇛


                       The Raspberry Pi is rather hard to get a hold of
                       right now (we have a few tips on where to buy a
                       Raspberry Pi and a list of best Raspberry Pi deals
                       if you have your heart set on one) but you can
                       still find alternatives on the market for example
                       the Khadas VIM 4.


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


          o § FSF⠀➾


                # ⚓ FSF ☛ FSD_meeting_recap_2022-07-08_—_Free_Software
                  Foundation_—_Working_together_for_free_software⠀⇛


                       Check out the great work our volunteers
                       accomplished at today’s Free Software Directory
                       (FSD) IRC meeting.


                       Every week, free software activists from around the
                       world come together in #fsf on Libera.Chat to help
                       improve the FSD. This recaps the work we
                       accomplished at the Friday, July 8, 2022 meeting.


          o § Programming/Development⠀➾


                # ⚓ Rlang ☛ Combine_project_management_and_data_analysis_using
                  Tiddlywiki_and_RMarkdown_|_R-bloggers⠀⇛


                       I have been looking for a simple and flexible tool
                       to manage projects, take notes, and track results
                       of data analysis with R, e.g. EverNote, OneNote,
                       Trac, JIRA, github, RMarkdown, bookdown, etc.
                       Recently, Tiddlywiki and Projectify pops up from
                       random goggling. Tiddlywiki is a non-linear
                       notebook for storing information. I found it is
                       very useful and simple to manage my research
                       projects and take notes of data analysis as a data
                       scientist and digital agronomist.


                # ⚓ Daniel Stenberg ☛ predef_is_our_friend_|_daniel.haxx.se⠀⇛


                       For C programmers like me, who want to write
                       portable programs that can get built and run on the
                       widest possible array of machines and platforms, we
                       often need to write conditional code. Code that use
                       #ifdefs for particular conditions.


                       Such ifdefs expressions often need to check for a
                       particular compiler, an operating system or perhaps
                       even a specific version of of one those things.


                       Back in April 2002, Bjørn Reese created the predef
                       project and started collecting this information on
                       a page on Sourceforge. I found it a super useful
                       idea and I have tried to contribute what I have
                       learned through the years to the effort.


                # ⚓ I Programmer ☛ Scratch_Can_Even_Do_Linux_Kernel⠀⇛


                       Is writing a Kernel module in Scratch, the block-
                       based programming language used primarily by kids,
                       possible? Absurd it may be, but yes, it is
                       absolutely possible!


                       Scratch is the original block-based programming
                       language and still the best known and most widely
                       used. It was invented in 2003 at MIT to make kids’
                       introduction to coding a much smoother experience.
                       That said, the educational value of block versus
                       regular text based languages is highly debated with
                       strong arguments on either side.


                       I encountered the case made for using text-based
                       languages opinion when reviewing CodeGuppy, a
                       platform that teaches kids (and teens and “creative
                       adults”) to code by writing Javascript.


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ The_Rust_Programming_Language_Blog:
                        Announcing_Rustup_1.25.1⠀⇛


                             The rustup working group is announcing the
                             release of rustup version 1.25.1. Rustup is
                             the recommended tool to install Rust, a
                             programming language that is empowering
                             everyone to build reliable and efficient
                             software.


    * § Leftovers⠀➾


          o § Hardware⠀➾


                # ⚓ IT Wire ☛ iTWire_–_Supply,_logistics_blamed_as_global_PC
                  shipments_down_again_in_2Q⠀⇛


                       Global shipments of traditional PCs fell 15.3% in
                       the second quarter of 2022 to 71.3 million units,
                       the technology analyst firm IDC says, adding that
                       the year-on-year drop was the second consecutive
                       decrease after two years of increases.


                       In a statement, IDC said the fall was worse than
                       expected, and blamed deterioration in both supply
                       and logistics due to the continued lockdowns in
                       China and macro-economic headwinds.


                       The company said traditional PCs included desktops,
                       notebooks, and workstations, but not tablets or x86
                       Servers.


          o § Linux Foundation⠀➾


                # ⚓ Linux Foundation’s Site/Blog ☛ Enabling_Open_Source
                  Projects_with_Impactful_Engineering_Experience_–_Linux
                  Foundation⠀⇛


                       I often talk about “engineering experience” and the
                       importance for open source projects to provide
                       fast, easy and impactful ways for open source
                       consumers to realise return on engagement. Just
                       like e-commerce stores that invest in user
                       experience to encourage repeat sales, successful
                       open source projects provide a slick installation,
                       well written contextual documentation and a very
                       compelling engagement model that encourages
                       collaboration.


          o § Security⠀➾


                # ⚓ Security Week ☛ ‘Raspberry_Robin’_Windows_Worm_Abuses_QNAP
                  Devices_|_SecurityWeek.Com⠀⇛


                       A recently discovered Windows worm is abusing
                       compromised QNAP network-attached storage (NAS)
                       devices as stagers to spread to new systems,
                       according to Cybereason.


                       Dubbed Raspberry Robin, the malware was initially
                       spotted in September 2021, spreading mainly via
                       removable devices, such as USB drives.


                       In a May 2022 report, Red Canary noted that the
                       malware primarily relies on msiexec.exe – the
                       legitimate executable program of the Windows
                       Installer – to communicate with its infrastructure,
                       using HTTP requests. It also uses Tor exit notes
                       for command and control (C&C).


                # ⚓ CISA ☛ Citrix_Releases_Security_Updates_for_Hypervisor_|
                  CISA⠀⇛


                       Citrix has released security updates to address
                       vulnerabilities in Hypervisor. An attacker could
                       exploit these vulnerabilities to take control of an
                       affected system.


                # ⚓ CISA ☛ SAP_Releases_July_2022_Security_Updates_|_CISA⠀⇛


                       SAP has released security updates to address
                       vulnerabilities affecting multiple products. An
                       attacker could exploit some of these
                       vulnerabilities to take control of an affected
                       system.


                # ⚓ USCERT ☛ Microsoft_Releases_July_2022_Security_Updates⠀⇛


                       An attacker can exploit some of these
                       vulnerabilities to take control of an affected
                       system.


                # ⚓ CISA ☛ Adobe_Releases_Security_Updates_for_Multiple
                  Products_|_CISA⠀⇛


                       Adobe has released security updates to address
                       vulnerabilities in multiple products. An attacker
                       could exploit some of these vulnerabilities to take
                       control of an affected system.


                # ⚓ IT Wire ☛ iTWire_–_Microsoft_patches_84_flaws,_including
                  one_exploited_in_the_wild⠀⇛


                       Microsoft has released patches for 84 flaws,
                       including four rated critical and one that had an
                       unknown status, on its monthly Patch Tuesday. The
                       other patches were all rated as important.


                       Commenting on the vulnerabilities, Satnam Narang,
                       staff research engineer at security firm Tenable,
                       said: “Microsoft patched CVE-2022-22047, an
                       elevation of privilege vulnerability in the Windows
                       Client Server Run-Time Subsystem (CSRSS). The flaw
                       was assigned a CVSSv3 score of 7.8 and is rated
                       important.


                       “According to Microsoft, this vulnerability has
                       been exploited in the wild, though no details were
                       available at the time patches became available.
                       Elevation of privilege flaws are valuable for
                       attackers that have already gained access to a
                       vulnerable system with limited privileges through
                       other means, including social engineering or
                       exploitation of a separate vulnerability. They
                       could potentially gain administrative privileges by
                       running a specially crafted application that
                       exploits this flaw.”


    * § Gemini* and Gopher⠀➾


          o § Technical⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ internet_points⠀⇛


                             I’ve spent the past decade chasing internet
                             points on Reddit, Github, and Twitter. I’ve
                             found that focusing on internet points
                             doesn’t actually yield favorable results. I
                             spent so much time trying to figure out what
                             other people want to see that I’ve lost sight
                             of what I want to see.


                # § Programming⠀➾


                      # ⚓ Miscellany_and_Batch_File_Dialog_Boxes⠀⇛


                             It’s summer and I have a lot of time off. For
                             the last week or so, I’ve


                             been getting up quite early to re-stain the
                             deck and fences. They’re


                             done, which is good, because it’s really
                             starting to warm up. Prior to


                             this week, it was cool and a bit rainy. I
                             like that.


                             Otherwise, I’ve been learning a bit of python
                             and some more bash and


                             batch scripting. I know a bit of Javascript
                             too, and there’s a great


                             deal of similarity among them all. I should
                             probably challenge myself by


                             turning to something really different in the
                             future, but I’m not sure


                             what. I guess that will depend on what I want
                             to do and in what context


                             (Windows for work, Linux at home).


                      # ⚓ When_Words_are_Used_to_Fear-Monger⠀⇛


                             My first impressions are that this post is
                             using a noticeable pattern of language-
                             change, creating parallels between that and
                             technological development, and then using
                             that to fear-monger the use of the word
                             “app”. And surely, it gets the history and
                             usage of the word “app” completely wrong.


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



                    ䷩ 𝚕𝚒𝚗𝚎 9574

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/07/2022:_Microsoft_Patch_Tuesday,_the_Latest_NSA_Back_Doors_Ready_to
Install⠀✐


Posted in News_Roundup at 9:16 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Politics
          o Technical
                # Science
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Apple_Maps⠀⇛


                       Apple Maps is a web mapping service that’s
                       available in over 200 regions around the world
                       offering curated guides.


                       While Apple Maps is free to use, it’s proprietary
                       software and not available for Linux. We recommend
                       the best free and open source alternatives.


          o § Instructionals/Technical⠀➾


                # ⚓ OpenSource.com ☛ How_I_create_music_playlists_on_Linux⠀⇛


                       I recently wrote a C program in Linux to create a
                       smaller random selection of MP3 files from my
                       extensive MP3 library. The program goes through a
                       directory containing my MP3 library, and then
                       creates a directory with a random, smaller
                       selection of songs. I then copy the MP3 files to my
                       smartphone to listen to them on the go.


                       Sweden is a sparsely populated country with many
                       rural areas where you don’t have full cell phone
                       coverage. That’s one reason for having MP3 files on
                       a smartphone. Another reason is that I don’t always
                       have the money for a streaming service, so I like
                       to have my own copies of the songs I enjoy.


                       You can download my application from its Git
                       repository. I wrote it for Linux specifically in
                       part because it’s easy to find well-tested file I/
                       O routines on Linux. Many years ago, I tried
                       writing the same program on Windows using
                       proprietary C libraries, and I got stuck trying to
                       get the file copying routing to work. Linux gives
                       the user easy and direct access to the file system.


                       In the spirit of open source, it didn’t take much
                       searching before I found file I/O code for Linux to
                       inspire me. I also found some code for allocating
                       memory which inspired me. I wrote the code for
                       random number generation.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ OpenSource.com ☛ A_guide_to_productivity_management_in_open
                  source_projects⠀⇛


                       Open source is one of the most important technology
                       trends of our time. It’s the lifeblood of the
                       digital economy and the preeminent way that
                       software-based innovation happens today. In fact,
                       it’s estimated that over 90% of software released
                       today contains open source libraries.


                       There’s no doubt the open source model is effective
                       and impactful. But is there still room for
                       improvement? When comparing the broader software
                       industry’s processes to that of open source
                       communities, one big gap stands out: productivity
                       management.


                       By and large, open source project leads and
                       maintainers have been slow to adopt modern
                       productivity and project management practices and
                       tools commonly embraced by startups and enterprises
                       to drive the efficiency and predictability of
                       software development processes. It’s time we
                       examine how the application of these approaches and
                       capabilities can improve the management of open
                       source projects for the better.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ TecMint ☛ Linux_Lite_–_An_Ubuntu-Based_Distribution_for
                  Linux_Newbies⠀⇛


                       Linux Lite is a free, easy-to-use, and open-source
                       Linux distribution based on the Ubuntu LTS series
                       of releases. By design, it is a lightweight and
                       user-friendly distribution that was developed with
                       Linux beginners in mind especially users migrating
                       from Windows.


                       Linux Lite provides a simple and familiar desktop
                       environment that Windows users will have an easy
                       time using. For instance, the start button is
                       clearly labeled. You also get app shortcuts on the
                       taskbar and an applet section in your bottom-right
                       area where you get volume controls, network, update
                       settings and so much more.


          o § Devices/Embedded⠀➾


                # ⚓ Raspberry Pi ☛ Are_you_technocentric? Shifting_from
                  technology_to_people⠀⇛


                       When we teach children and young people about
                       computing, do we consider how the subject has
                       developed over time, how it relates to our
                       students’ lives, and importantly, what our values
                       are? Professor Pratim Sengupta shared some of the
                       research he and his colleagues have been working on
                       related to these questions in our June 2022
                       research seminar.


                # ⚓ Hackaday ☛ Pi_Pico_Provides_Practical_PlayStation
                  Pointing⠀⇛


                       It’s not immediately clear to us why one would need
                       a mouse for the original PlayStation (though we’re
                       sure there’s no shortage of folks eager to jump
                       down into the comments and tell us), but if you
                       ever desire adding improved pointing capabilities
                       to the nearly three decade old console, this
                       project from [Vojtěch Salajka] is certainly one to
                       keep an eye on.


                # ⚓ Hackaday ☛ Hackable_OSHW_CardClock_Demands_Attention⠀⇛


                       When examining a project, it’s easy to be jaded by
                       a raw parts list. When the main component is an
                       ESP8266, we might say “oh, another 8266 project.
                       yawn!” But we’re certain that when you take a look
                       at [Will Fox]’s Foxie CardClock, it’ll surely grab
                       your attention.


    * § Leftovers⠀➾


          o ⚓ The Nation ☛ We_Are_All_God’s_Poems⠀⇛


                 We all want to be joined in holy metonymy. You are a part
                 of me, we want God to say, that stands for the whole of
                 me. Instead of immanent, just say man. Instead of
                 wishbone, just say wish.


                 Sound out the word, and we are all God’s onomatopoeia.
                 Gaga comes from God mad: Coo, coo at the one you love,
                 madman, across the carousel of the cosmos, these painted
                 horses circling the sun.


          o ⚓ The Nation ☛ A_Gilded_Age⠀⇛


                 The labor of magazine-making has never been less
                 glamorous, less stable, or less profitable. Prestige, as
                 the union organizers at Condé Nast have said, doesn’t pay
                 the bills. With the churn of digital publishing pushing
                 magazines into the financial and cultural doldrums, the
                 luster of the legacy media job has only gotten duller.
                 Yet there is still a magic in print magazines that does
                 not seem to exist in newspapers or book publishing. Be it
                 a weekly, a biweekly, or a monthly, a magazine can give
                 us a snapshot of cultural mores, a printed record of the
                 present, and a forecast of the future. “The more
                 fragmented we become as a culture,” Tina Brown once
                 observed, “the more the media holds us together.”


          o ⚓ Hackaday ☛ It’s_A_Bird!_It’s_A_Plane!_It’s…_A_Live_Air_Traffic
            Plane_Spotting_Simulation⠀⇛


                 Plane spotting has been a hobby of aviation enthusiasts
                 for generations. Hanging out by the airport, watching
                 aircraft come and go, maybe even listening to Air Traffic
                 Control on a scanner from your local Radio Shack. Yep-
                 we’ve been there, and it can be a lot of fun! But how can
                 those of us who don’t live near a major controlled
                 airport keep up on the action? As demonstrated by the
                 [Information Zulu] YouTube channel’s Live Stream, seen
                 below the break, the action may be closer than you think!


          o § Education⠀➾


                # ⚓ TruthOut ☛ The_Right_Wants_to_End_Teacher_Certification.
                  It’s_Already_Starting_to_Happen.⠀⇛


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Build_Your_Own…_Whatever⠀⇛


                       You can read all about making, say, a bookshelf or
                       bowling, but unless you’ve actually done it, you
                       don’t really know how it works. That’s the idea
                       behind [codecrafters-io] Build-Your-Own-X GitHub
                       repository. It is a collection of software projects
                       from around the Web that offer “step-by-step guides
                       for recreating our favorite technologies from
                       scratch.”


                # ⚓ Hackaday ☛ Weed_Eater_String_Made_From_Plastic_Bottles⠀⇛


                       For those who don’t mind constantly adding tiny but
                       measurable amounts of microplastics to their
                       landscaping, string trimmers are an excellent way
                       of maintaining edging around garden beds, trimming
                       weeds, or maintaining ground covers on a steep
                       hill. One problem with them, though, is that not
                       only is the string consumable but it can be
                       expensive. Plus, if you have a trimmer with a
                       proprietary spool you need to hope the company
                       never goes out of business. Or, you can simply
                       refill your string spool with this handy tool.


                # ⚓ Hackaday ☛ A_Handy_Tester_For_A_Mountain_Of_PS/2_Keybords⠀⇛


                       The hacking life is not without its challenges, and
                       chief among these is the tendency to always be in
                       acquisition mode. When we come across a great deal
                       on bulk equipment, or see a chance to rescue some
                       obscure gear from the e-waste stream, we generally
                       pounce on it, regardless of the advisability.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Counter Punch ☛ “Value-Based_Care”_is_a_Pretext_for
                  Privatization⠀⇛


                       They have no evidence to back up their assertions. 
                       But the scheme to move to value-based care and to
                       shove risk onto physicians imposes profit-making
                       managers into the system, shifts the profit
                       incentive from more care to denial of treatment,
                       and expands opportunities for venture capital,
                       private equity, and insurance companies.  This up-
                       coming corporate-sponsored extravaganza will
                       concentrate on promoting value-based care as the
                       bipartisan solution to our failed yet costly health
                       care system that has thrown 100 million into
                       medical debt as the nation suffered 338,000 deaths
                       from Covid that would not have happened had we had
                       a universal health care system.  Life expectancy is
                       plummeting as the profits climb.


                       Mark McClellan, George W. Bush’s head of the Center
                       for Medicare and Medicaid Services (CMS) will speak
                       on the wonders of Medicare Advantage, the
                       privatized part of Medicare that the HHS Inspector
                       General found denies necessary care and delays care
                       through unsupported demands for pre-authorization. 
                       McClellan serves on the board of Alignment Health
                       Care, a direct contracting entity–one of the plans
                       that seniors can be placed in without their consent
                       that can take up to 40% of Medicare money in
                       profits and overhead.  He is also on the Board of
                       Cigna, a company that raked in $143 billion in
                       profit over the 12 months ending March 2022.


                # ⚓ Scheerpost ☛ Newsom_Plans_to_Bring_Affordable_Insulin_to
                  California⠀⇛


                       Office of the Governor of California, Public
                       domain, via Wikimedia Commons By Dean Baker /
                       Center for Economic and Policy Research
                       California’s Governor, Gavin Newsom,
                       announced plans las…


          o § Security⠀➾


                # ⚓ Krebs On Security ☛ Microsoft_Patch_Tuesday,_July_2022
                  Edition⠀⇛


                       Microsoft today released updates to fix at least 86
                       security vulnerabilities in its Windows operating
                       systems and other software, including a weakness in
                       all supported versions of Windows that Microsoft
                       warns is actively being exploited. The software
                       giant also has made a controversial decision to put
                       the brakes on a plan to block macros in Office
                       documents downloaded from the Internet.


                # § Privacy/Surveillance⠀➾


                      # ⚓ EFF ☛ Congress_Probes_How_Location_Data_Brokers
                        Threaten_Reproductive_Privacy⠀⇛


                             Some good news: three members of Congress are
                             investigating this problem, and have sent
                             letters to five location data brokers. The
                             legislators are Rep. Maloney, chair of the
                             House Oversight Committee; Rep.
                             Krishnamoorthi, chair of the Consumer Policy
                             Subcommittee; and Rep. Jacobs, author of the
                             “My Body, My Data” bill. Four of these
                             location data brokers (Babel Street, Digital
                             Envoy, Gravy Analytics, and Safegraph) are
                             discussed in EFF’s recent deep dive on
                             federal government purchases of phone app
                             location data. The fifth broker is Placer.ai.


                             The letters begin by quoting EFF’s Eva
                             Galperin regarding the “unprecedented digital
                             surveillance” faced today by abortion
                             seekers. They also cite EFF’s reporting on
                             how the State of Illinois bought data from
                             Safegraph. Most importantly, the letters ask
                             the location brokers for information,
                             including a list of the phone apps the
                             companies use to gather location data, a list
                             of the business partners from which they
                             obtain this data, and a list of purchasers of
                             location data related to family planning
                             clinics.


                             The three representatives also sent letters
                             to the makers of five period tracking apps.
                             They ask for information about their data
                             collection and dissemination, and express
                             concern about “the potential misuse of this
                             sensitive, private data to invade the privacy
                             of those seeking reproductive health care.”


                      # ⚓ Pro Publica ☛ Pegasus_Spyware_Maker_NSO_Lobbying_to
                        Get_Off_U.S._Blacklist⠀⇛


                             Israeli cybersecurity company NSO Group, the
                             company behind the notorious Pegasus spyware,
                             has been conducting a broad campaign in the
                             United States to get off the U.S.
                             government’s blacklist.


                             Pegasus is a hacking tool that could be used
                             to vacuum up a phone’s contents remotely
                             without the target having to fall into a
                             phishing trap by clicking on a deceptive
                             link. The spyware can even use the phone to
                             remotely track and record its user.


          o § Defence/Aggression⠀➾


                # ⚓ Common Dreams ☛ ‘I’m_Going_to_Kill_You’:_Congresswoman
                  Jayapal_Targeted_in_Alleged_Hate_Crime⠀⇛


                       U.S. Rep. Pramila Jayapal reiterated Tuesday that
                       she and her family are safe after being verbally
                       attacked at their Seattle home by an armed area man
                       who told her to “go back to India” and threatened
                       to kill her.


                       Police arrested a 48-year-old man—who lives about
                       half a mile from the Washington Democrat and
                       Congressional Progressive Caucus chair—on Saturday
                       night at 11:25 pm, according to The Seattle Times.


                # ⚓ Pro Publica ☛ Bayraktar_TB2_Drone_Sales_from_Turkey_Growing
                  Despite_Western_Laws⠀⇛


                       Ethiopian Prime Minister Abiy Ahmed was in a tough
                       spot last August when he paid a visit to Turkey.
                       For nearly a year, his government had been at war
                       with rebels from the Tigray People’s Liberation
                       Front, which was now pushing south from its
                       stronghold near the Eritrean border and threatening
                       to move on the country’s capital of Addis Ababa.
                       Thousands had already been killed, and the United
                       States and the United Nations had accused all the
                       warring parties of blockading aid, committing
                       sexual assault and deliberately targeting
                       civilians.


                       With only a small, aging fleet of Soviet-era
                       military jets, Abiy needed a way to quickly — and
                       cheaply — expand his air campaign against the
                       rebels. Turkey had just the solution: a military
                       drone known as the TB2 that could be piloted from
                       nearly 200 miles away. China and Iran also supplied
                       drones, but the TB2, outfitted with cutting-edge
                       technology, had fast become the new favorite of the
                       world’s embattled nations, helping to win wars even
                       when it was pitted against major powers.


                # ⚓ Site36 ☛ German_interior_minister_cybers_the_Constitution⠀⇛


                       According to a new concept, federal authorities are
                       to be given hacking powers, with the Ukraine war
                       cited as the reason


                # ⚓ Common Dreams ☛ ‘$839_Billion_Military_Budget_Is_a_Policy
                  Failure,’_Say_Critics_as_House_Tees_Up_NDAA⠀⇛


                       With the U.S. House set to vote this week on
                       legislation that proposes a staggering $839 billion
                       in military spending, progressive lawmakers and
                       advocates said Monday that the bill exemplifies the
                       warped priorities of Congress at a time of growing
                       hunger, rising child poverty, an ongoing pandemic,
                       and other pressing crises.


                       “Until they can pass an audit, it’s time to stop
                       handing the Pentagon a blank check.”


                # ⚓ Common Dreams ☛ Opinion_|_The_Global_NATO_Alliance,_the
                  European_Left,_and_the_Crack_in_Everything⠀⇛


                       It is no secret that the United States and NATO are
                       engaged in a proxy war with Russia, perhaps to be
                       fought to the last Ukrainian. In June, as heads of
                       state gathered in Madrid for the Alliance’s annual
                       summit, I joined more than 10,000 activists from
                       across Spain and around the world for mega anti-
                       NATO peace conferences and a massive No to NATO
                       rally. Their focus was not only NATO’s roles in the
                       Ukraine War but also its transformation into the
                       world’s dominant GLOBAL alliance whose new
                       strategic concept also prioritizes containing
                       China. Highlighting this transformation, the Prime
                       Ministers of Australia, Japan, New Zealand, and the
                       Republic of Korea joined the summit for the first
                       time in the Alliance’s history.


                # ⚓ Common Dreams ☛ John_Bolton_Admits_on_Live_TV_He_‘Has
                  Helped_Plan_Coups_D’État’⠀⇛


                       Longtime Republican official John Bolton admitted
                       during a televised interview Tuesday that he has
                       helped plan coups outside of the United States.


                       Bolton, who served as former President Donald
                       Trump’s national security adviser, appeared on CNN
                       to discuss the congressional committee
                       investigating the January 6, 2021 attack on the
                       U.S. Capitol.


                # ⚓ Common Dreams ☛ Jan._6_Committee_Lays_Bare_How_Trump’s
                  Tweets_Fomented_Deadly_Insurrection⠀⇛


                       The congressional committee investigating the
                       January 6, 2021 attack on U.S. Capitol on Tuesday
                       detailed how former President Donald Trump used
                       Twitter to incite his violent followers ahead of
                       the deadly incursion—and how the social media giant
                       helped foment the insurrection.


                       “Trump’s intimate ties to far-right extremist
                       groups were a cornerstone of his presidency.”


                # ⚓ The Nation ☛ Trump_Was_the_“Central_Figure”_Who_Set_the
                  Coup_in_Motion⠀⇛


                       The January 6 hearings began with an assertion by
                       committee chair Bennie Thompson (D-Miss.) that
                       Donald Trump was at the center of a conspiracy to
                       implement a coup. The seventh hearing of the US
                       House Select Committee to Investigate the January
                       6th Attack on the United States Capitol, on
                       Tuesday, has been organized with an eye toward
                       confirming that assertion with devastating clarity.
                       In particular, it will provide details about the
                       former president’s participation in a December 18,
                       2020, White House meeting with what committee
                       member Jamie Raskin has described as a “group of
                       lawyers, of outside lawyers who have been
                       denominated ‘Team Crazy’ by people in and around
                       the White House.” At the meeting, which involved
                       Sydney Powell, Rudy Giuliani, and Michael Flynn,
                       among others, Trump’s most extreme associates
                       plotted to overturn the will of the people. They
                       discussed moves that are often associated with
                       coups, such as the seizure of voting machines from
                       states where Trump lost to Democrat Joe Biden.


                # ⚓ Common Dreams ☛ Jan._6_Panel_Refers_Trump_to_DOJ_for
                  Suspected_Witness_Tampering⠀⇛


                       Rep. Liz Cheney made a stunning revelation at the
                       conclusion of Tuesday’s House January 6 committee
                       hearing, informing the public that former President
                       Donald Trump called an unnamed witness in the
                       panel’s investigation following the June 28 hearing
                       and that the U.S. Department of Justice has been
                       made aware of Trump’s apparent intimidation tactic.


                       The yet-to-be-seen witness “declined to answer or
                       respond to President Trump’s call, and instead
                       alerted their lawyer,” said Cheney (R-Wyo.), vice-
                       chair of the House committee investigating the
                       January 6, 2021 attack on the U.S. Capitol.


                # ⚓ Scheerpost ☛ Biden_Falsely_Claims_US_Troops_Aren’t_Engaged
                  in_Combat_in_the_Middle_East⠀⇛


                       The president made the claim in an op-ed on his
                       upcoming trip to the region.


                # ⚓ Scheerpost ☛ Outrage_as_Biden_Reportedly_Considers_Lifting
                  Ban_on_‘Offensive’_Arms_Sales_to_Saudi_Arabia⠀⇛


                       “Saudi Arabia and the UAE are fabulously wealthy
                       oil states and do not need any aid,” noted one
                       progressive. “U.S. weapons transfers are intended
                       to throw our money to American ar…


                # ⚓ Common Dreams ☛ Opinion_|_Can_President_Biden_Make_Lemonade
                  out_of_Lemons_on_his_Middle_East_Jaunt?⠀⇛


                       Ah, lemonade! As we endure the summer swelter, is
                       there a more refreshing beverage? Making lemonade
                       out of lemons is a worthy and timely endeavor,
                       whether actually or metaphorically. 


                # ⚓ Counter Punch ☛ Biden’s_Janitorial_Venture_in_Israel_and
                  Saudi_Arabia⠀⇛


                       Dressed in blue or tan uniforms and pushing
                       janitorial cleaning carts, these hard-working men
                       and women (in Europe women clean men’s restrooms)
                       go about cleaning urinals, toilets, mirrors, and
                       restroom walls, doors, and floors. The trademark
                       blue plastic gloves and disposable paper caps are a
                       sharp contrast to the facial expressions of these
                       resolute folks who, in addition to wiping and
                       cleaning human grime, have to mop floors and fish
                       out cigarette butts, gumballs, and a variety of
                       face masks from urinals and floors. And the latter
                       is a sign of  COVID-times.


                       With stoic, almost robotic and often resigned
                       facial expressions, these men and women perform
                       their menial tasks to help put food on their
                       tables, pay medical bills, and pay rent and
                       utilities.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ EFF ☛ Victory!_Another_Court_Protects_the_Right_to_Record
                  Police⠀⇛


                       The case is Irizarry v. Yehia. Mr. Irizarry is a
                       journalist who records on-duty police. In 2019,
                       while he was recording a traffic stop, Officer
                       Yehia arrived, stood in front of Mr. Irizarry’s
                       camera, and shined a flashlight into the camera.
                       The Tenth Circuit ruled that “Mr. Irizarry was
                       engaged in protected First Amendment activity when
                       he filmed the traffic stop,” and that he “suffered
                       an injury when Officer Yehia stood in front of his
                       camera and shined a flashlight into it …”


                       We agree. Police violate the First Amendment when
                       they interfere with people who are recording them.
                       As we explained in our amicus brief filed in the
                       case: 


                       On-duty officers have also attempted to interfere
                       with publication of recordings, by loudly playing
                       popular music. Some online platforms use automated
                       filters to block content that contains copyrighted
                       materials. The officers hope these filters will
                       block publication of recordings of their on-duty
                       activity.


                # ⚓ Techdirt ☛ FBI’s_Crime_Data_Collection_Still_Being_Stymied
                  By_Major_Police_Departments_Not_Reporting_Crime_Stats⠀⇛


                       The FBI has switched to a new crime reporting
                       system to collect crime data from all over the
                       nation. Despite being given a long runway (the 2021
                       switch was announced in 2015), the FBI is still
                       seeing an incredible lack of contribution.


                # ⚓ Scheerpost ☛ Craig_Murray:_The_Film_About_Julian_Assange⠀⇛


                       Ithaka is a heart-rending film that offers an
                       important rebuttal to more than a decade of
                       propaganda aimed at dehumanizing the WikiLeaks
                       publisher.


                # ⚓ Scheerpost ☛ Whistleblower_Relief:_Dropping_the_Collaery
                  Case⠀⇛


                       The Anglo-Australian legal system has much to
                       answer for.


          o § Environment⠀➾


                # ⚓ Counter Punch ☛ Indigenous-Led_Organization_Opens_New_Salvo
                  in_Fight_for_Climate_Justice⠀⇛


                       “We often envision climate injustices first before
                       we talk about climate justice,” says Frederick.
                       “It’s because we see a lot of injustice in terms of
                       what has created climate change and continues to
                       exacerbate it, [along with those] in the front-line
                       communities that are most impacted, who happen to
                       be our people,” says Frederick.


                       The concept of climate justice conforms to the
                       belief that global warming and climate change are
                       social, economic and political issues as much as
                       they are environmental or scientific dilemmas. For
                       organizers like Frederick and her colleague, Jade
                       Begay, climate justice campaign director for NDN
                       Collective, climate justice is more than just an
                       acknowledgment that climate change is man-made and
                       rooted in socioeconomic issues, it stands for a
                       better future where the economy thrives while
                       ethical considerations are made for the environment
                       and all people—rich and poor, white or BIPOC
                       (Black, Indigenous, and people of color).


                # ⚓ TruthOut ☛ With_Stunning_Irony,_Environmental_Review_Is
                  Being_Used_to_Block_Climate_Action⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Climate_Insanity:_The_Biden
                  Administration_Wants_to_Drill_on_Alaska’s_North_Slope⠀⇛


                       The bitter end of the fossil fuel era is playing
                       out in one of the world’s wildest remaining places:
                       Alaska’s North Slope. And it’s not pretty.


                # ⚓ Counter Punch ☛ How_Climate_Change_is_Making_Flooding
                  Worse⠀⇛


                       In mid-June 2022, storms dumped up to 5 inches of
                       rain over three days in the mountains in and around
                       Yellowstone National Park, rapidly melting
                       snowpack. As the rain and meltwater poured into
                       creeks and then rivers, it became a flood that
                       damaged roads, cabins and utilities and forced more
                       than 10,000 people to evacuate.


                       The Yellowstone River shattered its previous record
                       and reached its highest water levels recorded since
                       monitoring began almost 100 years ago.


                # ⚓ Common Dreams ☛ Groups_Demand_Egypt_Uphold_Right_to_Protest
                  at_Global_Climate_Summit⠀⇛


                       Three dozen global human rights groups on Tuesday
                       called on Egyptian authorities to respect
                       international law by allowing peaceful protests at
                       the upcoming United Nations Climate Change
                       Conference—and not limiting dissenters to a
                       specific space where their impact will be weakened,
                       as officials have suggested they will.


                       “The Egyptian authorities should unconditionally
                       allow peaceful protests and gatherings around the
                       time of COP27, including in Cairo, the Egyptian
                       capital, and other cities.”


                # ⚓ The Nation ☛ Dear_Harvard,_It’s_Time_to_Reject_Fossil_Fuel
                  Money⠀⇛


                       In June, Harvard announced that it would establish
                       the Salata Institute for Climate and
                       Sustainability. The institute aims to connect and
                       bolster climate-change initiatives across the
                       university, in large part by supporting related
                       research. With this institute’s creation comes a
                       new and crucial opportunity for Harvard to
                       demonstrate climate leadership. Amid today’s
                       unprecedented climate emergency and a global energy
                       crisis, Harvard can lead the way in protecting the
                       integrity of the research we urgently need to usher
                       in a just, renewable energy economy and ensure the
                       academic freedom of researchers by implementing a
                       ban on fossil fuel industry funding for climate
                       research. Doing so would provide a vital safeguard
                       for our planet, communities, and futures.


                # § Energy⠀➾


                      # ⚓ Hackaday ☛ Airbus_A380_Completes_Flight_Powered_By
                        Cooking_Oil⠀⇛


                             Fossil fuels are making news for all the
                             wrong reasons of late. Whether it’s their
                             contribution to global climate change or the
                             fact that the price and supply hinges on
                             violent geopolitics, there are more reasons
                             than ever to shift to cleaner energy sources.


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ Federal_Logging_Projects_Put_10
                        Climate-Saving_Forests_on_Chopping_Block⠀⇛


                             Federal agencies are targeting mature and
                             old-growth forests for logging despite these
                             trees’ extraordinary ability to curb climate
                             change and President Biden’s directive to
                             preserve them, according to a new report
                             spotlighting the 10 worst logging projects in
                             federal forests across the country.


                             In the report released today, Worth More
                             Standing, the Climate Forests coalition
                             details federal logging proposals targeting
                             nearly a quarter of a million acres of old-
                             growth and mature forests overseen by the
                             U.S. Forest Service and Bureau of Land
                             Management. The report outlines “a pervasive
                             pattern of federal forest mismanagement that
                             routinely sidesteps science to turn carbon-
                             storing giants into lumber” and calls on the
                             Biden administration to pass a permanent rule
                             to protect these big old trees.


          o § Finance⠀➾


                # ⚓ Telex (Hungary) ☛ Major_tax_change_bill_pushed_through
                  parliament_in_spite_of_protests⠀⇛


                       It was proposed on Monday, debated on Tuesday, and
                       after a few hours of debate, the new law about the
                       taxation of small businesses was passed by 120
                       votes in favour, 57 against and 1 abstention. While
                       the debate was going on in parliament, spontaneous
                       demonstrations were held in several parts of
                       Budapest, with demonstrators blocking Margaret
                       Bridge and part of Elisabeth Bridge.


                # ⚓ Counter Punch ☛ An_American’s_Visit_to_Another_Planet:
                  Iceland⠀⇛


                       Like most Americans, I don’t get out much. Cost,
                       excessive work hours–all the reasons that keep one
                       close to home are part of my world. A plan that
                       started in 2019 allowed us to take a quick trip to
                       Iceland that only materialized this summer. I was
                       prepared for something radically different; I read
                       about other nations (unlike most Americans), but
                       the reality of seeing how other parts of the world
                       live has made the return home all the more
                       heartbreaking. To say we are off the rails in the
                       United States implies there are rails to go off of
                       (and we of course don’t want to pay for the
                       infrastructure of any high speed rails in the US).


                       Where to start–well, for one thing the entire time
                       we were there we did not see one homeless person.
                       I’m not saying that in a Karen-esque–oh, thank
                       heavens we didn’t have to view them. No, it’s a
                       clear indication that they are a nation with an
                       adequately functioning safety net, the likes of
                       which we have given up on in the US. I’m 52 years
                       old and (here we go….old person rant)–the increase
                       in people being forced to live on the streets due
                       to stagnant and unlivable wages, soaring real
                       estate costs, mental health and substance abuse
                       (because what the hell do you think will happen to
                       people in a nation not caring for them?)….the
                       difference in just my lifetime is staggering. It’s
                       become a given that lots of people are living in
                       the most dire circumstances. What a staggering
                       difference. It’s a clear indication of a lack of
                       soul in a nation. If you can’t care for your own or
                       consider so many to be disposable, what are you as
                       a people? It’s a question the right wing doesn’t
                       want to consider because they are too anxious to
                       impose a 100% fascist reality–that’s their desire
                       for the soul of the nation and the liberal left
                       will just frown about the sadness of it all, but
                       not really consider the implication that this is a
                       failed state.


                # ⚓ Common Dreams ☛ Opinion_|_Imperial_Detritus:_Henry_Luce’s
                  Dream_Comes_Undone⠀⇛


                       “The American Century Is Over.” So claims the July
                       2022 cover of Harper’s Magazine, adding an all-too-
                       pertinent question: “What’s Next?”


                # ⚓ Counter Punch ☛ 21st-Century_Comstockery:_Does_History
                  Repeat_Itself?⠀⇛


                       Today, the U.S. is witnessing a third repeat of a
                       long-fought morality war, this one being played out
                       not only at the Supreme Court but in local and
                       state legislations throughout the country. It
                       involves abortion and gun ownership as well as a
                       host of other “culture war” issues, including
                       immigration, racial equality, voting rights, gay/
                       trans rights, “critical race theory” and censorship
                       at schools and libraries.


                       Today’s struggle may be considered the third battle
                       over moral values during America’s “modern” and
                       “postmodern” eras – this one marked by vengeance.
                       The second battle took place during the post-WW-II
                       period and involved struggles over dissent (i.e.,
                       “communism”) and immorality, including pornography,
                       comic books (dubbed “Marijuana of the nursery”) and
                       illicit sexuality, including prostitution,
                       homosexuality and s&m/leather fetishes. Often
                       forgotten, the nation’s first modern morality war
                       took place in the post-Civil War era and culminated
                       with the passage of the Comstock Act in 1873.


                # ⚓ Counter Punch ☛ Out_of_It_on_the_Outdoors⠀⇛


                       The excise tax has been in place for over a
                       century. In 1937, the Pittmann-Robertson Act
                       directed that revenue back to the states for
                       habitat conservation, wildlife management, hunter
                       and safety education, and more. Combined with a
                       similar tax on fishing and boating equipment known
                       as Dingell-Johnson, these tiny taxes fund a huge
                       portion of Montana’s Department of Fish, Wildlife
                       and Parks’ annual budget and have long been
                       considered a vital and secure source of revenue for
                       the agency.


                       It’s highly doubtful that a single Montana hunter
                       or angler contacted Rosendale’s office to demand he
                       remove the tax since the money comes back in
                       improvements to our much-loved traditional
                       pursuits. In fact, it’s far more likely he’ll be
                       hearing from most Montanans who hunt and fish to
                       ask why he’s backing legislation that provides a
                       dubious “solution” in search of a non-existent
                       problem — and puts a long-standing, tremendously
                       successful program to maintain and improve the
                       nation’s fish and wildlife at tremendous risk.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ TruthOut ☛ Boris_Johnson_Spends_Last_Days_in_Office_Laying
                  Minefield_for_His_Successor⠀⇛


                # ⚓ Counter Punch ☛ Ecuador’s_unpopular_neoliberal_government
                  survives_for_now:_An_interview_with_David_Villamar⠀⇛


                       From 2007-17 Ecuador was governed by the leftist
                       government of Rafael Correa. In 2017 Lenin Moreno
                       won the presidency by campaigning as a Correa
                       loyalist but, once in office, immediately turned
                       into the exact opposite. For the past five years
                       Correaists have been brutally persecuted. Correa
                       himself has been given political asylum in Belgium.
                       Despite repression and dirty tricks by the
                       electoral authorities, Andres Arauz, the Correaiist
                       candidate in 2021, came fairly close to winning the
                       presidency. Correists also ended up being the
                       largest block in the National Assembly, though they
                       are not a majority.


                       In 2019, the indigenous federation, CONAIE, led
                       protests against Moreno’s government after having
                       collaborated with him during his initial years, and
                       applauding Moreno’s persecution of Correaists. Last
                       month, massive CONAIE-led protests broke out
                       against Lasso’s government which has only been in
                       office for a year. Eighteen days of protests led
                       Lasso to backtrack on some of his neoliberal
                       policies though the danger he will renege on his
                       agreement with CONAIE is very real.


                # ⚓ Common Dreams ☛ ‘People-Powered’:_John_Fetterman_Raises_$11
                  Million_in_Second_Quarter⠀⇛


                       Pennsylvania Lt. Gov. John Fetterman, the
                       Democratic nominee for the key battleground state’s
                       open U.S. Senate seat, raised $11 million in the
                       second quarter of 2022, his campaign announced
                       Tuesday.


                       Fetterman’s best-ever quarterly fundraising haul
                       smashed Pennsylvania’s previous record for money
                       raised by a Senate candidate over a three-month
                       period.


                # ⚓ FAIR ☛ National_Polls,_State_Ballots_Measure_Different
                  ‘Public_Opinions’⠀⇛


                       Nate Cohn, who covers politics and polling for the
                       New York Times, wrote an article last month (6/3/
                       22) comparing the results of national polls with
                       actual ballot measures in states. His major theme
                       was that national polls may be unreliable when they
                       show high levels of support for various policies.
                       The reason: When those same policies are voted on
                       at the state level, they uniformly perform worse
                       than what the national polls show.


                # ⚓ Common Dreams ☛ Survey_Reveals_How_Much_Voters_Dislike
                  Companies_Funding_Seditious_GOP_Lawmakers⠀⇛


                       New polling published Tuesday revealed that most
                       U.S. voters oppose corporate donations to
                       Republican lawmakers who tried to overturn the 2020
                       presidential election, with favorability ratings
                       plummeting by an average of 40% when participants
                       were informed of a company’s financial support for
                       backers of former President Donald Trump’s “Big
                       Lie.”


                       “Corporations quietly resumed funding these members
                       of Congress who voted to throw out legally cast
                       votes in favor of party loyalty.”


                # ⚓ Common Dreams ☛ Opinion_|_There_Should_Be_No_Path_Forward
                  to_Privatizing_Veterans_Affairs⠀⇛


                       When Joe Biden ran for president in 2020, he
                       marketed himself as a pragmatist, eager to
                       collaborate with Republicans and capable of
                       bridging divides because of his long experience in
                       the Senate and as vice president.


                # ⚓ Counter Punch ☛ Combating_Corporate_‘Pinkwashing’_During
                  Pride_Month_With_Mutual_Aid⠀⇛


                # ⚓ TruthOut ☛ AOC_Calls_on_Senate_to_Formally_Say_If_Supreme
                  Court_Justices_Lied_About_“Roe”⠀⇛


                # ⚓ Common Dreams ☛ AOC,_Lieu_to_Senate_Dems:_Say_on_the_Record
                  Whether_Gorsuch_and_Kavanaugh_Lied⠀⇛


                       Reps. Ted Lieu and Alexandria Ocasio-Cortez
                       demanded Monday that Senate Democratic leaders say
                       on the record whether they believe U.S. Supreme
                       Court Justices Neil Gorsuch and Brett Kavanaugh
                       lied under oath about their views on Roe v. Wade, a
                       1973 decision that both judges voted to overturn
                       last month.


                       In a letter to Senate Majority Leader Chuck Schumer
                       (D-N.Y.), Lieu and Ocasio-Cortez noted that neither
                       Gorsuch nor Kavanaugh contended during their Senate
                       confirmation hearings that Roe was “egregiously
                       wrong from the start,” a position that both
                       justices assented to last month by joining Justice
                       Samuel Alito’s majority opinion in Dobbs v. Jackson
                       Women’s Health Organization—a ruling that ended the
                       constitutional right to abortion.


                # ⚓ Counter Punch ☛ Militant_White_Identity_Politics_on_Full
                  Display_in_GOP_Political_Ads_Featuring_High-Powered_Weapon⠀⇛


                       Appearing with a shotgun and a smirk, Greitens
                       leads the hunt for RINOs, shorthand for the
                       derisive “Republicans In Name Only.” Along with
                       armed soldiers, Greitens is storming a house under
                       the cover of a smoke grenade.


                       “Join the MAGA crew,” Greitens says in the video.
                       “Get a RINO hunting permit. There’s no bagging
                       limit, no tagging limit and it doesn’t expire until
                       we save our country.”


                # ⚓ Counter Punch ☛ New_York_Times_attacks_U.S._Ambassador_to
                  Mexico_from_the_right!⠀⇛


                       And so, given that Lies of Our Times, founded by
                       Ellen Ray and with regular contributions from Noam
                       Chomsky, stopped publishing in 1994, it’s up to
                       amateurs like me to dissect the current crop of bad
                       reporting. Here we go:


                       The article opens with this:


                # ⚓ Common Dreams ☛ WATCH_LIVE:_Jan._6_Hearing_to_Focus_on_How
                  Far-Right_Extremists_Answered_Trump’s_‘Siren_Call’⠀⇛


                       The House committee investigating the January 6,
                       2021 attack on the U.S. Capitol is set to document
                       how far-right extremists answered former President
                       Donald Trump’s “siren call” to converge in
                       Washington for a lie-fueled “stop the steal” rally
                       that descended into violent chaos.


                       ​​”Big protest in D.C. on January 6th. Be there,
                       will be wild!” Trump tweeted just before 2:00 am on
                       December 19, 2020.


                # ⚓ TruthOut ☛ Trump’s_White_House_Counsel_“Corroborated”
                  Almost_All_Jan_6._Witness_Testimony⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ Democracy Now ☛ As_U.S._Funnels_Money_&_Arms_to_Ukraine,
                  Independent_Media_Faces_Pressure_to_Parrot_Official
                  Narrative⠀⇛


                       As the Pentagon authorizes an additional $400
                       million for Ukraine’s defense on Friday, bringing
                       estimated total U.S. security spending on Ukraine
                       under President Biden to a staggering $8 billion,
                       we speak to Joe Lauria, editor-in-chief of
                       Consortium News, about the pressure on news media
                       to follow a single approved narrative on the
                       Ukraine war. The independent media outlet recently
                       had their PayPal account shut down and received
                       notice from NewsGuard, a fact-checking group, that
                       they are under review for publishing fake news.
                       “American and European audiences have been fed the
                       idea that Russia has been failing in this war and
                       that Ukraine still has a chance to win, but I think
                       we’re starting to see reality seep into the
                       reporting,” says Lauria.


                # ⚓ Scheerpost ☛ VIDEO:_As_US_Funnels_Money_to_Ukraine,
                  Independent_Media_Faces_Pressure_to_Parrot_Official
                  Narrative⠀⇛


                       By Democracy Now! As the Pentagon authorizes an
                       additional $400 million for Ukraine’s defense on
                       Friday, bringing estimated total U.S. security
                       spending on Ukraine under President Biden to a …


                # ⚓ Techdirt ☛ Twitter_Sues_Indian_Government_Over_Orders_To
                  Block_Content⠀⇛


                       The government of India continues to hew closer to
                       the ideals of nearby China, led by the Mohdi
                       government, which has been pushing for greater
                       control of the country’s population. Its favorite
                       means and methods are surveillance and censorship —
                       the tool set of authoritarians all over the world.


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


                # ⚓ Common Dreams ☛ Biden_Urged_to_‘Demand_Justice’_for_Shireen
                  Abu_Akleh,_Jamal_Khashoggi⠀⇛


                       Ahead of U.S. President Joe Biden’s trip to the
                       Middle East this week, advocates pressured him to
                       seize the opportunity to “demand justice” for slain
                       journalists Jamal Khashoggi and Shireen Abu Akleh.


                       “Your administration has thoroughly failed to meet
                       the bare minimum expectation held by a grieving
                       family.”


                # ⚓ Common Dreams ☛ Opinion_|_Biden’s_Middle_East_Trip_Shows
                  His_Disregard_For_Journalists⠀⇛


                       Joe Biden is visiting Saudi Arabia and Israel, two
                       countries whose governments have made headlines for
                       murdering journalists. 


          o § Civil Rights/Policing⠀➾


                # ⚓ Scheerpost ☛ 28_Years,_160_Arrests:_What_One_Man’s_Record
                  Reveals_About_San_Diego’s_Broken_Justice_System⠀⇛


                       What do you do with people who are repeatedly
                       failed by social services and the legal system?


                # ⚓ Meduza ☛ ‘They_don’t_think_Russia’s_prisons_are_crowded
                  enough’:_Ilya_Yashin_faces_criminal_charges_for_speaking_out
                  against_the_war._Meduza_spoke_to_his_lawyer,_Vadim_Prokhorov.
                  —_Meduza⠀⇛


                       On the evening of July 12, lawyer Vadim Prokhorov
                       reported that the Russian authorities were bringing
                       criminal charges against his client, opposition
                       politician Ilya Yashin, for allegedly spreading
                       “disinformation” about the Russian military — a
                       crime that could carry a sentence of up to 15 years
                       in prison. Yashin is currently in jail, where he’s
                       serving a 15-day sentence for allegedly disobeying
                       a police officer. Meduza spoke to Prokhorov about
                       Yashin’s case, and about one of his other clients,
                       Vladimir Kara-Murza, another opposition figure who
                       refused to leave the country after February 24 and
                       now stands accused of spreading disinformation.


                # ⚓ TruthOut ☛ Sri_Lankan_Protesters_Occupy_Homes_of_President
                  and_PM,_Demanding_Their_Ouster⠀⇛


                # ⚓ Democracy Now ☛ How_Sri_Lanka_Protests_Led_to_a
                  “Reawakening_of_the_Citizen”_&_Pushed_Out_President_&_Prime
                  Minister⠀⇛


                       Thousands of protesters in Sri Lanka have stormed
                       the homes of the president and prime minister and
                       are refusing to leave until they officially resign,
                       as the president faces accusations of corruption
                       that bankrupted the country and led to a massive
                       economic crisis. President Gotabaya Rajapaksa is
                       set to formally step down Wednesday and has
                       reportedly tried to flee the country. We go to the
                       capital Colombo to speak with Bhavani Fonseka, a
                       human rights lawyer and a senior researcher at the
                       Centre for Policy Alternatives, who has been
                       participating in the protest. She describes the
                       months of peaceful protest that led to this moment.
                       “Considering the crisis and considering the demands
                       of the people that there has to be a change, we
                       need to look to general elections as soon as the
                       environment is conducive,” notes Fonseka.


                # ⚓ Democracy Now ☛ Abortion_Providers_in_Mississippi_&_Alabama
                  Post-Roe_Want_Biden_to_Federally_Codify_Right_to_Choose⠀⇛


                       Heeding outrage from reproductive rights activists,
                       President Biden signed an executive order Friday to
                       ensure access to abortion medication and emergency
                       contraception in the wake of the Supreme Court
                       overturning Roe v. Wade. We speak to the heads of
                       two major reproductive health centers in the Deep
                       South about how they are providing patient care now
                       that abortion is criminalized. Diane Derzis is CEO
                       of Jackson Women’s Health Organization,
                       Mississippi’s only abortion clinic, which was at
                       the center of the Supreme Court case that led to
                       the overturning of Roe. The clinic closed soon
                       after Roe was overturned last month, and plans to
                       reopen in Las Cruces, New Mexico. We also speak to
                       Robin Marty, operations director of the West
                       Alabama Women’s Center, which just reopened on
                       Monday to offer a selective range of sexual health
                       services after discontinuing abortion services.
                       “The only way to stop this is to absolutely pass
                       federal law that protects a woman’s access to the
                       most private decision in our lives,” says Derzis.
                       “We are going to be a safe place that does not ask
                       questions and simply sees people with bleeding
                       issues and does what we are legally allowed to
                       under the law,” says Marty.


                # ⚓ The Nation ☛ Self-Managed_Abortion_May_Become_More
                  Important_Than_Ever⠀⇛


                       In the Dobbs v. Jackson Women’s Health Organization
                       ruling, the conservative justices rejected the idea
                       that it is a fundamental human right for women to
                       have agency over their own bodies and ruled that
                       state lawmakers can exert control over part of what
                       is in fact a spectrum of reproductive health care
                       that all people who can become pregnant will likely
                       need to some degree. It’s a spectrum because all
                       reproductive health experiences are connected, and
                       the accessibility and safety of abortion care is
                       essential to ensuring that pregnancy, childbirth,
                       and miscarriage can be safe too. There aren’t some
                       people who have children and others who have
                       abortions; we’re the same people at different
                       points in our lives. 1


                # ⚓ Project Censored ☛ Did_Dobbs_Help_the_Left_Rediscover_How
                  Political_Change_is_Made?_–_Dispatches_from_Project_Censored:
                  On_Media_and_Politics⠀⇛


                # ⚓ TruthOut ☛ Federal_Judge_Blocks_Arizona_Law_Giving
                  “Personhood”_Rights_to_Fertilized_Eggs⠀⇛


                # ⚓ Common Dreams ☛ Judge_Blocks_Arizona_‘Personhood’_Law_Aimed
                  at_Criminalizing_Abortion⠀⇛


                       A federal judge on Monday barred enforcement of a
                       so-called “personhood” law in Arizona that advocacy
                       groups warned would be used to criminalize abortion
                       across the state.


                       The Center for Reproductive Rights—part of the
                       coalition that demanded and obtained the
                       injunction—noted in a press release that the 2021
                       law crafted by Republican legislators “classifies
                       fetuses, embryos, and fertilized eggs as ‘people’
                       starting at the point of conception.”


                # ⚓ TruthOut ☛ Warren_Asks_Facebook_&_Instagram_to_Stop
                  Censoring_Truthful_Posts_About_Abortion⠀⇛


                # ⚓ TruthOut ☛ No_State_Can_Deny_Abortion_to_Those_Needing
                  Emergency_Care,_Biden_Admin_Says⠀⇛


                # ⚓ The Nation ☛ The_Thin_Wall_Separating_Church_and_State
                  Comes_Tumbling_Down⠀⇛


                       Last month was shockingly painful, with each new
                       opinion from the Supreme Court worse than the last.
                       In one week, the court ruled that Maine must
                       subsidize tuition at private religious schools
                       along with nonreligious ones, and it struck down
                       Roe v. Wade. Taken together, these unrelated cases
                       highlight the power of the religious right and bode
                       ill for the future of civil liberties and civil
                       rights.


                # ⚓ The Nation ☛ Buffalo_Community_Activists_Show_How_to_Fight
                  Gerrymandering⠀⇛


                       A coalition of community activists here has once
                       again thrown a spanner into this city’s political
                       works.


                # ⚓ The Nation ☛ Mo_Farah_Reveals_That_He_Is_a_Survivor_of
                  Human_Trafficking⠀⇛


                       Sir Mohamed Farah is a track distance legend. The
                       British runner, born in Somaliland, holds an
                       unprecedented 10 global championship medals,
                       including four Olympic golds. There are statues of
                       him in England. He has honorary titles that have
                       been bestowed upon him by Queen Elizabeth II. And
                       this week, in news that has created shock waves in
                       our supposedly shock-free culture, Farah revealed
                       that he first came to England at the age of “8 or
                       9” as the result of human trafficking. In the
                       process, he rewrote what was assumed about his
                       history, his family, and even his name.


                # ⚓ The Nation ☛ Deadly_InHuman_Trafficking⠀⇛


                # ⚓ Scheerpost ☛ Roe_v._Wade_is_Gone._A_Wave_of_Criminalization
                  is_Coming.⠀⇛


                       With Roe v. Wade out of the way, the floodgates
                       have opened. States are rushing to pass new laws to
                       criminalize and surveil abortion, and the future
                       before us could be even grimmer than imagined.


                # ⚓ The Nation ☛ The_Republicans’_Agenda,_Hidden_in_Plain
                  Sight⠀⇛


                       “What are Republicans for?”


                # ⚓ Counter Punch ☛ Returning_to_Reno_After_Roe’s_Undoing⠀⇛


                       She just laughed.


                       “What’s so funny?” I asked.


                # ⚓ Common Dreams ☛ WATCH:_Hawley_Taken_to_Task_for_Transphobic
                  Questioning_on_Abortion_Rights⠀⇛


                       University of California, Berkeley law professor
                       Khiara Bridges reprimanded far-right Sen. Josh
                       Hawley during a congressional hearing on Tuesday,
                       accusing the Missouri Republican of asking
                       transphobic questions.


                       “You’ve referred to people with a capacity for
                       pregnancy. Would that be women?” Hawley asked
                       Bridges during a Senate Judiciary Committee hearing
                       on abortion rights titled, “A Post-Roe America: The
                       Legal Consequences of the Dobbs Decision.”


                # ⚓ Common Dreams ☛ ‘Not_Too_Late_to_Stop_This’:_Organizers
                  Mobilize_Against_Biden’s_Anti-Choice_Judge_Pick⠀⇛


                       Pro-democracy groups are ramping up efforts to make
                       sure President Joe Biden backs off his reported
                       plan to nominate an anti-choice Federalist Society
                       supporter to a U.S. District Court in Kentucky amid
                       news that the White House is moving forward with
                       the nomination.


                       “They’re defending it,” a source who was briefed on
                       the Biden administration’s judicial nomination
                       plans told HuffPost Tuesday regarding the
                       president’s choice of Chad Meredith, a conservative
                       lawyer who served as chief deputy general counsel
                       to former Kentucky Gov. Matt Bevin, a Republican.


                # ⚓ Scheerpost ☛ ‘The_Uber_Files’:_124,000+_Leaked_Files_Expose
                  Global_Dirty_Dealings_of_Ride-Hailing_Giants⠀⇛


                       Internal documents reveal how company “won access
                       to world leaders, cozied up to oligarchs and dodged
                       taxes amid chaotic global expansion.”


                # ⚓ Meduza ☛ ‘Life_here_is_going_downhill’:_How_forced
                  mobilization_has_transformed_the_Donbas_‘people’s_republics’
                  —_Meduza⠀⇛


                       The Kremlin-controlled “people’s republics” in the
                       Donbas have mobilized tens of thousands of people
                       since Russia began its full-scale invasion of
                       Ukraine in February. More than four months later,
                       these conscripts are faced with a lack of medical
                       care, military gear, and even food. Relatives who
                       dare to speak up on their behalf are persecuted by
                       the security services. Meanwhile, utility companies
                       and mines in the “DNR” and “LNR” are experiencing
                       disruptions due to personnel shortages. And the
                       risk of man-made disasters in the Donbas is higher
                       than ever before. For Meduza, journalist Gleb Golod
                       reports on how mass mobilization has sapped the
                       Donbas.


                # ⚓ Meduza ☛ ‘Brutal_crimes_are_a_result_of_brutal_policies’
                  Criminologist_Yakov_Gilinsky_on_a_life_spent_navigating_war,
                  crime,_and_state_censorship_—_Meduza⠀⇛


                       In the early 1970s, criminologist and lawyer Yakov
                       Gilinsky became the first Soviet academic to study
                       deviantology — the study of deviant behavior and
                       its causes. He was the first researcher in the USSR
                       to study how socioeconomic factors influence crime
                       and suicide rates. Today, Gilinsky continues to
                       teach and work in St. Petersburg. Bumaga spoke with
                       Gilinsky about the likely effects of the war, his
                       childhood in besieged Leningrad, and how he and his
                       colleagues evaded the Soviet censors. With Bumaga’s
                       permission, Meduza is publishing an abridged
                       translation of the interview.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Charter’s_Running_A_Fake_Consumer_Group_In_Maine
                  That’s_Killing_Community_Broadband–With_The_Help_Of_A
                  Democratic_Advisor⠀⇛


                       For decades, entrenched U.S. regional monopolies
                       have refused to deliver affordable, reliable, fast
                       broadband in any sort of uniform way. That’s just
                       kind of how monopolies work.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Techdirt ☛ How_Not_Overly_Enforcing_Its_IP,_Universal
                        Made_The_Minions_Ubiquitous_And_Beloved⠀⇛


                             No one is ever going to confuse Hollywood
                             giant Universal Studios with, say, EFF’s view
                             on more permissive copyright. However,
                             Polygon recently had a really interesting
                             article on how Universal’s comparatively
                             minimal focus on cracking down on the
                             incidental (and fun) uses of its Minions
                             characters have made the characters well
                             known, ubiquitous… and well loved. And, as
                             the article notes, a hell of a lot more
                             relevant today than Mickey Mouse, owned by
                             Disney — which is famous for its
                             unwillingness to allow anyone to make use of
                             its characters.


                      # ⚓ Techdirt ☛ Take-Two’s_War_On_Its_Own_Modding
                        Community_Continues,_Harming_Take-Two⠀⇛


                             Over the past couple of years, we’ve
                             discussed several battles in the war on the
                             modding community Take-Two and Rockstar Games
                             launched. I’ve never seen a coherent
                             explanation for why this war was needed at
                             all, from either the publishers or
                             speculators. Almost without warning, Take-Two
                             went on a DMCA blitz on sites hosting these
                             mods, many of which had been around for
                             years. And these aren’t merely mods that
                             allow people to cheat in online games. Many
                             of them are mods for the single-player game,
                             allowing players to do new and interesting
                             things. You know, making Take-Two’s product
                             more valuable, in other words.


                      # ⚓ Torrent Freak ☛ Movie_Piracy_Site_Operator_Faces_Five
                        Years_in_Prison_After_Arrest_in_Japan⠀⇛


                             A man suspected of operating a piracy site
                             offering links to over 3,300 local and
                             Western movies has been arrested in Japan.
                             The 51-year-old, suspected of infringing the
                             copyrights of companies including Bandai
                             Namco and King Records, told police that he
                             simply wanted to share his love of movies
                             with others. Under local law, he faces up to
                             five years in prison.


                      # ⚓ Torrent Freak ☛ Fake_Sky_Representative_Abuses
                        Copyright_Claims_Board_to_Target_Pirate_Streaming_App⠀⇛


                             The US Copyright Claims board officially
                             opened less than a month ago and there’s
                             already a highly suspicious claim on the
                             docket. The unknown “Copyrights Protection”
                             outfit filed a case against pirate streaming
                             app HA Sports Studio ‘on behalf’ of Sky.
                             However, Sky informs TorrentFreak that it has
                             absolutely nothing to do with it.


                      # ⚓ Techdirt ☛ Copyright_Is_Bananas:_Case_Over_Copyright
                        Of_A_Banana_Taped_To_A_Wall_Allowed_To_Move_Forward⠀⇛


                             How many times can we write about bananas and
                             copyright? Even assuming the monkey selfie
                             case doesn’t count, it’s come up surprisingly
                             often here on Techdirt. A few years ago,
                             there was a high profile copyright case about
                             whether or not a banana Halloween costume was
                             covered by copyright (it was). But, this
                             latest case is about whether or not there’s
                             copyright in the, um, artistic display of
                             taping a banana to a wall. Believe it or not,
                             this is not the first case we’ve even written
                             about regarding copyright questions around
                             bananas taped to walls. Two years ago, we
                             wrote about a different case, involving the
                             copyright on photographs of bananas taped to
                             walls, but that seemed like a pure trolling
                             case.


    * § Gemini* and Gopher⠀➾


          o § Politics⠀➾


                # ⚓ That_Time_Factory_Waste_Didn’t_Flow_Into_a_River⠀⇛


                       “Waste From Thousands of Old Industrial Sites May
                       Be Released by Floods”


                       This note made me remember a large fire incident
                       that I was witness too a few years ago.


                       Dalälven is one of Sweden’s seven biggest rivers,
                       and Malung is a small city at the edge of it.
                       Malung is known for its history of leather
                       workmanship and had an old abandoned factory that
                       had prepared leather from animal skin until a few
                       decades ago.


                       The thing about this old factory is that the old
                       way of doing this involved some pretty dangerous
                       chemicals. As a result the factory grounds were
                       polluted.


          o § Technical⠀➾


                # § Science⠀➾


                      # ⚓ Project_Hail_Mary_by_Andy_Weir⠀⇛


                             I immensely enjoyed Andy’s The Martian. A
                             tried to read his Artemis, but for some
                             reason I lost steam early on. I’m not sure
                             whether it was the book that did it or
                             extenuating circumstances (of which there
                             were many at the time). However I have heard
                             from many that Project Hail Mary is a gem.


                             And it really is.


                             We get to follow Dr Ryland Grace (who doesn’t
                             remember his own name when the book starts)
                             as he spends time in the Tau Ceti solar
                             system looking for a solution to an extreme
                             extinction level event going on back home.


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



                    ䷩ 𝚕𝚒𝚗𝚎 11335

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.13.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/07/2022:_Rust_Losing_More_People⠀✐


Posted in News_Roundup at 12:16 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Graphics_Stack
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Rust
    * Leftovers
          o Linux_Foundation
          o Entrapment_(Microsoft)
          o Security
                # Privacy/Surveillance
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ The Register UK ☛ Slimbook_updates_Linux_laptop_ranges_•
                  The_Register⠀⇛


                       Another vendor has refreshed its Linux laptop
                       lineup for the summer, and some of the new models
                       look strangely familiar.


                       Last week we covered the new Pulse G2 laptop from
                       Germany’s Tuxedo Computers. Close behind it are new
                       models from several other vendors of Linux laptops
                       with very similar specs.


                       In an unusual move that provides the FOSS project
                       with additional funding, the KDE organization sells
                       hardware under its own brand. A notable example is
                       the KDE Slimbook, and it just launched two fourth-
                       generation models of the Slimbook IV.


                       The specs of the Slimbook IV are much like those of
                       the Tuxedo Pulse G2: AMD Ryzen 7 5700U CPUs, with
                       eight cores and 16 threads. The CPU clock speed
                       varies between 1.8GHz and 4.3GHz according to load,
                       and there’s 8MB of cache. The onboard Vega8 GPU
                       runs at up to 1.9GHz.


                       The machines have two DDR4 SODIMM slots, and can
                       take up to 64GB of 3,200MHz memory, and also have
                       two M.2 slots for up to 4TB of NVMe storage. They
                       have both onboard Gigabit Ethernet and Wi-Fi 6 for
                       a maximum speed of 2.4Gb/s, plus Bluetooth 5.2.


          o § Server⠀➾


                # ⚓ The_Hidden_Cost_of_Fixing_Your_Kubernetes_Clusters⠀⇛


                       While the adoption of Kubernetes to speed software
                       development has become a recipe for success in the
                       containerized world, many organizations working to
                       streamline and optimize their processes are
                       encountering a major issue—namely, a heavy cost for
                       repairs. When defects and other code issues occur
                       without a cost-awareness and savings plan in place,
                       the price of Kubernetes ownership can go through
                       the roof. The good news is, cost optimization in
                       Kubernetes boils down to two key words—proper
                       configuration.


          o § Graphics Stack⠀➾


                # ⚓ 9to5Linux ☛ DXVK_1.10.2_Brings_Fixes_for_Dead_Space,_Myst
                  V,_Godfather,_and_Many_Other_Games⠀⇛


                       DXVK 1.10.2 fixes bugs and crashes in many video
                       games, including Beyond Good and Evil, Dead Space,
                       Myst V, Day Z, Dirt Rally, Godfather, Limbo, Return
                       of Reckoning, Scrapland Remastered, and Planetary
                       Annihilation: TITANS.


                       The Star Wars: The Force Unleashed II, Star Wars:
                       The Old Republic, Majesty 2, Onechanbara Z2: Chaos,
                       Plants vs. Zombies Garden Warfare 2, Small Radios
                       Big Televisions, Sonic Adventure 2, Supreme
                       Commander, and SpellForce Platinum Edition video
                       games also received improvements.


                # ⚓ Low-resolution-Z_on_Adreno_GPUs_–_Danylo’s_blog⠀⇛


                       Now, a year later, I returned to this feature to
                       make some important improvements, for nitty-gritty
                       details you could dive into Mesa MR#16251 “tu:
                       Overhaul LRZ, implement on-GPU dir tracking and LRZ
                       fast-clear”. There I implemented on-GPU LRZ
                       direction tracking, LRZ reuse between renderpasses,
                       and fast-clear of LRZ.


                       In this post I want to give a practical advice,
                       based on things I learnt while reverse-engineering
                       this feature, on how to help driver to enable LRZ.
                       Some of it could be self-evident, some is already
                       written in the official docs, and some cannot be
                       found there. It should be applicable for Vulkan,
                       GLES, and likely for Direct3D.


          o § Instructionals/Technical⠀➾


                # ⚓ Its FOSS ☛ 9_Rather_Unknown_Ways_of_Using_Neofetch_in_Linux
                  –_It’s_FOSS⠀⇛


                       Neofetch is a simple command-line tool that
                       displays an ASCII logo of the distribution along
                       with a few system information in the terminal. It
                       looks beautiful and you can easily show which
                       distribution, desktop environment, and themes you
                       are using when you share the screenshots of your
                       desktop in various Linux communities.


                # ⚓ OSTechNix ☛ Enable_Nested_Virtualization_In_Proxmox_VE_–
                  OSTechNix⠀⇛


                       Proxmox is my preferred hypervisor to deploy
                       various containers and VMs. Sometimes, I want to
                       create a VM inside another VM. Meaning – I just
                       want to host a guest hypervisor(i.e VM) in my
                       physical Proxmox hypervisor. Have you ever wondered
                       how to setup a guest hypervisor in a host
                       hypervisor? In this guide, I will show you how to
                       enable nested virtualization in Proxmox VE and then
                       enable VT-X in the guest hypervisor.


                # ⚓ How_to_perform_CRUD_functionalities_in_Django_Rest
                  Framework_–_NextGenTips⠀⇛


                       An API (Application Programming Interface) is a set
                       of rules shared by a particular service. These
                       rules determine in which format and with which
                       command set your application can access the
                       service, as well as what data this service can
                       return in the response. It acts as a layer between
                       your application and external service.


                       REST API (Representational state transfer) is an
                       API that uses HTTPS requests for communication with
                       web services. From the python site, the REST API
                       can be viewed as a data source located on an
                       internet address that can be accessed in a certain
                       way through certain libraries.


                # ⚓ Make Use Of ☛ How_to_Use_the_New_Chromebook_Linux
                  Interface⠀⇛


                       If you recently upgraded your version of Chrome OS,
                       you may have noticed something different when you
                       launch the Linux environment in Chrome OS version
                       103 and higher. Here’s how to use the new Chrome OS
                       Linux interface.


                # ⚓ HowTo Forge ☛ How_to_Install_NFS_Server_and_Client_on
                  Ubuntu_22.04⠀⇛


                       NFS or Network File System is a protocol that
                       allows local users to access remote data from
                       multiple disks and directories in the same way as
                       local access. In this tutorial, you will learn how
                       to install the NFS Server and Client on the Ubuntu
                       22.04 Server. You will also learn how to mount the
                       NFS shared directory automatically at system boot
                       on the client machine.


                # ⚓ ID Root ☛ How_To_Install_qBittorrent_on_Fedora_36_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       qBittorrent on Fedora 36. For those of you who
                       didn’t know, qBittorrent is a free open-source
                       cross-platform P2P BitTorrent client. The software
                       also has an integrated RSS reader so that it can be
                       used to download files directly from RSS feeds.
                       This application is known to work effectively and
                       efficiently on many operating systems such as
                       Linux, Microsoft Windows, and FreeBSD. It is
                       written in the C++ language.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the qBittorrent BitTorrent client
                       on a Fedora 36.


                # ⚓ Video ☛ Install_DTOS_on_ArcoLinux_(Now_With_Awesome_and
                  Qtile!)_–_Invidious⠀⇛


                       DTOS now comes with the option to install any (or
                       all) of three window managers: XMonad, Awesome and
                       Qtile. I have also been fixing a lot of bugs with
                       DTOS in recent days, so I thought I would do a test
                       run. Today, I’m installing DTOS on top of
                       ArcoLinuxB Awesome Edition.


                # ⚓ Tips On UNIX ☛ Install_Audacious_4.2_On_Ubuntu_/_LinuxMint
                  /_Fedora_&_Alma_Linux_|_Tips_On_UNIX⠀⇛


                       This tutorial will be helpful for beginners to
                       install Audacious 4.2 on Ubuntu 22.04 LTS, Ubuntu
                       20.04 LTS, Linux Mint 20.3, AlmaLinux 9, Rocky
                       Linux 8, and Fedora 36.


                # ⚓ Linux Handbook ☛ Convert_Hex_to_ASCII_Characters_in_Linux
                  Bash_Shell⠀⇛


                       Got a bunch of hexadecimal characters and want to
                       convert them to a readable decimal system (ASCII)?


                       There are multiple ways to convert hex to ASCII in
                       Linux. You may also use these methods in your shell
                       script if required.


                # ⚓ ID Root ☛ How_To_Install_Ansible_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Ansible on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, Ansible is the simplest way to
                       automate apps and IT infrastructure. It runs on
                       many Linux operating systems and is configured
                       quite easily. It uses the open SSH service to
                       perform the various networking tasks ensuring a
                       well secure and protected communication
                       environment. Nowadays IT environments are very
                       complex and often need to scale extremely quickly.
                       Automation makes system administrators’ and
                       developers’ jobs easier and allows them to focus
                       attention on other tasks that add value to an
                       organization.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of Ansible on Ubuntu 22.04 (Jammy
                       Jellyfish). You can follow the same instructions
                       for Ubuntu 22.04 and any other Debian-based
                       distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Red Hat ☛ Install_storage_in_your_application_cluster_using
                  Rook_|_Red_Hat_Developer⠀⇛


                       Developers running applications in the cloud have
                       traditionally separated their applications from
                       storage, but recent services such as the Rook
                       Operator for Kubernetes make it easy to create
                       storage in the cloud. This article shows how to use
                       Rook for object storage. Our example runs a single-
                       node Red Hat OpenShift cluster on your laptop or
                       desktop using Red Hat OpenShift Local (previously
                       known as CodeReady Containers). We’ll install Rook,
                       create object storage on OpenShift Local, and
                       perform some bucket notifications.


                # ⚓ Red Hat Official ☛ How_to_troubleshoot_your_network_with
                  Nmap_|_Enable_Sysadmin⠀⇛


                       Expert troubleshooting skills are a must for
                       sysadmins. Understanding how to identify and
                       resolve problems that you come across is crucial to
                       creating the best resolutions. Tools help you be
                       successful in the quest for answers. Nmap is a
                       helpful tool for security and IT professionals.


                       Without understanding what network ports are open,
                       it would be impossible to assess a system’s
                       security. System administrators use Nmap to check
                       if systems are online and help discover any
                       problems in their network. You can also detect
                       operating system versions, determine whether
                       services are online, test embedded network stacks,
                       and even identify aggressive network traffic.


                # ⚓ Linux Shell Tips ☛ How_to_List_All_Existing_Groups_in_Linux
                  System⠀⇛


                       Being able to manage users and groups in a Linux
                       operating system environment is an important
                       milestone in terms of Linux administration and
                       security. Under Linux, each user account is
                       automatically associated with a single primary
                       group. A Linux user cannot be a member of two or
                       more primary groups, only one.


                       However, when it comes to secondary groups, it’s a
                       different case. A single Linux user account can be
                       associated with more than one secondary group (up
                       to 15).


                       In summary, a primary group is OS-assigned to each
                       Linux user account and is linked to user-created
                       files whereas secondary groups can be associated
                       with multiple Linux user accounts and are not
                       always automatically assigned.


                # ⚓ Trend Oceans ☛ How_to_Install_Metasploit_Framework_with_GUI
                  Method_on_Linux_–_TREND_OCEANS⠀⇛


                       Rapid7 and the open-source community manage the
                       widely used penetration testing framework,
                       Metasploit. It is a very powerful tool used by
                       cybercriminals as well as ethical hackers to test
                       and create exploits for networks or servers.


                # ⚓ Linux Shell Tips ☛ How_to_Determine_the_Number_of_Linux_RAM
                  Slots_in_Use⠀⇛


                       A RAM is important in determining the performance
                       spectrum of your Linux-powered machine. On the
                       other hand, think of a RAM slot as the main memory
                       socket or slot that physically exists on the
                       computer’s motherboard to hold installed/inserted
                       and compatible RAM.


                       These RAM slots determine/specify the number and
                       type of RAM compatible with the Linux-powered
                       machine you are using. SDRAM (Synchronous DRAM),
                       DDR (Double Data Rate), and DIMM (Dual In-Line
                       Memory Module) are examples of some common RAM
                       types. It is the computer motherboard that
                       determines the existing number of RAM slots.


                       Therefore, when the term RAM is mentioned, we
                       should always think of RAM modules and RAM slots.
                       Each RAM slot is compatible with a specific RAM
                       module. Examples of popular RAM modules include
                       DDR1, DDR2, DDR3, DDR4, and SDRAM.


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ Zizo_partners_with_SUSE_to_harness
                  the_power_of_open_source [Ed: Shipping proprietary software
                  while seeking to "harness the power of open source" for
                  openwashing]⠀⇛


                       It can help assist in making data-driven decisions,
                       which can in turn, act as a catalyst to accelerate
                       the digital transformation journey. In a nutshell,
                       we can say that data is the new lifeblood of any
                       digital enterprise – but it is only valuable when
                       it is the right data, in the right format, and
                       available at the right time. Therefore, in a world
                       where data is growing exponentially, Zizo, a
                       leading provider of big data and edge analytics,
                       decided to build solutions that are flexible,
                       adaptable and cost effective; with the ability to
                       be deployed either at the edge, or in the data
                       centre.


          o § Fedora Family / IBM⠀➾


                # ⚓ Venture Beat ☛ Red_Hat’s_new_CEO_to_focus_on_Linux_growth
                  in_the_hybrid_cloud,_AI_and_the_edge_|_VentureBeat⠀⇛


                       When IBM acquired Linux vendor Red Hat for $34
                       billion in 2019, Paul Cormier took the reins as Red
                       Hat CEO. After three years, Cormier is now handing
                       those reins over to a new leader.


                       Yesterday, Red Hat announced that long-time
                       engineering leader at the company, Matt Hicks, will
                       now be the company’s president and CEO. Cormier
                       will move to the chairman role, where he will
                       continue to be an active participant in the
                       company’s activities.


                       In an interview with VentureBeat, both Cormier and
                       Hicks emphasized that now is the right time for a
                       CEO transition.


                # ⚓ Red Hat Official ☛ RHEL_9_networking:_Say_goodbye_to_ifcfg-
                  files,_and_hello_to_keyfiles⠀⇛


                       In my first Red Hat Certified Engineer (RHCE) fast-
                       track training in 2002, we were using Red Hat Linux
                       7.2, and I learned to love the network
                       configuration files in /etc/sysconfig/network-
                       scripts. Later, Red Hat Enterprise Linux (RHEL) 6
                       introduced NetworkManager (also known as ‘NM’).


                # ⚓ Red Hat Official ☛ Red_Hat_Shares_―_Special_edition:_Red
                  Hat_Summit_2022_recap⠀⇛


                       The Red Hat Shares newsletter helps IT leaders
                       navigate the complicated world of IT―the open
                       source way.


                # ⚓ Enterprisers Project ☛ Cloud_migration:_3_top_business
                  advantages⠀⇛


                       Despite the global trend toward cloud migration,
                       some businesses are pushing back, claiming the
                       productivity and cost savings aren’t living up to
                       their expectations. In fact, a recent McKinsey
                       survey found that 75 percent of respondents went
                       over budget on their cloud migration process and 38
                       percent were behind schedule.


                # ⚓ Enterprisers Project ☛ Digital_transformation:_3_things
                  successful_CIOs_know⠀⇛


                       CIOs leading digital transformation initiatives are
                       fundamentally changing the way their business
                       operates.


                       Digital transformation starts with the business,
                       not the technology, and it’s no easy feat.
                       According to a BCG report, “only about a third of
                       transformations meet or exceed their target value
                       and achieve sustainable change: these are the
                       companies in the win zone. Worry-zone companies
                       create some value but do not meet their targets and
                       produce only limited long-term change.”


                       Digital transformation is the implementation of new
                       technology, people, and processes to improve the
                       business. Any business IT strategy should the
                       following three tenets in its digital
                       transformation initiative.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Neowin ☛ Linux_Mint_21_beta_ISOs_pass_tests_meaning_their
                  release_is_imminent_–_Neowin⠀⇛


                       The Cinnamon, MATE, and Xfce editions of Linux Mint
                       21 beta have been approved for release by the Linux
                       Mint project according to its community website. In
                       an announcement last week, the Linux Mint project
                       leader said that the beta was due last week, but
                       there were issues with the beta ISOs which meant
                       they received a “Rejected” status during the tests.
                       Now that they have been approved, their release
                       should be imminent.


                       Typically, the beta period lasts about two weeks
                       for any last minute issues to be tested by a wider
                       audience. Following the beta, the final ISOs are
                       made available to the public. In-place upgrades are
                       sometimes enabled soon after the release and other
                       times they are delayed to give more time for
                       testing to be done of the new operating system
                       version.


          o § Devices/Embedded⠀➾


                # ⚓ peppe8o ☛ Neopixel_(Addressable_RGBs)_LEDs_strip_with
                  Arduino⠀⇛


                       To have colored animations for beautiful displays,
                       Neopixel is good as it can give any color
                       combination. It looks like a RGB LED, but can work
                       with one pin to control all in series. It’s cheap
                       and easy to install for room decoration.


                # ⚓ CNX Software ☛ WeAct_RP2040_board_adds_16MB_flash,_USB-
                  C_port_to_Raspberry_Pi_Pico_form_factor_–_CNX_Software⠀⇛


                       If the Raspberry Pi Pico’s 2MB of QSPI flash is not
                       quite sufficient for your needs, and you’d not
                       quite a fan of micro USB ports, the WeAct RP2040
                       “clone” comes with up to 16MB flash and a USB Type-
                       C port for power and programming.


                       Another improvement is the addition of a reset
                       button, which can be convenient for flashing UF2
                       firmware, and the pinout remains mostly the same.
                       The price is not quite as low as the original
                       Raspberry Pi Pico, but the board sells for an
                       affordable $5.99 with 2MB flash, while the 16MB
                       flash variant goes for $8.99 with shipping included
                       in both cases.


          o § Open Hardware/Modding⠀➾


                # ⚓ CNX Software ☛ Pixel_Pump_is_an_open-source,_manual_pick-
                  and-place_machine_(Crowdfunding)_–_CNX_Software⠀⇛


                       Pixel Pump is an open-source hardware vacuum pump
                       that should be easier to use than a pair of
                       tweezers to pick and place SMT components, and
                       suitable for prototypes and small production runs.


                       The system comes with a pen with five exchangeable
                       stainless-steel nozzles to match the size of
                       components, a foot pedal, and several tactile
                       silicone buttons with RGB backlighting to control
                       the unit.


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


          o ⚓ Medevel ☛ CalDavZAP:_A_Self-hosted_Open-source_CalDAV_Server⠀⇛


                 CalDavZAP is an open source CalDAV web client
                 implementation released under GNU Affero General Public
                 License (version 3.0).


                 [...]


                 The project is released and licensed under the GNU Affero
                 General Public License (version 3.0).


          o § Programming/Development⠀➾


                # ⚓ Ubuntu Pit ☛ Coding_vs_Programming:_An_In-depth
                  Comparison⠀⇛


                       Coding vs. Programming, the debate regarding the
                       two terms being the same or not, has been going on
                       for decades. It is a question that every tech
                       beginner always considers and confuses. Sometimes,
                       even the experts use the terms interchangeably
                       because they do not believe that the differences
                       matter much.


                       But in reality, coding and programming are
                       different. There are many factors where they
                       differ, and it takes people years of experience to
                       truly understand them. However, the IT industry
                       uses both these fields to develop softwares that
                       impact our daily lives – so they’re equally
                       important.


                # ⚓ Ubuntu Pit ☛ Top_10_Best_Programming_Tools_for_Kids_in
                  2022⠀⇛


                       Kids are, by default, curious beings. Everything is
                       new to them, and they love to explore. In this era
                       of technology, keeping children up-to-date is also
                       a part of parenting. Introducing them to
                       programming is a great start, and there are tons of
                       programming tools for kids to make it a fun
                       experience.


                       Studies suggest that the best age to start with
                       programming or coding is around five to seven
                       years, depending on the kid’s understanding and
                       reading capability. Like mathematics, programming
                       also helps children open to problem-solving methods
                       and think more logically, which can benefit them in
                       the future.


                # ⚓ Qt ☛ Qt_for_Android_Automotive_:_Outrun_Demo_Integration⠀⇛


                       The Outrun project was started to demonstrate the
                       development process when using the unified design
                       and development tools that Qt offers, by creating a
                       digital cockpit from early design to UI
                       implementation, visual effect creation, building
                       connectivity, and finally running it on various
                       environments.


                       The last step in the Outrun project development is
                       connecting the UI to the vehicle platform.
                       Currently the Qt for Android Automotive module
                       provides vehicle properties through both C++ and
                       QML APIs. It also offers a submodule to access
                       Android notifications (to be released later). If we
                       analogize the project to solving a jigsaw puzzle,
                       connecting the UI to the vehicle would be the last
                       pieces of the puzzle. You probably know that
                       placing the final pieces of a jigsaw puzzle should
                       be much easier than the first pieces.


                # ⚓ Qt ☛ Compiling_QML_to_C++:_Fixing_unqualfied_access⠀⇛


                       This is the eighth installment in the series of
                       blog posts on how to adjust your QML application to
                       take the maximum advantage of qmlsc. In the first
                       post we’ve set up the environment. You should read
                       that post first in order to understand the others.
                       We’re going to learn how to avoid unqualified
                       access now.


                       You will see quite a few warnings on unqualified
                       access when compiling Qt Creator with qmlsc
                       enabled. An access to a name in QML is called
                       “unqualified” if the name is neither found in the
                       directly surrounding QML scope, nor an ID or a type
                       name. Usually this means you’re accessing members
                       of the root element of a component, context
                       properties, or undeclared signal parameters. Most
                       of those are easy to fix. Let’s look at the
                       TimeMarks.qml file in the tracing library.


                # ⚓ gfldex:_Coercive_bits⠀⇛


                       Altreus was looking for a way to convert a list of
                       bitmask names, provided as a string by the user, to
                       a bitmask. He wished for BUILDARGS, as provided by
                       Perl’s Moose but was given good advise how to solve
                       the problem without making object instantiation
                       even more complex. Nobody can stop me from doing
                       just that.


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ Changes_at_the_Clippy_Team [Ed: Rust
                        exodus continues, but this is the spin (as people step
                        down). Rust is too focused outsourcing itself and
                        sending developers into the jaws of Microsoft. It is
                        something to avoid.]⠀⇛


                             With the new additions to the team, we should
                             be able to handle our long PR queue better.


                             [...]


                             At the same time, we recently granted some of
                             our oldest members the well-deserved alumni
                             status. We want to thank Pascal Hertleif and
                             Martin Carton for all their contributions,
                             especially in the early days. People joining
                             today probably never worked with them on
                             Clippy, but without them, we probably
                             wouldn’t be here.


                             We also want to thank Philipp Hansch for
                             their contributions to Clippy and all of the
                             review work they’ve done over the years. To
                             this day phansch is one of the most active
                             Clippy contributors (measured by the number
                             of commits).


                             And finally, thank you to mikerite, who
                             stepped down from an active reviewer/team
                             member position but will be staying on as a
                             contributor. We’re looking forward to
                             continue working with them!


    * § Leftovers⠀➾


          o ⚓ Tedium ☛ Why_Digital_News_Outlets_Haven’t_Nailed_Alt-Story-Form
            Journalism⠀⇛


                 I have a bone to pick with one of the best-known news
                 outlets on the internet, and pick it I shall. Since 2017,
                 Politico cofounders Jim VandeHei and Mike Allen, along
                 with a cast of notables, have taken a brevity-driven
                 approach to writing about the news of the day, no matter
                 what form it takes, on a site called Axios. Much of the
                 content is written in bullet points that are designed to
                 focus points of communication. The company has branded
                 this approach as something called “Smart Brevity.” Now,
                 it would be one thing to write everything in a quick hit
                 format, but they’ve gone further than that, attempting to
                 sell the communication approach to businesses and even
                 writing a book about it, as if VandeHei is friggin’
                 running IBM over here. As someone who once ran a popular
                 website that specialized in brevity, I first watched this
                 state of affairs with a sense of cynicism, then
                 bemusement. I have written Twitter threads to remind
                 people that, hey, they weren’t first. I can’t help but
                 think about, given all the tools they have, how little
                 they do with brevity! Today’s Tedium is questioning
                 whether that alternative story form journalism has a
                 place on the internet besides bullet points. —


          o § Linux Foundation⠀➾


                # ⚓ Linux Foundation’s Site/Blog ☛ Open_Mainframe_Project
                  Announces_Schedule_for_the_3rd_Annual_Open_Mainframe_Summit
                  on_September_21-21_in_Philadelphia,_PA [Ed: IBM mainframes
                  are proprietary, but 'Linux' Foundation gets paid to lies to
                  you about it (openwashing). The lies are products and
                  service.]⠀⇛


                       The Open Mainframe Project, an open source
                       initiative that enables collaboration across the
                       mainframe community to develop shared tool sets and
                       resources, announces the schedule for the 3rd
                       annual Open Mainframe Summit, which will be in-
                       person in Philadelphia, PA, and streaming online
                       for global attendees. This year’s theme focuses on
                       security, which is top of mind for every company
                       that uses mainframes.


                # ⚓ Linux Foundation’s Site/Blog ☛ SODA_Foundation_Announces
                  2022_Data_&_Storage_Trends_Survey [Ed: Nothing to do with
                  Linux, nothing to do with research (just spam and
                  marketing)]⠀⇛


                       To address evolving Data and Storage needs
                       throughout the industry, SODA Foundation, in
                       partnership with Linux Foundation Research, is once
                       again conducting a survey to provide insights into
                       challenges, gaps, and trends for data and storage
                       in the era of cloud native, edge, AI, and 5G. The
                       results will serve to guide the SODA Foundation
                       technical direction and ecosystem.


                # ⚓ Linux Foundation’s Site/Blog ☛ Jamie_Thomas:_What_is_the
                  OpenSSF [Ed: Linux_Foundation now works for/with Microsoft
                  shills_like_Shimel; this is a catastrophe]⠀⇛


                       Jamie Thomas is the General Manager, Systems
                       Strategy and Development at IBM and is also the
                       OpenSSF Board chair. She sat down with Alan Shimel
                       of TechStrong TV during OpenSSF Day in Austin to
                       share about OpenSSF and how the open source
                       community is rallying together to increase the
                       resilience of open source software.


                # ⚓ Linux Foundation’s Site/Blog ☛ FDC3_2.0_Drives_Desktop
                  Interoperability_Across_the_Financial_Services_Ecosystem_–
                  Linux_Foundation [Ed: This is not a community, it's not "Open
                  Source", it's a carte of banksters diluting the "Linux" brand
                  so that Zemlin and his cohorts can steal a lot of money
                  (monetising an attack on brands we built)]⠀⇛


                       The Fintech Open Source Foundation (FINOS), the
                       financial services umbrella of the Linux
                       Foundation, announced today during its Open Source
                       in Finance Forum (OSFF) London the launch of FDC3
                       2.0. FDC3 supports efficient, streamlined desktop
                       interoperability between financial institutions
                       with enhanced connectivity capabilities.


          o § Entrapment (Microsoft)⠀➾


                # ⚓ The Register UK ☛ Get_over_it:_Microsoft_is_a_Linux_and
                  open_source_company_these_days [Ed: Get over it. Steven J.
                  Vaughan-Nichols works on Microsoft payroll via LF and
                  ZDNet]⠀⇛


                       In 2001 then CEO Steve Ballmer declared: “Linux is
                       a cancer.” Later, Microsoft sponsored SCO’s
                       copyright attack on Linux; claimed that Linux
                       violated unnamed Microsoft patents; and forced
                       Linux-based Android vendors to pay for dubious
                       patent claims. Bill Gates and Ballmer’s Microsoft
                       wanted to see Linux and open-source software (OSS)
                       dead and buried.


                       They did it because, as Microsoft’s Halloween
                       documents show, they believed “OSS poses a direct,
                       short-term revenue and platform threat to
                       Microsoft, particularly in server space.”


                # ⚓ Bleeping Computer ☛ Microsoft_July_2022_Patch_Tuesday_fixes
                  exploited_zero-day,_84_flaws⠀⇛


                       Today is Microsoft’s July 2022 Patch Tuesday, and
                       with it comes fixes for one actively exploited
                       zero-day vulnerability and a total of 84 flaws.


          o § Security⠀➾


                # ⚓ Ghacks ☛ Patches_for_new_Retbleed_AMD_and_Intel
                  microprocessor_vulnerability_may_have_significant_overhead_–
                  gHacks_Tech_News⠀⇛


                       Researchers at ETH Zurich discovered the
                       vulnerabilities, which they named Retbleed. The
                       attacks exploit vulnerabilities in retpoline, a
                       mitigation introduced in 2018 to mitigate certain
                       speculative execution attacks.


                # ⚓ LWN ☛ Security_updates_for_Wednesday_[LWN.net]⠀⇛


                       Security updates have been issued by Fedora (xen),
                       Mageia (x11-server), SUSE (chromium, kernel, pcre,
                       pcre2, squid, and xorg-x11-server), and Ubuntu
                       (gnupg, gnupg2, uriparser, xorg-server, xorg-
                       server-hwe-16.04, and xorg-server, xorg-server-hwe-
                       18.04, xwayland).


                # ⚓ Reproducible_Builds_in_June_2022_—_reproducible-
                  builds.org⠀⇛


                       Welcome to the June 2022 report from the
                       Reproducible Builds project. In these reports, we
                       outline the most important things that we have been
                       up to over the past month. As a quick recap, whilst
                       anyone may inspect the source code of free software
                       for malicious flaws, almost all software is
                       distributed to end users as pre-compiled binaries.


                # ⚓ QSB-083:_Retbleed:_Arbitrary_speculative_code_execution
                  with_return_instructions_(XSA-407)⠀⇛


                       We have just published Qubes Security Bulletin
                       (QSB) 083: Retbleed: Arbitrary speculative code
                       execution with return instructions (XSA-407). The
                       text of this QSB is reproduced below. This QSB and
                       its accompanying signatures will always be
                       available in the Qubes Security Pack (qubes-
                       secpack).


                # ⚓ XSAs_released_on_2022-07-12_|_Qubes_OS⠀⇛


                       The Xen Project has released one or more Xen
                       Security Advisories (XSAs). The security of Qubes
                       OS is affected. Therefore, user action is required.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Bruce Schneier ☛ Post-Roe_Privacy⠀⇛


                             This is an excellent essay outlining the
                             post-Roe privacy threat model. (Summary:
                             period tracking apps are largely a red
                             herring.)


                      # ⚓ Medium ☛ Fear,_Uncertainty,_and_Period_Trackers⠀⇛


                             You have probably been seeing a lot of scary
                             news coverage about period tracker apps and
                             databases, and you might be wondering whether
                             or not you should be deleting your period
                             tracking app. If you use a period tracker,
                             but your threat model does not include the
                             additional risks of say: helping other people
                             get abortions, we don’t currently have
                             evidence of imminent threats of large-scale
                             preemptive investigation of you based on
                             personal health app data. The biggest threat
                             of criminalization is that a third party
                             (like hospital staff or a relative) reports
                             someone to the police for their pregnancy
                             outcome — not that police find their period
                             data in a database.


          o § Civil Rights/Policing⠀➾


                # ⚓ DaemonFC (Ryan Farmer) ☛ Illinois_DCFS_kills_one_child
                  every_month_while_investigating_parents_for_allowing_kids_to
                  walk_the_dog._–_BaronHK’s_Rants⠀⇛


                       I think one can reasonably argue that the kids are
                       dead due to DCFS, which was found in contempt by a
                       state judge and is still in contempt of court
                       today, months later.


                       I think that there’s something poetic about the
                       State holding itself in contempt 12 times. I mean,
                       nothing happens because the State can’t punish
                       itself. How does a State that has no money except
                       what it stole from me and my spouse and millions of
                       other Illinoisans fine itself? Where does the money
                       it takes from itself even go? This is the kind of
                       bullshit that only happens in government. When the
                       judge throws the director of DCFS in prison for
                       contempt until things start getting better or he
                       resigns, I’ll be impressed. Until then, what is
                       even the point?


                       None of this should be a surprise. Illinois is
                       managing child services as effectively as the State
                       Police manage gun control (the FOID Act) and as
                       effectively as they’re managing the roads. Letting
                       us drive over pot craters while they’re busy
                       causing an 11 year traffic jam at US 41 and Grand
                       Avenue in Gurnee, because it will “help with
                       climate change”.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ BBC ☛ Are_internet_shutdowns_evolving?⠀⇛


          o § Monopolies⠀➾


                # ⚓ TechRadar ☛ Campaigners_urge_US_Senate_to_address_Big
                  Tech’s_monopoly⠀⇛


                       Digital rights campaigners are urging US Senators
                       to address what they consider “the fundamental
                       problem that plagues our online ecosystem.”


                       From Alphabet (parent company of Google and
                       YouTube) to Meta (Facebook, Instagram, and
                       WhatsApp), Apple, and Amazon, just a handful of US
                       companies – known as “Big Tech” – monopolize the
                       market.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ GeminiLoggBookOberDadaisticus:_Against_Interpretation⠀⇛


                # ⚓ SpellBinding:_ACXMOTI_Wordo:_QUAKE⠀⇛


          o § Technical⠀➾


                # § Programming⠀➾


                      # ⚓ The_File_Chooser_Button⠀⇛


                             I am a great admirer of Gtk+ and have always
                             felt that it is simply the best and most
                             comprehensive toolkit available in the open
                             source ecosystem. One might argue that it’s
                             the best toolkit period. That said, there
                             have been a few things over the years that
                             have left me scratching my head, and one of
                             them was that when Gtk4 was released it saw
                             the deprecation of the GtkFileChooserButton.


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


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 12457
    ➮ Generation completed at 02:42, i.e. 163 seconds to (re)generate ⟲