Unicorn But Calm Emojis & Text

Copy & Paste Unicorn But Calm Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣰⢢⢀⡶⣠⠖⡱⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣰⢢⢀⡶⣠⠖⡱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠉⠇⣴⣿⠾⡁⡝⠁⠀ ⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⢖⡒⣮⠀⢼⣠⠆⢷⡑⠁⠊⠗⠀⠀ ⠀⠀⠀⠀⠰⠋⠀⠠⠀⠀⠵⡨⠥⠐⠊⢀⢠⠀⠀⠀⠀⣴⠀⠀ ⠀⠀⡰⠛⡹⠀⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⠉⠀⠀⠀⠀⠀⠑⡀ ⢀⡔⠁⡀⡇⠀⠀⠀⠀⠀⠀⡠⠁⠀⠣⣀⣀⣀⠀⠀⠐⠀⣡⠁ ⠀⡀⢂⠄⠑⠂⠞⡇⢀⣀⣈⣉⢹⣷⠀⠀⠀⠀⠈⣷⣖⣸⣷⠀ ⠀⠑⢕⣦⠬⠤⠞⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀

Related Text & Emojis

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢁⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⡉⢠⠟⢷⡀⢀⣴⣿⣦⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⡏⠁⣠⡿⠛⠉⠁⢀⡼⡻⠛⡞⡷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⢯⠟⠂⠀⢹⣞⡟⠁⡠⠔⢒⡾⡼⠁⠀⡇⣇⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⡼⠻⡇⢸⢀⣴⣿⣱⠁⠀⢀⠇⡏⠑⢄⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠳⢌⣾⡷⠀⠁⠀⠀⡼⢀⣧⡀⠈⢣⡀⡼⠉⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢳⠤⠴⠟⠁⣰⣿⠛⢶⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠞⠉⠀⠀⢀⣾⡋⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣠⣴⡾⡟⠉⠣⡀⠹⡄⠀⠀⠀ ⠀⣠⠞⠋⣽⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇⠀⠀⣇⠀⢿⠀⠀⠀ ⢰⠏⢿⡆⠸⡄⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⡞⣰⢧⡀⠀⢸⠀⠸⣆⣴⡆ ⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢴⠿⠚⢇⠀⠳⣄⡀⠳⠤⢤⡾⠃ ⠘⢧⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⠢⣄⡀⠉⠙⢻⠛⣧⠀ ⠀⠀⠙⠒⠦⠼⠗⠒⠲⠦⢤⣀⠀⠀⠀⣀⣠⣶⠇⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠀⠀⠉⢦⠀⢸⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠈⢳⣄⠀⢸⢀⣾⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢴⣴⣚⡁⣀⡠⠊⣨⣧⡾⢫⠃⢀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡾⠓⢲⠋⠉⠁⠀⡎⢀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡎⠀⠀⠀⠀⢇⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢣⠀⠀⠀⠀⠀⠉⣹⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠓⠤⣀⣀⠤⣶⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠒⠚⠋⠙⠲⠦⠤⠤⠶⠛⠁⠀⠀⠀
⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢰⢦⡀⠀⢰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣎⠙⠲⢤⣀⠀⠀⠀⡌⠈⣗⣄⡌⠘⣷⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⡀⠀⠈⠙⠲⢄⣣⡖⣯⡷⣧⠀⢸⢿⣦⡀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⣿⣼⣯⣄⣿⣦⣸⢸⣏⠻⣤⣀⣈⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢤⠤⠴⠻⣯⠈⠋⠙⠃⠀⠈⣿⠻⣾⡿⠛⠁⠉⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠈⠷⣤⡛⠛⢿⣿⡟⢹⡄⠀⠀ ⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢻⠿⠿⠀⠀⠀⠀⠀⠈⢻⡙⢹⡏⠿⣆⣹⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⡞⠁⣀⠙⢿⠂⠀ ⠀⠀⢀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣿⠀⢸⡄⠀ ⠀⠀⡞⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⣷⣾⠇⠀ ⠀⢸⠈⠿⠀⠙⠲⣄⠀⠀⢀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⣼⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⣘⠷⠊⠉⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢴⣶⠿⠖⠛⣿⡄⠀ ⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠙⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠹⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⣴⣶⣶⣾⣟⠟⠀⠀⠠⠃⢠⠎⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⣟⢿⣷⣶⣶⣶⣤⣤⣀⠀ ⠀⠸⣿⣿⣿⣿⣿⡿⢻⠋⠀⠀⠀⠁⡰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠈⢺⠛⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢿⣿⣿⣿⡿⢳⠃⢀⡀⠀⠀⡼⠁⠠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠑⠄⠀⠳⡛⢿⣿⣿⣿⡟⠀ ⠀⠀⢸⣿⣿⣿⣤⡇⠃⠀⠀⠀⢰⠃⠀⢡⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⢱⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⣿⣿⢫⡟⠸⠀⠀⠀⠀⡏⠀⠀⡎⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⣄⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢦⠀⠀⢫⡹⣿⡟⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⣏⠀⠀⠀⢸⠁⠀⡸⠀⠀⣼⠟⡇⠀⠀⠀⠀⠀⠀⠘⣼⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⢧⠀⠀⢻⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠮⠀⠀⠀⡏⠀⠀⡇⠀⡰⠧⠤⠼⡀⢰⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡀⠀⠸⡄⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⢠⡟⡄⠀⡳⠀⠀⢰⠇⠀⣼⠁⡰⢁⣀⣀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠙⣌⠛⠦⡀⠱⡙⢦⡀⠀⢣⠀⢣⠀⠀⢇⠀⠈⢏⣏⠛⢖ ⠀⠀⢠⢳⠃⡇⠀⢑⠀⠀⢸⠀⡜⢉⣦⣯⡵⠶⢦⣌⠐⠜⢄⠳⣄⡀⠀⠀⠀⠈⢲⣈⣭⣵⣿⣑⠳⣄⠈⡇⠘⡆⠀⢸⠀⠀⢸⠘⡆⠀ ⠀⣠⠃⡞⠀⢱⠀⢸⠀⠀⢸⡜⢠⣿⠟⢁⠐⢿⣷⣌⢳⡀⠀⠑⠸⠯⠉⠑⠒⢢⡟⠁⠘⣿⣶⡍⠻⣬⡷⣧⠀⢳⠀⠨⡄⠀⢈⠆⢹⡀ ⡜⠁⣼⠇⠀⠈⡆⠈⡆⠀⢸⠐⣾⠃⠀⣿⡖⣶⡽⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⣶⣷⣹⣿⠀⢹⡾⢾⢀⣾⡀⠀⡇⠀⢸⠀⠀⢣ ⣠⡾⢼⡁⠀⠀⠹⡄⢱⠀⢸⠐⣻⠀⠀⣿⣏⣿⣧⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⢿⣿⢿⣻⠀⠀⡷⠞⠉⣯⡇⢀⡇⠀⣸⠀⠀⠘ ⣿⡝⣾⠀⠀⠀⠀⢳⠈⢇⠸⡀⠹⡄⠀⠘⢇⣐⡨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⣂⡸⠃⠀⢸⠓⠂⢰⢿⡇⢰⠀⢀⡇⠀⠀⠀ ⣷⣛⣼⠀⠀⠀⠀⠀⠣⡈⢆⢇⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠋⠁⢀⡷⢫⣗⡸⠀⡼⠀⠀⠀⠀ ⢷⣝⣾⡄⠀⠀⠀⠀⠀⠑⣌⢾⡀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⠀⠀⠁⠁⠀⠀⠀⡜⠛⣫⣷⠃⡼⠁⠀⠀⠀⠀ ⠸⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢸⣧⢿⢿⡟⡸⠃⠀⠀⠀⠀⢀ ⣧⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢠⡿⣼⡹⣾⡟⠁⠀⠀⠀⠀⠀⢸ ⠈⠁⠈⠻⡽⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣴⣟⡳⢧⣻⡽⠀⠀⠀⠀⠀⠀⢀⡯ ⣿⣶⣤⣄⣹⡽⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠉⠀⠀⠀⢀⣠⣴⢯⡳⣞⣿⣷⣹⡇⠀⠀⠀⠀⠀⢀⣾⢳ ⣿⣿⣿⣿⣿⣿⣯⠷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣒⣦⢤⣤⣠⣀⣄⣠⣤⣤⣴⣶⢻⡽⣻⣮⣗⣻⢼⣻⡟⢾⡇⠀⠀⠀⠀⢀⡾⣭⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢦⣀⠀⠀⠀⠀⠀⠹⡏⠁⠉⠓⠦⣉⡉⠛⣙⣩⠵⢚⠩⠳⣽⣽⣼⣿⣾⣷⣷⣿⣿⠆⠀⠀⠀⣠⣾⣻⣾⣿
⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⠀⣠⡀⢀⣠⣴⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⡟⠋⢀⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⠆⣠⣾⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀ ⣼⣿⡿⠻⠂⢹⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣀⠀ ⠀⠀⠀⠀⠀⢼⣿⣿⡿⠁⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣰⡟ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⠀⣠⠶⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄⠀⠀⣸⣅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠁⠙⣿⣿⡇⠀⢸⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠏⠀⢀⣿⡏⠀⠀⠀⠉⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠁⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡄⢫⠉⢩⠃⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡞⠳⡜⠦⠚⠘⠒⠋⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠉⠉⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀ ⠀⠀⠀⠀⣶⣦⣤⠘⣿⣿⣆⠀⠀⢿⠇⣼⣿⣿⣿⣿⠛⢸⡇⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠈⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣁⠀⠻⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣇⡀⣾⠃⠀⠀⢠⣿⣿⣿⡇⠀⡔⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⠟⠀⠀⠱⠤⣀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⡗⡤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣫⢸⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⢀⣠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣷⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⢿⣿⡿⣿⣥⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⠟⠛⠛⣻⣿⣿⣏⠁⠀⠹⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⠟⠁⢀⣠⣾⣿⡿⣿⣿⣄⠀⠀⠉⠙⠛⠿⠿⠿⠟⠙⠹⠿⠿⠿⢿⣿⣿⣿⣶⣄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⢸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠉⠚⠋⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀ ⠀⠀⢀⣠⣴⣶⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠋⠓ ⠀⣴⣿⠇⠉⠉⠛⠛⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀ ⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡏⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠻⣿⣦⣀⣀⣴⣾⠿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⠰⣿⣿⢉⣿⠟⢿⣿⠁⢾⣿⠉⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠀⠘⢿⣦⣍⣀⣾⡟⠀⠈⢿⣦⣄⣠⣾⡿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠉⠙⠋⠉⠀⠈⠻⣿⣄⠀⠀⠀ ⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀ ⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⣸⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄⠀⠀⠀⠀⠸⣿⠀ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢣⡀⠀⠀⠀⠀⠀⣰⠁⡼⠀⠀⠀⠀⠀⠀⣿⡆ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠉⠒⠦⠤⢤⠞⢁⡼⠁⠀⠀⠀⠀⠀⢰⣿⢡ ⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀ ⠀⠹⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠏⠀⠀ ⠀⠀⠙⢮⣷⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⡿⠿⣶⣤⣤⣄⣀⣀⣀⣀⣀⣸⣷⣄⣀⣤⣤⣴⣶⠿⠛⣿⣇⠀⠀⠀⠀⠀ ⠀⣀⣠⣴⣿⡿⠁⠀⠀⢈⣉⣿⡞⠛⠛⠛⠛⠻⣿⣟⠛⠉⠉⠀⠀⠀⢀⣿⡿⣦⡀⠀⠀⠀ ⠀⢻⣉⣼⠛⣷⠄⠠⢟⠋⣽⠻⡖⠀⠀⠀⢠⡾⢻⡛⠳⣶⠒⠒⠒⠴⠟⠁⡇⢈⡛⣀⡀⠀ ⠀⠈⠉⠛⠒⠻⠀⠤⠬⠴⠯⢄⣷⣀⣀⡀⣜⣡⣼⡧⠤⠁⢀⠠⠤⠄⠠⠀⠀⠒⠂⠀⠛⠃
⣰⡿⠿⠿⣷⣦⣠⣤⣾⠟⠛⠳⣦ ⡏⢀⢀⣠⣶⠟⣹⣿⠷⣦⡀⢀⢘⡇ ⢣⣤⣴⠿⠃⢀⡿⢿⡆⠈⠻⠿⠟⠁ ⠀⠀ ⠀⠀ ⣠⠃⠈⠳⡄ ⠀⠀ ⣰⡟⠁ ⠀⠀ ⣸ ⠀⠀⢰⡏ ⠀⠀⠀ ⢠⡟ ⠀⠀⠘⣇ ⠀⠀⠀ ⢸⡇ ⠀⠀ ⢿ ⠀⠀⠀⠀⠈⢷⡀
.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⡁⡇⢸⡇⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⡇⣿⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢸⣧⣤⠤⠤⢤⣤⣿⠦⣄⣀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣶⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣾⠀⣿⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢫⠀⣿⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢈⡴⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠤⠀⠠⠄⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⢆⣧⠀⠀⢀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⢦⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⠒⠲⡏⡰⠁⠀⠀⢰⢸⡾⢹⠀⠀⠈⡇⢠⠠⢷⡻⣖⠒⠤⣀⠀⠈⡆⠀⢷⣤⣤⣴⣶⣦⣤⣤⣼⠀⢿⣤⣤⣤⣤⣤ ⣀⣀⣠⣤⣄⣠⣤⣤⡼⢠⠃⡀⠀⠀⣼⣾⠛⠚⢇⠀⠀⠸⡼⠀⠀⠑⣿⢦⡀⠈⡗⠄⠸⡀⠘⡇⠀⠀⠀⠀⠀⠀⢹⠀⣿⠉⠉⠉⠉⠉ ⠿⣉⠉⠉⠉⠉⠛⢻⣇⡿⢰⠁⢀⡞⡟⣿⠀⠀⠈⢦⠀⠀⢣⠀⢠⣶⣾⣷⣿⣄⡇⠀⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⠀ ⡀⠙⢦⡀⠀⠀⠀⣼⡺⠁⢸⠀⠈⣇⡇⣿⣶⣿⣿⡜⣷⡀⠈⣆⠘⢹⣿⣿⡎⢻⡇⡄⠀⢸⠀⠀⢳⡀⠀⠀⠀⠀⢀⡆⡇⠀⠀⠀⠀⠀ ⠙⣦⠀⠹⣦⠀⠀⣿⡄⢸⠘⡄⠀⢿⣿⡟⣿⣿⣿⡀⡟⠑⢄⢸⡄⠘⢿⣯⠇⠀⣷⡇⠀⢸⠀⠰⡈⢿⠿⠿⠿⠿⢿⡇⣿⣷⣶⣶⣶⣶ ⠀⠀⠱⣄⠈⠳⣄⣼⡇⢸⡄⣷⣄⢾⡟⠃⠘⠿⠿⠃⠀⠀⠀⠙⠻⠄⠀⠀⠀⢀⣿⠀⠀⢸⢀⠀⣹⣌⢧⠀⠀⠀⢸⠇⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠈⠻⡇⠀⣷⣻⣿⣎⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⢻⠀⠀⢸⠘⡆⢳⡟⢪⣷⣄⠀⢸⡀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠄⠘⠀⡟⢻⣿⣿⠻⣿⠁⠀⠀⠀⣴⡾⠋⠉⠛⢿⠂⠀⠀⢀⡎⠀⠀⣸⠀⢳⠈⣿⣶⣿⣿⣶⣾⠁⣿⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⣠⠞⢁⣴⡆⣸⣡⡟⢹⠸⡄⡏⢣⡀⠀⠀⠘⠦⣀⡠⠴⠋⠀⢀⣠⠞⡇⠀⠀⡿⡇⠈⡆⠸⡏⠉⠉⠉⢹⠀⣿⠉⠉⠉⠉⠉ ⠀⢀⡴⠛⢁⣴⡿⢻⡷⠛⠁⡇⢸⠀⢸⣷⠀⢹⡦⣤⣀⣀⡀⠀⢀⣠⠴⡏⠀⢶⢁⠀⢠⠃⢷⠀⠸⡀⢻⡀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠔⠉⣠⡶⠟⠉⠀⢸⡇⠀⣿⠀⢸⡧⣴⣼⡀⢸⡇⡇⠀⠘⣯⠉⠉⠀⢠⣧⡀⡞⡘⠀⣸⠧⣼⣇⡀⢣⠀⢳⡀⠀⢸⡀⣿⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⢸⡇⠐⡏⢀⢎⡴⢋⡹⣷⠚⢶⣷⠴⠚⠡⠤⠤⠚⠁⠀⣹⣧⠇⢀⣇⡴⡉⠣⡘⡌⢆⠈⢷⣶⣾⡇⣿⣤⣤⣤⣤⣀ ⡋⠀⠀⠀⠀⠀⠀⢸⡇⡸⠀⣎⠈⠀⠉⡠⢿⡄⣼⡏⠐⠲⠤⡄⠀⠤⠒⠉⢸⡟⠀⢸⡟⠢⡘⠂⠈⣡⠈⢆⠈⢯⢹⡇⣿⠉⠉⠉⠙⠛ ⠓⢤⡀⠀⠀⠀⠀⠸⣧⠃⠀⣿⡄⠀⠈⠀⣜⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⡷⠀⠁⠀⡠⠙⡄⠈⢢⠈⢻⡇⢹⠀⠀⠀⠀⠀ ⡀⠀⠙⢦⡀⠀⠀⢰⠇⠀⣸⢯⡘⣆⠀⠀⢸⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠁⠀⠀⢰⡃⣠⠟⣷⠀⢣⡀⠹⣾⡀⠀⠀⠀⠀ ⠉⠲⣄⠀⠈⠳⣤⠏⠀⣰⠏⠀⣿⣏⠣⢄⣸⠀⢹⡈⠓⠦⣤⣤⣤⣤⣴⣾⠃⠀⢸⣿⣄⣀⣤⣾⢿⣇⠀⢈⣧⠀⠑⣄⠘⢿⡿⠿⠿⠿ ⠀⠀⠈⠑⢄⢀⠎⠀⣰⣿⣀⣴⡏⢹⣦⣤⡞⠀⠈⣧⣀⡔⣢⣴⣾⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠁⣸⠛⢾⡟⢻⠀⠀⠈⣢⡈⠳⡄⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⣾⡾⠋⠀⢻⣴⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣼⠋⠀⠀⢻⡿⢧⡀⠀⠱⡑⣄⠙⢦⠀ ⠀⠀⢀⡠⠁⠀⣸⡟⢻⠃⠀⠀⠀⢹⡟⠱⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⠈⢻⡄⠀⠱⡈⢷⣌⠳
⠄⠐⠀⠀⠀⠀⠈⠇⠀⡇⡇⠀⠀⣠⡐⠀⠈⢸⠁⠉⢉⠉⠉⠉⠉⠙⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠉⠁⠀⠉⠁⠉⠑⠺⣤⠤⠤⠤⣤⣤⣤⡆⢸⣤⣤⣤ ⠀⠀⠀⠀⠀⢀⢀⠜⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀ ⠀⠀⠀⣀⣀⣸⠃⠀⢀⢐⢆⠀⢠⠈⢆⣀⣀⠀⠐⡄⢃⡀⣀⣀⠀⢸⢸⠀⠀⠀ ⣀⣠⣤⣤⣤⢂⢡⠀⣸⡞⠚⡄⠈⡄⠈⠺⡦⡈⡂⢰⠈⡏⠉⠉⠉⢹⢸⠉⠉⠉ ⠑⢄⠀⠀⢸⠎⠀⠰⠀⣧⣴⡌⡄⠰⠘⢿⣯⢳⣇⠀⡄⠰⡀⠀⠀⢸⢸⠀⠀⠀ ⠑⢄⠳⡄⢻⠘⢰⠀⡿⡟⣿⡇⠏⠢⢣⠘⠛⠀⡟⠀⡇⠠⣹⠛⠛⢻⢸⠻⠟⠓ ⠀⠀⠑⢌⠻⡀⣿⣷⣽⣄⠀⠀⠀⣀⣀⡀⠀⠰⡇⠀⡇⡘⣗⢵⡄⢸⢸⠀⠀⠀ ⠀⠀⢀⠜⣡⢀⣳⢻⠏⡧⡀⠀⠫⣁⡠⠃⠀⡰⠇⢀⢇⢠⢹⠛⠛⢻⢸⠛⠛⠛ ⡠⢔⣡⠞⢹⠊⡼⢸⢀⡇⢸⠒⠀⡤⠤⠐⡏⢸⡀⢸⢸⡀⠆⢇⠀⢸⢸⠀⠀⠀ ⡠⠋⠀⠀⢸⠀⠇⢌⢈⢿⡚⣦⡔⠣⠤⠂⣉⣎⠁⣆⢎⠫⠜⡈⢶⣼⢸⣤⣤⣄ ⢆⡀⠀⠀⢸⡘⢸⡄⠀⢊⢷⡏⠀⠁⠀⠁⠀⡏⢰⡇⠁⠁⠶⠐⡈⢾⢸⠀⠀⠀ ⢄⠉⠢⡀⡘⠀⡜⢌⢄⠀⡏⡧⣀⠀⠀⢀⣠⠁⢸⡁⠀⣨⡔⠱⡈⢄⠻⣤⣤⣤ ⠀⠉⠂⡸⠁⡾⡤⠏⢧⣼⠀⢡⣠⣩⣽⣿⡟⠀⢸⣿⣿⢁⠗⢞⣃⠀⠡⡙⢄⠀ ⠀⠀⠐⠀⡾⡏⠀⠘⡿⠃⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⠋⠀⢸⡏⢦⠈⢎⢮⡢
⣿⣛⢿⡹⣟⡽⣫⢟⡽⣫⢟⡽⣫⡝⣯⡝⣯⠽⣭⠯⡽⣭⢻⣭⢻⣭⢻⣭⢻⡭⢯⡽⢭⢯⠽⣍⢯⡝⡭⢯⡝⣭⠯⡽⡭⢯⡝⣭⢯⡹⣍⢻⡜⣣⢏⡭⣋⠷⣩⢳⡙⣎⠳⣍⠳⣍⢳⣙⢮⣙⢮⣙⢮⡙⢮⡙⢮⡙⢮⣙⢮⡙⢧⢫⣍⠻⣜⢣⢏⡽⢭⢯⣹⠹⣎⡝⣣⠝⣎⠵⣹⣌⡷⠽⠿⠛⠛⠛⠛⠛⠓⠛⠾⠷⠭⣮⣵⣩⢎⡵⢫⡜⣥⢋⠷⣩⠳⣍⢳⡙⢮⣙⢎⡳⣙⢎⡳ ⣷⢫⣞⡳⣝⢾⡱⣏⢷⡹⣎⢷⣣⢟⡶⣹⢎⡟⡶⣫⠷⣭⢳⣎⠷⣎⠷⣎⢷⡹⣓⢾⡹⣎⡟⡼⣓⣞⡹⢦⣛⡜⣳⢭⣓⢏⡞⣱⢮⡱⢎⡳⢼⡱⢎⡵⢋⡞⣡⠧⡹⣌⠳⣜⡹⣌⠳⡜⢦⣙⢦⡙⣦⡙⢧⣙⢣⡝⢦⡙⢦⡙⣎⠳⣌⠗⣮⣹⠾⠾⠧⣾⣔⣏⡶⣙⢦⣻⠼⠛⣉⠀⠆⡐⠰⠈⡄⢡⠂⡡⢘⠰⢀⠆⡐⢄⠠⢉⠙⠓⠷⢼⣆⡻⡜⣥⠻⣌⢧⡙⢧⢎⢧⡝⢮⡹⣜ ⣷⢫⡞⣽⣚⢧⡻⣜⢧⡻⣜⢧⣛⢮⡳⣝⢮⣝⡳⣭⢳⣭⢳⢎⡿⣜⡻⣜⢧⣛⡭⢶⣹⠲⣝⡳⣭⠶⣹⠳⣬⠝⣎⠶⣩⠞⡼⡱⢎⡵⢋⡼⣡⠳⣍⢖⢫⡔⡣⢞⡱⣌⠳⣬⠱⢎⡳⣙⠮⡜⢦⡙⢦⡙⢦⡙⠶⣘⠧⣙⢦⣹⣬⣷⢞⣛⣉⣀⣀⣀⣀⣀⠀⠈⠉⢹⠞⢁⢂⠑⡠⠘⡠⢁⠊⡁⡐⣀⠂⡁⢄⠈⡄⢂⠌⢠⢈⠐⡈⠐⡄⢂⠈⡙⠳⣮⣓⠮⣎⡝⣎⠞⣦⠹⣖⠳⡜ ⡷⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡭⡞⣵⢫⣞⡲⣝⢎⡷⢬⣓⢏⡶⢭⠶⣙⣎⢮⠵⣋⣖⠻⣌⡗⣎⡳⢣⠟⡴⣛⢬⠳⣍⢞⡱⡝⡎⢶⢩⢖⣡⠛⡴⢊⠧⡘⢥⢃⠳⣌⠳⣌⡛⣬⠱⢎⡱⢎⡣⡝⢦⡙⢦⡙⢧⣙⣮⢗⡿⠽⠛⠉⡉⢡⠀⡄⠠⡀⢄⠈⡉⠕⠲⠧⣌⡂⠌⡐⠠⢑⠀⢆⠐⠡⠐⣀⠂⠡⢂⡘⠠⠁⠌⠂⢄⠂⡑⠂⢄⢁⠊⢄⡁⠠⠙⠻⣴⡹⣌⠻⣔⢫⡜⣣⠝ ⣟⡱⣏⢾⡱⣏⡞⣵⢫⢞⡵⣋⢶⡹⣒⢏⢶⡹⢎⡾⣜⣣⡝⢮⡜⢧⣫⠳⣜⠮⣝⡱⣎⢻⡜⡼⣡⢯⣙⠾⡱⣍⢎⡳⡜⢮⡱⢣⠝⣊⠖⡎⡴⡙⡔⣋⠖⡩⢆⡍⠳⡌⡓⠴⣩⢆⡹⣌⠳⣊⠵⣉⣶⡭⢶⠛⣍⠼⡚⢉⡀⠒⡈⠐⡐⢂⠒⡈⡐⠄⢊⡐⠐⡠⢁⠢⠐⢉⠓⢦⣌⠄⡘⠄⡈⢄⠡⠄⡈⣔⡾⠇⢠⠡⢈⡐⠂⠄⠡⢈⠂⠂⠌⠠⢀⠅⢂⠡⢈⠳⣏⡽⣌⠳⡜⡥⢞ ⡷⣹⢎⡷⡹⢶⡹⣎⡽⢎⡶⣹⠲⣍⡳⢎⡧⣝⠳⣜⠶⣱⡚⢧⣹⠳⡜⣝⢮⡹⡜⡵⡭⢶⡹⣜⡱⢎⡜⣣⠳⣌⠧⣓⡹⢆⡳⢍⢎⡱⢚⠜⡰⠱⡘⡔⢪⡑⢎⡜⡱⢌⡱⢍⠲⣜⣴⠾⠗⠋⠉⠁⠀⠀⣸⣺⣷⡠⠐⠠⢀⣡⣠⣡⡆⠄⠒⢠⠐⡈⢄⡐⢂⠰⢀⠢⠉⡔⢨⠀⠌⡙⢦⣔⠈⠄⣒⡴⠚⢅⢂⡘⢀⠂⠆⡐⢈⠐⡁⠆⡈⠄⡁⠒⡀⠒⣀⠡⠂⡐⠌⢻⣮⡝⣺⢱⣋ ⢯⠵⣎⢳⡝⣣⣛⡴⡹⢎⡵⢣⡻⣌⢗⡫⢖⡭⣛⣬⢓⢧⡹⢣⢇⡟⡜⣎⠶⣩⡓⢧⡝⡲⡝⢦⡙⢮⠜⡥⣛⢬⢚⠥⣎⠳⣌⢋⢦⢱⡉⢎⡱⣅⡓⠌⡆⣿⡦⢶⣥⣊⣼⠜⠋⠩⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠋⠉⠉⠉⠁⣀⡼⠃⡘⡈⠄⡐⢀⠂⠐⡈⠄⢊⢀⠡⢀⠂⠌⡐⣀⠂⣌⡿⠞⠡⢁⡘⢀⠂⢄⠃⡌⠐⡀⠆⢂⠐⡐⠄⠒⠠⢁⠂⠡⡀⡐⢠⠐⠄⠂⡙⢾⠥⠷⣬ ⣏⡞⣜⢣⢞⡱⢎⠶⡹⣍⢞⡣⢗⡭⢮⣙⢮⡱⢣⢎⡝⢦⡙⢧⡚⡼⡱⢎⡳⢥⢛⢦⡹⢱⡙⢦⡙⢮⣙⢲⢱⠪⡍⢞⡰⣋⠴⣋⠆⣧⣘⣆⣒⣙⣯⣛⠶⢭⣷⣄⠠⠉⠛⠲⣤⣀⢿⢧⡀⢸⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣄⡂⠐⡐⢂⠐⡄⠨⠐⠠⢈⠄⢂⠒⠠⠈⠆⢁⣠⠞⠋⢄⠘⡐⢂⠐⠂⡌⢀⠂⠄⡡⠐⡈⠄⠒⢠⠈⢂⡑⢄⠈⡐⠠⠐⡠⠈⠄⢡⠀⠌⢳⡀⠀ ⡞⣜⢎⡳⢎⡵⢋⡞⡱⢞⡬⢳⡍⣞⡱⢎⠧⣝⢣⡞⣜⢣⡝⢦⡙⢶⡙⢮⡱⢋⡞⣢⠝⡥⢛⠦⣙⠦⢣⡝⢢⡛⡜⢢⡱⣷⣟⡛⠋⢉⠉⠄⢂⡁⠡⢉⠉⠄⡉⠙⠠⠁⠎⡐⠈⠛⠛⠳⢽⣾⠤⠜⣢⡀⠀⠀⠀⠀⠀⠀⠚⠚⠒⠒⠛⠓⠦⢤⣢⠀⠅⠩⠐⢂⠨⠐⡈⠡⡈⣰⠞⠡⡘⢈⠐⢂⡐⠂⠌⢂⠐⠠⡈⠔⠠⡁⠢⠘⡈⢄⠘⢠⠀⢂⠂⢄⠁⢂⠄⠡⠈⠄⡘⢀⠂⡹⡄ ⡝⡎⣮⢱⢫⡔⢫⡜⢱⢫⡜⢣⡞⣦⠙⡎⢳⡌⢳⡜⣬⢳⠘⣧⠙⣦⠙⣦⠙⣧⠚⣥⠚⢱⢫⡜⣥⢫⢱⡜⢣⡜⡌⢣⣶⣥⣮⣿⣷⣦⠈⠂⡆⠐⢡⠈⠐⢢⠐⠁⡆⠁⠂⡄⢡⡌⢠⠁⠂⢠⠐⢠⠈⡝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣮⠁⠘⢠⠂⠑⢠⢡⡞⢡⠘⠐⢠⠃⠈⠐⢠⠁⡌⠀⠊⣤⠁⠊⢡⠐⢡⠑⠐⠀⡎⠀⡜⠀⠘⢠⠈⡄⠂⢡⠈⠒⠈⡄⠒⠀⣵ ⡳⡝⣬⢓⢮⡱⢫⡜⣣⢎⡵⢋⠶⣉⠷⣙⢦⢛⢦⡓⡭⢎⡳⣌⠳⣎⠳⣌⠳⣌⢳⡩⢞⡱⢪⠕⣎⠮⣑⢎⠦⣷⡿⣿⣯⠉⡉⢈⠉⠡⢈⠐⠠⢁⠂⠉⠄⠂⠄⠡⢀⠡⠈⠄⠡⠐⠂⠜⡐⡈⡐⢂⡐⢀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⡁⠂⠌⢂⣲⠋⢄⠣⠠⠁⠌⠠⠉⠄⡁⠢⢈⠁⠎⠠⠘⡈⠤⢈⠄⠢⢁⠡⠀⠅⠠⢉⠐⡈⠤⠐⡈⠄⠌⠠⠑⠠⠈⠄⡡ ⡝⢮⡱⣋⠶⣉⢧⢚⡥⢺⡜⣭⢚⡥⣛⢬⡚⡜⢦⡹⣜⢣⠳⣌⢳⣌⠳⣌⠳⣌⠳⣜⡡⢏⡥⢛⡴⢋⡜⣬⡷⠞⠋⡉⠄⠒⡈⠤⠉⠄⠡⢈⠁⠂⠌⡐⢈⠐⡈⠐⡀⢂⠡⠈⠄⠡⢈⠐⠠⠐⠠⢁⠰⢀⠂⠻⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢷⡌⢐⡾⢁⠘⡀⠆⠡⡈⠄⠃⠌⡐⠠⠡⠌⠌⠨⠄⢡⠐⣁⠂⢌⠰⠀⠆⠡⠌⠰⠀⢆⠐⠄⠡⠐⡈⠄⢡⠈⠡⠉⠄⡁ ⣝⢣⠳⣍⠞⡱⢎⡣⢞⡱⣚⠴⡫⢴⡩⢖⡹⡜⣣⠕⣎⢧⡛⣬⠳⣌⠳⣎⠳⣌⠳⡆⡝⡢⢍⣣⡼⢷⣏⣅⠠⣨⡅⠐⡨⠄⢁⠂⠡⠌⠰⠀⠌⠨⠐⠠⢈⠐⡈⠰⠈⠠⠂⡉⠤⢁⠢⠌⠁⠜⠠⢁⠂⡌⢠⠁⠄⠠⢉⡒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⡐⠠⢁⠒⠌⡐⠠⠉⠌⡐⠤⠑⡰⢈⠌⠡⢘⠠⠂⠔⠨⠐⣠⣡⣬⣴⣬⣤⣡⣂⣈⠐⠡⡁⠔⡈⠄⠌⡠⠉⠄⡀ ⣎⢧⢛⡴⢋⡵⢋⡼⢡⠧⣙⢲⡙⢦⡙⢮⡱⢎⡵⢚⡜⢦⡙⢦⢛⢬⠳⣌⠷⣌⣳⣭⠶⠛⠉⢁⡴⠋⢉⡽⠟⠡⢈⡐⠁⠰⠀⠌⡐⠌⢠⠡⠌⢂⠉⠰⠈⡐⢈⠰⠈⠤⠡⠐⠠⠂⠔⡈⠡⠌⡐⢀⢣⡐⠠⢉⠢⡁⠆⡀⠡⢈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠠⠁⣂⡬⠶⠖⠛⠛⠒⠒⠦⢥⣐⠈⡈⠱⡈⠔⠉⣠⡵⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⢆⡐⠰⡀⢌⠐⠄⠩⠐⡀ ⡞⡜⠮⣔⢫⡔⣫⠲⣍⠞⣡⠧⣙⢦⡙⢦⢳⢩⠖⣭⢚⢦⡙⢮⡩⢲⣭⠶⠛⠋⠁⠀⠀⣠⣴⠋⠄⣨⡟⢁⠨⠐⣁⠈⡁⢂⠡⠂⠌⡈⠤⢈⠰⠈⠌⠠⠡⠈⠄⠂⠌⡐⠠⠉⠤⠉⠄⠄⠃⠔⡀⠂⣿⣿⣔⠠⢀⠱⡈⠔⡡⢂⠌⡡⢀⠹⠲⣄⡀⠀⠀⠀⢰⠃⢄⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡁⡀⢂⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠐⣈⠰⢈⠡⡁⠄ ⡝⣜⠳⣌⠳⣜⣡⠳⣌⡛⡴⠹⣌⠶⡙⣎⠮⣱⢚⡴⢋⣶⠽⠖⠋⠁⠀⠀⠀⠀⠀⢀⡼⠃⠠⢈⣴⡟⠠⠌⢂⠥⠐⡈⠄⠂⠤⠉⡐⢈⠰⠈⠄⡉⠌⠠⠡⠈⠌⡈⠰⢀⠡⢈⠰⠈⠌⠄⡉⡐⠠⢁⢻⣿⣿⣷⡄⢂⠱⣈⠐⢂⠂⣁⠢⠄⠡⢀⠙⠲⣄⠀⣾⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⠂⢆⠰⢀⢂ ⡳⣌⠳⣌⠷⣘⢆⡛⣤⠛⣬⠳⡜⣪⠕⣮⣑⡧⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠠⢈⣴⣿⡿⠖⠁⢂⠡⢂⠡⠐⡈⠌⠄⠃⠌⡠⢂⠉⡐⠈⠤⠡⠈⠌⡐⢈⠐⠠⠈⠄⠢⠈⠌⠤⠁⠤⠑⠤⠀⢿⣿⣿⣿⣆⠐⡀⢊⠄⠒⠠⠐⡈⠔⡈⠤⠁⠌⡙⢷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢂⠰⣡⢾ ⡵⢪⡝⡬⣓⠭⢎⡵⢪⡝⢦⣳⡽⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠄⡈⢤⣿⣿⣿⡇⠈⢄⠃⡐⠤⠈⠡⢐⡈⠌⡘⠠⡐⠠⠈⠄⡉⠐⠠⢉⠐⠠⠈⠤⠁⠌⡈⠤⠉⠰⠀⠍⠠⠡⡘⠄⢂⢻⣟⣿⣿⣇⠐⠌⡠⠃⠌⡐⠰⠠⠘⢠⢉⡐⠤⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⣶⢫⣗⣫ ⣜⢣⠎⡵⡩⢞⣱⡮⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠄⢂⣴⣿⣿⣿⣿⡇⢈⠂⡌⠐⠄⠡⠂⡔⠠⠈⠤⢁⠰⠁⡉⠐⡈⠌⡐⠈⠤⠁⠌⡐⢈⠐⠠⢂⠡⠌⡈⠌⡐⠡⠐⡈⠆⠠⢻⡟⣿⣿⣆⠂⠔⡈⡐⠠⢁⠆⠉⠄⢂⠐⣀⠃⠌⠠⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣿⡹⡞⣼⢣ ⣬⢣⣛⠴⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠡⢈⣾⣿⣿⣿⠿⢻⡆⠰⡀⠌⡐⢡⠈⠡⢀⠃⡌⠰⠈⠤⠁⠌⡐⠠⠂⠌⡐⠠⢉⠐⠠⠈⢄⠡⢂⠐⠤⠐⡈⠤⠁⡌⠐⡈⢡⠀⣿⡭⣿⣿⣆⠈⡔⠠⢁⠌⡀⠃⠌⡀⠒⠠⠘⡈⠤⠑⠠⢙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠉⠛⠿⣜⣫ ⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣤⠿⢙⠐⡈⢡⣿⣿⣿⠛⣁⡀⢸⡇⢁⠂⡌⠐⡂⠌⡐⠌⡰⢀⠡⠌⡠⢉⠐⠠⠡⠘⠠⠐⡁⠂⠌⡐⢁⠂⠰⠀⠌⢄⠡⠐⡠⠡⢀⠃⠄⡁⢂⠸⣟⡽⣿⣻⡄⠠⣁⠂⡐⠠⠑⠠⢀⠉⠄⠡⠐⠠⢉⠐⠠⢈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⢋⠉⠄⣁⡾⢋⠠⢈⠐⣰⣿⣿⣿⡧⠚⠁⠀⢐⣿⠀⢂⠌⢂⠡⡀⢁⠊⡐⠤⢁⠢⠐⡠⠉⢄⠑⡈⠤⠁⢄⢁⠒⡀⠆⡘⠠⢉⠐⠤⠘⡐⢠⠁⠂⢌⠂⡐⠀⠎⣿⡼⣻⣿⣿⡀⠄⡂⠄⡑⢈⠁⠢⠌⡠⠁⡑⠐⡈⠄⡡⠂⠐⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠴⠲⠮⠉⢌⡀⢢⠈⠄⣈⡶⢋⠐⠄⠂⢄⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⣇⠂⢌⠰⠠⡁⢄⠃⡐⡁⠂⡄⢂⠡⢀⡁⢂⠌⡐⠄⡁⠆⠂⠔⡐⠐⠠⢁⠂⡁⠂⠅⡐⡁⢌⠁⠢⠐⡌⠡⢸⣟⡷⣹⣿⣿⣷⠠⠘⡠⢐⠀⡊⠐⡈⢐⠠⢀⠑⡈⢄⠡⠠⢁⠐⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⢷ ⠀⠀⠀⠀⠀⢀⣴⡚⠉⡈⠄⡨⠐⣉⠠⠐⠠⢌⡶⢋⠠⢃⠘⠠⢡⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢻⡔⢈⠂⡑⢐⢀⠒⠠⢀⠡⠐⡀⢂⠂⡐⠄⢂⠅⢂⠁⠆⡁⢢⠐⡁⠢⢈⠐⠠⡁⢂⠡⢐⡈⢄⢃⡘⡀⠂⣾⢿⣜⣳⣿⣿⣿⣧⠐⠰⡈⠐⠠⢁⡐⢈⠐⢠⠂⠌⡀⠂⡅⠢⢈⠐⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⣮⠟ ⠀⠀⠀⠀⠀⢸⣿⢀⢂⡐⢂⠐⠡⢀⢂⣱⠼⠋⠰⢀⠒⠈⠤⣱⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢂⠐⢤⣦⠄⡑⠂⢡⣆⣥⣦⠀⠒⢠⠈⡔⢠⠁⡌⢂⠁⢂⣴⣞⠲⠖⠈⡁⢐⣤⣶⣿⡦⠂⢂⠰⠀⢡⣿⣻⡼⠛⠉⠀⢹⣿⣆⠁⢆⠉⡐⠠⠐⣀⠊⠠⠘⡀⠤⠑⠠⠑⡈⠰⢀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣭⠟⠁⠀ ⠀⠀⠀⠀⠀⠈⠻⣂⠄⠐⢂⡘⢀⠂⡘⠡⢈⢂⠱⠠⢈⣴⣾⣿⣿⣿⡟⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⡇⠠⠌⠻⣿⣷⣦⣥⣿⣿⣿⣿⠃⠌⢂⡐⡀⢂⠔⢠⠁⠌⡀⠛⠿⢿⣿⣿⣿⡿⠿⠋⡁⠄⣁⠊⡐⠌⣺⠟⠁⠀⠀⠀⠀⠀⢻⣿⣧⠀⢊⡐⠠⢡⠀⢂⡁⢂⠐⠠⢈⠐⢡⠠⢁⠂⡐⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⣴⣿⡻⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍⣠⠐⡐⠂⠄⡁⠂⢄⣂⣵⣾⣿⣿⣿⣿⣿⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⢿⢇⡁⢂⠡⢀⠉⡙⢋⠙⡉⢁⠂⠌⡐⠠⣀⣔⠈⠄⡂⠌⡐⢠⢁⠂⡄⠂⡁⢂⡐⠄⡒⢐⡀⢂⠐⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢀⡐⢁⠂⠌⠠⠐⠂⡈⠐⡠⢈⠐⡐⢀⠆⠠⡁⠘⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⠀⠀⣰⣿⠿⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠥⣶⣶⢿⣿⣛⣯⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⠀⠀⠀⠀⠀⠀⠈⢿⣣⠀⠒⢌⠒⡐⠠⠒⢠⠁⢊⠐⠠⠡⣿⡿⢇⡐⠐⠄⡐⠡⢀⠑⠠⠑⡄⠡⢐⠂⣁⠂⠔⡀⢢⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡐⢈⠰⢈⠠⢁⠂⡄⠡⠐⡀⠒⡈⢄⠘⡀⠆⡉⠰⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢸⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠿⣿⠿⡇⢠⢸⠛⡆⠀⠀⠀⠀⠀⠀⠀⠳⣌⠈⡐⠢⠌⠡⠉⠠⢈⡄⣈⣤⣁⠨⠉⠄⡐⠈⡔⠠⡁⠂⠌⠠⡁⠤⢁⠂⠌⢠⢈⣐⣴⠿⠤⠤⠤⠤⠤⣀⣀⣀⣀⡀⠀⠀⠀⢻⣟⣷⡠⢈⠂⡐⢀⠂⡄⡁⠂⡄⠡⠐⢠⢁⠐⢂⡁⢂⠰⠹⡄⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠋⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠃⡀⣇⠀⣼⠀⢧⠀⠀⠀⠀⠀⠀⢀⠀⠸⣇⡠⢀⣘⣤⠿⠿⠛⠛⠛⠘⠛⠛⠿⢤⣀⢃⠀⠄⡀⢃⠘⠄⡠⠠⠘⢠⣸⡼⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡀⠛⠣⣄⠀⠀⢿⡿⣿⡀⡘⠠⢘⠠⢀⠀⠇⢀⠃⠜⡀⠄⠸⢀⠠⡘⠠⠀⢻⡤⠤⠀⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢏⠀⠆⠡⠐⣹⡼⠻⡄⠈⢆⠀⢰⠀⠀⠀⠀⠉⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⠓⠒⠶⢥⡐⢀⣡⡶⠋⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⠱⣄⠘⠻⣽⣿⣄⢁⠢⢄⠡⠈⠄⠡⠌⡐⠠⠌⠰⠈⠄⡂⠱⢈⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠫⠔⠠⢁⢂⠘⡈⠔⢡⠀⡑⢈⠹⣄⠘⠀⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠙⡶⠋⠀⠊⢀⣀⣤⣀⡀⠀⠀⠀⠀⡦⡀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠘⢾⣿⣷⡄⠂⠆⢡⠈⡐⠄⡁⠆⠌⠡⠌⠠⡁⠆⠡⠌⠐⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⣨⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣗⡿⠆⢈⠐⠂⢂⠡⢈⠰⡀⠒⣀⢂⣬⣾⣧⡀⢸⡌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠚⢀⣰⠖⠻⠓⠓⠦⢤⣈⠑⠢⣀⠀⣇⠈⠑⠦⣀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠹⢿⣿⣦⣈⠐⢂⡐⠠⠡⠈⢌⠰⠈⠡⠐⡈⠡⡘⠄⡐⢙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡠⢐⣼⠎⠐⠠⠈⠄⠂⢄⣡⣶⡟⣟⣶⣳⣿⣦⣷⡀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡴⢋⡀⠢⠁⡌⢢⠐⠠⢈⠙⠦⣄⠑⠘⠀⠀⡄⠀⠉⠒⠤⣀⡀⠣⣄⠉⠑⠲⠄⣀⠙⢿⣻⣦⡂⠌⡑⢠⠉⠄⢂⠡⠌⠡⢈⠡⠐⠌⡐⠠⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣅⠠⠑⠂⢡⣨⣶⢿⣛⣧⣿⣾⣿⠽⠶⠟⠛⢿⣦⣀⠈⠑⠢⢄⡀⠀⠀⠀⠹⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠐⠂⡌⢂⢁⠂⢂⠉⡐⠂⡌⡐⢈⠙⡦⣀⠀⠹⣶⣤⣤⣀⣀⡉⠀⠈⠑⠦⣀⣀⣀⣀⣀⣭⣿⣿⣦⣄⠁⡘⠈⡄⠒⡈⠤⢁⠢⠉⠤⠑⠄⢂⢈⣷⠶⢶⣤⣴⣦⣴⣶⡶⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⣿⡿⠿⠛⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣤⣈⡁⠒⠂⠄⠁⠀⠉⣶⠤⢄⣀⠀⠀⠀⠀⡠⢊⡁⠌⡌⠡⠐⡀⠆⡈⠤⠘⠠⠁⠆⣁⠂⠡⣀⣽⣷⣦⣽⣯⠞⠛⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠾⠶⠭⠿⣿⣷⣦⣅⡠⢁⠐⢂⠂⢂⠉⡐⢁⠊⠄⣢⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠿⢷⣦⣤⣀⠀⠀⠙⣷⣦⣀⠉⠉⣲⠎⡁⢂⡐⢂⠔⢁⠂⠡⠐⠠⠄⡡⢑⠨⠐⣀⣬⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠦⠬⠤⠦⠤⠦⠼⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⣹⠛⠻⣿⠛⢁⠐⠄⡂⠐⠠⠈⠄⡈⠡⢈⠁⡂⢁⢂⣤⣷⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣠⠞⣡⠈⠄⡈⠐⠠⢁⠂⡁⢂⠁⠢⢁⣌⣰⣶⣿⣿⡿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣦⢳⡬⣟⢻⣦⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠜⣧⣯⡽⢾⠳⣞⡻⣛⠟⡿⢿⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡯⡟⡝⣦⣙⡮⠛⣝⠲⣍⢞⣱⢍⡞⣥⣛⢻⣦⣄⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣋⠶⣹⢜⡱⡄⢆⣡⡝⠷⡼⠞⢹⡎⡖⢦⢻⠦⣭⠹⣷⡟⣻⢫⣽⠭⡧⣧⣍⣛⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡲⣍⢾⡱⢎⣽⠵⣋⠶⡽⡹⣜⡧⣞⡹⡜⣣⢻⡳⢬⡗⡭⢿⣶⡟⣖⣫⣶⡷⢣⣾⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⢻⢱⡎⣵⡞⢣⡝⣮⢱⢫⡜⣽⢱⢳⡌⢳⣬⢳⠙⣦⣿⢹⡖⣽⢸⡍⣿⣯⢹⣽⣦⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢿⣜⣺⢣⡝⣼⢣⢏⠶⣩⠞⣬⡷⣋⠗⣎⡝⣦⠟⣬⢓⢮⠋⢷⢯⣽⢣⣙⢻⣿⣾⢹⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢞⠫⡝⣢⠝⣦⣿⢣⠳⣼⣏⣳⣮⡷⠵⣛⢟⡱⣍⠞⡴⣽⢏⡝⢦⣫⠃⠀⠘⡾⣼⢣⢎⣽⣿⣿⠛⣼⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⣌⠳⡌⣥⢫⣷⡏⣧⢋⡿⠛⠉⠀⣤⣚⠵⣪⣕⡮⢝⡻⣋⢞⡼⠋⠉⠙⢆⠀⣟⡿⣘⠮⣼⣿⣿⣡⢴⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠰⣀⠳⡘⢴⣿⣿⢫⢳⣍⢧⣶⣤⣄⣒⣚⠉⠁⠀⠀⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⣿⠳⣍⠞⣼⣿⢾⣯⣷⣾⡁⠀⠀ ⠀⠀⠀⢀⣤⣼⣧⠑⡠⢃⠜⣸⡿⢾⡩⢎⡏⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⢠⣭⣒⠄⠀⠀⠀⠀⢀⣏⢳⢬⢫⣟⣯⣿⢯⡟⣽⣷⡀⠀ ⠀⠀⠀⣿⠋⢿⣿⠄⡱⢈⠜⣸⠀⠈⣷⢩⣧⠤⠤⣄⡀⠀⠀⠓⠶⠤⣀⠄⠀⠉⠛⡿⢿⠶⢆⣠⠻⣌⠳⣎⣽⣿⣻⣽⣿⠸⣌⢿⣷⠀ ⠀⠀⠀⣿⣇⢂⡙⠒⠖⢃⡘⡼⡳⠶⠛⡏⠀⠀⠀⠀⣳⠶⠒⠶⠤⢤⣀⠀⢀⣀⣀⠀⠀⠘⠯⢼⡷⣋⠷⣼⡟⣷⣻⣷⠏⡵⣊⢖⣻⡇ ⠀⠀⠀⠘⣧⣓⠦⣉⠘⣤⢼⡋⠤⠄⠂⢛⡶⣦⠶⠟⠃⠤⠤⢀⣀⠀⠈⢹⠉⠀⠈⠙⢦⣀⣤⢟⡲⣭⣾⢻⡼⣗⣿⠏⣜⠱⣘⠲⡰⡇ ⠀⠀⠀⠀⠈⠙⢻⣿⠟⢡⠊⠀⢀⠤⠐⠊⠉⢀⠀⠀⡀⠀⠀⠀⠀⠈⠹⠿⢤⣤⣀⣀⣨⠿⢵⣮⢿⣻⡉⠁⢀⡿⢃⠞⣠⠋⡔⢣⣱⡃ ⠀⠀⠀⠀⠀⣰⡟⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠄⠁⠀⠂⠐⠄⢀⠀⠄⠀⠈⠹⣫⢥⣋⠦⡙⠶⣤⡀⣠⠞⡰⢁⠎⡄⢣⠘⣴⠏⠀ ⠀⠀⠀⠀⣴⠏⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠌⠐⠒⠤⣀⠱⣢⠏⠛⠍⡉⠑⣽⠃⠜⣄⢃⠒⣨⣴⣿⠉⠀⠀ ⠀⠀⢀⣼⠏⠀⡰⠁⠀⡀⠢⠄⠀⢠⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠉⢳⠀⢆⡀⠈⠢⢻⡌⢂⠌⡓⠼⠿⠟⣻⡇⠀⠀ ⠀⢀⣼⠋⠀⠰⠁⠀⠀⠄⠀⠀⠀⠀⠀⠈⡀⠐⠀⠠⠂⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠈⠊⢄⠇⢸⣷⣌⠲⣈⣔⡡⣶⠟⠀⠀⠀ ⠀⣼⡟⠀⠀⡇⡀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⡀⠀⠀⠀⠀⢀⠧⠀⠀⠀⢸⠀⠀⣿⠿⣧⣤⣤⠿⠃⠀⠀⠀⠀ ⢰⣟⠀⠀⠀⠉⠂⠴⣀⠆⣀⠀⡀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠐⢂⡤⠊⣀⠀⠀⢀⠇⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢶⣄⡀⠀⠀⠀⠀⠉⠐⠊⠥⣀⡂⠤⢀⡀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣠⠖⣩⢇⠃⠉⠚⠤⡜⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠉⠐⠒⠩⠄⣂⣁⠠⢀⣠⢴⣋⠖⣩⠇⠂⠀⠀⠀⡰⠁⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠙⠋⠚⠒⠋⠭⠥⠤⣀⣀⣀⣠⠃⢠⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠳⠶⠶⢶⠴⣶⢾⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⣤⣈⠙⠛⠋⣁⣴⣿⣷⣄⡉⠛⠛⠉⣀⣴⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠉⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⣀⡀⠀⠀⠀⠀⣀⣀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡆⠈⠛⠷⣦⣤⣴⠾⠋⠀⠈⠻⢶⣤⣤⣶⠿⠋⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠸⠿⢿⣿⣿⣿⣿⠿⠿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠢⠐⠁⠀⡤⢠⠃⠀⢀⢎⠮⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢱⠀⢂⠀⠀⠂⠀ ⠀⠀⠀⡠⠊⢀⡾⠀⢠⢣⠃⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⣧⠈⣧⣾⠀⡄⠀⠀ ⣠⠘⠭⠄⢊⢿⠃⡠⣱⠍⢂⠀⠀⠾⠈⠃⠀⠀⠀⢀⣀⡠⣼⠀⣿⢻⣇⡇⢸⣿ ⠀⠉⡇⠐⡇⡆⢰⣽⠋⠀⠀⠁⠒⠒⠂⠀⠀⠀⠐⠋⣭⠀⠀⠀⡿⠈⡏⠁⡀⢻ ⠀⠀⡡⢊⣱⢀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⡆⠁⠀⣃⠀⠃⠀ ⠀⢈⡩⢒⢼⠞⠂⠇⠀⠀⠀⣾⣍⡀⠒⠀⠄⡀⠀⠀⠈⠉⠁⡇⡆⢰⡝⢸⡲⠖ ⠐⡡⠂⡡⠎⣀⠀⠈⡄⠀⠀⢿⣿⣿⣷⣶⣤⣬⣴⠀⠀⠀⢀⡇⡇⣿⡇⡆⠀⠀ ⠊⡠⠞⠛⠛⡳⠞⡟⠈⢆⠀⠘⡕⢌⣉⣻⣿⡿⠋⠀⠀⢠⡪⡇⢠⠫⡷⢭⠀⠀ ⢰⣀⣀⣀⡠⠵⢶⠁⡀⠸⠱⣄⠈⠒⠒⠂⠉⠀⣀⠤⠊⠃⠣⢀⡎⠢⡈⢆⠀⠀ ⠈⠀⠀⠀⠀⠀⡄⠀⠐⢄⢣⠙⠛⠒⢀⠤⠋⠁⣮⢶⡄⡆⢀⠎⠣⠀⢱⠈⡄⠀ ⠀⠀⠀⠀⠀⢠⣀⠠⠄⢰⠢⢑⣀⠒⠁⠀⠀⡸⢜⡤⠏⠑⢢⠀⠀⠀⠀⠀⠁⠀ ⠀⣆⡘⡀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠓⡀⠀⢠⠁⠀⠈⠒⠄⣈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠓⠶⣤⣀⡀⠀⡼⠀⡜⠁⠀⠘⢄⠂⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣿⡁⠈⠁⢸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⢂⠟⠀⠀⠀⢿⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡿⠀⢿⡏⠀⠀⠀⠀⠀⠀ ⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠟⠀⠀⠂⢸⠀⢸⡟⠀⠀⠀⠀⠀⣀⢀⣦⡎⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣼⡿⠛⠛⠉⠉⠉⠛⠛⠛⠉⠙⠓⠲⢦⣼⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣶⣶⣶⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡏⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢂⡼⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢇⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡟⠀⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⣀⠀⠀⠀⠀⡀⣸⢠⣿⡀⠀⠀⠀⡆⠀⡇⠙⡄⠀⣀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⢻⠇⡸⠁⠀⠀⠀⠀⡇⣿⡞⠀⡇⠀⠀⠀⢹⠀⡇⠠⠿⣟⢻⣍⠓⠲⠤⣀⠀⠀⠸⡄⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠀⢸⣧⣤⣤⣤⣤⣤⣤ ⠀⠀⢀⣀⣀⣀⡀⣀⣠⣤⣤⡏⢠⠇⢀⠀⠀⠀⣰⣷⣿⠓⠒⢳⡀⠀⠀⠈⣧⡇⠀⠀⠈⢣⣻⢳⡀⠀⠈⡗⠄⠀⢻⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⢸⡏⠉⠉⠉⠉⠉⠉ ⣿⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⢠⣿⠀⡞⠀⠀⣴⣿⢯⡏⠀⠀⠀⢳⡀⠀⠀⠸⡇⠀⠀⣠⢄⣹⣷⣝⣦⠀⣇⠀⠀⠈⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠈⠻⣆⠀⠀⠀⠀⠀⠀⢸⡏⡞⠙⢀⡇⠀⢰⡇⣿⠸⣧⣀⣤⡤⣄⢹⣄⠀⠀⢱⠀⠘⣷⣿⣻⣷⣝⢿⣧⣿⠀⠀⠀⢧⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⣄⠀⠘⢷⣄⠀⠀⠀⠀⣸⣧⠃⢠⠈⡇⠀⠀⡇⣏⣼⣿⣿⣿⣿⡷⠌⣿⣆⠀⠀⢧⠀⠁⣿⣿⣿⣿⡀⢿⢻⢸⠀⠀⢸⠀⠀⠀⢻⣆⣀⣀⣀⣀⣀⣀⣸⡆⣿⠀⠀⠀⠀⠀⠀⠀ ⠙⢷⣄⠀⠙⢷⡄⠀⠀⢿⣾⠀⢸⠀⢧⠀⠀⢷⣿⣿⠋⣿⣿⣿⣿⠀⣿⠈⠳⣄⠸⣇⠀⠹⣿⣧⡿⠀⠀⡾⣿⠀⠀⢸⠀⠀⢧⡀⢿⡿⠿⠿⠿⠿⠿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⢷⡄⠀⠙⢦⡀⢸⣿⠀⢸⡄⢸⣤⡀⣿⣿⠻⠀⠹⣯⣦⡿⠀⠁⠀⠀⠈⠓⢮⣃⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⠀⡀⠀⢳⡈⢳⡄⠀⠀⠀⠀⢸⠀⣿⠇⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠙⢿⣿⠀⠘⣷⢸⣧⣷⡘⢿⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⢿⡆⠀⠀⢸⠀⢧⠀⡎⡿⣦⡻⣄⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⡄⠀⣿⣧⣏⣿⡿⣌⢿⢦⡀⠀⠀⠀⠀⠀⣀⣀⠤⢤⣤⣤⣀⠀⠀⠀⠐⠋⢸⠁⠀⠀⢸⠀⢸⡀⢹⣿⣈⠻⢿⣷⡄⠀⢸⠀⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⠖⠀⠃⠀⡟⢈⣿⣿⢳⠉⢾⣧⠁⠀⠀⠀⠀⣿⠿⠛⠉⠀⠉⠙⣿⠀⠀⠀⠀⢀⣾⠀⠀⠀⣼⡄⠈⣧⠀⣿⣿⣾⣿⣿⣿⣿⣿⠀⢸⣷⣶⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⢀⣴⠛⠁⣠⣶⠀⣸⣣⣾⠋⢿⠸⡄⢸⠉⢧⡀⠀⠀⠀⠈⠳⣄⡀⣀⣤⠞⠁⠀⠀⢀⣴⠏⡇⠀⠀⠀⡇⣷⠀⠸⡆⠘⣿⠉⠉⠉⠉⠉⢻⠀⢸⡏⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⣠⡶⠋⠀⣠⣾⠿⣿⣰⠷⠋⢹⠀⢸⠀⠀⢧⡆⠀⠳⣦⣀⡀⠀⠀⠀⠉⠁⠀⠀⢀⣠⡶⠋⠀⣦⠇⡀⠀⢠⠇⢹⡄⠀⢳⠀⠸⣆⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢀⡤⠞⠁⢀⣤⣾⠟⠁⠀⣿⠁⠀⣦⡟⠀⣾⡄⠀⠛⣧⠀⠀⣧⠈⡏⠉⠓⣶⠶⠶⠶⠖⠉⠀⣟⠀⠀⣿⢠⠇⠀⣾⡄⠈⣧⠀⠈⣇⠀⢻⡆⠀⠀⠀⣿⠀⢸⡇⠈⠀⠀⠀⠃⠀ ⠋⠀⢠⣾⡿⠋⠀⠀⠀⢠⣿⠀⠀⣿⠃⠀⣿⠗⢺⣽⡹⡄⠰⡟⢰⠃⠀⠀⣹⠇⠀⠀⠀⢀⣰⠿⣦⣠⡏⡼⠀⢀⡟⠓⣶⣿⠦⣄⠘⡆⠀⢻⡄⠀⠀⢻⡄⢸⡇⠀⠀⠀⠀⠀⠀ ⢀⣴⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠐⡏⠀⡼⢁⡴⠋⣠⠿⣿⠛⠓⣾⣶⠶⠛⠉⠦⠤⠤⠖⠋⠀⠀⣈⣿⣢⠇⠀⣸⢀⡼⣅⠙⢧⡘⣆⠹⡄⠀⢿⣿⣶⣿⠁⢸⣧⣤⣤⣤⣤⣤⣀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠁⢰⠣⠋⠀⠚⠁⣠⢿⡄⢠⣿⡏⠒⠦⠤⣄⡀⠀⢀⡤⠖⠋⠁⣸⡟⠀⠀⣿⠛⢦⠈⠳⠄⠉⢸⡀⠹⡄⠈⢻⡉⢹⡇⢸⡏⠛⠛⠛⠛⠛⠛ ⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠇⠀⢸⣇⠀⠀⠠⠞⠁⣸⣿⣾⣿⠁⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⣿⠁⠀⢰⡿⣄⠀⠓⠀⠀⢀⠿⣇⠀⠹⡄⠈⢳⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣻⠏⠀⢀⣿⠟⣦⠀⠀⠀⠀⢳⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⣿⠛⠀⠀⠀⢀⡎⠀⠸⣄⡀⠙⣆⠀⠙⣧⢸⡇⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠈⠻⣦⡀⠀⠀⢠⡟⠀⠀⣸⠟⣦⡈⣧⡀⠀⠀⢸⡄⢹⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠀⣿⡏⠀⠀⠀⠀⣾⡀⣠⡞⠙⣷⡀⠈⢦⡀⠘⢿⣧⡀⠀⠀⠀⠀⠀ ⠈⠳⢦⡀⠀⠈⠙⢧⣠⡟⠁⠀⣰⠏⠀⢈⣿⣯⠻⣄⣀⢸⠁⠈⣷⠈⠛⢶⣤⣀⣀⣀⣠⣤⣶⢾⡿⠀⠀⠀⣿⣧⣀⣀⣀⣴⣿⢿⣧⠠⠀⢘⣧⠀⠀⠳⡄⠈⠻⣿⡿⠿⠿⡿⠿ ⠀⠀⠀⠙⠦⡀⠀⢀⡽⠀⠀⣴⣿⡀⢀⣼⡏⠹⣦⡀⢈⡽⠀⠀⢻⡆⠀⠀⠤⢀⣀⣤⣶⣶⣿⣿⠇⠀⠀⠀⣿⣿⣿⣶⣶⡿⠃⢸⡟⢷⣴⡷⢿⡃⠀⠀⠘⢦⠀⠙⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢢⠞⠁⠀⣘⣿⣹⡷⠟⠹⣇⠈⣿⣿⣿⠃⠀⠀⠘⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⣠⡿⠀⠈⠻⣦⣬⣧⠀⠀⠀⢣⠱⣄⠈⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠀⢀⢬⣿⣿⡏⠀⠀⠀⠻⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠟⠀⠀⠀⠀⢹⡏⠛⣷⡄⠀⠀⢣⡈⢷⣄⠙⢦⡀ ⠀⠀⢀⢀⡠⠀⠀⠀⣸⣟⠃⣿⠀⠀⠀⠀⠀⢙⡿⠋⠿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⡇⠀⠉⢿⡆⠀⠀⢳⡈⠻⡷⣌⠛
⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣾⣿⣧⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠉⠉⢹⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠿⠛⠉⢸⡏⠁⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⢿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⢠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣀⣾⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠻⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣹⣿⠃⠀⠈⣿⣿⣴⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠀⠀⠀⠀⠘⠉⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢂⡗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣸⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠆⡏⢂⠀⠄⡀⢀⢀⡀⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢶⣄⣈⣣⠀⠟⢄⡐⠀⢠⠊⡜⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⡡⡅⠹⣀⡸⠁⠜⠁⠀⠄⡆⢆⠑⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⠞⡡⡞⢹⢤⠊⠙⠃⠀⠀⠈⡆⢣⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠙⡰⠀⡸⢸⠀⠀⠀⢀⡄⠠⣀⠋⠰⠈⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠾⢯⠀⠎⠑⢼⠀⢀⣾⣿⠇⢀⢱⠰⠁⠰⠉⡖⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡾⠀⠀⠀⠀⠈⠉⠁⠀⡸⠈⢃⠘⢱⣄⠇⢸⣀⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡸⠒⢋⠎⠀⠸⠑⢌⠐⠠⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⡠⠊⢀⡔⡡⢄⠀⠀⠀⠈⡆⠀⢱ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡰⠁⠸⠀⠰⢀⠔⠸⠸⣀⡄⡇⠀⢀⡴⠁⠀⠧ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⣤⢤⢠⠃⠀⠀⠃⡰⠁⠀⠀⠑⢠⠒⢁⠊⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠠⠴⠗⠁⠀⠀⠀⠸⠀⡀⠄⠒⠉⠀⠑⠺⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⠓⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡒⠤⣀⡀⠀⢀⡴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠉⠑⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢀⡤⠋⣀⣀⣀⣤⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⣶⣆⠀⠀⢠⠈⢇⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠀⠀⠀⣏⣧⠈⠟⠀⠀⠀⠀⠀⠀⠽⡿⠆⠀⠀⠀⢀⣿⣿⣦⣶⣶⠟⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣯⢧⠤⢤⣤⣴⠦⠀⠀⠀⠁⠀⠀⠛⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠙⠯⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣄⣠⡇⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣆⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⢿⣿⠟⠒⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⠿⠺⢝⡯⢧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠓⠁⠀⠀⠀⠉⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡒⠒⠛⠁⠀⠘⠒⠒⢲⡶⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠈⢢⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⢠⠇⢀⡤⣀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁⠀⠈⠳⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠀⠀⢀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣟⠁⠀⠀⠺⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⠓⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⡏⢀⣼⠟⠉⠀⠀⠀⠸⣷⠇⠀⠀⠈⢻⣆⠸⡏⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⢰⡇⣾⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡄⢷⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢻⣾⡄⠀⠁⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⣀⣀⣻⣶⣤⣄⣀⠉⠻⢷⣦⣄⡉⠓⢦⣄⣀⠐⠦⣤⣀⣀⠀⠀⢀⣀⣀⣀⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠾⠛⠋⠉⠁⠀⠀⠀⠀⠉⠙⠳⣶⠿⠦⠉⠙⠒⠛⠻⠟⠓⠒⢿⣿⠿⠛⠛⠋⠉⠉⠙⠛⠛⠿⣦⣄⠀⠀⠀⢠ ⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢠⡿ ⢠⣿⠀⠰⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠈⢿⣾⠃ ⠀⢿⢧⡀⠀⢀⣠⡤⠤⠄⠤⣄⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⣸⡏⢀ ⠀⢈⡿⣽⡶⠋⠁⠀⠀⠀⠀⠈⢷⣤⣴⠟⠁⢤⣀⣀⠀⠀⠀⣀⣀⣀⠀⠙⠷⣦⣄⣠⠞⠉⠁⠀⠈⠙⠳⣦⣀⣴⡿⠟⠋ ⠀⢸⠇⣽⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠓⢲⠶⠤⠭⠭⣭⣭⣭⡭⠤⣤⠤⠖⠚⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⡇⠀⠀ ⠀⢸⠀⠹⣄⠀⠀⠀⠀⠀⠀⡾⠋⠘⢧⣄⣘⡇⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⣠⣿⣻⣦⠀⠀⠀⠀⠀⠀⠀⣼⠈⡇⠀⠀ ⠀⢸⡇⠀⠉⠓⠦⣤⠤⠄⠀⠀⠀⠀⠀⠠⠿⠷⢤⡀⠀⢸⠀⠀⠀⢀⡇⣰⣞⣉⠀⠀⠀⠀⠀⢀⣀⣀⣤⠾⠃⠀⡇⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠒⠾⣦⡖⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⣹⢻⣇⣀⠀⣸⠇⠀⠀ ⠀⠀⠈⠿⣦⡀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠉⠁⣴⠟⠀⠀⠀ ⢀⣠⠴⠖⠋⢉⣩⣥⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣶⣾⠋⠀⠀⠀⠀ ⠈⠙⠛⠚⠛⢉⡿⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢦⣄⣉⣛⣶⣄⠀⠀ ⠀⠀⠀⢀⣴⢋⣠⣴⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠙⠻⣍⡉⠁⠀⠀ ⠀⠀⠀⠘⢋⣿⠋⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣿⠲⠼⠿⠆⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⢀⣾⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠗⢲⣤⠾⠧⢶⣿⠛⠛⠛⠛⢻⠃⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⡶⠶⠶⠶⠶⠤⣾⡟⠀⠀⢸⡇⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣠⡖⢳⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⣠⠆⠀⠀⠀⣰⣿⠁⠀⠀⠀⣠⠞⠃⣰⠋⡇⠀⠀⠀⠀⢀⡇⠸⣆⠀⠀⠀⠀⠙⣧⡀⠀⠈⠒⢦⡀⠀⢳⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣴⡟⠀⠀⢀⡴⢋⡇⠀⠀⣠⠞⠁⢀⡾⠁⠀⢡⠀⠀⠀⠀⡾⣏⠀⣿⡙⠲⢤⡀⠀⢸⣿⢦⡀⠀⠘⣿⢦⣀⠱⢄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⣾⣿⠃⠀⢠⠞⠁⢸⠁⣠⠞⠁⠀⣠⢿⠀⢀⠀⠘⣆⠀⠀⢰⠃⣿⡄⠁⠛⢦⡀⠙⠳⣄⠻⡆⠙⢦⡀⠘⣖⣯⠓⢦⣁⠂⠘⢷⡒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢇⠀⢠⡞⣽⢹⠀⣰⠋⠀⠀⣧⠞⠁⣀⣤⣶⡿⢿⡷⢾⣧⡀⠹⡀⠀⣾⠀⣿⢧⡄⠐⢦⡿⣶⣶⣪⣤⣹⡄⠀⠙⢦⡘⠯⠳⣖⠚⠛⠋⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢸⢡⠏⠀⡇⠇⡼⠃⠀⠀⢀⣇⡴⠚⢉⣿⡟⠀⠀⣧⠈⣇⠀⠀⠻⡄⢻⠀⢿⠘⣧⠀⠀⠑⢌⠳⣄⠈⠙⢿⣤⠀⠀⠙⠒⠀⠈⠳⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡾⠈⠀⢸⠁⠈⠀⠀⠀⠀⣸⠁⠀⢀⣾⣿⡇⠀⢀⣸⣆⣸⡄⠀⠀⠙⠎⠀⠸⣧⢹⠀⠀⣀⣀⣀⡈⢷⡀⠘⡏⠻⡆⠀⠀⠀⠀⠀⠈⠓⠶⠦⣤⡤⠤⢀⠄⠀ ⠀⠀⠀⠀⠄⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢀⣟⠀⣿⣷⣭⣭⣭⣿⡿⣿⣆⠀⠀⠀⠀⠀⡟⣯⣿⣿⣭⣶⣶⣿⣯⣿⣖⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡟⢀⡾⢈⣿⠿⣿⣿⣏⢹⡿⡟⣿⡝⣦⡀⠀⠀⠀⢻⡘⣿⣿⢿⣿⣽⡇⢹⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⣄⣿⣿⣿⣼⡇⠀⠘⢧⡈⣷⣤⡀⠀⠘⡇⠘⠃⣴⣾⣿⣿⣼⡇⠹⣿⣯⡻⣗⠒⠲⣶⠖⠛⠉⠁⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⠿⢿⠀⠀⣿⠛⢿⡿⢛⡇⠀⠀⣰⣇⣈⣙⣛⣶⣾⣹⡄⠀⣿⠛⢿⡟⢻⡇⠀⡿⢿⣿⣮⣷⣦⣸⡆⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⢉⡁⠀⠀⣿⡿⠛⠛⠛⠻⣿⡉⠁⠀⣿⠀⠀⠀⣉⠁⠀⠀⣸⣿⠏⠈⡏⢹⡟⠲⡶⢶⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡄⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠚⠓⠒⠒⠛⠁⣀⣼⡿⠀⠀⠀⠀⠀⢻⣧⣀⠀⠘⠓⠒⠶⠿⠂⢀⣼⡿⡟⠀⢠⣇⡿⠇⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⠁⠀⠀⠀⠀⠀⢻⡟⠿⠷⠶⠤⠤⠶⠶⠿⠿⠛⠋⠀⠀⢠⡆⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⢰⠀⣠⢟⡾⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠚⣡⡾⠁⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⢤⡀⢳⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⡾⡟⠀⢀⡟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠙⣾⡇⠀⠀⠀⠀⠀⢹⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠷⠶⠶⢶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣇⡇⠀⡾⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡇⠀⢸⣿⠀⠀⢸⣿⡀⠀⠀⠀⠀⠻⡇⠙⣿⣦⡀⠀⠀⠀⠀⠀⣿⣥⠶⠶⠒⠶⠶⢴⣿⡏⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⣿⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠄⠀⠸⣿⠀⢸⣿⡀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢳⠀⢸⠙⠻⣦⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⣠⣴⠛⢹⠀⠀⠀⣿⡇⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢂⠀⢻⡆⢸⠀⡇⠀⠀⡇⣿⣇⠀⠀⠀⠀⠸⣆⡜⠀⠀⢨⡟⢷⣦⡀⠀⠀⠉⠙⠒⠛⠉⠁⠀⢀⣤⣶⡚⢿⠸⡇⠸⡇⠀⠀⢿⣇⠀⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢄⠀⢻⡇⠀⡇⠀⠰⣇⠸⡞⣦⠀⠀⠀⠀⢿⡇⠀⠀⣼⠑⣦⡏⠻⣷⣄⡀⠀⠀⠀⢤⣶⣿⡿⢻⣿⠁⠈⡇⢻⡄⢷⠀⠀⢸⣸⠀⢸⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢆⢠⠻⣦⣇⠀⠀⣿⣄⢻⡾⣧⠀⠀⠀⠘⡷⠤⣴⡇⠀⠘⢧⡀⠈⠻⣿⣿⣶⣿⣿⡿⠋⢀⡼⠁⠀⠀⣧⣀⣳⣼⣆⣀⣼⠿⠞⠛⣧⣱⠀⡟⠲⢦⡀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠘⣧⡼⠋⣹⡇⠀⣿⠹⣎⡿⠋⢳⡄⠀⠈⢹⡀⠀⣧⠀⠀⠈⠙⢦⡀⠈⢻⣿⡿⠋⢀⡤⠟⢀⣶⠀⢀⡇⠀⠀⠉⣯⠁⠀⠀⠀⡼⢻⢸⡆⢱⡀⠀⢸⠆⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠈⢧⣠⠇⠇⠀⢸⣠⠞⠁⠀⣴⠟⣦⠀⠀⢻⡀⠸⠀⠀⠀⠀⠀⢉⣷⡄⠀⢀⡶⠋⠁⣴⣿⣿⡆⡾⠀⠀⠀⠀⠘⣧⠀⠀⢠⠇⠘⡄⢧⠈⠧⠤⠼⠀⠀⣇⡀⠀ ⠀⠀⢀⡤⠶⠦⠤⣄⢀⣠⠖⠋⠉⠳⢶⡚⠁⢠⠞⢳⣄⠀⢳⡀⡇⠀⠀⠀⠀⣸⠀⢧⠀⢸⠁⢸⡀⣿⣿⠟⣱⠃⠀⠀⠀⠀⠀⠘⣦⢀⡴⠒⠒⠣⢬⣵⣂⣀⡤⠖⡋⠉⠙⢦ ⠀⢸⠃⠀⡄⢀⡠⠞⠉⢀⣠⢶⣄⠀⠀⠹⣶⠋⣴⡿⢻⠷⣌⢷⣸⡀⠀⠀⢀⡇⠀⠘⣆⡼⠀⢨⡇⠻⠋⣰⢷⡀⠀⠀⠀⠀⠀⠀⣨⢏⡴⠉⠳⢤⣀⣀⣈⣉⣻⠀⠀⡀⠀⠀ ⠀⡴⠒⠺⡷⣼⣶⣶⣚⣯⠶⢯⣈⡳⣄⠀⢹⠟⠉⠀⣸⠀⠈⠻⣷⣷⡀⠀⣼⠻⣆⣀⣻⣇⣠⠟⣧⠀⣰⠋⠀⢷⡀⠀⠀⠀⠀⢀⡏⣸⠀⠀⠴⠶⠶⢶⡶⠾⣋⡴⠛⠉⠀⠀ ⠀⣇⠀⠀⠀⠀⠈⢻⣴⣏⡴⢫⡇⠀⣻⠀⠈⡇⠀⢰⠇⠀⠀⠀⠈⠛⢧⣴⢻⡶⠋⠀⠀⠈⠃⢤⡾⠶⠃⢀⡠⠄⠳⡀⠀⠀⠀⢸⠁⡇⠀⠀⠀⢸⡆⠸⣦⡞⠁⠀⠀⠀⠀⠀ ⠀⠿⣶⣤⣤⣤⡤⠞⠛⠉⠀⣼⠀⠀⣿⠀⠀⡇⢠⠏⠀⠀⠀⠀⠀⣄⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⣰⠋⠀⠀⠀⠙⢆⠀⠀⢸⡀⡇⠀⠀⠀⠘⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠏⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠸⡄⠀⢠⡀⠀⡞⠀⡴⠃⠀⠀⠀⠀⠀⠈⢳⡀⠈⢳⡁⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡿⠀⠀⠀⠘⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢹⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡃⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠻⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠄⠄⢀⠀⠀⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠁⠁⣡⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⢀⣰⢞⣿⡿⣯⡀⠀⠀⢤⠀⢀⡴⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⠀⢀⣾⠏⠀⠀⣻⢯⡞⡿⠁⢸⡇⠀⠀⠀⣷⠟⠀⠀⠀⠈⢻⡄⠀⠀⠄⠒⠶⣤⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢀⣴⠏⡾⢰⣇⡀⠈⠃⠀⠀⣰⢿⡇⠀⠀⠀⠀⠈⠇⠀⢠⠀⠀⠀⠈⢳⡀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣼⢧⣼⣿⠛⣿⡿⣿⣦⡀⠉⠁⣾⣿⣺⣿⣗⣶⣤⡀⠀⠈⢧⡀⠀⠀⠈⠇⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣿⣶⢻⣿⣠⣾⣿⣾⣿⣷⣶⢾⣿⣿⣿⣿⣶⣭⣿⣟⠖⢶⡄⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⡳⣿⠟⠛⠛⠻⣿⣿⣿⣦⣿⣿⣿⠛⠿⣿⣿⣿⣨⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠸⣿⣷⠋⠄⠄⠀⢠⠞⠋⠀⠺⣿⡀⠀⠀⠠⠲⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⢻⡟⠷⣦⣤⣤⢿⡀⠀⠀⠀⠈⠻⡷⣶⡶⠾⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⡠⠄⠾⣄⡀⠀⠀⣀⣠⣸⣧⠀⠀⠀⢠⣤⣅⣀⡠⠤⠐⢫⠀⢸⠁⠀⠀⡇⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⡄⣀⣙⣶⣾⣏⠀⢻⡘⢦⠀⠀⠈⢿⣆⠀⢣⠀⠀⢀⡷⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢲⠃⠀⣠⢿⣏⡁⠀⢹⣿⡶⠞⠁⠈⠳⣄⡀⠀⠈⠑⠚⠓⠂⠁⠀⠀⠀⢀⣴⢿⡄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢻⣀⣎⠀⣠⣇⠀⠀⠉⠓⢏⢹⡀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠈⣧⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣿⣄ ⢀⡷⢯⠁⠀⢉⣡⡜⠓⢦⡤⠀⠀⣿⣿⣀⣠⣤⣄⣀⣀⠀⠈⠉⠳⡶⠶⣾⣿⣏⣀⠤⡴⠚⢻⡄⠀⠀⠀⠀⠀⣿⠴⠶⠶⠶⠦⣄⣸⠘ ⠾⣥⣤⠷⣞⣁⠀⣱⣠⠋⠁⠀⠀⣿⡏⠁⠀⠀⠀⠀⠉⠉⠛⠓⠚⢧⠀⢹⡁⠀⠀⠀⠹⡄⠈⡧⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠻⣄ ⠀⠑⢪⡽⠶⠞⠋⠀⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢣⡀⠀⠀⣀⡽⢾⡟⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⣀⡘ ⠀⠀⠀⠹⡄⠀⠀⠀⠉⠀⠀⠀⠀⡟⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠗⠚⠉⠁⢀⣼⠁⠀⠀⣀⡾⠁⠀⠀⢀⣤⡞⠋⠁⠀⠀ ⠀⠀⠀⠀⠈⣲⡆⠀⠀⠀⠀⠀⢠⣷⣄⠙⣻⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⣞⣉⣠⡤⠞⠋⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠋⣽⠃⠀⣀⣀⡤⠴⠚⢳⣼⠛⠉⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⢀⣀⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡏⠉⠉⠀⢸⡄⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣴⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣄⣳⠀⠀⠀⠀⢇⢀⣠⠶⠛⣿⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠈⠉⠓⠒⠒⠒⠋⠉⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⠀⠔⠋⠀⠀⠀⢀⠀⢰⠏⠀⠀⠀⢀⡔⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡆⠈⣇⠀⠀⣄⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⢉⡽⠋⢀⣿⠀⠀⠀⣠⠎⡴⠋⠉⠑⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⢹⡆⠀⣿⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠋⠀⢀⣾⠇⠀⠀⡰⢃⡞⠀⠀⠀⠀⠈⠳⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⡄⣿⡇⠀⡄⠀⠀⠀⠀ ⠀⠀⣰⡶⠊⠁⣀⡤⢞⣿⠿⠀⠀⡴⢡⠏⢳⡀⠀⠀⠀⠀⣴⡄⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿⣿⣿⣿⢠⣿⠀⢸⣦⣤ ⠶⣯⡁⠒⠚⠉⠀⢠⠎⡏⠀⠀⡼⣱⣿⠃⠀⠳⣄⠀⠀⠀⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⡴⠶⠶⢾⡇⠀⣿⡿⠸⣿⡌⢿⠀⠸⣿⣿ ⠀⠀⠉⢻⠁⠒⠒⡏⢰⠁⠀⡾⣵⡿⠁⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠞⠋⢉⣅⠀⠀⠀⡇⠀⣸⡇⠀⣿⡇⢸⠀⠀⠸⣿ ⠀⠀⠀⢸⠀⢀⡼⢧⡜⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⠋⠀⠀⠀⠀⠀⡿⠀⠀⢻⠁⢸⢠⠃⠀⠙ ⠀⠀⠀⣠⡷⢋⣀⣼⡇⢀⣎⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⣸⠀⠇⠀⠀⢨⡇⠀⢸⠀⠀⠀ ⠀⠀⠚⠛⣏⣉⠤⣾⢠⠿⣍⣠⡇⠀⠀⠀⠀⠀⣶⣶⡒⠒⠢⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⢹⠀⡆⠀⢀⡏⠇⠀⡶⣶⣲⣴ ⠀⢀⡠⠖⢉⡠⠞⣻⠏⠀⠀⠀⢡⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣄⡀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⣼⣿⠀⢰⠷⠛⠉⠀ ⠐⠉⢀⠴⠋⢀⣴⠏⠀⢀⠀⠀⠀⢣⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣭⣦⠀⠀⠀⠀⠀⠀⣸⠀⡞⢰⣿⣹⠀⣾⠀⠀⠀⠂ ⡠⠞⠁⢀⣴⣮⣤⣒⣻⣋⣤⣤⣶⠋⠱⡀⠀⠀⠀⢿⢿⡛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⡴⢿⠀⠁⢸⡟⢻⣴⢻⠄⠄⠀⠀ ⠀⢀⡴⠋⠉⠉⠉⠉⢩⠞⠉⠉⡏⠀⠀⢱⢄⠀⠀⠈⢢⡙⠲⠤⢤⣈⠿⣿⡿⠟⠁⠀⠀⠀⠀⣠⣾⡴⠿⠀⢀⡞⠈⠺⡏⠻⡇⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⣘⣲⣴⡾⠀⡀⠀⠈⣏⠳⣄⠀⠀⠙⠢⠤⠤⠒⠒⠉⠀⠀⠀⠀⣀⡤⠚⡏⠈⢧⡆⢀⡞⠙⢄⠀⠙⣄⠀⠀⠀⠀ ⠀⠗⠚⠛⠛⠛⠛⠉⠉⠀⢠⠃⠀⠑⡄⠀⠸⡀⠹⣷⣤⣀⣀⠀⢀⣀⣀⣠⠤⠔⢲⣯⡁⠀⠀⡀⠀⠈⡇⣼⣇⠀⠈⠳⡀⠈⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠦⡀⢳⡀⠙⠛⠛⠋⠉⢉⡤⠚⠁⠀⠀⣼⡤⢿⣦⡀⡇⠀⠀⡿⠉⠛⠆⠀⠀⢱⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣀⣀⡀⠳⣀⠀⢀⡠⠖⠉⠀⠀⠀⠀⣰⡏⣇⠀⢹⠙⠳⢤⡀⠁⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⠤⠒⠊⠉⠁⠀⡏⠈⠓⠲⠬⢥⡀⠀⠀⠀⠀⠀⢠⠇⠙⠮⣟⠋⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⡆⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡴⠛⣄⠀⠀⠀⠀⡎⠀⠀⠀⠈⠓⠦⣄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠳⢶⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠟⠁⠀⠈⢦⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣤⣄⣀⠀⢀⡼⠃⠀⣴⠁⠀⠀⠀⠀⠈⢣⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡟⣇⢀⣠⣶⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢧⣛⢾⡹⣏⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⣭⢷⣫⣟⣽⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠟⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⡼⣽⣚⣧⣟⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⢀⣽⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡳⣝⡯⣗⡿⣾⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⡶⢧⡖⣯⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢳⡟⣭⢷⣯⣿⣿⣿⢿⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡽⣞⡿⣸⡱⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣭⢷⣫⡿⠿⠛⠷⠾⣮⣓⠜⢢⠣⡙⢎⠻⡝⠿⡿⣷⣦⣤⣀⠀⠀⣠⣿⣿⢷⣻⡽⡞⣥⢻⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⣳⡘⣤⢣⡌⣅⢣⢃⠿⣹⢿⣶⣤⣿⣿⡿⣯⢷⣻⡝⢴⣫⣿⡇ ⠀⠀⠀⠀⠀⣠⣼⣿⠟⠁⠀⠀⢠⡴⠒⠲⣶⣄⠀⠀⠀⠈⢿⣝⢮⣳⣞⣼⠿⠛⠛⠛⠿⢿⣿⣿⣿⡿⣽⣏⡷⣊⢧⣟⣿⠄ ⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⢰⣿⡄⠀⣰⣿⣿⣷⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣚⡷⡭⣞⣾⡿⠀ ⠀⠀⢀⣿⣿⠿⠁⠀⠀⠀⠀⢸⡽⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠛⣷⣦⡀⠀⠀⠹⣷⣏⡾⣵⣻⣿⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠻⠯⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣀⣀⣾⣿⣿⡄⠀⠀⢻⣾⣽⣳⣿⡟⠀⠀ ⠀⢰⡇⠀⣀⣠⣤⣴⣾⡟⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡛⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣾⣽⣿⠇⠀⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⣛⠉⠀⠀⠀⠀⠈⢻⣦⣤⣤⣤⣤⣤⣶⣄⠀⠀⠈⠉⠉⠛⠻⣿⣋⡥⠞⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀ ⢀⣼⣿⡿⣧⢏⣿⣟⢿⣿⣄⠀⠀⠀⠀⠘⣿⡿⢛⠛⡛⠿⠿⣿⣷⣤⣀⠀⠀⣰⠆⠂⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀ ⢼⣿⣿⣟⣧⢿⣹⣏⡾⣼⣻⣆⠀⠀⠀⠀⢹⡷⢈⠒⢠⢂⡐⠤⣙⣻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀ ⠈⣿⣿⣿⣞⣯⢷⡞⣵⢧⣻⣿⠀⠀⠀⠀⠀⢿⣄⠋⡄⠢⡐⢥⣾⡟⠁⠀⠀⠀⠀⠀⠀⣴⡿⣦⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⢿⣿⣿⣿⣞⣯⢿⡽⣞⡵⣻⣧⡀⠀⠀⠀⠈⠻⣧⣔⣡⣼⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀⣙⣿⣽⣿⣦⣀⡀⠀⢸⠇⠀⠀⠀ ⠀⠘⣿⣿⣿⣟⣾⣯⢿⡽⣯⣽⣿⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣛⣟⡻⣿⣿⣿⣿⣻⣿⠀⠀⠀⠀ ⠀⣰⣿⢩⡙⢏⠛⠛⠛⠛⠛⠉⣿⣷⢈⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡿⣹⢮⣗⢮⣷⣿⢳⣞⣿⣿⠇⠀⠀⠀⠀ ⣴⣿⡏⢦⡙⢎⠲⢤⣀⡀⠀⢠⡿⠸⣷⣌⡆⠤⣉⠒⠥⠒⡔⠒⢆⠩⡙⣿⣿⣽⣻⣽⣻⣞⣯⢾⣼⣻⣾⣿⡟⠀⠀⠀⠀⠀ ⣿⠟⡌⢧⢸⡉⢗⠢⡜⡸⢡⣿⢧⠓⡬⢙⠻⠷⣶⢯⣶⣭⣴⡭⢆⡑⣶⠏⠻⣷⣟⣾⣳⣟⣾⣻⣞⣷⣿⠿⠃⠀⠀⠀⠀⠀ ⢫⠜⡱⢊⠦⣙⡌⠳⣌⠱⣡⡿⢇⡘⠔⢣⠘⡔⠤⢂⡔⢠⢢⡐⣢⣾⠟⡀⠀⠈⠛⠿⣷⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⣴⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⡀⠀⣴⣿⣿⠁⠀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡉⠛⠛⠿⠿⠋⣁⣴⣾⣿⣿⣿⣀⠘⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠚⠛⠛⠻⠿⠗⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠿⢿⡿⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⠖⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⠟⠁⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣶⣶⣶⣄ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠙⠛⢿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⠋⠁⠀⠙⢷⡄⠀⠀⠀⣠⡾⠛⠛⠻⣶⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⢰⣶⠀⠀⣿⠀⠀⣸⡏⢀⣤⡄⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡝⠿⣿⣿⠀⠈⣷⡀⠀⠀⠀⣠⡿⠀⠀⣿⠀⠈⠋⠁⠀⢠⡿⢰⣿⣿⣿⡿⠋⡉⠙⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣾⠁⠀⠈⠀⠀⠀⠈⠛⠷⠶⠞⠋⠀⠀⠀⠘⣷⣀⣀⣀⣴⠟⠁⢸⣿⣿⣿⡇⠸⣧⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠻⠿⠿⠀⠀⠹⣷⠤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⢰⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠘⢷⡀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⣠⡟⠀⡀⠀⠀⠀ ⡤⠤⠤⠤⠴⠏⠀⠀⣿⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠉⠛⠛⠶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣠⣾⠏⢰⡟⠻⣧⣀⠀ ⠀⠀⠀⠀⠀⣴⡟⢻⡏⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣧⣀⠀⢻⣆⠈⠉⠛ ⠀⠀⠀⠀⣾⠟⠀⣼⣷⣄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣶⣦⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣦⣄ ⠀⠀⢀⣼⣏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿ ⠀⠀⣸⡇⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⡿⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⡞⢩⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡹⠁⢰⠃⣩⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠿⣉⣩⠛⠲⢶⡠⢄⠐⣣⠃⣰⠗⠋⢀⣯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣠⠬⠦⢤⣀⠈⠓⢽⣾⢔⣡⡴⠞⠻⠙⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣳⠖⠉⠉⢉⣩⣵⣿⣿⣒⢤⣴⠤⠽⣬⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣟⠟⠋⢡⡎⢿⢿⠳⡕⢤⡉⡷⡽⠁ ⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⡾⣥⣏⣖⡟⠸⢺⠀⠀⠈⠙⠋⠁⠀⠀ ⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠘⠿⣯⣮⢦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠒⠠⢄⠀⠀ ⠀⠀⠀⡠⠄⢀⣄⡀⠀⢀⡀⠤⠀⠀⠐⠂⠀⠀⠒⠤⣠⢋⠀⠂⠅⠢⡀⠡⠀ ⠀⠠⢀⠄⢊⠡⠀⡸⠊⠁⠀⠀⠀⠐⢣⡔⠍⠠⠀⠀⠈⠒⠊⠲⢄⡈⠂⣢⠃ ⠀⡗⡡⠂⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢞⡦⠊⠀ ⠀⠻⣀⠤⠊⡌⠀⠀⠀⠀⠀⠀⡔⠿⠦⠔⠛⠛⡄⢈⠄⠀⠀⠀⠀⣄⢡⠀⠀ ⠀⠀⡈⠐⢲⠁⠀⠀⢀⢀⣤⣒⣑⠄⠀⠀⠀⢀⣧⡪⠻⠀⣠⡇⠀⠸⠽⠀⠀ ⠀⠀⠁⠀⠇⠀⠀⠀⠀⢁⣴⠷⠶⡀⠀⠀⠀⣿⢭⣍⢷⣬⣮⠁⢠⡸⠆⠀⠀ ⠀⠐⠀⡠⢶⠀⠠⠄⢼⣽⢁⢻⢾⡅⠀⠀⠀⢻⠾⡟⡆⠟⢣⠔⣟⠅⠘⠀⠀ ⠀⣀⠔⡠⠊⠁⢤⢲⡅⠙⠘⣹⣀⠇⠀⠀⡀⠀⢚⣜⡁⠀⣌⢀⢿⢌⢆⠃⠀ ⢀⠃⠔⠀⡇⢀⣈⣂⡪⡄⠈⠐⠀⠀⠀⡶⢴⡆⠀⠀⠀⢠⢷⣁⡈⡈⠎⠎⠀ ⢀⠊⠀⠀⡗⠙⢄⢏⠀⠉⠒⣤⠀⠀⠀⣘⠾⠁⠀⡠⠶⡛⡄⣾⠈⢃⠈⠌⡇ ⠀⠀⠀⢰⠀⣀⠈⢪⢂⠀⢠⠁⡍⠒⠈⠈⢢⣤⡾⠁⠀⠈⢊⡇⠀⢸⡆⠈⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⢷⡗⠇⠱⡸⣤⣀⠀⠀⢙⠁⠀⠀⣠⠊⠁⠀⠀⠇⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠈⠻⡘⡠⠋⠁⠑⠊⢐⡞⡦⠔⠊⠈⢾⠀⠀⠀⠘⡀⠀ ⠀⠀⠀⠢⠀⠀⠀⠀⠔⠒⠋⠀⠀⠓⠄⣀⣈⡿⢿⣛⣀⠠⠃⠈⠢⣀⡀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣯⡿⣽⡷⣿⢿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣽⣷⡟⣯⣿⣽⣯⣿⣽⠂⠀⢠⣶⣿⡟⣦⠀⣶⣶⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⣻⠏⠀⠈⣿⣞⠟⢀⣴⣿⣻⢾⣽⣟⡿⣯⢿⣽⢯⣷⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⢀⠻⣾⡽⣷⠀⠀⠸⣻⠀⣸⣟⠾⣽⣯⠷⣻⣽⣟⡿⣾⣻⢧⠀⠀ ⠀⠀⠀⢠⣾⣇⣀⢧⣨⣇⣏⡙⠯⣧⡄⠀⣟⠀⡿⠀⠀⠈⠀⠀⢀⣿⢾⣻⡷⣟⣿⠃⠀ ⠀⠀⠀⠘⢷⡏⠐⠊⠰⠃⠈⠛⢷⡷⣄⡀⠀⠀⡅⠀⢀⣠⣶⡿⠻⠏⢛⡓⠛⠋⠁⠀⠀ ⠀⠀⢀⣤⣦⣴⡶⣶⢶⣴⣤⣀⠀⠙⢟⡿⣦⠀⠀⠀⠛⣉⣴⡴⣞⡿⣟⣿⣻⣗⣦⠀⠀ ⠀⢀⣾⡿⣽⣯⢷⠛⠈⠉⠛⠛⠂⠀⠘⢷⣻⠀⠀⠀⠒⠛⠉⠁⢻⡷⣟⣯⡿⣽⢿⡄⠀ ⣠⣿⢯⣟⣷⣻⢿⣤⣤⡤⠤⠶⣶⠆⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠙⢻⣽⣻⢯⣟⡿⡄ ⠙⠋⢿⣻⣞⣯⣿⣽⠚⢁⣤⡾⠁⠀⠀⠀⣾⠀⣿⣇⠀⠀⢰⣦⣀⣠⣼⢯⣟⡿⣽⣻⢿ ⠀⠀⠀⢿⣽⠳⠏⣠⡾⣟⣷⢿⣦⣤⠀⠀⢸⡄⢸⣯⢿⣶⣻⢾⣟⡿⣞⣿⣽⣻⢯⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣾⣯⡷⣟⣧⣤⣿⣻⡀⠹⣟⣾⡽⣿⣞⡿⣯⠃⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠻⢿⣧⣟⡿⣿⣻⢧⣟⣧⡇⠀⠘⠟⣿⣧⢿⠻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣿⣳⣿⣻⣽⢯⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⣽⡾⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⢀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀ ⠀⠀⠀⠀⠀⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⡔⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⢀⡤⠶⢯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⣛⣋⡭⠭⣭⣟⠓⢲⡞⣵⢸⣤⡞⠛⠓⣲⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⣡⠶⠋⣡⠴⠒⠛⢉⣩⣭⣿⣸⡿⣼⠈⠉⢛⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⣡⠞⠁⡴⠋⠀⣠⡴⠋⢁⣠⠞⣼⠈⠁⠙⢿⡛⢿⡌⠙⣆⠀⠀⠀⠀ ⠀⢠⡏⡼⠃⠀⡼⠁⢀⡼⢃⡤⠞⠋⠀⣠⠃⠀⠀⠀⠀⢳⡄⠹⡄⢸⡄⠀⠀⠀ ⠀⡞⣸⠃⠀⢸⠃⠀⡼⢁⣮⡴⠒⠚⠋⠁⠀⠀⠀⠀⣶⣦⠙⣆⡙⣆⡻⣄⡀⠀ ⢸⢁⡏⠀⠀⢸⠀⠀⡇⢸⡏⠀⠰⡆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⢲⡷⠶⠟⠋ ⣸⢸⠃⠀⠀⠸⡇⠀⡇⢸⡀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⢹⠸⡇⠀⠀⠀⢳⡀⢹⡌⢧⡀⠀⠀⣹⠦⣤⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⢳⡄⠀ ⠘⡆⢷⠀⠀⠀⠈⢳⡀⠙⢮⣝⣿⣻⣏⠀⠹⣆⠀⠀⠈⢷⡀⠘⢦⠀⢠⠏⣿⠀ ⠀⢻⡘⣧⠀⠀⠀⠀⠹⣆⠀⠉⠣⡀⠙⢷⡀⠈⠳⣤⡀⠀⠙⠦⠬⠷⠾⠚⠁⠀ ⠀⠈⢧⠈⢧⡀⠀⠀⠀⠈⠳⣦⡀⠙⢦⡀⠹⣆⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⢸⡿⣄⠀⠀⠀⠀⠈⠻⣆⠈⢳⡀⠘⣦⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣇⡼⠃⠈⠛⢦⣀⣄⡀⠀⠘⣧⠀⢷⠀⠘⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⡞⢁⡞⢛⡀⠀⣹⠀⢸⠆⠀⢻⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠓⠋⠀⣠⠏⢀⡞⢀⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠴⠾⠷⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣀⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⠶⡏⣶⢎⡿⢻⡏⠶⢞⡇⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠙⠐⠚⠁⠀⠛⠲⠛⠙⢷⡄⠀⠀ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⢠⢲⠀⠀⠀⢿⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠤⢀⡠⢃⠎⠀⠀⠀⣬⠀ ⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠁⠀⠀⠀⣰⠏⠀ ⠀⠘⠵⣴⣆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⡾⠋⠀⠀ ⠀⣀⣠⡿⠉⠛⣳⣶⠶⠶⠾⣿⠶⠛⠋⠉⣹⣧⡀⠀⠀ ⠈⠫⣎⣷⠀⠋⡜⢳⠀⠀⠞⢫⣑⠂⠀⠐⠁⢃⣉⢠⠄ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡠⢺⢀⠞⠁⠀⠀⣿⠀⠀⠙⡌⡏⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⢸⡎⠀⠀⠀⠀⢸⠀⠀⠀⢱⣣⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠽⡀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⢀⡠⠤⠒⠊⠉⠑⠲⢭⢯⡒⠨⠷⠦⠭⢶⡶⠶⠖⠒⠶⠾⣄⡀⠀⢀ ⢠⡏⣀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⡄⠙⣆⡞ ⠸⣧⡀⣠⠤⠄⠤⡀⠀⣠⠏⠀⠀⠀⠀⠈⢇⠀⠀⢀⡠⠤⣀⠀⠀⣸⣁ ⠀⡏⡎⠀⠀⠀⠀⣹⡞⠥⡤⠒⢒⣒⣒⣂⡠⠽⣶⠃⠀⠀⠀⠙⡶⡏⠁ ⠀⡇⠣⣀⡀⠀⠐⠁⠑⢤⣇⠀⠀⠁⠀⢸⢀⡤⠯⠣⠀⠀⠀⢀⠇⡇⠀ ⠀⢣⡀⠀⢳⠀⠀⠀⠀⠀⠐⠓⠒⢤⡐⠚⠋⠉⠀⠀⠀⢉⢻⡥⢠⠇⠀ ⢀⡠⠕⠂⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⢤⣤⠋⠀⠀ ⠉⠉⢉⡝⣁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠲⢬⠽⠆⠀ ⠀⠀⢛⠞⠉⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⡆⠽⠆⠀ ⠀⢀⠯⢄⣼⢡⡷⠤⠤⠤⠀⠠⠤⠤⠤⠤⠤⡤⠤⠤⣠⡇⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀⠀⠀⠀⢀⡴⠋⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠞⠉⠀⠀⠀⠉⠙⢷⣄⣠⡿⠀⠀⣶⣦⡼⠋⠙⣦⣀⣀⠀⠀ ⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢿⣀⡀⣿⣟⠀⠀⠀⣯⠈⠉⢻⡇ ⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⢧⣤⡼⢿⠇⢠⡾⠁ ⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠦⢴⣿⠁⠀ ⠠⠼⣿⡶⠶⡄⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠚⠛⣾⠟⠃⠀ ⠀⠀⣈⣷⣶⠆⠀⠙⠋⠀⠀⠀⢴⡦⠀⠀⠀⠙⠋⠀⠀⢙⡾⠿⠶⠆⠀ ⠀⠀⠀⣀⣿⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠧⣄⡀⠀⠀ ⠀⠀⠀⠋⠀⠈⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⢀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠿⠟⠛⠉⠉⠉⠁⠀⠈⠉⠙⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀ ⠀⣸⠏⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⡄⠀⠀ ⢠⡏⠀⠀⣀⣘⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠘⣧⠀⠀ ⠈⡇⠀⠀⣰⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⢻⡄⠀ ⠀⡇⠀⠰⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠈⣷⠀ ⠀⣷⠀⢸⣟⣚⣫⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⣾⠟⠀⠀⣿⡆ ⠀⢻⡆⠈⠙⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⣿⠃ ⠀⠀⢳⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⣷⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠘⣷⡀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀ ⠀⢰⠟⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠈⣧⠀⠀⠀ ⠀⡿⠀⠀⠀⠀⠀⠈⠙⠶⠶⠖⠒⠒⠚⠒⠲⠛⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀ ⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⠋⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⣋⣉⠅⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠄⠀⣰⠓⠠⣮⢿⠋⡆⠀⢱⡔⠉⠙⢢⠀⠀⠤⢄⠘⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢠⣞⣮⣮⣤⡁⠀⢞⣇⣠⣀⡈⠀⢠⠀⠀⢣⠀⠈⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢺⣞⣧⣼⣿⣾⣦⢾⣿⣿⣯⣿⣒⢤⠁⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠸⣷⠏⠀⠈⡹⠋⢿⡋⠁⠩⢙⡷⠋⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⠀⠀⣀⡇⠀⠀⠀⢹⠓⠒⡚⠄⠀⢀⠹⢂⠒⢻⠁⠀⠀⡀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠎⠀⣈⡳⣶⡍⣋⢆⠀⠙⢏⠹⠀⡈⠊⠀⢈⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⢀⢴⣹⠀⣜⠑⠢⢜⡏⠁⠀⠑⠢⣀⠀⠀⠀⣀⡴⠋⢣⠀⠀⠀⢱⠀⠀⠀⠀⣄ ⣸⠱⣀⠄⢎⡱⠆⠈⣿⠄⠒⠠⠤⢄⣉⡖⢿⠯⠐⢂⠹⡄⠀⠀⢸⠒⠚⠒⠢⡏ ⠘⢫⡾⠓⠡⡁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠱⣈⡄⢀⡀⢶⠇⠀⢀⡜⠀⠀⢀⡀⠌ ⠀⠀⠑⢤⠀⠀⠀⢠⣌⠢⣤⠄⠀⠀⠀⠀⠀⠉⣀⣠⣞⣀⠴⠊⠀⢠⠞⠁⠀⠀ ⠀⠀⡎⡯⠤⢤⠒⠈⣾⠉⠀⠀⠀⢠⣶⣦⠀⣠⣤⡄⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀ ⠀⢀⢇⣇⠀⠀⣆⠠⠚⡧⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ ⠀⠎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⢱⢂⢷⡀⣠⣦⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢼⡄⠈⡤⡞⢉⠀⣔⠍⠁⡗⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⡠⠛⡄⣡⡾⠌⠀⡄⡏⠢⠈⡦⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠊⢀⣀⣈⠉⠁⠀⠀⠐⠑⠤⠕⢁⣿⠢⡄⠀⠀ ⠀⡠⢒⠃⠀⠀⣿⣾⣽⠇⠀⠀⠀⠀⠀⢱⢸⢹⠀⢡⠸⠀⠀ ⢸⠘⠂⢆⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣤⣂⣌⡞⢄⠘⡀⠃⡇ ⠘⢄⡀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡀⠑⠤⡁⠒⡞⡄ ⠀⠀⠈⠉⠀⠈⠉⠒⠒⠒⡝⠀⠀⠀⠀⠀⡜⠒⣄⢈⣠⠃⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠒⠯⡤⡪⠜⠊⡍⡰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠳⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⠀⠀⠀⠈⣄⠑⠤⠀⣤⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⣶⢻⣗⣻⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣦⡟⣷⢯⡷⠻⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢬⣿⣳⣿⠝⠉⠀⣠⣄⣤⣶⣤⣠⣄⡀⠀⠀⠀⠀ ⠀⢼⣿⣳⡯⠀⢀⣰⣿⣻⣽⣻⣞⣷⣻⡾⣽⢶⡄⠀⠀ ⢰⣿⣟⣿⠁⢀⣾⣿⣷⠟⠉⣠⣀⣀⠀⠙⢿⣟⣿⣖⠀ ⢸⣿⣿⡅⠀⣿⣿⣿⡖⣠⣿⣿⣿⣿⣿⣄⠀⢺⣿⣿⡇ ⢸⣿⣿⡧⠀⣿⣿⣿⢃⠉⠿⠿⠛⣿⣿⣿⡆⢘⣿⣿⣟ ⠘⣿⣿⣿⠄⠈⢿⣿⣿⣶⣤⣠⣴⣾⣿⡿⠃⢼⣿⣿⡏ ⠀⠨⣿⣿⣯⣂⠘⠻⢿⢿⣿⣿⣿⣟⠟⢃⣰⣿⣿⡿⠁ ⠀⠀⠈⢿⣿⣿⣾⣄⣠⢀⣀⣀⡀⣠⣴⣿⣿⡿⡟⠁⠀ ⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢏⡤⠶⢦⡀⠀⠀⣀⠤⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⢉⡿⣿⣿⡿⢸⠁⠰⠀⢹⠀⢰⠃⣤⠀⢳⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡼⢠⠆⠙⠃⠈⠳⠤⠴⠋⠀⠸⣄⢀⣠⠞⢸⣿⡟⢰⠈⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⢿⡀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠈⠛⠃⠀⡗⠚⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⡀⠳⣄⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀ ⠀⠀⠀⣀⣀⠀⠣⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡸⠁⠀⠀ ⠒⠒⠒⣣⢤⠇⠀⠙⢦⣄⠀⠈⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⡞⠁⣏⠣⠤ ⠀⠀⣰⠋⣸⣦⣀⣀⣀⣈⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣷⣮⡳⣄ ⠀⢰⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞
⠀⠀⠀⢠⡾⠲⠶⣤⣀⣠⣤⣤⣤⡿⠛⠿⡴⠾⠛⢻⡆⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠉⠁⠀⢀⣿⠐⡿⣿⠿⣶⣤⣤⣷⡀⠀⠀ ⠀⠀⠀⢹⡶⠀⠀⠀⠀⠀⠀⠈⢯⣡⣿⣿⣀⣸⣿⣦⢓⡟⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣍⣭⣾⠁⠀⠀ ⠀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣤⡀ ⠈⠉⠹⣏⡁⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠆⠀⢀⣸⣇⣀⠀ ⠀⠐⠋⢻⣅⣄⢀⣀⣀⡀⠀⠯⠽⠂⢀⣀⣀⡀⠀⣤⣿⠀⠉⠀ ⠀⠀⠴⠛⠙⣳⠋⠉⠉⠙⣆⠀⠀⢰⡟⠉⠈⠙⢷⠟⠉⠙⠂⠀ ⠀⠀⠀⠀⠀⢻⣄⣠⣤⣴⠟⠛⠛⠛⢧⣤⣤⣀⡾ Search '' kwroppiicafe '' for more!
⠀⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⠟⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠋⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⣷⡄⠀ ⠀⠀⢀⣠⣶⡿⠿⠿⣿⣿⠛⠿⠿⠟⠛⠛⠙⢿⣿⣯⠁⠙⢿⣿⣧⠀⠙⠛⠁⠀ ⠀⢀⡾⠋⠁⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠄⠀⠈⠻⣷⣄⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢠⣴⠾⠋⠁⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠉⠶⠤⠄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⠀⠀⠈⡢⢀⣀⠀⠀⠀⠀⢀⡠⠗⠂⡝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠙⠢⣀⠀⢇⠀⢠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠀⢩⡀⠀⠀⠀⣀⣰⠀⠈⢦⠀⠑⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡦⠤⠥⠀⠀⢸⣿⡏⠀⠀⠀⢣⢰⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⡄⠹⡢⢰⡀⠀⣀⢆⡘⠟⠁⠀⠀⠀⠘⠇⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠈⠒⠵⣄⢱⡀⠹⠚⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣂⡀⠀⠀⠑⠇⠀⠀⠈⢳⠠⢄⣀⣀⣀⠤⠋⠀⠀ ⠀⠀⠀⣀⠤⢤⠔⠩⢟⠳⡤⡤⠴⡤⠠⡶⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠁⠀⡟⠀⠀⠀⢢⠃⠀⠠⠦⡄⠌⠑⣠⠤⠷⣖⠒⠢⡄⠀⠀⠀ ⠀⠀⣇⠀⠀⢧⠀⠀⠀⠀⢱⡀⠀⠀⠸⠀⠈⣀⡀⠀⠈⢧⠀⡷⠀⠀⠀ ⠀⠀⢸⠄⠀⡼⡧⠀⣀⣠⠴⢓⡶⠒⠒⠊⠉⠁⠘⣦⠤⢺⠽⠃⠀⠀⠀ ⠐⠶⠯⠴⠊⠀⢗⣂⣸⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣨⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢰⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠃⢀⡿⢷⡄⠀⠀⣠⣶⣦⣄⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠈⣿⡤⠞⠀⢸⢿⣦⡴⠟⠛⠓⢻⣷⢿⣵⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣧⡀⠀⠀⢸⡆⢀⣴⡿⠋⠁⠀⠀⠀⣰⠟⡵⠋⢸⠈⣯⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡾⠋⠁⠀⠀⣷⢋⡞⠁⢀⡴⠒⠋⣹⠟⡞⠁⠀⢸⠀⣿⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⡿⢿⡇⢰⡏⢀⣠⣼⡟⣸⠁⠀⠀⢸⠀⣿⠙⢦⡀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡾⠋⠀⠈⢷⡈⢧⣸⣧⡘⠓⠇⠀⠀⠀⡞⠀⣿⠀⠀⠹⣄⠀⠈⡿⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠙⠓⠛⠋⠁⠀⠀⠀⠀⠸⠃⢸⡟⣧⠀⠀⠘⣆⣼⠇⠀⡾⣷⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢘⡷⠶⠖⠛⠁⠀⣴⣷⠏⠉⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⢀⣾⣿⠉⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣤⣶⣿⡞⠉⠙⣆⠀⠹⣦⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠉⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣤⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠈⡇⠀⡇⠀⠀⠘⡇⠀⢻⡆⠀⠀⠀ ⠀⣰⢟⣑⡀⠸⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⡇⢠⡇⠀⠀⠀⢷⠀⠘⣇⠀⢀⡀ ⢰⡏⠀⠿⠏⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⢀⡞⣠⡟⢹⣄⠀⠀⢸⡀⠀⠻⠶⢾⡇ ⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⣾⠷⠚⢹⡄⠀⠙⢦⣀⠀⠹⠦⠤⢤⣾⠃ ⠀⢿⣄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠹⢦⡀⠀⠈⠛⠲⠶⡞⠻⣧⠀ ⠀⠈⠻⢧⣄⣀⠀⣸⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠉⠓⢦⡀⠀⠀⣿⠀⢹⡇ ⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠉⠙⠛⠶⢤⣤⣀⣀⣠⡤⠾⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣤⡀⠀⠀⠀⢹⡀⢀⡿⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢙⣷⡄⠀⢸⢁⣾⡇⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠴⠞⠋⠀⢀⣠⠞⢀⣽⣠⡾⢛⡿⠀⢀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠭⣿⣿⣭⣤⠴⠛⠙⠉⠀⡸⠁⢀⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⡿⠀⠀⠀⠀⢰⡇⠀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠀⠀⢳⣸⣇⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⣹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠙⢦⣀⡀⠀⠀⣀⣠⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⡼⠷⣤⣀⡀⠈⠉⢉⣉⣭⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠴⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀ ⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⢠⠃⢀⣸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠈⡇⠀ ⢸⠀⢰⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢸⡀ ⠸⡆⢾⣒⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⠃⠀⡇ ⠀⢣⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡇ ⠀⠀⢦⠀⠘⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⡼⠀ ⠀⠀⠈⠣⡀⠀⠀⠉⠙⠛⠒⠲⠶⠖⠚⠋⠁⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠶⠶⠖⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡇⠀⣴⡿⢋⠋⠀⠀⠀⠀⠻⣇⣼⠀⠀⠀⠂⠙⣷⡄⠘⣿⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣾⠟⠀⣿⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡄⢸⡇⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢰⣿⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠙⣷⡈⣷⠀⠀⢈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢹⣧⢻⡆⠀⠈⠲⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡇⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠈⠢⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣎⡇⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣴⣤⣄⡀⠀⠀⠤⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡇⠀⣀⣤⣤⡼⠿⠿⠶⢶⣤⣀⣀⠙⠻⣿⡷⣶⣄⣀⠙⠷⣶⣤⣀⠈⠛⠷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⠾⢿⣦⡈⠉⠛⠓⠶⠿⠿⠟⠛⠳⠶⢾⣿⣿⠿⠛⠛⠋⠉⠉⠉⠙⠛⠛⠻⢿⣶⣄⠀⠀⠀⠀⠀⢠ ⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀⢠⣿ ⠀⢀⣾⠏⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠹⣷⣀⣾⠇ ⠀⢸⣿⡇⠈⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢻⣿⡿⠀ ⠀⠘⣿⢳⡀⠀⠀⠀⣀⣴⡶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀ ⠀⠀⠘⣧⡙⢧⣴⡿⠋⠁⠀⠀⠀⠀⠀⠘⢷⡀⢀⣠⣾⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⡀⠀⢀⣴⠟⠛⠉⠉⠉⠛⠿⣦⣄⠀⠀⣠⣿⣿⡾⠟ ⠀⠀⢰⡏⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢯⣅⣀⣈⡙⠛⠶⠦⠤⠤⠤⠴⠶⠶⠖⠂⠀⠀⣈⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⡏⠁⠀⠀ ⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣇⠀⠀⠉⣟⠙⠛⠒⠒⠒⢶⡶⠶⠶⠒⠒⢺⡟⠛⠉⠉⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⣧⠀⠀⠀ ⠀⠀⢸⡇⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠠⢹⣷⣄⡀⢿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⣟⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⣿⠀⠀⠀ ⠀⠀⢸⡇⠀⠈⠛⢶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣿⣧⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣠⣶⠟⠋⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣿⠀⠀⠀ ⠀⠀⢹⣿⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣙⣷⣤⣀⣿⡀⢀⣀⣠⣴⣧⣴⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠶⠶⣿⢿⡟⠉⠀⠀⢰⣿⠀⠀⠀ ⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠙⠻⣯⡉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣼⣧⣶⠄⢀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠹⢷⣄⡀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠁⠀⢀⣾⠏⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⠶⠛⠙⠛⢋⣡⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣦⣤⣴⡿⠋⠀⠀⠀⠀⠀ ⠠⠾⣿⣥⣄⣤⣤⡶⠾⣿⡟⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⠈⠙⠻⢷⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⢿⣶⣶⣤⣬⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⣠⣴⣾⠟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠈⠻⢶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠛⢛⣿⡿⠋⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⢿⣶⠦⣤⣽⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⣠⣶⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⣆⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⣼⡟⠁⠀⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⠟⠛⢻⣷⠶⢿⠷⠾⢿⣛⠋⠉⠉⠉⠉⢙⡟⠁⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠿⠶⢶⣿⡿⠀⠀⠀⢠⣿⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠾⠟⠹⣷⠀⠀⠀⠀⠀⠀⠀⣰⡾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⣀⣤⣴⠿⣷⠀⠀⠀⠀⠀⣼⡟⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣶⢦⣤⡀⠀⠀⠀⢨⣿⡶⠿⠋⠉⢀⣠⣿⣦⣄⠀⢀⣾⠏⠀⣠⠖⢸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⠃⠀⠹⣷⣄⠀⢀⣸⣯⣠⣤⣴⢾⡿⠋⠁⠈⢻⣷⣿⠏⠀⢰⡟⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡟⠘⣆⠀⠈⣿⣶⣿⡟⠉⠉⠀⢀⠀⣠⡞⢠⡆⢸⣿⡿⠀⠀⣿⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣸⡇⠀⢻⣦⣾⣿⣷⡿⠃⣠⢂⣴⡿⣾⠊⣴⣿⣧⢾⣿⡿⠀⠀⣘⣃⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣷⣀⣼⣿⢿⣿⣟⣵⣿⣿⠿⣡⠟⣡⣾⣿⣿⣯⣿⡿⠁⠀⠀⠹⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⣵⣿⣿⣧⣾⠷⠟⠛⣽⣿⠿⠋⠸⢁⣀⠀⠀⢄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠿⠛⢻⡏⠉⠉⢉⣤⣤⡀⠀⠀⠈⠛⠁⠀⠀⢰⠛⣿⣿⡄⠈⢆⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣏⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠘⡄⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠹⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠐⢈⠙⠛⠿⠶⣦⣤⣤⣤⣤⡶⠶⠟⠛⠉⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢿⣷⡀⠀⠀⠀ ⠀⣠⣾⡿⠷⠶⢶⣤⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣠⣿⣷⣄⠀⠀ ⣴⡿⠋⠀⠀⠀⠀⠈⢿⡆⠘⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⣴⠟⠋⠉⠉⠛⢦⡀ ⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⡄⢻⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠇⢠⡿⠃⠀⠀⠀⠀⠀⠀⢣ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢈⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸ ⠙⣷⣄⠀⠀⠀⠀⠀⣰⣿⡿⠛⢻⣿⠟⠛⠛⠛⠛⢻⣿⠻⠷⠶⠟⠛⢻⣿⠻⣿⣧⡀⠀⠀⠀⠀⠀⢀⡞ ⠀⠀⠛⢿⣶⣦⣶⣾⠟⠉⠀⠀⠈⠻⢧⣄⣀⣀⣀⣼⡿⣤⣀⣀⣀⣠⡿⠃⠀⠈⠙⠻⣦⣄⣀⣤⣴⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠶⠶⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀ ⠀⠀⢠⡾⠁⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡙⢷⡀⠀⠀ ⠀⢠⡟⠀⠀⠀⣰⣿⣿⡇⠀⠀⠙⢷⡀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠹⣮⢿⡀⠀ ⠀⣾⠀⠀⠀⢰⡏⠙⠛⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⣸⠋⠛⠋⠀⠀⠀⢹⠈⣧⠀ ⢸⡇⠀⠀⠀⠘⣧⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣾⠀⢹⡆ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⣸⠇ ⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⡟⠀ ⠀⠘⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣾⠁⠀ ⠀⠀⠘⢷⡀⠀⠀⢻⣿⡻⠋⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡿⠃⠀⢠⡾⠁⠀⠀ ⠀⠀⠀⠀⠻⣦⡀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠀⣀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠉⠛⠓⠒⠒⠒⠚⠋⠁⣠⣤⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⠶⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠛⠛⠉⠉⠙⠛⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠠⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠆⠀⠀⠈⠱⣄⠀⠀⠀ ⠀⠀⡰⠃⠀⢀⣀⣀⣀⣀⣭⣿⣷⠆⠀⠀⠰⣾⣿⣭⣀⣀⣀⣀⣀⠀⠈⢢⠀⠀ ⠀⡸⠁⠀⡴⠁⠀⠀⠛⢋⠉⠁⢀⣀⠀⠀⢀⡀⠈⠉⢙⠛⠁⠀⠀⠱⡄⠀⢧⠀ ⣿⠇⠀⠀⣇⠀⠀⠀⠀⣸⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⢸⡀⠀⠀⠀⢠⡇⠀⠈⣇ ⣿⠀⠀⠀⠈⠲⠤⠤⠖⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠑⠦⠤⠴⠊⠀⠀⠀⢿ ⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿ ⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣉⠑⠒⠤⢤⣤⣀⣀⣤⣤⠤⡖⡺⣛⡀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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