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- JoinedDec 18, 2021
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  sweettooth ₍₍ (̨̡⸝⸝´꒳`⸝⸝)̧̢ ₎₎   
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Statistics
All Anime Stats Anime Stats
Days: 33.8
Mean Score:
6.46
- Watching1
- Completed191
- On-Hold17
- Dropped38
- Plan to Watch399
- Total Entries646
- Rewatched54
- Episodes1,830
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Anime (10)
Character (10)
-
Akemi, Homura
Mahou Shoujo Madoka★Magica
-
Iwakura, Lain
Serial Experiments Lain
-
Reki
Haibane Renmei
-
Lawliet, L
Death Note
-
Osaki, Nana
Nana
-
Nagisa, Kaworu
Shinseiki Evangelion
-
Crona
Soul Eater
-
Anarchy, Stocking
Panty & Stocking with Garterbelt
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Mitsukai, Dokuro
Bokusatsu Tenshi Dokuro-chan
-
Naoko-san
Yuri Seijin Naoko-san
All Comments (26) Comments
⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀
⠀⠀⣰⣾⣏⠩⡉⠰⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀
⠀⣰⡇⠈⠙⠤⣽⣧⣹⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘
⢰⣟⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀
⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀
⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣿⣿⡶⠤⢕⡄⠀⠀⠀
⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀
⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠐⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣾⣷⡤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢎⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣿⣿⣿⣿⣷⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠣⡈⠲⡀⠀⠀⢀⣠⣴⣦⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣶⣤⣤⣤⣶⣾⣶⢿⡞⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢆⠈⠻⢿⣿⣯⢿⣽⣾⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠳⡀⠀⠙⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣉⢻⣿⡿⠿⣿⣿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⣀⣠⣤⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⠳⣷⡾⡷⢶⠷⣶⠶⣿⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠳⡆⢒⠢⡑⡘⡐⠢⠌
⠀⠻⠴⣌⡦⠼⣤⠡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠶⠶⣦⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠹⣆⢣⠱⡱⡘⢥⢋
⣔⡀⠀⢀⠠⠔⡚⢓⡇⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠈⠉⠁⠉⠐⠒⠒⠂⡄⠀⠘⢧⢣⠱⡍⠞⡬
⣙⠿⣛⠯⡘⠆⠙⣼⠳⠛⠉⠉⢉⣩⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠈⢷⣳⠈⠓⡒
⣈⣼⢦⡙⠔⡋⠟⣼⠀⣠⡴⠞⢋⣽⠋⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⢻⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠈⢷⢋⡛⠴
⠙⣋⠛⣉⠛⡌⠓⣸⠀⠃⠀⢠⡾⠃⠀⠀⠠⣤⣴⠿⠛⠉⠀⠀⠀⠀⠀⣿⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣿⠢⣍⠒
⢠⠡⡘⠤⡁⢎⠱⢘⣇⠀⣴⡟⠁⢠⢄⡀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠈⠓⢤⢋
⠐⣃⠈⡕⢈⠤⠋⣄⣻⡀⠛⠀⠀⠀⠀⠈⢣⡀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⢆⡾⠁⠀⠀⠀⢀⠮⣜
⣁⠎⡴⡉⠔⢊⠱⣄⠺⣇⠇⠀⠄⠀⠀⠀⣰⠇⠀⠹⣷⣄⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⢀⠠⡀⢆⠬⡑⡌⠆⢸⡼⠁⠀⢠⠂⠄⢎⠼⣌
⡌⠒⡤⠙⡢⣉⠶⢤⡉⢿⠀⢂⠀⣀⡤⠞⠁⠀⠀⠀⠈⠻⢷⣦⣄⣀⣀⣼⡏⢋⡰⢌⢢⡱⠸⢌⠲⢑⣬⣰⠏⠁⠀⣈⢂⠡⢊⡌⡒⢬
⣘⠱⣆⢋⡔⣡⠒⡜⣠⢋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⡩⢏⢛⡹⣌⢣⡜⣎⠣⠜⡁⠸⣯⠞⠋⠀⠀⢀⠰⡀⠆⢧⠘⢶⡩⢖
⢢⠹⢤⢣⡜⠠⣋⠴⡁⢊⠔⣠⠀⣄⠠⡄⢤⡐⢢⣌⡱⢌⡳⣌⠖⣯⢎⡳⢌⠣⡜⠠⠍⣲⠚⡿⠃⠀⢀⢠⠰⡌⠒⢥⠋⢦⠛⠤⠱⡉
⢎⠱⡌⢆⡘⢄⠂⢣⠅⢃⠠⠀⠛⡘⠳⡙⠶⡙⢇⠊⡁⠋⡔⠀⡂⠘⣏⠖⣉⠒⡌⠱⠀⠳⢧⣴⣤⣎⡑⠊⠱⡄⠱⣈⠘⠀⠜⣠⢡⠐
⡞⢠⠋⠦⢑⠂⠨⠄⠈⠄⠂⠈⠄⢡⠃⢥⠃⢥⠈⠐⣡⠐⡀⠀⡔⡌⢣⠚⡄⢣⠈⠄⠁⠀⣠⠄⠀⠹⡔⢨⠑⡠⠡⠀⢂⡁⢚⠄⡎⠄
⠚⠤⠉⠒⢈⠀⠰⠀⠆⠠⠑⡠⠐⢡⠋⣆⠱⢂⡑⢠⠂⢐⠢⢁⠢⡘⡴⢃⠜⠠⢈⠀⢠⠞⠁⠀⠀⠀⢻⡠⢋⠀⢓⠈⢆⡐⠣⢌⠘⢂
⠙⠬⡁⣜⠠⠘⠐⠰⠀⠑⠀⠠⢀⠐⠨⠐⡃⠉⡔⢂⡵⠊⠀⢀⢲⠱⣁⠊⠌⡐⠠⠀⠁⠀⠀⠀⠀⠀⠀⢷⠀⠜⠠⣉⠰⠈⠒⠌⠼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠘⢝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣱⠱⠤⠤⠖⠒⠲⠦⠤⣄⡴⠋⠀⠀⠀⠀⡳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠀⠹⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠴⠶⠶⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣀⣀⣤⣤⣤⣤⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣶⡛⠛⠛⠛⠓⠙⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠈⠉⠉⠉⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣭⡛⠛⠲⠶⣤⣄⠘⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣠⡶⠞⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣀⣀⣀⣀⡀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠉⠀⠸⡄⠀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡽⠉⠀⠀⠀⠉⠙⠢⡀⠀⢸⣿⠋⠉⠉⠈⠉⠉⠉⠉⢻⣿⠀⡠⠒⠊⠐⠈⢿⣶⡄⠀⠀⣇⠀
⠀⠀⠀⠀⠀⠀⢸⠃⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢸⠀
⠀⠀⠀⠀⠀⠀⡟⠀⠻⣄⣀⣀⣀⠀⠀⠀⠐⠊⠁⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⢳⢸⡇
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠠⠞⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⣴⣦⡤⢤⡀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠶⠋⠁⠀
⠘⣿⠬⢭⣶⣿⣭⣿⣶⣖⡦⠤⣈⠉⠙⠒⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀
⠀⠘⣦⠀⠀⠢⡈⠻⣉⣻⡿⢷⣮⣗⢾⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠧⢤⡴⠋⣉⣲⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠳⡄⠀⠑⢄⠠⡀⠀⠀⠳⣝⠷⣭⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⢞⡯⠟⠛⠛⡻⠿⣿⠿⠷⢶⣯⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢦⣄⣀⣁⣁⣀⣠⠤⠾⠒⠚⢹⠇⠙⠉⣩⠉⠙⠛⢋⠴⠋⠀⠀⠀⣸⣄⠀⠘⡄⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⠃⠀⡠⠞⠁⠀⠀⠀⠀⠀⡏⠙⠮⣁⠀⠀⢀⣇⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣎⡴⠊⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⢉⣩⠽⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠄⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⣀⣤⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡄⢀⡴⠚⠉⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠹⡏⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣳⣄⣠⠤⠤⠶⠶⠒⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢃⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠮⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡤⡴⠃⠈⠦⣀⠀⠀⠀⠀⠀⠀⢀⣷⢸⠀⠀⠀⠀⢀⣀⠘⡄⠤⠤⢤⠔⠒⠂⠉⠁⠀⠀⠀⠑⢄⡀⠀⠀⠙⢦⡀⠀⠀⠀
⠀⠀⠀⠀⣼⠃⠀⠀⢠⣞⠟⠀⠀⠀⡄⠀⠉⠒⠢⣤⣤⠄⣼⢻⠸⠀⠀⠀⠀⠉⢤⠀⢿⡖⠒⠊⢦⠤⠤⣀⣀⡀⠀⠀⠀⠈⠻⡝⠲⢤⣀⠙⢦⠀⠀
⠀⠀⠀⢰⠃⠀⠀⣴⣿⠎⠀⠀⢀⣜⠤⠄⢲⠎⠉⠀⠀⡼⠸⠘⡄⡇⠀⠀⠀⠀⢸⠀⢸⠘⢆⠀⠘⡄⠀⠀⠀⢢⠉⠉⠀⠒⠒⠽⡄⠀⠈⠙⠮⣷⡀
⠀⠀⠀⡟⠀⠀⣼⢻⠧⠐⠂⠉⡜⠀⠀⡰⡟⠀⠀⠀⡰⠁⡇⠀⡇⡇⠀⠀⠀⠀⢺⠇⠀⣆⡨⢆⠀⢽⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠁
⠀⠀⢸⠃⠀⠀⢃⠎⠀⠀⠀⣴⠃⠀⡜⠹⠁⠀⠀⡰⠁⢠⠁⠀⢸⢸⠀⠀⠀⢠⡸⢣⠔⡏⠀⠈⢆⠀⣇⠀⠀⠀⢸⠘⢆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⡜⠀⠀⢀⡜⡞⠀⡜⠈⠏⠀⠈⡹⠑⠒⠼⡀⠀⠀⢿⠀⠀⠀⢀⡇⠀⢇⢁⠀⠀⠈⢆⢰⠀⠀⠀⠈⡄⠈⢢⠀⠀⠀⠈⣇⠀⠀⠀⠀
⠀⠀⢸⡀⠀⢰⠁⠀⢀⢮⠀⠇⡜⠀⠘⠀⠀⢰⠃⠀⠀⡇⠈⠁⠀⢘⡄⠀⠀⢸⠀⠀⣘⣼⠤⠤⠤⣈⡞⡀⠀⠀⠀⡇⠰⡄⢣⡀⠀⠀⢻⠀⠀⠀⠀
⠀⠀⠈⡇⠀⡜⠀⢀⠎⢸⢸⢰⠁⠀⠄⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⣶⣿⡿⠿⡛⢻⡟⡇⠀⠀⠀⡇⠀⣿⣆⢡⠀⠀⢸⡇⠀⠀⠀
⠀⠀⢠⡏⠀⠉⢢⡎⠀⡇⣿⠊⠀⠀⠀⢠⡏⠀⠀⠀⠎⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠀⡇⠀⢰⡆⡇⢸⢠⢹⠀⠀⠀⡇⠀⢹⠈⢧⣣⠀⠘⡇⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⡇⠀⡇⢹⠀⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠠⠟⡯⣻⣇⢃⠇⢠⠏⡇⠀⢸⡆⠀⢸⠀⠈⢳⡀⠀⡇⠀⠀⠀
⠀⠀⠀⣇⠀⡔⠋⡇⠀⢱⢼⠀⠀⡂⣼⡇⢹⣶⣶⣶⣤⣤⣀⠀⠀⠀⣇⠇⠀⠀⠀⠀⣶⡭⢃⣏⡘⠀⡎⠀⠇⠀⡾⣷⠀⣼⠀⠀⠀⢻⡄⡇⠀⠀⠀
⠀⠀⠀⣹⠜⠋⠉⠓⢄⡏⢸⠀⠀⢳⡏⢸⠹⢀⣉⢭⣻⡽⠿⠛⠓⠀⠋⠀⠀⠀⠀⠀⠘⠛⠛⠓⠀⡄⡇⠀⢸⢰⡇⢸⡄⡟⠀⠀⠀⠀⢳⡇⠀⠀⠀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⢙⠌⡇⠀⣿⠁⠀⡇⡗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠁⠀⢸⣼⠀⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⢀⡠⠔⠚⠉⠉⢱⣇⢸⢧⠀⠀⠸⣱⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠦⡔⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⡏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠋⠀⠀⠀⢀⡠⠤⣿⣾⣇⣧⠀⠀⢫⡆⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣠⠇⠀⠀⢀⡠⣶⠋⠀⠀⡸⣾⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠠⠊⠁⠀⠀⢸⢃⠘⡜⡵⡀⠈⢿⡱⢲⡤⠤⢀⣀⣀⡀⠉⠉⣀⡠⡴⠚⠉⣸⢸⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠚⣤⣵⡰⡑⡄⠀⢣⡈⠳⡀⠀⠀⠀⢨⡋⠙⣆⢸⠀⠀⣰⢻⡎⠀⠀⡎⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⢌⣳⣵⡈⢦⡀⠳⡀⠈⢦⡀⠀⠘⠏⠲⣌⠙⢒⠴⡧⣸⡇⠀⡸⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⠢⡀⠀⠀⠀⠠⠄⡖⠋⠀⠀⠙⢿⣳⡀⠑⢄⠹⣄⡀⠙⢄⡠⠤⠒⠚⡖⡇⠀⠘⣽⡇⢠⠃⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡼⣄⠀⠀⠀⠀⠀⠑⣽⣆⠀⠑⢝⡍⠒⠬⢧⣀⡠⠊⠀⠸⡀⠀⢹⡇⡎⠀⡿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠻⣺⣧⠀⠀⠀⠰⢢⠈⢪⡷⡀⠀⠙⡄⠀⠀⠱⡄⠀⠀⠀⢧⠀⢸⡻⠀⢠⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⣿⠀⠀⠀⠀⢣⢇⠀⠑⣄⠀⠀⠸⡄⠀⠀⠘⡄⠀⠀⠸⡀⢸⠁⠀⡾⢰⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
__|__
| |__ ╲ ╲ ╲
|ロ | ╲╲ /\~/\
|ロ | ╲ ╲( •ω • )
|ロ | ╲⊂ づ
|ロ | ╲ ╲ ⊃⊃╲
|ロ |___ ╲| ___ ╲|____
⠀⢀⣀⣈⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢨⠀⠈⡏⢉⠀⣿⡇⠀⡠⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡔⡩⢆⣭⣶⣽⡀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⣿⣿⢺⣶⡾⠷⠚⠂⠉⠉⠉⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠈⢷⣡⢛⣿⡼⣽⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣶⠳⣄⢻⡿⠚⠁⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠘⣇⠎⡴⡙⢏⠢⣿⠳⢄⠀⠀⠀⠀⠀⠀⠈⠒⢦⠤⣄⡈
⣿⣿⣿⣿⣿⣿⡟⡠⢉⠛⢿⣿⣿⢣⠿⣌⢿⠼⠋⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠘⢿⡞⡰⣉⢎⣱⡟⢷⣌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀
⣿⣿⣿⣿⣿⣿⡧⡑⢎⡘⠤⡙⢧⡿⠽⢾⠋⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠘⢦⠀⠀⠀⠀⠈⢷⡱⢌⣲⢏⡜⠬⡙⢧⣳⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡙⢢⡑⢎⣔⢣⡙⡶⠁⠀⠀⠋⠈⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⢆⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⢷⣿⡇⢎⡌⢣⡙⢦⠹⣷⡀⠀⠀⠀⠀⡇⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⡜⡥⢺⠏⠉⢳⡞⢁⠤⠤⠤⠤⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢱⠀⠈⣧⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠘⣏⠖⣸⢡⠚⡤⢓⡜⢧⠀⠀⢀⢰⠃⠀⠀⠀
⢸⣿⣿⣿⠟⠉⢠⡗⡜⡏⠀⠀⡿⡱⠃⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣧⠈⣇⠀⢸⠳⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢻⡜⣡⠎⣷⡌⢣⠜⣩⢳⡀⠄⢸⠀⠀⠀⠀
⢠⡿⠋⠁⡀⢁⢺⣇⡿⠀⠀⣰⢃⡏⠀⢰⠃⠀⠀⣠⡯⠔⠈⢱⡤⣁⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠶⢺⠈⠻⡃⠒⠲⢼⣧⠀⠀⠀⠀⠈⡷⡡⢞⣹⡿⣕⢪⠔⣣⠳⡄⢸⠀⠀⢃⠀
⣡⣴⢲⡟⢁⠂⢘⡷⠁⠀⢠⢏⡾⠁⢀⡏⣀⠴⠒⠁⠀⠀⠀⠂⠀⡸⡄⢀⡇⠀⠀⠀⠀⢸⡇⣋⢇⢸⠀⠀⠑⡄⠀⢠⠿⡄⠀⠀⢀⠀⢿⡱⣊⠼⣿⡽⣧⡫⡔⢣⡽⢺⠀⠀⢸⠀
⠀⢰⡞⠐⡠⢨⡾⠁⠀⢠⣿⣿⣃⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⢸⢻⠀⠀⠀⠀⡆⢹⠆⢸⣸⠀⠀⠀⢱⡀⢸⠀⣧⠀⢀⠂⠄⡸⣷⣉⠶⣹⡿⣵⣿⣼⡏⣀⢻⠀⢠⠃⠀
⠀⢸⠁⠒⣰⠋⠤⠤⠊⠉⠉⠉⠀⠀⠀⡠⠔⠈⠀⢀⠄⠀⠀⢀⢼⡏⠀⡏⠈⡆⠀⠠⢈⡇⢸⡇⠈⣇⣠⣴⡦⢦⣧⣼⠀⢸⡀⢀⠂⠔⡀⣿⣜⠲⡥⢿⣟⡵⣺⠃⢄⣾⠀⠈⠀⠀
⠀⡞⣠⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢍⡧⣀⡀⠄⠊⠀⢀⡠⡞⠁⣸⠹⡀⠇⠀⠸⡀⠐⢸⠁⢸⠀⠐⠻⠟⠰⢾⣶⣄⠋⠻⣮⣅⠂⠌⢂⠔⣻⡯⢷⠚⣿⣽⣿⣹⠃⢼⡇⠀⠘⠀⠀
⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢀⣤⠖⢹⡕⢱⠀⡇⠀⢻⠀⠀⠀⢳⠈⡝⠀⠎⠀⠀⠀⠀⢴⣾⣿⣿⣦⠀⠙⣯⡐⠌⢂⠄⢻⠳⡈⢣⢸⡿⣷⣻⡅⣺⡇⠀⠀⠀⠸
⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠈⡠⣼⠁⢈⣿⡿⣿⣛⠣⠀⠀⠀⢣⠃⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⠹⡆⠀⡿⡇⠌⡂⢌⢹⣦⢋⠞⣸⡟⢻⣽⠆⡿⡇⠀⠀⠀⡐
⣇⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡞⢈⣇⠒⡀⡏⠀⣾⠛⢀⣹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣦⠼⠃⠀⣿⡗⢠⠑⡌⢾⡡⢊⣴⣿⣷⣾⣿⡃⣷⡇⠀⠀⡐⠀
⣜⣳⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠢⢈⢷⠀⣧⢰⣿⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣏⠄⢣⡜⢻⣤⣾⠿⣿⣿⠿⣿⣼⠋⣱⠀⠰⠀⠂
⠙⢾⡽⣷⣌⠑⢄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠳⠬⣷⣸⠈⢿⡀⠀⢿⡛⠿⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣸⣏⡘⣰⣧⢹⢿⡿⠉⠉⢧⡀⢸⣿⠀⣠⣇⠀⠀⠀
⠀⠀⠙⢯⣿⡶⣤⣕⣄⠀⠀⠀⢀⣀⣠⣤⡤⣀⡀⠀⢙⣧⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⣠⢧⡷⠠⣽⣛⣾⠒⠉⠋⠒⠐⠚⠐⢿⠙⠙⢚⡀⠀⠀
⠀⠀⠀⠀⢸⣿⡽⣿⢹⣟⡿⣻⢯⣻⣿⢿⢳⠤⣩⢹⡋⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡒⢩⠁⢆⡈⢧⠀⠀⠀⣠⡿⢯⡟⢰⠇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⣍⡻⣿
⠀⠀⠀⠀⠸⣿⣹⡏⢦⣿⣽⣳⢯⣿⣿⡏⣸⡇⢦⠹⡷⢤⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⠘⠤⡉⠆⣬⠏⠀⢀⣴⢭⣾⣿⡇⣿⡒⣾⢿⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣧⣿⣧⣼⣿⣷⣫⣟⣯⣷⣧⠟⣻⡤⢋⣿⠒⣤⡜⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠓⠋⢁⣠⣶⣵⣾⣿⣿⣿⣼⡿⢿⠻⡀⠁⠀⠀⠀⣠⠔⠀⡠⠁⠰⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⡿⣁⣸⢧⣷⣻⣾⠟⡟⠉⠉⢀⣳⢡⣿⣶⣿⣿⣟⣉⡉⣉⠛⢋⣓⣒⣲⣶⣶⣶⣯⣿⣿⣿⣿⣿⣿⠿⠋⠉⣽⠇⠀⠸⡀⢃⠀⠀⢀⠞⡇⡀⡰⠁⠀⡄⠀⠀⠀⠀
⢠⣆⡴⡄⢸⣥⡧⠚⠋⡏⠙⣷⣏⣤⣥⣿⣿⣿⣿⣧⢺⣀⡼⢄⡠⠔⠋⠉⠛⢗⢒⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠉⠈⢀⠤⠚⠁⠀⠀⠀⢇⠈⡆⢠⠣⢌⡟⢠⠁⢀⢾⠁⠀⠀⠀⠀
⣸⠋⠉⡏⠒⣀⣃⣤⣴⣾⢿⣿⣯⡿⠙⠛⠋⠂⠀⠛⢿⠶⠿⠋⠀⠀⠀⢠⣖⣦⡽⠽⡿⠿⠛⢉⣀⡀⠀⣿⣷⠀⡞⠁⠀⠀⠀⠀⠀⠀⠘⡄⠰⡇⠣⡼⢁⠆⢀⠎⣼⢀⠔⠀⠀⠀
⣇⣤⣶⣶⣿⣟⣫⣿⡟⠹⣯⣧⠞⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠸⠟⢹⠀⡜⠁⠀⠈⠁⠀⠈⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠹⣴⠃⡌⠀⡎⠄⡈⠁⢄⢀⣷⣾
⡟⠛⠛⠛⠛⠉⡿⠛⠻⢿⡦⣴⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠇⠀⠀⠀⠀⠀⠀⠀⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄⣳⠒⢣⣼⡀⢰⠁⠂⠄⠡⢈⣸⣿⡿
⣆⣀⣠⣲⣿⣟⡲⢤⣀⡀⠈⠛⣶⣶⣦⣀⡀⠀⠑⠄⠫⡒⠢⣀⠀⠀⠀⠀⡄⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠏⠀⠀⢀⣀⡔⠂⠉⠀⠀⠈⢈⣀⠀⠀⠈⣿⡀⠡⠈⠄⠠⣿⡟⢹
⠿⠛⠛⠛⠉⠙⣭⢳⡍⡷⡄⠀⠈⢻⣽⣿⣿⢶⡤⡀⠀⠑⢅⠠⠑⠦⡀⠀⢣⠂⢘⣀⣀⣀⡤⢀⢀⣀⠀⠀⠺⠇⣠⡔⠁⢈⠤⠐⠊⠉⠀⠀⣏⡀⡏⠉⠉⣿⣷⣀⣁⣀⣐⡿⣅⡇
⠀⠀⠀⠀⠀⠀⢈⣧⣻⠼⠇⠀⠀⠀⣿⣿⣿⣧⠉⠛⠷⣦⣀⠳⣌⠠⠉⣆⠨⠟⠙⢄⠐⠀⠃⠀⠙⠀⠉⢹⠧⡿⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⣿⡞⡿⣿⠁⢀⡈⠸⣷
⠀⠀⠀⠀⠀⠀⢸⡶⣹⣆⠀⠀⠀⡘⣀⢻⣿⣿⣧⠈⠄⠠⠙⠛⠪⠲⣄⡧⢀⣡⠖⢺⠈⠉⠉⠉⠉⠉⠐⢰⢇⡧⠊⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣯⡟⣽⣿⠀⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠹⣿⣟⡿⣶⣎⣰⠃⠀⣿⣿⣿⣧⠈⠀⠁⠂⠁⡀⠈⢳⡎⢨⠦⠇⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣸⢷⡻⡵⡟⠀⠀⠸⠊⢨
＼ ', !-─‐-i / /´
／｀ｰ' L/／｀ヽ､
/ ／, /| , , ',
ｲ / /-‐/ ｉ L_ ﾊ ヽ! i
ﾚ ﾍ 7ｲ｀ﾄ ﾚ'ｧ-ﾄ､!ハ| |
!,/7 '0' ´0iソ| |
|.从" _ ,,,, / |./ |
ﾚ'| i＞.､,,__ _,.イ / .i |
ﾚ'| | / k_７_/ﾚ'ヽ, ﾊ. |
| |/i 〈|/ i ,.ﾍ | i |
.|/ / ｉ： ﾍ! ＼ |
kヽ>､ﾊ _,.ﾍ､ /､!
!'〈//｀Ｔ´', ＼ ｀'7'ｰr'
ﾚ'ヽL__|___i,___,ンﾚ|ノ
ﾄ-,/ |___./
'ｰ' !_,.:
⠀⢀⣜⣴⠟⢀⠄⢀⠴⠊⡁⠀⣠⠞⢁⠆⢀⠜⠋⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠢⡀⠀⠀⠀
⠀⣾⠟⠁⠐⠁⠀⠀⡠⠊⠀⠔⠁⠀⡜⠀⠀⢀⠀⢀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢢⣀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠂⡀⠀
⣼⠃⠀⠀⠀⠀⣠⢞⣠⠄⢲⢂⡔⣸⠀⠀⣠⡇⠀⠘⡇⠀⠀⠀⠈⢦⠀⠀⠀⠀⢸⠀⠈⠉⢀⣍⣈⢻⣦⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⢦
⠁⠀⠀⠀⢀⡴⠋⢘⡇⢠⡾⠋⠀⡇⠀⢠⠃⠀⠀⠀⠻⡄⠀⠀⠀⠈⠳⡀⠀⠀⠈⡆⠀⢰⡟⠁⠈⠳⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠁⠀⢴⡞⣡⠋⠀⠀⢸⠁⠀⠏⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠱⡄⠀⠀⠘⣄⠀⠹⡗⢤⡀⠈⠳⡄⠀⢹⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠋⡴⠃⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⢦⡀⠙⣄⠙⢦⣤⣾⡆⠀⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡞⠁⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢰⡀⠀⣆⠀⠱⣄⣸⡇⠀⠘⠿⢻⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⢳⠀⣠⠟⠀⠀⠀⡇⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⡄⠀⠈⢛⢧⣀⡀⠂⣸⠀⢸⠀⠀⡄⠀⠀⠀
⠀⠀⠀⠻⣏⡀⠀⠀⠀⣷⠀⢸⣿⣿⡀⢢⠀⠀⡀⠀⠀⠀⠀⢧⠀⠀⠀⡇⠀⣼⡇⢠⠇⢹⣄⠀⠘⡆⢈⠉⠛⠁⠀⢸⠀⠀⠟⢆⠀⠀
⡇⠀⣤⠀⠹⣷⡀⠀⠀⣿⡄⢸⣿⠻⣧⠈⢧⠀⠹⡀⠀⠀⠀⠈⣆⠀⠀⣧⢰⠇⡇⣸⠀⠀⠹⣆⠀⣿⣼⡄⠀⠀⠀⢸⡆⢸⠀⠘⣆⠀
⢹⡀⣿⣧⡀⠹⣷⡀⠀⢹⣷⢸⣿⡆⠹⣧⡘⣧⠀⠱⡄⠀⡀⠀⠸⡆⠀⢹⡏⢀⣿⣧⡠⠤⠴⢿⡇⣻⣿⣇⠀⠀⠀⢸⡇⡜⠀⢀⡏⠀
⠘⣧⠀⢸⣷⣄⢻⣷⣄⠈⣿⣿⣿⣉⡛⢻⡷⣿⣇⠀⢹⣦⣱⡄⠀⢹⡖⢻⠋⣹⣿⣥⣴⣶⣶⣶⣿⣿⣉⣿⡄⠀⠀⢸⣵⠃⠀⣸⡇⠀
⠀⠹⡆⢸⠻⣿⠮⢿⣿⣷⣾⣿⡿⠋⢛⣻⣿⣿⣿⣧⠈⣿⣿⣿⣦⡀⢻⣼⠘⣿⠟⠉⢴⣾⣿⣿⡟⠻⡇⢹⣧⠀⠀⣾⡏⡰⢰⡇⠀⣠
⠀⠀⠹⣼⡄⠘⣷⡀⠙⢿⣿⡿⣇⠀⠈⢻⣿⣿⡿⠻⣷⣼⡏⢻⣟⠻⣾⣿⡄⠁⠀⠀⠈⠛⠛⠋⠁⠀⢠⣿⣿⡀⢠⣿⠟⢡⣿⠃⣾⠃
⠀⠀⠀⠙⣧⠀⣿⢷⣄⢀⣹⣿⣿⣅⠀⠈⠁⠀⠀⠀⠈⣿⣿⡄⠙⠦⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣴⣫⡾⣿⡇⣼⠋⣴⣿⣿⡞⠁⠀
⠀⠀⠀⠀⠈⠀⣿⣤⣝⠋⠛⢿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠁⠙⢆⠀⠀⠀⠙⢌⠂⠀⠀⠀⣠⡴⢻⡿⠋⣰⣿⣷⣧⣾⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠈⠛⣿⣍⡛⠛⠓⠢⠤⠀⠀⢀⣷⠈⠀⠀⠀⠀⠀⠀⠠⠔⠋⠁⣠⣏⣴⠞⢋⣸⣿⣯⣿⣏⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡹⣷⣤⣽⣾⣽⣢⢤⣀⠀⠀⠀⠊⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠭⠔⠒⠛⠛⠛⠿⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣌⠻⣍⠉⠛⢿⣟⠛⠛⠓⠀⠀⢀⣈⣀⣀⡀⠀⢀⣠⡶⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣿⣿⠳⣜⢷⣄⠀⢿⣿⣦⣄⡀⠀⠀⠈⠉⠉⠉⠁⠈⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣇⠈⠳⢿⣷⣼⣿⣿⣽⣿⣶⣄⠀⠀⠀⠀⠀⠈⢨⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠑⠿⣿⡎⠛⢧⠈⠙⠙⠦⣄⣠⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠚⢳⡿⠻⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣴⠟⠃⠀⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣧⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⠃⠀⢀⣼⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⣿⢷⡟⠢⡀⠀⠀⠀⠀⠀⠠⠄⠉⠛⠛⢭⣴⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢊⢀⡟⢸⡟⢸⣷⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠎⣸⡇⣿⢇⠏⠹⣿⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⢀⡴⣿⠟⣡⠋⠀⠀⢹⣷⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡴⠋⣼⠏⠀⣿⠀⢀⠔⠉⠙⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢿⠀⡎⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⣿⣤⣤⣿⡆⠀⢸⣦⢃⡴⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠘⣄⠀⠀⢠⣿⣿⠻⣿⣿⠇⢀⣼⠿⠋⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣿⣈⡶⠋⣹⣿⣧⡈⡿⠀⣠⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⣀⣤⠴
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢲⣤⣠⣤⣄⣠⡀⠀⠙⢯⡀⠀⢸⣿⣿⡿⠁⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢠⣶⡿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣾⣿⠠⠀⠀⠈⠻⣶⣄⠀⠙⠲⣿⡹⠏⠀⣰⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣴⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠦⠚⠉⠀⠀⠀⠐⠀⠀⠈⢿⡷⢤⠴⠛⠁⠀⠀⢈⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣉⡤⠖⠊⡏⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⢱⠦⣄⡀⠙⢦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡞⠁⠀⣠⢞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⣇⠀⠙⢆⠈⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢧⡠⣾⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⣧⠀⢸⠂⠀⣧⠀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⢸⠈⢇⠀⢰⠀⠀⠀⠀⠀⡇⢠⠃⢻⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡇⠀⠀⠈⡵⠦⡼⠶⢾⣷⣸⣧⠀⠀⠀⣸⣧⣯⡶⣾⡴⡏⢀⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇⠀⠀⡼⠁⠀⣀⣀⡀⠀⠉⠉⢦⠀⢠⠋⠉⠁⠀⣉⣸⣗⣉⡈⠳⣄⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣴⡀⠀⠀⢃⣠⠞⣿⡷⡿⠛⣿⣿⣿⢶⡄⠈⠳⠋⠀⠀⣰⢾⠛⢻⣿⣿⡿⣿⡈⡟⠂⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠁⠀⠸⡇⢿⣽⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⢿⡵⣿⣿⣯⡇⠏⡹⠁⠀⠀⢀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠹⣌⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠀⣰⠃⠀⠀⠀⣠⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢀⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⢀⡜⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠑⢆⡀⠀⠈⠻⡍⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⣀⣤⣟⠁⣠⠔⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣿⠛⣻⣶⣤⣤⣤⣀⣠⣤⢤⣤⣴⡶⠫⠿⣿⡚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣶⡄⢰⢳⠃⢀⣷⣿⠦⢯⣿⡗⠀⢧⠹⡄⠀⣤⣽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣶⣿⣄⣾⠏⠀⠈⠑⢦⡀⣤⠞⠉⠀⠈⠱⣧⢠⣼⣿⣦⣽⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣻⣿⣿⣿⡿⠟⢹⣿⡄⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡟⠓⢍⠻⡿⠏⠁⠀⢸⢿⡟⠲⠶⠚⢱⠋⢲⠑⠒⠒⠊⣟⡩⢾⡇⠙⢿⣿⡿⢋⡼⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠙⢤⡀⡻⠁⠀⠀⠀⡌⠶⣷⡶⠶⢦⠘⣗⠏⢀⠒⢒⣒⡻⠆⢸⡇⠀⠀⢻⡕⠉⠀⠀⠳⡀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⣧⠀⠀⠉⠉⠉⠀⢸⠀⠈⠉⠉⠀⠀⠀⣠⡇⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠚⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠈⠑⠢⣄⡀⠈⠁⠀⣀⠴⠋⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⠀⠀⠀⠀⠉⣷⠒⡋⠀⠀⠀⠀⢫⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠤⡄⠀⠀⠀⡇⠀⣇⠀⠀⠀⡤⢦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠞⠀⠹⣄⠀⢸⠀⠀⢹⣀⣠⠞⠀⠘⠦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣉⡟⠀⠀⠀⡏⠀⠀⠀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠉⠉⠀⠈⡇⠀⠀⠀⡏⠉⠉⠉⠁⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⣆⣠⠇⠀⠀⠀⣧⠀⣠⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠶⠛⠁⠀⠀⠀⠀⠈⠻⠿⣦⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠈⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⢀⠀⠀⠀⠈⠀⢀⡰⣊⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠠⠈⠂⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣍⠄⡂⡺⡀⡰⢄⡀⣔⡲⢞⡩⢥⡰⠂⠀⠀⠀⢀⢀⠒⡤⠜⠠⢔⣈⠣⠄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠹⠞⡾⠀⠀⠀⡝⢦⡙⡵⣀⠦⣑⢫⡏⣴⣣⡜⠔⠁⡢⢉⣴⡋⢄⠢⡜⣢⠳⠔⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢨⢟⡄⢸⢀⡗⣩⢶⣒⢦⣙⣮⠵⢫⡜⢧⢒⠐⣀⠀⣆⡲⡎⠸⡞⣋⣙⠃⠒⣲⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣯⢷⠀⠸⠜⠑⠉⠁⠀⠒⠂⠒⠂⠐⢸⡌⠳⢤⡹⠐⠴⠠⢁⡐⣠⠤⢤⣊⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡭⠑⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⢳⡍⡖⣝⢪⡡⠄⠜⠘⠡⢒⢀⣀⢏⡫⠭
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠈⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣁⡄⠀⠀⠈⡄⠀⡀⠀⠂⠠⠀⠀⠀⠀⠀⠹⣜⢆⣳⡥⡌⠃⡴⣠⠎⢙⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡏⣿⡟⡏⢿⡿⣿⣿⢢⢀⠆⢀⡇⠀⢹⣈⠐⠀⠠⠄⢁⣂⣐⠂⠈⣳⢧⡘⢝⡦⡀⢡⠀⠄⢀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡿⡁⡾⢠⣿⠳⣇⠈⣇⣹⡏⠆⣾⢃⠞⠼⡀⠸⣇⣆⠰⣢⢀⠀⡈⡀⠠⠐⠙⢫⣵⡰⡝⠻⡦⣔⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⡛⠃⢄⠋⠸⢱⣿⡍⠹⢻⢠⠻⡶⣄⠈⢇⠰⠌⢮⡉⠻⣧⡐⠠⠏⠤⣀⠀⠘⣽⣵⡐⡀⠊⠹⠫⣒⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠻⣿⣿⣿⣿⡄⠟⠿⠧⠁⠀⠀⠀⠈⠿⠃⠀⣟⣸⠸⢰⣟⠀⢘⠤⠀⢶⠿⣤⡻⣧⡁⣟⠰⣀⠣⣬⣘⣯⠣⡘⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣙⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡿⢿⠀⠈⠂⠀⠀⠘⠀⠁⣶⣿⣧⠳⣷⢸⡐⣦⡿⣳⡫⠂⠀⠈⠢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⡀⠐⠀⠀⢀⣴⣿⠃⢸⡀⠀⠐⠀⠀⠀⠀⠉⢯⡽⠁⠜⡜⠳⡜⢆⡿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣂⠤⠀⣀⣤⣾⣿⡿⣟⣤⠀⣛⡦⡈⠂⡀⣀⠀⠀⠀⢀⣌⠞⣈⠽⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢁⡡⠀⠘⡅⠡⠤⠤⢀⡀⠀⢤⡮⢒⣴⣭⣶⡶⣾⣞⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢏⡳⣙⠮⡜⡻⢿⣿⣿⣿⣿⣿⡟⢣⠀⠀⡁⢶⠀⠀⠀⠄⢀⠨⠻⢿⡫⠔⠁⠀⠙⠿⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢏⡚⡴⡩⢖⠭⣓⢭⣛⣿⣿⣿⡟⢠⢨⠀⠌⢡⢰⡦⠀⠄⠀⢃⢠⠂⠃⠀⠀⠀⠀⠀⠐⡀⠉⠋⠞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣮⣟⠭⣓⠯⣞⡡⢖⠦⣙⣿⣿⡇⠸⠀⠀⠀⠆⢸⡡⠂⣀⢢⡿⠋⡈⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⠿⠋⢡⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢛⡲⢝⡺⢥⣣⣾⣿⠁⠀⠀⠀⠀⢠⠃⡎⣫⠡⣱⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⣄⠙⡳⢏⣾⡿⡀⠀⠀⢀⣶⠝⠈⠭⠁⠀⡱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⠀⠠⠕⢥⢀⣼⣷⣿⣷⠎⠉⠀⠀⠈⠁⠀⡴⠃⢀⡀⢽⣶⣶⣬⣡⡄⣢⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠑⠢⠠⢂⣽⣿⣿⣿⣿⠀⠀⠀⠀⠰⡰⠈⢼⡉⡗⠀⠀⢂⠉⠉⠙⢉⣀⠁⢂⠄⢀⡀⠀⠀⢀⢀⡤⠦⠠⠓⠒⢶⡖
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⢀⢪⡔⢸⣿⣿⣿⣿⡄⡣⠀⠀⠀⡆⠛⢧⡜⡙⡟⡦⠀⠀⣠⣄⣀⣰⡾⠝⣠⡞⠍⠋⠄⠐⠀⠀⠀⠀⠀⠈⠐⣳
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠃⡎⠄⡾⠋⢻⣿⣿⣷⢺⡘⡆⢂⠁⠀⠀⠑⠵⠁⠘⠻⢛⠳⡩⢍⣹⠀⡰⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠐⡐⠀⠘⠁⠀⠀⠻⣿⡟⠂⡐⢨⡑⢄⠀⠀⠀⠀⠀⠀⢀⠎⡵⢱⠊⠀⢈⢂⠀⠀⢀⠠⢂⢌⢂⣦⣵⡿⠟⠓⠈⠁
⡿⠟⣰⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⢋⣁⣀⣀⠀⠇⠀⠀⠀⠀⠀⠄⠈⢀⠄⡧⠸⠐⠁⠀⠄⠀⠀⠀⢀⢎⡚⡔⢋⡞⣍⠫⡜⢭⠲⣅⣫⣼⣾⡿⠋⠁⠀⠀⠀⠀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠠⠈⡆⠀⠀⠠⣒⡤⣃⠎⡴⠋⢸⠜⣰⢋⡜⡆⣏⠼⡍⠥⠍⠈⠙⡒⠶⣤⣀⠀⠀
⠀⣿⣿⣿⠿⡻⢵⡚⢯⠭⣭⠹⣌⡲⣳⣵⣿⣿⣿⣿⡄⠀⠀⠀⠀⠂⣁⢲⣷⡄⠁⣷⡄⠀⠀⠠⣻⡔⣩⠁⠀⣨⢻⢏⡚⡴⣩⢆⡳⡼⠀⠀⠀⠀⠀⠀⠐⠈⡓⣦
⡰⡿⢓⡕⢮⡱⢣⡝⡬⢳⡤⣓⠵⣩⢓⡬⡝⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⣿⣿⡄⢸⣿⣆⠀⠠⠢⣻⢴⡒⢶⣫⣝⣾⡻⣝⣣⢾⣹⢏⡝⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠋⡴⡹⣜⢣⡝⣣⢜⠵⡉⣤⠓⣮⢱⡩⢖⡩⢞⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢿⡿⢂⢴⡹⢥⢣⡟⣻⠱⣎⢿⢯⣛⠛⠮⠵⠫⠵⡉⠄⣀⠀⡀⢀⠀⡈⠤
⡝⣲⠱⣎⠳⣜⠕⣁⠲⣍⠶⣙⠴⢣⡱⢫⡔⣻⡿⣿⣿⣿⣆⠀⠀⠀⢠⣿⣿⣿⣿⣿⠊⠀⠀⠣⡓⢎⡣⢞⣡⠳⣘⢾⡻⣌⠳⣕⠨⡑⢢⠑⡌⢄⣣⣌⣢⡼⠶⠛
⠈⠥⢟⣬⣓⠁⣴⢩⠳⣌⠳⡥⡛⣆⢳⠱⢼⡿⢲⡹⣿⣿⣿⡄⠀⠀⣸⣿⣿⣿⣿⠁⠀⠀⠀⢀⡌⠣⣓⠮⡔⣫⢜⠃⢱⣊⢷⠜⠻⡛⠚⠛⠛⠛⠉⠉⠁⠀⠀⠀
⢀⣾⣅⠀⠀⠀⡱⣍⠳⣌⢳⡑⡳⣌⢇⣫⣿⡓⢧⡱⡹⣿⣿⣷⡀⠀⣿⣿⣿⣿⠇⠀⠀⠀⢠⡼⣣⠀⠀⠙⠓⢥⠏⠀⠀⢳⡞⠀⠀⠈⠢⠐⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⢠⠋⢀⡏⠑⠎⣧⡙⡖⣥⢚⣼⡯⢜⢥⢣⢓⡏⢿⣿⣧⢠⣿⣿⣿⡏⠀⠀⠀⣠⠟⢠⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀
⢠⡛⠛⠻⣷⣶⣦⣬⣕⡒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣳⠖⢋⣩⣭⣿⣶⡤⠶⠶⢶⣒⣲⢶⣉⣐⣒⣒⣒⢤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠉⣩⣭⣽⣶⣾⣿⢿⡏⢁⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⢭⣯⣟⡿⣷⣘⠢⡀⠀⠀⠀⠀⠀
⠹⣷⣿⣿⣿⣿⣿⢟⣵⠋⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣦⣾⣢⠀⠀⠀⠀
⠀⠹⣿⣿⣿⡿⣳⣿⠃⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣵⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⣯⡇⠛⣽⣦⣿⠀⠀⠀⠀⢀⠔⠙⣄⠀⠀⠀⠀⠀⠀⣠⠳⡀⠀⠀⠀⠀⢿⡵⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⠿⢿⠟⠀⠀⠀⢀⡏⠀⠀⠘⡄⠀⠀⠀⠀⢠⠃⠀⠹⡄⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⠒⠤⢤⣀⣘⣆⠀⠀⠀⡏⢀⣀⡠⢷⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠸⣿⣿⠟⢹⣥⠀⠀⠀⠀⠀⣸⣀⣀⣤⣀⣀⠈⠳⢤⡀⡇⣀⣠⣄⣸⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠁⠀⢸⢟⡄⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⠁⠀⠈⠙⠙⣯⣿⣿⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⢨⢞⢆⠀⠀⠀⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⡿⡇⠀⣠⢟⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⠀⢈⡏⢎⠳⣄⠀⡇⠙⠛⠟⠛⠀⠀⠀⠀⠀⠀⠘⠻⠛⢱⢃⡜⡝⠈⠚⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣅⠁⢸⣋⠈⢣⡈⢷⠇⠀⠀⠀⠀⠀⣄⠀⠀⢀⡄⠀⠀⣠⣼⢯⣴⠇⣀⡀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⡌⠛⣶⣆⣷⣿⣦⣄⣀⠀⠀⠀⠈⠉⠉⢉⣀⣤⡞⢛⣄⡀⢀⡨⢗⡦⠎⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣿⠁⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⢸⠀⠀⠀⠄⠙⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡉⢳⡄⠡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣠⣧⣤⣄⣀⡀⡰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⢀⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣠⠖⠒⠒⠛⢿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠤⠴⠞⢋⣵⣿⢿⣿⣿⣿⣿⣿⣿⠗⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡼⣶⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⢛⣿⠀⠙⠲⠽⠛⠛⠵⠞⠉⠙⠳⢦⣀⣀⡞⠀⠀⠀⠀⡠⠋⠐⠣⠮⡁⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣎⡀⢀⣾⠇⢀⣠⡶⢶⠞⠋⠉⠉⠒⢄⡀⠉⠈⠉⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠘⢁⡴⢟⣯⣞⢉⠀⠀⠀⠀⠀⠀⢹⠶⠤⠤⡤⢖⣿⡋⢇⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⠗⠺⠟⠖⢈⡣⡄⠀⠀⠀⠀⢀⣼⡤⣬⣽⠾⠋⠉⠑⠺⠧⣀⣤⣤⡠⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠦⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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░░▄▀▒▒▒▒▐░░░░░▐▒▒▒▒▐░░░░░▄█▄▒▐▒▒▒
▄▀▒▒▒▒▒▄██▀▄▄░░▀▄▄▀░░▄▄▀█▄░█▀▒▒▒▒
⣿⣿⣿⣿⣿⣿⣷⢳⠛⣿⣾⣿⣿⠀⢹⠀⡥⠸⣿⣿⣿⣿⡿⣿⣷⣌⠻⢻⣼⣿⣿⣿⢹⡏⠿⢻⣿⣿⠣⠀⢤⣤⣤⣿⣿⣥⣰⡿⠛⠑⢿⣿⠿⠋⢀⣸⣿⢻⡇⢻⣟⠗⠀⠀⠘
⣿⣿⣿⠛⢻⣿⣿⣿⡆⡜⣿⣿⡇⠀⠀⢚⢴⣾⣿⣿⣏⣿⣷⣽⣿⣿⣷⣾⣿⣿⣿⣿⣾⣯⣾⣿⣿⣿⣀⡀⢲⡟⢹⣿⣿⣿⣿⣿⣦⡀⠀⣹⣿⡾⢠⣿⣿⣿⡇⣼⡿⠃⠀⠀⠀
⣿⣿⣇⠀⢸⣿⣿⡇⣷⡇⢹⡟⠁⣲⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣮⡡⢀⣸⣿⣿⣿⣷⣿⣿⠃⢈⡀⡆⠀
⠻⣌⣧⡄⠀⢻⣿⣷⢿⣷⣽⣿⣼⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⡟⢫⣿⣿⢠⣿⣾⠃⠀
⠀⠈⠻⣿⣆⢸⢻⣷⢨⣿⣇⣷⡝⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢱⢿⡏⠈⢹⣿⡿⢋⣼⣿⠋⠀⠀
⠀⠀⠀⠈⢿⣦⣛⣿⣷⣿⣿⣿⣿⣾⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣴⣿⡿⠁⣸⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣷⡿⠁⠀⠀⠀
⠀⠀⠀⠀⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⠇⠀⠀⡰⠐
⠀⠀⠀⢠⢿⣧⠀⢘⢿⣿⢿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡏⠀⠀⡀⠀⠈
⣄⠀⠀⠐⣯⡛⣧⣾⡿⢻⣦⣭⣛⠿⣷⣾⣿⣿⣿⡿⠟⠛⢉⣿⣿⣿⣿⣿⣿⣿⡿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠘⠟⠻⣿⣿⣿⣿⢏⣨⣟⢀⣴⣼⠁⠀⠀
⠹⣶⡤⠗⣿⣿⡿⢻⣴⣿⢿⣿⣿⣿⠿⢿⡿⣟⣁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠋⠻⠻⠿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠐⣶⣿⠋⣹⢋⣿⣿⠃⠻⢓⣿⡾⠀⠀
⠀⢘⣿⣦⣼⣿⣷⣿⢣⠀⠀⢹⡟⠁⠀⠸⡽⣿⣿⣿⣿⣦⠿⠿⠿⠛⠁⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠈⢻⣿⣿⣿⡏⠀⣰⣿⠃⣴⠃⢋⣿⠃⠀⣴⣾⣟⣁⣠⣀
⣼⣿⠟⠻⣿⢹⡅⠹⠷⠀⠀⢸⡄⠀⠀⠀⢛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⢹⣿⢿⣅⣴⣿⠃⣴⣣⣆⣾⣧⠴⠚⣻⣿⠟⠛⣠⠟
⡿⠁⠀⣄⣻⣿⣿⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠘⠁⠀⠈⠛⢿⣾⡛⢻⣿⠛⢠⣴⣾⡟⠁⢠⢞⠁⢠
⠀⠀⣀⣸⠿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣙⠻⡇⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡎⢁⣠⣾⠟⠉⢀⡴⣣⢦⣾⣿
⠀⠐⠛⣡⣾⡿⠆⠀⠀⠀⠀⠀⣀⡼⠞⠚⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⠿⣃⣠⢴⣫⠾⠀⠿⠛⣿
⠀⠰⠿⣿⣿⣷⠷⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢯⣿⠞⣫⡷⠟⠉⠀⣀⣿⣶⣿
⠀⠀⠀⠙⠛⠃⢀⣉⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠛⢦⣦⣤⣤⡤⠴⠶⢛⡽⢻⣟⣡⡞⠁⠀⢀⣴⣿⠿⠋⣿⣿
⠀⠀⠀⢀⣤⣾⣩⢿⣿⡿⢿⣆⣀⣀⠀⢀⣀⣤⢶⣿⣿⣿⣿⣶⣦⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡟⠀⠀⠀⠀⠈⠙⠿⣄⡀⣠⠟⢀⣴⠟⣩⠀⣠⣶⠿⠟⠋⠀⠀⣿⣿
⣀⡤⠚⢻⣭⣷⣿⠋⣡⣴⣦⡾⣟⣯⡿⢿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⡃⢐⣋⡷⠎⠉⠁⠀⠀⠀⠀⠀⣽⠿
⠏⠈⢠⣿⣿⣽⣿⡶⢿⣯⠵⠚⢭⣼⠋⡿⠛⡀⣼⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣟⢯⡓⣦⣄⡀⢀⣀⣀⣀⠀⠀
⠀⢠⣉⣱⣤⣴⣶⣿⣿⡇⠀⢹⡇⠀⠀⠰⢿⣳⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡈⢻⡻⣿⢿⣭⠟⠋⠉⠉⠙⠒
⠀⠀⠈⠁⠀⠾⠿⣷⡟⠃⠃⠀⠁⣤⣤⣶⡿⠟⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢦⣄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣿⣿⡞⠁⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠜⠁⣀⣤⣾⠿⠟⠻⢙⣀⢠⡄⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⡖⠉⣿⣶⣤⠴⠾⠟⠉⠉⠛⠛⠿⠿⢤⣤⣤⡄⢚⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣶⣯⣿⣯⣁⣠⣶⣶⢋⣽⢋⣠⣾⣿⣯⠈⠁⠋⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣧⡏⣠⣾⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀
⠂⠀⠀⠀⣤⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣾⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡿⣾⣿⣯⣿⣷⣿⣼⣎⣿⣻⣾⢫⣾⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠄⢼⣧⣿⠟⢛⣽⣶⣾⣿⡽⢛⣱⡾⣻⣏⣿⠿⣿⢳⣿⣿⣿⣿⣿⣿⣿⠟⢋⢙⣿⣤⣉⣈⣉⣡⣴⣾⣿⠟⠁⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⠷⠶⢦⠤⢄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠚⣉⣤⣾⣿⣿⢟⣿⣿⣠⡾⣿⣿⣽⡿⢿⣿⢧⣽⣿⣿⣿⣿⣿⣻⣟⠻⠿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⢿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣿⣿⣿⣟⣵⡾⣿⣽⣿⣡⣿⣿⠿⠋⠀⣼⢃⣿⣿⣿⡟⣛⠻⣿⣿⣿⣿⣿⡿⠿⠛⠛⣛⠛⢻⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠈⠛⢛⣉⣹⣿⣷⢿⡟⢿⣟⠛⣿⠀⢀⣿⣿⢸⡿⣿⣿⣷⢹⣇⣽⣿⡟⢻⣿⣇⡿⣴⠀⣽⡇⣀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠐⠀⠀⣀⣾⣿⢿⡿⠉⡄⢸⣿⣇⡏⢀⣿⣿⠁⣾⣷⢸⣿⣿⡟⣹⡿⠛⠀⠚⢛⣿⣷⠿⡿⠁⠸⡃⠀⠘⢏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⢠⡿⢿⠟⠀⠀⠀⠃⠀⢿⣿⡆⢿⣿⡿⠰⣿⢷⠞⣿⡏⠱⠟⠏⠀⢦⡄⠀⠙⢿⡏⠀⠀⠀⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⠀⠱⣄⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠘⣇⢀⠇⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡤⣄⣀⠀⢹⣼⠀⢰⠏⠀⠈⢻⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡓⠦⢤⣀⣠⠴⠚⠉⠀⣀⣀⣤⣴⣿⣿⣿⣟⠉⠙⠲⢄⣧⠤⣼⡀⠀⠀⣸⣠⣤⣀⠀⠀⢸⢹⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⢀⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢼⣞⡉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡞⠁⠀⠈⠓⠀⢐⠋⠀⠀⠙⡆⠀⠸⡆⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡞⠙⠺⢦⡀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣾⠛⠻⣿⠿⠿⠛⠻⢿⢿⣿⣷⡀⠀⣀⣥⠐⠳⡤⣤⣀⡴⠃⠀⠀⣧⣱⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⢀⣠⠼⠿⠉⠀⠀⠀⢸⡿⠶⠾⠃⠀⠀⠀⠀⠈⣯⣿⠁⠉⢹⢹⠁⠀⠀⢳⠀⠀⠀⠀⠀⢠⡏⢷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⠟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⣿⠘⢦⣄⣀⡞⠀⢸⠀⠀⠀⢸⢀⣼⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⠒⠒⠒⠚⠯⠊⠓⠢⠤⣤⣠⣤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣀⠤⠄⠤⢄⡀⠀⡼⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠉⢸⠇⠀
⡄⠀⠀⠀⠀⣴⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⠀⠀⠀⠀⠙⣶⣻⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡟⢀⣟⡇⠀
⣳⣀⣀⣀⠀⠻⣿⣿⣿⡟⡩⠶⢿⣿⣿⡿⠟⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⣤⡄⠘⠉⠹⡇⠀⠀⢿⡇⠀⠀⠀⠀⣸⠁⠀⠀⢀⣧⠟⢸⡇⠀
⠁⣿⠁⠉⢷⣀⣿⠿⠻⢦⡳⢦⣾⡟⠉⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠤⣄⣴⠖⣇⠀⠀⠘⣧⠀⠀⠀⢠⠃⠀⠀⠀⢸⠁⠀⢸⠁⠀
⠂⠹⣄⠀⠀⢻⠃⠀⠀⠀⣷⠘⣟⠀⠀⠀⠀⢀⡤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠁⢀⣿⡄⠀⠀⠈⠓⠀⢠⠏⠀⠀⠀⢠⠇⠀⠀⢸⠀⠀
⢰⡴⠚⠓⠂⠀⠀⣤⣶⣾⡁⠀⠈⢷⡄⠀⡰⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠞⠁⠻⣆⠀⠀⠀⣰⠋⠀⠀⠀⢀⡾⠀⠀⠀⢸⠀⠀
⢸⡇⠀⠀⣸⡇⠀⠀⢻⠘⢾⠢⢄⠀⠙⠳⣧⣀⡀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⡾⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⠀⠀
⠀⣟⠶⠴⡏⢧⡀⠀⣼⠀⠈⣷⡈⠋⠉⠿⠂⣈⣄⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⢠⠟⢧⡀⠀⠀⠸⠀⠀
⠀⠸⡄⠀⠹⣸⡝⠚⠙⡄⠀⢏⢷⡀⢰⠒⠲⠏⠀⣻⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠻⣴⢾⣋⠙⠶
⠀⠀⣷⡀⠀⠹⡇⠀⠀⠹⣄⢸⠈⣷⠘⢧⣀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⣀⣤⠀⣸⠋⠀⠀⠀⠀⠈⠛⣿⠀⠀
⠀⠀⡇⢧⠀⠀⣇⠀⠀⠀⠘⢮⣆⠸⣖⠈⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠿⠒⠒⠛⢉⣴⣧⠞⠁⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀
⠀⠀⡇⠀⢣⡀⢹⠀⠀⠀⠀⠀⠉⠛⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀
⠀⠀⠇⠀⠀⠳⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⠀⠀⠀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠛⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠰⢮⣁⡈⡏⢻⠒⠦⢽⡄⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⡼⠳⣾⣿⣿⣦⡤⢤⣤⣀⣀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⡴⣤⣀⣠⡤⠞⠁⢣⢸⠀⠀⠀⢻⡄⠀⠈⢿⡓⠒⣒⣶⠶⠚⠋⠁⠀⠀⠀⡼⠁⠀⣿⠩⣔⡲⠶⠶⣢⡤⣉⠛⠶⣄⡀⣠⠟⠀⠀⠀⠀⠀⠀
⠈⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⢻⡄⠀⠈⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⣟⡭⣔⠶⠤⠴⢖⣬⡛⢕⣤⣈⡽⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⠀⢸⢰⠀⠀⠀⢀⣼⢷⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣼⠓⠉⠀⠀⠀⠀⠀⠙⢿⣦⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⠇⣠⡴⠞⠉⠀⠸⣇⠀⠀⢹⡆⠀⠀⠀⠀⢀⡼⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡴⣏⠉⢲⠤⣀⣀⡀⢿⠀⠀⠀⢷⠀⠀⢀⣠⡾⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣼⡁⠹⣆⠀⠳⡑⢜⢮⡻⡆⠀⠀⠸⡏⠉⢩⡞⠁⠀⠀⣰⣯⠤⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡏⢣⠀⠙⢧⡀⠈⠪⡳⢕⡇⠀⠀⠀⣻⣠⠏⠀⠀⠀⣰⠏⠀⠀⡿⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⣆⠀⠀⠙⢶⣄⡈⠢⣿⠀⠀⣀⡽⠃⠀⠀⢀⣴⠋⠀⠀⢸⠃⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣳⣿⠁⠉⠛⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡾⣯⣿⣿⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⡇⠈⠫⠟⢿⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⡿⠛⢿⢿⣷⠀⠀⠀⠀⠈⢿⣯⣖⣂⣤⣄⣤⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⠟⠿⢯⡯⣿⣟⠉⠁⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⢻⣿⡿⠀⠀⢀⣏⣟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣧⡀⠘⠛⠃⠀⣠⣞⣿⡯⠃⠀⠀⠀⠀⠀⠀⢀⣄⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣮⣦⡀⡀⣴⣷⡟⠃⠀⠀⠀⠀⠀⠀⠀⡴⣟⣛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡿⠋⠀⠀⠀⡤⣄⣤⣤⣄⣾⡟⠀⠀⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣷⡏⡏⠉⠉⢿⡇⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡮⡦⣀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⢯⣵⣿⠿⠶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠵⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀