Cool Very Cool Goofy Nerd So This Is Best. Best Nerd Evar .ty For Seeing This!say Hello Emojis & Text

Copy & Paste Cool Very Cool Goofy Nerd So This Is Best. Best Nerd Evar .ty For Seeing This!say Hello Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⢀⣀⣠⣶⣾⣿⣆⣀⣀⣀⣀⣼⣿⣶⣦⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣀⢀⡀⢀⣀⣠⣶⣾⣿⣆⣀⣀⣀⣀⣼⣿⣶⣦⣀⡀⣀⢀⡀⣀⠀⠀ ⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⡿⠋ ⠀⠸⣿⠀⡀⠀⣾⣿⣿⡦⠄⠀⣸⣿⣿⣆⠀⢠⢼⣿⡥⠐⠄⠀⠀⣿⠇⠀ ⠀⠀⣿⡇⠁⢾⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠡⢻⣾⣿⣟⣧⡆⠀⢸⣿⠀⠀ ⠀⠀⠹⣿⣆⣀⣙⠻⠟⢋⣠⣾⣿⠛⠽⣿⣷⣣⡙⠿⢿⢋⣀⣴⣿⠋⠀⠀ ⠀⠀⠀⠏⠛⠿⠿⠿⠿⠿⠿⠋⡁⠎⡐⢈⠛⠿⠿⠿⠿⡿⠿⠛⠇⠀⠀⠀ ⠀⠀⠀⢠⠀⢁⠀⠀⠓⠀⢀⣄⣐⣂⣁⣂⣠⡀⠀⠖⠀⠋⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⢊⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⡿⠃⠀⠀⠀⠂⠠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢌⢔⠠⡀⡐⢈⠃⠶⡐⠌⠤⣁⢂⡐⢀⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠣⠒⣥⢊⡜⣤⢃⢎⣱⣐⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠐⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
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⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⢉⣳⣿⣯⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⠀⢻⣯⣇⣁⣠⠞⠓⠒⠚⠧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢶⣾⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢖⠙⠻⣦⠴⠦⠶⠖⠺⠚⠉⠹⠚⠛⠓⢲⠞⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡆⠀⠈⢆⠀⢀⡠⣤⣤⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢷⣀⠀⠘⡄⠈⠑⠾⠋⠀⠀⠀⠀⢰⡃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢽⣆⠀⠸⡄⠀⠀⠀⢀⡀⣴⣾⣿⠭⣧⣾⢦⣀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠂⠈⠲⠓⠓⠚⢉⣿⣋⣻⣤⢌⠳⡄⠀⠻⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⡀⣏⠋⠀⡛⠙⢦⡀⠁⠀⠀⠘⠀⠀⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⡧⢤⣄⠀⣷⡼⠾⣖⣏⠉⠉⠛⠓⠶⠶⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀ ⠀⠀⠀⢀⣴⠛⠁⠀⢀⡼⣇⠻⣿⣦⡀⠀⠈⣳⣤⠀⠐⠲⠦⠀⠀⠀⠀⠀⠀⢣⣄⠀⠀ ⠀⠀⢠⠛⠀⠀⠀⠀⠬⣆⠘⠉⢹⣿⣅⣀⣻⣟⣸⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠂⠀ ⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⣣⣿⢯⣽⡇⠉⣿⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠄ ⣰⠇⠀⠀⠀⠰⢶⣒⡆⠀⠒⣤⡾⢏⠽⠺⠿⠆⠀⠉⠐⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣿⣧⡇⠀⡶⣤⡀⠘⠋⠠⢶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠛⠋⠁⠀⠀⠿⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀
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⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣷⣦⣄⡀⣿⣱⡀⠀⠀⠀⠀⠀⠀⢸⢿⣧⣠⣴⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⢷⣿⣟⡿⠿⠿⡟⣓⣒⣛⡛⡛⢟⣛⡛⠟⠿⣻⢿⣿⣻⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⢻⡭⠖⡉⠥⣈⠀⣐⠂⡄⠔⢂⢦⡹⢬⡕⠊⠳⠈⢿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣷⣋⠲⢮⣁⠀⣐⠆⡤⢊⣜⡀⡾⣀⠀⢠⢻⣌⣤⣥⣓⣌⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣟⣽⢳⣯⣝⣦⡀⠓⡤⢆⠇⠂⠄⠤⡝⣂⠋⠖⢋⠀⣡⣶⣾⡿⡷⣽⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡜⢯⣿⣿⣿⣷⣿⣤⣧⣶⣬⣝⣃⣓⣈⣥⣶⣿⣾⣿⣿⢣⠇⢻⡞⣯⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡔⡯⢧⢟⣟⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡼⡼⢁⡌⢼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢇⡼⢃⡿⣼⣛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⣡⣫⣢⢏⣼⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡾⢕⣻⣽⣵⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢷⣮⣿⡼⢭⡟⠳⠞⡖⢛⣶⣷⣯⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠛⠛⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⡿⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⢃⣴⣿⠿⣻⢼⣲⠿⠭⠭⣽⣿⣓⣛⣛⣓⣲⣶⣢⣍⠻⢿⣿⣿ ⣿⣿⣿⡿⢁⣾⣿⣵⡫⣪⣷⠿⠿⢿⣷⣹⣿⣿⣿⢲⣾⣿⣾⡽⣟⣷⠈⣿⣿ ⣿⣿⠟⠁⣚⣿⣿⠟⡟⠡⠀⠀⠀⠶⣌⠻⣿⣿⠟⠛⠉⠉⠉⢻⣿⣿⠧⡙⢿ ⡿⢡⢲⠟⣡⡴⢤⣉⣛⠛⣋⣥⣿⣷⣦⣾⣿⣿⡆⢰⣾⣿⠿⠟⣛⡛⢪⣎⠈ ⣧⢸⣸⠐⣛⡁⢦⣍⡛⠿⢿⣛⣿⡍⢩⠽⠿⣿⣿⡦⠉⠻⣷⣶⠇⢻⣟⠟⢀ ⣿⣆⠣⢕⣿⣷⡈⠙⠓⠰⣶⣤⣍⠑⠘⠾⠿⠿⣉⣡⡞⠽⠗⡉⡀⠘⣶⢃⣾ ⣿⣿⣷⡈⢿⣿⣿⣌⠳⢠⣄⣈⠉⠘⠿⠿⠆⠶⠶⠀⠶⠶⠸⠃⠁⠀⣿⢹⣿ ⣿⣿⣿⣷⡌⢻⣿⣿⣧⣌⠻⢿⢃⣷⣶⣤⢀⣀⣈⢀⣀⠀⡀⠀⠀⢸⣿⢸⣿ ⣿⣿⣿⣿⣿⣦⡙⠪⣟⠭⣳⢦⣬⣉⣛⠛⠘⠿⠇⠸⠋⠘⣅⣁⣴⣿⣿⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠒⠭⣖⣩⡟⠛⣻⣿⣿⣿⣿⣿⣟⣫⣾⢏⣿⠘⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⡛⠿⠿⣶⣶⣿⣿⣿⣿⣿⣾⣿⠿⣰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⣉⣛⣋⣭⣥⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠙⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⣠⣴⣿⡿⠟⠋⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⣾⣏⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣿⣫⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⢿⣿⣿⡟⢿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡎⠘⣿⣿⣷⠀⠻⣿⣿⣧⠀⠀⠀⠀ ⢸⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡰⠁⠀⣿⣿⣿⠀⠀⠹⣿⣿⣧⡀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠂⠀⠀⣻⣿⣿⡄⠀⠀⠹⣿⣿⣿⣦⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⠀⠀⣿⣿⡿⢿⡇ ⠀⠛⢿⣿⣯⡍⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣦⣤⡈⠀⠀⣀⣼⣿⡟⠻⡿⠀⠀⣠⣿⣿⠃⠈⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠘⠻⠿⠟⠀⠐⠇⠀⠘⠿⠛⠋⠄⠀⠀
DO YOU TRUST ME pt. 20 𝖠𝗎𝗍𝗁𝗈𝗋'𝗌 𝖣𝗂𝗌𝖼𝗅𝖺𝗂𝗆𝖾𝗋 𝖭𝗈𝗍𝖾 𝘐 𝘧𝘪𝘯𝘥 𝘸𝘳𝘪𝘵𝘪𝘯𝘨 𝘢 𝘨𝘰𝘰𝘥 𝘰𝘶𝘵𝘭𝘦𝘵. 𝘐'𝘮 𝘰𝘯 𝘵𝘩𝘦 𝘚𝘱𝘦𝘤𝘵𝘳𝘶𝘮 𝘮𝘺𝘴𝘦𝘭𝘧. 𝘐 𝘦𝘯𝘫𝘰𝘺 𝘸𝘳𝘪𝘵𝘪𝘯𝘨 𝘧𝘢𝘯𝘧𝘪𝘤 𝘪𝘯𝘤𝘭𝘶𝘥𝘪𝘯𝘨 𝘮𝘺 𝘧𝘢𝘷𝘰𝘶𝘳𝘪𝘵𝘦 𝘤𝘩𝘢𝘳𝘢𝘤𝘵𝘦𝘳𝘴 𝘢𝘯𝘥 𝘴𝘰𝘮𝘦𝘵𝘪𝘮𝘦𝘴 𝘐'𝘭𝘭 𝘢𝘥𝘥 𝘮𝘺 𝘰𝘸𝘯 𝘧𝘦𝘢𝘳𝘴 𝘪𝘯 𝘵𝘩𝘦 𝘴𝘵𝘰𝘳𝘪𝘦𝘴. 𝘚𝘰 𝘴𝘰𝘮𝘦 𝘥𝘢𝘳𝘬𝘦𝘳 𝘤𝘰𝘯𝘵𝘦𝘯𝘵 𝘮𝘪𝘨𝘩𝘵 𝘵𝘳𝘪𝘨𝘨𝘦𝘳 𝘴𝘰𝘮𝘦 𝘱𝘦𝘰𝘱𝘭𝘦, 𝘢𝘶𝘵𝘪𝘴𝘮 𝘪𝘮𝘱𝘢𝘤𝘵𝘴 𝘦𝘷𝘦𝘳𝘺 𝘪𝘯𝘥𝘪𝘷𝘪𝘥𝘶𝘢𝘭 𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘵𝘭𝘺. 𝘞𝘦 𝘢𝘳𝘦 𝘯𝘰𝘵 𝘢 𝘮𝘰𝘯𝘰𝘭𝘪𝘵𝘩, 𝘢𝘯𝘥 𝘦𝘷𝘦𝘳𝘺 𝘱𝘦𝘳𝘴𝘰𝘯 𝘩𝘢𝘴 𝘵𝘩𝘦𝘪𝘳 𝘰𝘸𝘯 𝘷𝘢𝘭𝘪𝘥 𝘴𝘵𝘰𝘳𝘺. 𝘠𝘰𝘶 𝘮𝘢𝘺 𝘧𝘪𝘯𝘥 𝘪𝘯𝘧𝘰𝘳𝘮𝘢𝘵𝘪𝘷𝘦 𝘤𝘰𝘯𝘵𝘦𝘯𝘵 𝘰𝘯 𝘩𝘰𝘸 𝘰𝘯𝘦 𝘮𝘪𝘨𝘩𝘵 𝘣𝘦 𝘢𝘧𝘧𝘦𝘤𝘵𝘦𝘥 𝘣𝘺 𝘵𝘩𝘦 𝘢𝘤𝘵𝘪𝘰𝘯𝘴 𝘰𝘧 𝘰𝘵𝘩𝘦𝘳𝘴. 𝘐 𝘥𝘰 𝘯𝘰𝘵 𝘤𝘰𝘯𝘥𝘰𝘯𝘦 𝘢𝘣𝘭𝘦𝘪𝘴𝘵 𝘮𝘪𝘤𝘳𝘰𝘢𝘨𝘨𝘳𝘦𝘴𝘴𝘪𝘰𝘯𝘴. 𝘛𝘩𝘢𝘯𝘬 𝘺𝘰𝘶. ( emojicombos.com/neurofabulous ) Karen's arms wrap around him, her hands gentle on his back as she whispers words of comfort, her voice a balm to his frayed nerves. "You're safe, baby," she says. "You're safe with me." Plankton's sobs slow, his body relaxing marginally in her embrace. His antennae still thrash, but with less urgency, when Plankton's main dentist comes in. Dr. Musselman, Plankton's main dentist, rushes into the room, his eyes wide with concern at the sight of his patient's distress. Karen quickly explains the situation, her voice tight with emotion. "He's having an autistic shutdown," she says, her hand on Plankton's trembling back. "He's sensitive to sensory overload." He nods. "You can come into my exam room, follow me." The doctor's exam room is dimmer, the air cooler, and the smell less intense. The change in atmosphere is like a gentle caress against Plankton's overstimulated sensors. He lets out a shaky sigh, his antennae unfurling slightly. Dr. Musselman's eyes are kind, his voice a soothing balm. "Hi, Plankton," he says, his tone gentle. "Remember me?" Plankton's gaze flickers to him, his antennae stilling. "You're my other dentist," he whispers, his voice hoarse from the sobbing. The doctor nods, his smile reassuring. "That's right. I know you don't like surprises, so I'm sorry for that, for Jill. But we're going to take it slow, okay?" Plankton nods, his antennae twitching slightly. "We need to finish your cleaning," Karen says, her voice gentle. "But we'll do it with Dr. Musselman. He'll always work here, and can be your dentist instead of Jill from now on!" "Okay," Dr. Musselman says, his voice calm and measured. "We're going to take some x-rays now. It's quick and painless." Plankton's antennae perk up slightly at the mention of painlessness. He nods, his eye searching the doctor's face for any sign of deception. The doctor leads them to a small, enclosed space, the whirring of the x-ray machine a soothing constant. Karen holds Plankton's hand, her grip firm but gentle, as he sits in the chair. The doctor explains the process, his words clear and concise. Plankton nods, his breathing slowing slightly as he tries to comfort himself. The x-ray machine's cold metal touches his jaw, and he jolts. "It's okay," Karen whispers, her hand on his shoulder. "It's just a little picture of your teeth." Plankton's eye closes, his antennae stilling. He nods, his trust in his wife a beacon in the storm of his fear. Dr. Musselman's movements are careful, his voice calm. "Open wide," he says. Plankton's mouth opens slightly, his teeth clenched. The x-ray film slides into place, cold and slightly sticky. He tastes the metal, feels the pressure. But it's not the same as the probe. It's bearable. The machine whirs to life, the sensation of the x-rays a gentle buzz against his skin. His antennae quiver, but he doesn't pull away. Karen's hand squeezes his, a silent promise of support. "Good job," she murmurs, her voice a warm whisper in the cool air. The doctor's voice is steady. "Almost done," he says, his eyes on the machine's readout. Plankton nods, his breaths shallow but even. The fear has receded to a dull throb, a distant echo of the panic that had consumed him. The x-ray machine clicks off, the buzz of its operation silenced. Dr. Musselman gently removes the film, his movements careful not to startle Plankton. "Good boy," he says, his voice a warm caress. Plankton's antennae twitch in response, a tentative sign of trust.
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢠⡞⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⡁⡀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⡅⡇⠀⢹⣷⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠐⡇⢇⠀⢸⣿⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⡇⠸⡀⢀⣿⠏⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⣸⠀⢣⣼⡡⠒⢁⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠷⠶⠶⠶⠶⢤⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣻⣧⡀⠋⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡄⠀⠀ ⠀⠀⠀⢀⣴⠞⠋⡩⠃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀ ⠀⠀⣰⡿⠁⢀⠞⢀⠞⠙⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⡶⠿⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀ ⠀⣸⡏⠀⢀⠎⢀⠏⠀⢠⣿⠙⠻⠭⣉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⣀⣴⡾⠻⣷⣤⡀⠀⠀⠀⠀ ⢠⡿⠀⠀⣸⠀⡎⠀⠀⣼⣿⣄⠂⢤⣀⠉⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣶⣾⡟⠋⠁⠀⠀⠀⠙⠿⣷⣤⡀⠀ ⢸⡇⠀⠀⡇⢸⠀⠀⢰⡿⠈⠻⣷⣄⠀⠉⣲⣦⠠⠤⣈⡉⠐⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡟⠀⠀⠀⠀⠀⠀⠉⣻⡷ ⠘⣇⠀⠀⡇⠘⠀⠀⢸⡇⠀⠀⠀⡽⠗⢋⣠⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⢀⣀⣤⡴⠚⠉⠀ ⠀⢻⣄⠀⡇⢰⠀⠀⣿⠃⠀⠀⣀⠵⠚⠛⠉⠙⢻⡿⠷⠶⣦⣤⣤⡴⠶⠶⠟⠛⠿⣷⠲⠶⠶⠚⢻⣿⠿⣿⣦⣄⡀⠀ ⠀⠀⢻⡄⢸⠘⡆⠀⣿⢀⠔⠋⢀⣠⣴⣶⣾⣿⣦⢱⠀⠀⠀⢀⡏⣹⣷⣶⣦⣤⣀⠀⠉⠢⡀⠀⢸⣿⣀⣤⠾⠛⠁⠀ ⠀⠀⠀⠹⣿⡄⠈⢠⣿⠈⠂⢾⠙⣿⣿⣿⡿⣿⣿⢀⠇⠀⠀⢸⡄⢿⣿⣾⣿⣿⣿⠉⡟⠒⠃⠀⣾⡏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣆⡘⣿⠀⠀⠘⢦⡙⠿⠛⢋⣉⡡⠞⠀⠀⢀⠀⠳⠬⣉⣉⠙⠛⢃⡜⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠉⠋⠉⠁⠀⠀⠀⣴⣟⣻⣻⡆⠀⠀⠀⠉⠉⠉⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣀⣤⠶⠒⠒⢲⣴⣞⠉⠀⠉⢳⣄⣀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢉⣹⣿⣦⠀⠈⣿⣁⣈⣷⣴⠚⢉⣹⡟⠛⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠛⠉⠀⣽⣷⣦⡼⠋⠉⠀⠉⣿⡛⠉⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢻⣧⡤⠤⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣼⠋⠀⠀⠀⢹⠏⠉⠉⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿⣧⡀⠀⢠⠏⠀⠀⢀⣾⣯⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡁⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠛⠻⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⡀⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⣴⣾⣶⣶⣿⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠞⠉⣀⣠⠦⠴⠆⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⡻⣿⡶⣦⡀⠀⠀ ⠀⠀⣴⠋⣠⣶⠟⢋⡤⠶⠶⠶⢶⡀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢉⣿⡶⡍⠀⠀ ⠀⣼⠁⠚⠛⠁⢠⠏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢠⡏⠀⠀⠀⠙⠛⠁⣇⠀⠀ ⢰⡇⠀⠀⠀⣠⣼⠀⣾⣿⡆⠀⠀⢸⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⣀⡼⢻⡀⠀ ⣸⠀⠀⠀⠈⠉⠎⠳⢭⣉⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⢙⡿⠛⠉⠉⠛⢾⡇⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠤⠤⠤⠤⠤⢲⡟⢁⣴⠋⠛⢳⡄⠹⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡿⠀⣾⣹⣋⣏⣟⣷⠀⡇ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡏⠀⠀⠀⠀⣹⢠⠇ ⢹⡄⢣⠀⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⢠⠇⡾⠀ ⠈⣧⠈⢃⢹⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣿⠀⡇⠀ ⠀⠸⡆⠀⢇⢃⠀⠈⡆⠀⠀⠀⠀⠨⢕⣄⠀⠀⠀⡟⢸⣃⡀⠀⠀⢿⠀⢹⠀ ⠀⠀⢻⡄⠈⡌⣆⠀⢡⠀⠀⠀⠈⠉⠓⢬⡑⠀⣸⠁⣾⠀⠈⠙⢦⢸⡇⢸⠀ ⠀⠀⠀⢳⡀⠘⠌⢄⠀⠑⢄⠀⠈⠉⠓⠦⡉⠂⣿⠀⣿⠒⡖⡖⡖⢻⠃⢸⠀ ⠀⠀⠀⠀⠻⣄⠈⠢⣑⠢⢄⠑⠤⡀⠀⠀⠈⠳⣿⠀⠹⣏⠙⠓⣷⠟⠀⣼⠀ ⠀⠀⠀⠀⠀⠙⠳⣄⡀⠑⠂⠍⣂⠤⠀⢀⣀⠀⠹⣄⠀⠈⠛⠛⠉⣀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠈⠁⠐⠒⠀⠀⠉⠙⠒⣶⠶⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢤⣤⣠⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠷⢤⣀⡀⠀⠀⠀⠀⣀⣤⠼⡟⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡾⠀⠀⠈⣧⠀⠀⠀⣰⠏⠀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⠀⠀⠀⢸⡄⠀⣰⠏⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠉⢙⣦⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣀⣷⢠⠏⢀⣀⣀⠀⢸⢀⡇⠀⠀⠀⠀⠀⢠⣿⡑⢾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣋⡼⢧⡀⠀⠀⠀⠀⠀⣿⢧⠘⢿⣴⠼⠇⣿⠈⣷⠯⢤⠼⠇⢸⣿⡇⠀⠀⠀⠀⣰⡟⢄⣨⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣴⢛⣷⡄⠀⠀⠀⠀⣿⠘⣧⠀⠀⣠⡞⠁⠀⠈⢧⡀⠀⢀⡾⢻⠇⠀⠀⠀⣰⠯⣉⢲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡽⢿⣄⠀⠀⠀⢹⡆⠈⢷⡴⠋⠀⠀⠀⠀⠈⠳⣤⠞⠁⣼⠀⠀⠀⣰⡟⠢⣬⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡞⣹⣆⠀⠀⠈⣷⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡇⠀⣰⡏⠀⠀⣰⠣⣌⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣵⢛⣦⠀⠀⠘⣧⠀⢸⠀⠀⠀⠀⠀⠀⢸⣁⣰⡟⠀⠀⣰⣋⠀⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣡⠾⢧⡠⣼⣟⢷⡽⠀⠀⠀⠀⠀⢀⣨⡿⣫⣿⡄⣰⠓⠀⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣯⣿⢻⣯⣻⠿⣷⣤⣤⣴⣞⣛⣡⠖⣫⣾⡿⣯⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠶⠚⠉⠁⠙⣾⡏⠙⠓⠶⣬⣍⣉⣉⣭⡴⠞⠋⣿⠃⠀⠙⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠁⠈⠉⠻⣦⠀⢀⣤⡶⠛⠻⣦⣄⡀⠀⠀⠈⠉⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠉⢉⣷⡶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣤⣤⣀⣀⣀⣈⣙⡓⠶⣶⣶⣖⣻⠟⠁⠀⠀⠀⠀⠀⠀⣠⡟⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣡⠟⠲⠤⠤⢤⣈⣉⡉⢻⣿⣿⠛⠛⢻⡄⠀⠀⠀⠀⠀⢠⡾⢻⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⠀⠀⢈⡿⠶⣤⡤⠤⠶⠻⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡞⠋⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⠀⢰⠏⠀⣠⠟⠀⠀⠀⠀⢹⡆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠀ ⠀⢀⣿⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⢹⣤⡏⠀⡼⠃⠀⠀⠀⠀⠀⠀⠹⠾⡿⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⢀⣿⣥⠶⢦⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡏⢹⡆⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⠀⡿⢁⣠⡤⣤⣴⣾⣿⡈⠻⣦⠳⣄⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⡇⣿⠏⠀⡼⠁⠀⠀⠀⣀⡤⠴⠚⠋⠁⢠⣷⠛⢧⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⣼⣟⣫⣽⣷⣿⣲⢿⣌⠙⠦⣌⠻⣿⣦⣀⠀⢸⠁⠉⠛⠲⠤⢤⣷⠋⢀⣞⣁⣠⡤⠴⠺⡏⠀⠀⠀⠀⠀⣼⠃⠀⠈⣧⠀⠀⠀⠀⠀⢸⠇⠀ ⠹⣯⠞⠉⠀⠘⠛⠛⠛⠓⠒⠛⠛⠛⠒⠫⠷⢾⣤⣤⣀⣀⣀⣴⣧⣤⣾⡭⠽⠗⣾⠓⣦⣇⢀⣀⣀⣀⡀⡇⠀⠀⠀⠘⠳⠲⠦⢤⣄⣸⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢼⡇⠹⡉⠉⢧⠀⠈⠙⡿⣄⢀⣠⠶⢖⣺⣗⡶⢤⡉⣻⡄ ⠘⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠶⠒⠋⠉⠉⠀⠀⡼⠁⠀⡇⠀⠈⣇⣀⣠⠿⠾⠟⠚⠋⠉⠁⠈⠙⢳⣝⣯⠀ ⠀⢻⡿⣍⠛⠒⠦⢤⡤⠴⠒⠒⠒⠚⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣀⣼⣥⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⠆ ⠀⠀⢳⠈⢳⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀ ⠀⠀⠈⠳⢼⣄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡟⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠒⠶⢦⣤⣤⣤⡤⠤⠴⢶⣏⣉⡁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠓⠒⠶⠤⣄⣀⣀⣤⠤⠴⠶⠚⠉⣁⡴⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠙⠲⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣥⠾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣇⠀⠀⠀⣀⣀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠤⠤⠤⠤⠴⠖⠒⠒⡖⠒⠚⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⣖⣾⣭⡍⠉⠹⣿⣗⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠶⢶⣶⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣾⣕⡦⣄⡀⠀⠀⠀⠀ ⠀⠈⣧⣧⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣿⡿⣿⣿⣷⣯⣳⡀⠀⠀ ⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠀⣿⡆⠀⢹⣿⣿⠛⣷⡀⠀ ⠀⠀⡴⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣿⣇⣸⣿⠟⠁⠀⠉⣧⠀ ⠀⠀⣷⠂⠀⠘⣮⠙⠛⠒⠒⠛⠀⠀⢠⡏⠀⢰⣿⣿⣿⠏⠀⠀⠀⠂⢸⠀ ⠀⠰⡏⠀⠀⢰⣿⣷⣤⣄⢀⣀⣤⡜⠋⢀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠀ ⠀⢸⣇⡀⠀⠈⠛⢿⣿⣿⣷⣶⠯⢭⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⡄ ⠀⢺⣉⡍⢹⡆⠀⠀⠀⠉⠀⠈⠀⠀⠻⠛⠟⠛⠛⠋⣁⠀⠀⠀⠀⠀⣈⣿ ⠀⡟⠂⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠤⠀⠐⠀⢸⡟ ⢀⣧⡀⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢸⡇ ⣼⣃⡀⠀⠀⠻⠻⢿⣿⣷⣤⣤⣤⣄⣀⠀⣀⣀⣀⣴⡆⠀⠀⠀⠀⠀⢸⣇ ⣿⢀⠁⠀⢠⡆⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⡏ ⢻⡜⠳⢶⣼⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇ ⢸⣿⡀⠀⠀⣿⣿⣿⣿⣿⢗⡶⢤⣤⣀⣀⣀⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⣿ ⠸⣏⢇⠀⠀⣿⣿⣿⣿⣿⠀⠉⠉⠉⠛⠾⣿⣿⣿⣿⣷⣤⣤⣤⡴⠤⢤⣿ ⠀⠘⢮⣁⣰⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⣸⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡿⣿⡟⠁⣰⠇⠀⠀⠀⡀⣿ ⠀⠀⠀⡰⣻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⡿⠋⢀⡄⠴⣚⡵⠛ ⠀⠀⣾⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠖⠋⠉⠀⠀ ⠀⠀⠹⡽⣿⣿⣿⢏⠟⠀⠀⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠉⠛⠉⠀⠀⠀⠀⠀⠀⢸⣱⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⡿⠿⠿⠽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠚⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⢠⣤⣶⣾⣧⣤⣤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠴⠶⠤⢤⡀⣧⣀⣀⠀ ⠻⠶⣾⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢹⣿⣭⣽⠇ ⠀⠀⠙⠤⠴⢤⡤⠤⠤⠋⠉⠉⠉⠉⠉⠉⠉⠳⠖⠦⠤⠶⠦⠞⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⣀⣀⣤⠶⠖⠛⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⣿⣿⣿⣿⣿⠏⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢻⣿⣿ ⣿⣿⣿⣿⢟⣀⠔⠃⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠉⠀⠀⢀⠀⣴⠟⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣦⣤⣤⣀⣃⠃⢀⣤⣶⣿⣿⠟⠋⠉⠀⠀⠀⣀⣹⣿⣿⣿⣿ ⣿⣿⣿⠁⠀⠀⢀⣀⣿⠁⢠⠀⠀⠀⢙⡆⢀⣀⡠⠖⠊⠙⠾⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⡟⢿ ⣿⣿⣿⠀⠀⠛⠛⠞⣷⣴⣾⣷⣦⣶⣿⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣅⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸ ⣿⣿⡿⠀⢀⣀⡾⢣⣿⠉⢉⣿⠋⠉⠙⡿⣆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸ ⣿⣿⠇⠐⠂⠀⠐⡀⡟⠒⢧⡈⠳⠄⣤⡇⠸⣇⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸ ⣿⡟⠀⠀⠀⠀⠀⡇⡇⠀⠀⠑⣠⡾⠋⠀⠀⢻⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠃⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠀⠀⠀⢸ ⣿⡇⠀⠀⠀⠀⠀⡇⢻⠀⣠⡴⠋⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣤⣄⡤⢠⣴⣺⣿⡿⠃⠀⠀⠀⠀⠈⠉⠙⢉⣭⣿⣿⠃⠀⠀⠀⠀⠀⣼ ⣿⡇⠀⠀⠀⠀⣸⢁⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣶⡿⠿⠛⠁⠀⠀⠀⢀⣀⣠⡤⠶⠚⢉⣧⣿⠃⠀⠀⠀⠀⠀⢠⣿ ⡏⠑⠦⠤⣀⣴⢿⡟⠀⠀⠀⠐⠀⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠴⠶⠚⢛⡟⠉⠁⣈⣀⡤⠶⠋⣡⠃⢀⡞⠀⠀⠀⠀⣾⣿ ⣿⣶⣤⣤⢤⠴⠞⠁⠀⠀⠀⠀⠀⠋⠁⠓⢾⡿⣦⣤⣀⠀⠀⢠⣀⠀⠀⣀⣥⣠⡤⢴⠟⢒⠚⠉⠀⠀⢀⣸⠋⠀⢾⠇⠀⠀⣀⣾⣿⣿ ⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣍⣩⣹⠋⠉⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣦⠏⠀⡆⣠⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢍⡛⠢⠤⢀⣀⣀⣀⣠⣴⡦⠴⠒⠋⠀⠀⢠⣾⠋⢀⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⣀⣀⣴⡞⠁⣀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⣀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⠀ ⠀⠀⠀⢰⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⢼⣿⣦⡄⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⠿⠿⠿⠿⠿⠆⠀⠀⠿⠿⠏⠀⠀⠀⠀⠀⠹⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠛⠛⠉⠉⠛⠛⠿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⢀⡾⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢿⡄⠀ ⠀⣾⠃⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠈⣿⡀ ⢸⡏⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⢸⡇ ⣼⠇⠀⢰⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠘⣿ ⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿ ⢻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡟ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠘⢿⣿⣿⣿⣿⠟⠉⠀⠀⡐⠂⠀⠀⠀⠀⠰⢢⠀⠀⠉⠻⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠙⠻⣿⡇⠀⠀⠀⠀⣷⡆⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⢸⡿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠘⠿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢦⣤⣤⣤⣤⡶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠄⣺⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⢚⠄⠊⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣔⣤⢲⣋⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⡔⠻⣿⢡⠼⢧⠀⠀⠀⠀ ⣾⣷⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⠋⠀⣙⣀⣰⣽⡀⠀⠀⠀ ⠙⠻⣤⠐⢺⡗⠤⡀⠀⠀⠀⠀⠇⢀⢃⣴⡿⢋⠤⠾⠯⢽⣄⠀⠀ ⠀⠀⠀⠙⠢⢄⠀⠐⠴⣄⠀⠀⣰⣻⡿⢛⡉⠉⠀⠀⠐⠀⢿⡀⠀ ⠀⠀⠀⠀⠀⠀⠙⢴⠁⣠⣵⢶⣿⣾⢭⡭⠤⣀⠀⠄⢀⠁⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠁⠈⠫⠻⣷⣝⡢⢄⠀⠀⠀⠈⠱⣾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠈⠻⢿⣶⣤⣄⣀⣀⣴⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⡄⠹⣦⠈⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠽⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠉⠙⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⠀⠀⠀⣠⣴⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣤⡴⠟⠋⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠛⣷⣤⣴⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⣻⡿⠀⠀⠀⠀⠀⢀⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣠⣾⡿⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡾⢫⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⠟⢡⡟⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⠟⠁⢠⡿⠀⢿⡄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢠⣾⠋⠀⢀⡿⠁⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣴⢿⡟⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣾⠋⠘⣧⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢈⡁⠅⠈⠉⠐⠒⠤⣈⢳⣄⠆⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⢎⠵⠊⠁⠀⢀⣠⡤⡶⣶⣶⣦⡷⢿⣦⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣺⠜⠁⠀⣀⣤⣾⣿⣿⣿⣿⣷⣭⣻⢵⣀⢿⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⡋⢐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡹⡉⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣧⠈⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠟⠃⣸⠃⠠⢽⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⡯⣿⣶⢄⡰⠋⠠⣶⣾⢼⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⠉⡿⣿⣇⠈⠉⠀⠀⠀⠀⠉⠁⢠⣿⡿⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢦⡀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⠋⡷⣦⣴⠾⡏⠣⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣹⡟⡅⠟⠻⣝⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠊⢡⢃⡿⢿⣿⣤⣤⣿⣿⠿⡞⢇⠑⠢⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⣾⠁⠀⠀⣇⣞⡻⡿⣿⣿⢻⣿⣿⣿⣳⣸⠀⠀⠀⣷⠤⡀⠀⠀ ⢆⠈⠁⡜⠁⢑⣒⡆⠋⠉⡼⣾⢷⣏⣘⣷⢷⡷⡈⠙⢰⢒⡒⠁⠙⡀⠉⣀ ⠀⠉⢰⠓⠉⠪⣛⠣⢄⠜⣼⣏⣿⠇⠀⣿⡞⣷⠑⡀⠜⢘⠣⠊⠐⢇⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢄⣀⠀⠀⠀⣀⠠⠀⢀⣠⣿⠀⠀⠀⢨⣆⠈⠢⡀ ⠀⠀⠀⠀⢀⣀⣀⠠⢰⠊⢬⠗⠀⠠⢔⣂⡡⡄⠊⣿⣿⠙⠀⠀⢀⣾⣿⣧⡀⢇ ⠀⠀⠈⠀⠀⠸⡀⢰⡥⠊⠊⣠⠖⡅⠀⡡⠋⠀⠼⢿⡯⢁⡴⣸⣿⣿⣿⣿⢈⢀ ⠀⠀⢀⡠⢤⡄⡠⣀⠄⠒⣡⠮⢤⠴⢁⡤⠂⡊⠔⠚⠲⣿⣿⣿⠛⠉⡙⠻⢌⠜ ⠀⢐⠋⠀⣐⣁⠀⠉⢀⡼⠃⢐⠌⢴⠺⡉⣹⠁⠀⠀⠀⢸⣿⠁⣔⡉⠎⠃⣣⣹ ⠀⠈⠁⠉⡡⠁⠀⠀⠈⠁⢀⣯⠊⠘⣇⠇⠃⠀⠀⠀⠀⠀⠁⢸⣑⠂⡘⢠⠛⠯ ⠀⡐⡄⡖⠉⠙⣱⢦⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢜⠔⢡⣗⠤⠚ ⠾⠌⡆⢻⣠⡋⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⠋⠀⠀⠀ ⡀⢼⡞⢠⢉⡓⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⣿⠈⡆⠀⠀⠀ ⠀⠸⢇⢸⡆⠱⠀⠀⠀⠀⢀⡠⣤⣤⠄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⠙⠋⠀⢣⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠱⠀⠀ ⠀⠀⠀⠀⢀⣠⡄⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣣⣀ ⡆⣀⣴⢾⡇⢸⣧⠗⠃⠁⠂⢄⠀⠀⠀⡠⠚⠢⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿ ⣿⣽⡏⢛⠗⠉⠀⠀⠀⠀⠀⠠⠈⠒⠈⠀⠀⠀⠱⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿ ⠟⠋⠋⠶⢬⣼⣄⡠⠐⠈⠀⠀⠀⠀⠀⠀⡀⠄⠂⠑⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠟⠀⣴⠏⠀⣿⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⡟⢀⡼⠁⠀⠀⢼⡆⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⢹⠃⠚⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽⠋⠉⠉⢩⣾⣿⣿⠛⠛⠛⠶⠦⠤⣤⣿⣄⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣇⣼⣷⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣰⠏⣽⣼⠧⠴⠒⠛⠻⢷⡢⠤⢹⣏⢻⠓⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣷⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⡞⠉⣸⣷⡃⠀⠀⠀⠀⠀⠀⠹⠄⠘⣿⠈⠆⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⢼⣿⢿⣧⡿⠇⠻⢻⣿⡽⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣀⣴⣿⣿⣿⣿⣿⣭⣭⣹⡷⠶⢤⣄⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣿⠟⠋⠉⠛⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣈⣻⣄⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣿⣿⣶⣾⣿⣿⣿⣌⣻⣾ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⡦⢤⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠗⠈⠻⣷⣄⡹⠀⠀⠘⣿⣿⡄⠀⠀⢸⠀⠀⠀⠐⣴⣿⣿⣿⣿⣿⣿⣿⣇⠉⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠃⠀⠀⢀⣽⣿⣟⠀⠈⣿⡿⠋⠛⠛⠋⠉⠛⠛⠓⠒⠀⠈⠋⠉⠀⠀⠀⠘⢻⣿⣄⠀⣾⠀⠀⢠⣟⣾⣿⣿⣿⣿⠟⠛⠛⠛⠀⠀⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠁⠀⠀⣠⣴⡿⠟⢛⣿⣦⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡇⠀⢠⣾⡟⠉⠛⠉⠁⠀⠀⠁⠀⠀⠀⢰⣿⣧⣿⡀ ⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⣠⣾⡿⠟⠁⢀⣿⡿⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⢦⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⣿⣿⣇⢳ ⠀⠀⠀⠀⠘⠉⠀⠀⠀⣀⣤⣾⣿⣿⣃⣠⡴⠟⠋⠀⠀⣾⠉⠙⠛⢶⡶⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⣴⣿⠟⠃⠀⠀⠀⠒⠚⠲⢶⡶⠶⠿⣏⢀⡿⣾⢻⡄ ⠀⠀⠀⠀⣀⣠⣴⣶⣤⣍⣭⣭⣭⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠸⣆⠀⠀⠀⠀⠘⢧⠀⠘⠉⣿⣿⡏⠀⣇ ⠶⠶⠛⠛⢋⣧⣤⡿⠟⠋⠉⢻⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⠀⠀⠹ ⠚⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠴⠞⢫⡇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣾⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢠⣏⠀⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⣼⡟⠀⢸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠃⠀⢸⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⣰⠏⣿⣀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⡈⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⣠⣤⡴⠶⠛⠉⣉⣿⡟⠋⠀⠀⠀⢀⡾⡯⠀⠋⣿⠀⠀⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⢸⡇⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠋⠑⠋⠀⠀⠀⠀⣠⡟⠁⠁⠀⠀⣿⡄⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣇⢿⡄⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠋⠀⠀⠀⢀⣼⡋⠀⠀⠀⠀⠀⣿⡇⠀⠸⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠹⣮⣿⣆⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⢠⡀⠀⠀⠀⢸⣿⣿⠀⠀⠃⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡟⠀⢸⡇⠀⠀⠀⢸⣿⣿⡆⠀⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡜⣿⠀⠀⠈⠻⣿⡻⣦⡀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢸⡇⠀⠈⣧⠀⠀⠀⢾⣿⣿⣿⠀⢸⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⣿⡆⠛⢷⣄⠈⠻⢮⣻⣦⣄⣀⣀⣀⠀⠀⠈⠌⣿⡏⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠸⡇⠀⠀⢿⠀⠀⠀⢸⣿⢿⣿⡆⠸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⣷⢸⣷⠀⠀⠙⠷⣤⣀⠉⠉⠉⠉⠋⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⠈⣿⡿⡖⠶⠤⠤⠶⠛⠉⠀⠀⠀⠀⣧⠀⠀⢸⡀⠀⠀⢸⡿⠈⣿⣧⠀⠋ ⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⢻⢿⣷⣿⡇⠀⠀⠀⠈⠙⠛⢶⣤⣀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇⠀⠀⣾⡇⠀⠘⢿⡆⠀ ⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⣿⠙⠶⢦⣀⡀⠀⠀⠀⠈⠉⠛⠷⠶⠤⣶⣿⣿⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡇⠀⠀⢿⣷⣄⠀⢸⣇⣀ ⠀⣸⡇⠀⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠉⠉⠀⠠⠤⣄⣀⠀⠀⠀⢰⡇⣿⡀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢿⡀⠀⢸⣷⡙⠿⣟⣻⡏ ⢀⡿⣿⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠾⠷⣼⣧⡄⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢸⠇⠀⣼⠉⠻⢦⣟⣿⣟
⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⠶⠒⡖⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣷⣟⣿⡾⠷⢾⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⡿⣛⢛⡛⣿⣧⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣳⣟⣯⣟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣷⣤⣤⣾⣿⣿⠟⠙⠋⠉⠉⠁⠀⠀⠈⠙⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⢭⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠏⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⢿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⠛⢿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡴⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣾⣶⣤⣤⣀⣀⣀⣤⣶⣼⣶⣼⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠔⢒⡉⠡⠘⢌⠡⢋⠽⡇⠀⠀⠀⢠⠞⣉⠋⠱⠡⠌⡙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣧⡲⣌⡉⣄⠉⣄⣣⣮⠿⠃⠀⠀⠀⢯⡔⡡⣈⠁⢂⡐⣀⢡⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠉⠉⠉⠉⠉⠉⠁⣀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠛⠓⠓⠚⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⡄⠀ ⠀⣼⡿⠁⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠹⣿⡄ ⢠⣿⠀⠀⠀⠀⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠃⠀⠀⠀⢻⣧ ⢸⡏⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿ ⠀⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠙⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⡏ ⠀⢻⣧⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⢠⣿⠁ ⠀⠘⣿⡄⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⣾⡏⠀ ⠀⠀⢻⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⠁⠀ ⠀⠀⣰⣿⣿⣿⣛⣋⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢠⣨⣉⣉⣛⣿⣿⣿⣷⠀⠀ ⠀⠀⣿⣿⣿⣿⠿⠟⢿⣿⠟⢛⣿⣶⣤⡀⠀⠀⠙⢿⣿⡿⠟⠀⠀⢀⣠⣴⣿⡟⠻⣿⡿⠛⠿⢿⣿⣿⣿⡇⠀ ⠀⠐⣿⣿⣿⠁⠀⠀⠸⣿⠀⠸⣧⣿⣿⠟⣧⡀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣶⣿⡿⠀⢸⡇⠀⠀⠀⢻⣿⣿⡇⠀ ⠀⠀⣿⣿⣧⠀⠀⠀⠀⢻⣧⡀⠉⠉⠁⠀⣸⣧⠀⠀⠀⠀⠀⢰⣿⡀⠈⠉⠉⢀⣠⡿⠃⠀⠀⠀⢸⣿⣿⡇⠀ ⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠉⠛⠳⠶⠶⠟⠛⣿⠀⠀⠀⠀⠀⢸⡟⠛⠷⠶⠶⠛⠋⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀ ⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣷⣄⡀⠀⢀⣀⣠⣤⣶⣦⡘⢿⣿⣿⣿⣿⠏⢠⣶⣤⣄⣀⡀⠀⠀⣀⣴⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠸⠿⡟⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣷⣄⠀⠀⠀⠀⣀⣴⡟⠋⠻⢷⣄⡀⠀⠀⠀⢀⣤⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣾⣋⡁⠀⠀⠀⠀⣉⣿⡶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠛⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠤⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⣤⣾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠣⠅⡀⡸⣀⠀⠀⡌⣉⣄⣀⣸⢘⣟⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠃⠌⣐⢹⣿⣀⠟⠉⠉⠝⣁⠤⠤⠭⡉⢻⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⡕⠒⠂⢊⡟⠁⠀⠀⠀⢀⠎⠀⣀⣀⠀⠈⠢⢧⠐⠃⠀⠀⠀⠀⠀⠀⠀ ⣰⠁⠬⠄⣀⣀⠎⠀⠀⠀⠀⠀⠈⠀⡎⣴⣶⢱⠀⠀⡇⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠒⠦⠤⣀⠀⠀⠀⠐⡖⠀⠘⡀⠑⠬⠥⠊⠀⢀⠃⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣄⠀⠈⠢⠄⠀⠀⠔⠁⠀⠀⣏⢢⡤⢔⣦⠰⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢹⠛⣑⡠⢀⠀⠀⠀⠀⠀⡀⢀⠯⠐⠈⠀⢫⢑⣷⡄ ⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠱⢤⠨⡈⢂⢯⣭⣭⠋⢀⠎⠀⠀⠀⠀⠀⠅⠫⠆ ⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠈⠀⠀⠐⠈⢈⡴⣃⠀⠀⠀⣀⡤⣀⢨⡐⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢻⠒⠦⠤⠤⠤⢶⠊⢣⠀⢡⣆⣀⢼⡣⣑⠎⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡜⠀⠀⠀⠀⠀⠀⠳⠈⡆⠀⠙⠉⠀⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠋⡜⠀⠀⠀⠀⠀⠀⠀⡜⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢰⠁⠀⠀⠀⠀⠀⠀⡸⠁⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡃⢀⢌⠳⡩⢆⠀⠀⠀⢰⣁⠀⠁⠀⢻⠪⠻⣢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠚⠤⠦⠗⠚⠀⠀⠀⠀⠀⠉⠉⠉⠈⠒⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⡇⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣏⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣿⣀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣳⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣄⣶⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⢈⣍⣽⣇⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣤⡴⠾⡷⢶⣤⡀⠀⠠⡿⣿⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣠⠞⠉⠉⠁⠀⠀⢀⠀⢹⣧⠀⠀⠼⣿⣃⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠛⠉⠛⠳⣄ ⠀⣰⠏⠃⠁⠙⠛⠒⠢⢤⡄⠘⠀⠘⣿⡄⠠⢤⣿⡍⠜⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡋⠀⠀⠀⠀⣀⣤⡿⠟ ⢠⡇⠀⣆⠀⠀⠀⠀⢶⡘⣿⡆⠀⡈⣿⣿⠒⣶⠛⡇⢐⣦⢿⣧⡀⠀⠀⠀⢀⡴⠞⠁⠀⠙⢂⣀⣴⣾⠛⠉⠀⠀ ⠈⣇⡈⠯⠳⣄⢲⡀⠀⠉⠿⣿⣾⡷⣿⣿⣆⣃⡀⡗⢰⣷⡀⠳⡿⣷⠴⠞⢻⠀⠀⠀⠀⣲⣴⡿⠏⠀⠀⠀⠀⠀ ⠀⢹⢿⡓⠲⠾⢾⣷⡀⠀⠀⣻⣿⡇⠻⢹⡏⠈⣿⣷⣿⡏⠁⠀⠀⢸⣄⠀⠀⢣⣀⣤⣾⡿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠈⠹⣟⠁⣻⠟⢻⣿⠟⢶⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢿⣀⣤⣼⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡃⠀⠀⠀⠀⠀⠻⣆⣻⡶⢿⣿⣄⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣱⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣇⠀⠀⠀⠀⠀⠀⠉⠛⠷⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠀⠀⣀⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢜⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠄⠈⢓⣯⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢤⢤⡴⠧⠀⠀⠈⠀⠀⠀⠀⢀⡟⢹⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⣒⡶⠚⠉⢁⡌⠳⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⢦⡴⠊⠁⠀⠀⠈⠀⢀⡠⠔⠛⠢⡄⢹⣇⠀⠀⠀⢿⣏⠙⣄⣀⣀⣠⠤⠒⠋⠉⣿⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠞⠁⠀⠀⣀⡤⠔⠊⠉⠀⠀⠀⠀⠘⢆⠈⠢⡀⠀⠀⠨⡆⠀⣴⣻⣍⣱⠚⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢠⡎⠁⠀⠀⠀⣀⣀⣤⠔⠒⠒⢹⠀⠀⠑⡄⠀⠀⢣⡈⢻⡧⣦⣽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠘⣇⡠⠴⡖⢿⣿⡿⢸⠂⠀⠀⢸⠀⠀⠀⢹⣆⠀⠀⢧⠸⡏⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠙⣄⠀⠐⠦⠭⠴⠋⠀⠀⡰⠃⠀⠀⠀⠀⢻⡀⠀⠸⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣇⠄⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⣷⢤⣀⣇⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠺⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⢀⣇⣀⠈⠙⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⠖⠉⠀⣀⣠⡄⠀⠀⠀⠀⠹⣿⣯⠒⠢⠤⠤⠤⠤⠤⠴⠒⢊⣁⠇⠀⠀⠀⢸⠃⠈⠉⠙⠒⠚⠃⠀⠀⠀⠀⠀ ⢠⡟⠁⠒⠶⣏⡁⠀⢳⡀⠀⠀⠀⠀⠈⠢⣉⠩⣗⢚⣝⠒⢛⣻⣿⠖⢦⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠒⠤⠤⣀⣉⡓⠒⠷⠤⠤⣀⡀⠀⠀⠈⠉⠚⠻⠤⠽⠥⠤⠛⠚⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⢄⠀⡰⠋⠓⣶⠤⢤⣀⣀⣀⣀⡤⠴⠒⠻⢿⣄⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣾⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡦⠤⠬⠧⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠹⠿⢭⣍⠿⡷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡿⢻⡾⡏⠁⠀⠀⢀⣀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠦⠤⠤⣾⣉⣳⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⠄⢸⠟⢋⡛⢻⣿⠒⣿⠛⠟⡛⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⣤⣤⣴⣿⠒⣉⡅⢸⣿⠀⣿⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣄⣉⣥⣈⣿⣀⣿⣄⣼⣿⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⣀⣀⠀⣀⠀⠀⣀⢸⣿⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⢸⡏⠉⣿⡇⣿⠀⠀⣿⢸⣿⠉⠹⣷⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⣿⡇⢿⣦⡼⣿⢸⣿⣦⣼⠟⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⣻⣟⣛⣁⣿⠁⠀⠀⣼⣿⣿⣿⠛⠻⠟⠉⠰⣿⣿⡇⢀⡤⣤⣤⣽⣿⣿⡿⠿⣟⣷⣿⣿⣿⣮⣾⡗⠒⠒⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⢐⣿⣿⡿⢋⣿⣿⣿⠟⢉⣴⢾⣻⣿⣿⣭⣭⣽⣿⣿⣿⣯⣿⣿⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣉⣽⣯⣿⣿⣽⣿⡇⠀⢰⣻⣿⣿⡿⠷⠀⠀⢀⣴⡞⣿⣿⣧⣿⣿⢟⣴⡾⠿⠿⢿⣿⣷⣾⡿⠿⠿⠿⣿⣿⣿⣿⣯⡻⣿⡻⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠿⠄⢠⣯⣿⣿⣟⠂⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣿⠟⣡⠤⣤⣄⡀⠈⠛⢿⣟⢦⡀⠀⢠⣤⣍⣙⡻⣿⣦⡹⣷⡿⣿⣦⡀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀ ⣭⣽⣭⣿⡿⠀⠀⠀⣾⣿⡿⠛⠃⠀⠀⣾⡿⠋⢀⣈⣉⠻⣿⣿⡏⠀⠛⠿⠟⠻⠻⢦⡀⠈⢿⡆⠙⣿⣟⣻⡽⢿⣯⣝⣿⣧⠹⣿⡻⣽⣟⡿⢯⣅⡹⢿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠁⠀⠀⣼⣽⣿⡅⠀⠀⢀⣼⡟⠀⣾⣿⡿⡯⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢿⡆⠘⣯⣿⣿⣷⣾⣭⣟⣿⣧⡹⣿⣿⣿⣿⣷⢾⠿⠟⠋⠀⠀⠀⠀⠀⠀ ⣶⣿⡿⠁⠀⠀⢸⣷⣿⡟⠀⠀⢀⡞⡟⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣿⠀⢸⣿⣷⣽⣿⣿⣿⣿⣿⣷⣽⣿⣾⡱⠝⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⠁⠀⠀⢀⣿⣿⣟⣿⣶⡀⡾⢸⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢿⡆⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣦⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠀⠀⢀⣾⣿⣿⣿⣿⣿⢱⠃⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⡙⣿⣽⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⠄⠀⠀⣼⣿⣿⣿⣿⣿⠃⢸⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠧⣙⣿⣮⣛⢕⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⣰⣿⣿⣿⣿⣿⡏⠀⡏⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⢰⣿⣿⣿⣿⣿⣿⡷⠆⡇⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠿⠋⡇⣿⠀⢸⣿⣿⣿⣿⣿⠟⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣞⣿⣿⣿⡿⠟⠉⠀⢰⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠛⠉⠁⠀⣀⣠⣿⡟⠀⣼⣿⡏⢻⣯⠏⠀⣠⡦⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⢸⣷⠀⠀⠀⡷⠶⠾⠿⠿⠛⢻⣦⡀⠀⠀⠀⠀⠀⠀⢠⡶⠛⢉⣁⣀⣼⣧⣀⣿⣿⡇⠈⣿⣧⡮⡉⣦⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⣽⣿⢻⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⠇⠀⢀⣀⣀⣤⣄⣙⠻⣆⠀⠀⠀⠀⠀⠘⣿⠛⢻⣿⣷⣿⡇⠘⣿⣿⡇⠀⣿⡿⠴⠁⡏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⢸⣿⠀⠀⠀⠀⠀⢸⢿⡄⠀⢸⠀⣛⣭⣤⣤⡤⣴⢿⡟⠺⡄⠀⠀⠀⠀⠀⢹⠀⢸⡽⣿⣯⡇⠀⢁⡇⡇⢀⣿⣶⡄⢸⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⣸⣽⠀⠀⠀⠀⠀⢸⢸⣷⠀⢸⠀⢿⠁⠸⣿⣿⣽⡄⠹⡄⢻⠀⠀⠀⠀⠀⠈⠺⠶⠿⠿⠀⡇⢸⣸⠁⡇⠈⣹⣼⠦⠇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⢸⡀⣿⠀⢈⣇⠸⢦⡀⢿⡿⣿⣷⠶⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠟⢰⠁⠐⠛⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢡⢾⠀⠀⠀⠀⠀⢸⠃⢿⠀⣸⢹⣆⢈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⢸⠀⢀⣤⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⢻⣿⣼⣸⠀⠀⠀⢀⣤⢻⡆⢸⠀⢿⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡀⠀⡸⠀⢸⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⠀⢀⣠⣿⠁⢸⡇⣼⠀⣬⢳⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠇⠀⡇⠀⡏⠀⡇⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣤⣿⣿⣾⣄⢸⢣⢻⠀⡿⠁⠉⠉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣿⠹⠀⢀⣇⠜⠁⠀⣧⣀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⢹⣿⣿⣿⣿⣿⣿⠋⠀⣿⡜⡟⢰⠁⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠉⠉⠋⠁⢠⣿⡇⠀⢸⠃⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⡀⢀⣿⡇⠁⡸⠀⠀⠀⠀⢀⡆⠙⠳⢤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢸⣯⡇⠀⣾⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⡿⣿⣿⣿⣀⣼⣿⡇⠀⡇⠀⠀⠀⣴⠟⠁⠀⡀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⡾⢻⡇⢠⣿⠀⠀⠀⣴⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢸⡿⢠⣿⣿⠟⠉⡞⣿⠃⣸⢇⠀⢠⡾⠃⠀⢀⡼⠀⠀⠀⠀⠀⠈⠙⣷⣦⣀⣠⠴⡞⠁⡇⣸⣇⡇⣿⢀⣴⣾⣿⣿⣿⡄⠈⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡸⢠⣷⠟⠁⠀⢰⣟⡟⠀⣿⢸⣴⡿⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⢿⣿⣿⣷⡛⢧⢞⣿⣿⡏⡇⢻⣿⣿⣿⣿⣿⣿⡇⢸⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⢿⣧⠘⠃⠀⠀⠀⢾⣿⠀⢰⣿⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⠈⠻⣿⣿⣿⣿⣿⣿⠞⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡼⠋⠀⠀⠀⠀⠀⢸⡏⡎⢸⢹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢿⣿⣿⣿⣿⣿⣿⢳⣯⢰⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⢸⣼⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠻⣿⣿⣿⣷⣰⣺⣿⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⣈⣏⠻⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠈⣿⣿⣿⣶⣷⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠟⠁⢻⡹⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣦⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢰⠇⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀ ⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠈⣷⣿⠘⣷⡤⠀⠀⠀⠀⣀⣤⠞⠁⠇⠙⠷⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡠⠶⠟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡀⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⠀⠀⠀⠀⠔ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡄⠀⠀⢠⣾ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⣿⣿ ⠀⠀⣰⢻⣿⣿⣿⡟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠉⠻⣿⣿⣿⣿⣿⣿⡻⣿⣿⣷⣄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⠀⠀⣿⣿ ⠀⣼⠃⣼⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣠⠿⠿⣿⣿⣿⣿⣦⣙⢿⣿⣧⠀⠀⠙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡀⠀⠘⣿ ⣸⠃⢀⣿⡇⣿⣿⣴⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣱⠿⠛⢟⣛⣧⣼⣿⣿⡿⢿⢿⠿⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⠀⠸⣇ ⡏⠀⢸⠏⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⡞⠁⢀⣴⣿⠿⠛⠉⠀⢀⠀⣾⣟⣷⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡇⠀⣯ ⠀⢠⢸⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢐⣿⠟⠽⠳⣄⢈⣠⣤⠶⠞⠛⠉⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⠀⣷⢸⣿ ⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣆⠘⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠉⠀⣰⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄⢹⣼⣿ ⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠻⣿⣧⡀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣷⡀⢘⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠙⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡀⢳⡀ ⠀⢰⣟⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⡍⠀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠈⢻⣿⣿⣿⣄⢹⣿⣿⣿⡇⢸⣿ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⠻⣿⣿⠟⣴⣾⣿⢿⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⣷⣄⠀⠻⣿⣿⣿⣾⣿⣿⣿⣧⠀⣿ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢇⣾⡿⠃⠐⢹⣿⠏⠀⠀⠈⠀⠀⠠⡀⠀⠀⠀⠀⢀⣀⡤⠶⠖⠒⠒⢻⣧⡀⠀⠀⠀⠀⠳⡄⠈⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⡆⢻ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣡⣔⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣠⣤⣶⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⢦⠘⣿⣿⣿⣦⣿⢻⣿⣿⣿⣿⣿⣇⠸ ⠘⠀⢹⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⣿⡀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡄⠀⠀⠀⠀⠀⠓⠙⣿⣿⣿⣿⣦⣝⢿⣿⣿⣿⣿⠀ ⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡷⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡆ ⢀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣼⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠠⠘⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⣍⠙⣷⡇ ⢸⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢶⣿⣿⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⣯⡻⣿⣿⣿⡇⠸⣷ ⠸⠀⣼⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣻⠄⠀⠀⠀⠀⠀⢀⣾⠀⡜⢻⣿⣦⡙⠿⣷⡄⢻ ⣆⢼⡟⠀⣿⡆⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⣀⠔⢁⡾⠋⡟⠂⠀⠀⠀⠀⠀⣼⡿⢠⡇⠀⠙⠿⣿⣦⡈⠓⠘ ⣿⣿⡁⠀⢹⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣶⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⠤⠔⠋⢁⡜⠁⠀⠀⠀⠀⠀⢠⣿⠇⣸⠃⠀⠀⠀⠈⠉⠁⠀⠀ ⣻⣿⣿⣤⠿⣿⣿⣿⣿⣟⣾⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣭⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠁⠀⣠⠞⠀⠀⠀⢀⡿⠏⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⡙⠻⢿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠁⠀⠀⠀⡀⣼⠗⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏⠀⠙⢿⣿⣷⣦⡀⠀⠙⠛⠿⢿⡍⠛⠓⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⢀⣞⣡⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⢏⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⣿⣶⣤⡀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⠒⠒⠢⠤⠴⠒⠚⠋⠉⠉⡿⠉⠀⠀⠀⣿⣿⣶⣦⢤⣄⡀⠀ ⣿⣿⣿⣿⣾⣿⣧⢻⣿⣿⠏⣸⣿⣿⣿⠋⠻⣷⣄⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠒⠀⣸⣿⣿⣿⠋⠀⠀⠋⠙ ⣿⣿⣿⣿⣧⢿⣿⡟⣿⣏⢀⣿⣿⣿⣿⠀⠀⠈⠻⣷⣦⣀⠈⠻⣿⣿⣿⣿⣿⣿⣽⣃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⡀⠀⢀ ⣿⣿⣿⣿⣿⡌⣿⣿⠊⡻⣼⣿⣿⣿⣿⢳⣄⠀⠀⠈⠻⣿⣿⣦⡝⢿⣷⣝⠻⠿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠟⠿⠿⣿⣯⣀⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⣿⣿⡆⠈⠨⡻⣿⣿⣿⡇⠙⢦⣄⠀⠀⠀⠙⠻⣿⣄⣙⣿⣿⣦⣄⡉⠁⢘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣼⠠⢀⣰⣿⣿⣿⠛⠛⠛⠟⠛⠿⠿⠿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢔⣶⠶⢶⠒⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢉⡠⡴⠋⠀⠀⠀⠑⣤⡄⢀⣀⡉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡰⢋⡜⠀⠀⠀⣀⡀⠀⠘⢯⢁⡠⠭⢝⣦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠞⠀⡜⠀⠀⣰⠋⢀⣩⣵⣄⠀⠀⠀⠀⠀⠈⠹⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡰⠃⠀⡜⠀⠀⢰⡏⠉⠉⠉⠙⠛⢦⣴⣶⣦⡄⠀⠀⢱⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⡜⠀⠀⢠⡿⠤⠀⠀⠀⠀⠠⠶⠷⠦⠬⣿⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢀⠞⠀⢀⡾⠁⠀⠀⡜⠀⠠⡀⠀⠀⠀⡖⠀⠀⠀⠀⢸⠀⠀⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣥⠋⠀⢠⡿⠁⠀⠀⣸⢥⡀⠀⢵⠀⠀⠀⡟⠀⣠⠤⣠⢼⡇⠀⢸⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠁⠀⣰⠋⠀⠀⠀⢠⣿⣦⣀⠀⠘⠇⠀⠀⠀⢈⣴⣾⣿⣿⡇⠀⢸⣻⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⡴⠁⠀⠀⠀⢀⡾⣿⣿⣿⡦⠀⠀⠀⠀⢠⣿⣿⣿⠏⣈⡇⠀⢺⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⢀⡜⠀⠀⠀⠀⣠⠞⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⡇⠀⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡀⡜⠀⠀⠀⣠⡞⣧⠀⠀⠀⠀⠀⠀⢀⡄⢀⣄⠀⠀⠀⠀⠀⠠⣷⠀⢹⡅⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡇⠀⠀⡔⠁⠈⠙⡇⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⢠⣿⡄⠈⣿⡀⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⡀⠈⣇⠀⠀⠀⢹⣆⠀⠀⠐⠦⣴⠾⠶⣶⡤⠂⠀⠀⣠⠞⢻⣇⠀⠘⣷⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⡉⠒⠬⠷⢤⡇⠘⡇⠑⢦⣀⠀⠈⠛⠟⠉⠀⢀⡤⠞⠁⠀⢸⠈⠢⡀⠈⠇⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠀⡇⠀⠀⠀⢰⠁⢸⣇⠀⠀⢹⡟⠢⠤⠠⠴⠚⡟⠀⠀⠀⠀⡆⠀⠀⠈⠁⢸⠀⠐⣄⠀⠀⠀ ⠀⠀⠀⣠⡿⢁⠞⡇⠀⠀⣠⡏⠀⣼⡏⠀⠀⠀⣷⣶⣤⣤⣴⣾⡇⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸⠄⠀⠈⢆⠀⠀ ⠀⠀⣰⡟⢡⠎⢀⣧⣤⣴⣹⡧⠤⣟⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣸⡤⠤⣄⣀⣤⣬⡀⠀⢠⠈⢇⠀ ⠀⢰⡟⡰⠃⢀⣾⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡄⠀⢆⠈⡄ ⢀⠏⠸⠁⠀⣾⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡀⠸⡀⣇ ⢸⠀⡇⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣇⠠⡇⣿ ⢸⠀⠁⠀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀ ⣤⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⣿⠁⢻⣿⣿⠇⠀⠀⠀⣴⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠷ ⠀⢻⠀⢀⣿⣿⠀⠀⠀⠀⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀ ⠀⠘⡆⠘⣿⡇⠀⠀⠀⠀⠘⠛⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀ ⠀⢀⣼⣶⣾⣧⣤⣤⣄⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⣧⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠀⠈⠉⠉⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⣾⠁⠠⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢰⣿⡷⣀⣄⡀⠀⠠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠶⣼⡏⠘⠛⠁⢴⣦⡇⡀⠀⠙⠛⠛⠁⠖⠚⠉⠀⠀⠀⠀⢸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠒⣿⠀⠀⠀⠳⠼⠧⠤⠝⠁⠀⠀⠀⠐⠒⠲⠆⠀⠀⠀⠀⠑⠘⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢳⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠙⠷⣦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠈⢻⣷⣦⣿⡇⠀⠀⠀⠀⠀⢦⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠠⣄⢀⡾⠁⠈⢹⣧⠀⠀⢀⠀⠀⠈⢛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⣀⣽⠟⠀⠀⠀⠀⠻⣧⡀⠘⢦⡀⢀⣾⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣈⣻⠿⠁⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⡽⠿⠶⠦⣤⣄⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⣀⡀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⡥⠾⠂⠀⠀⠀⠀⠀⠀⠀⢰⣹⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢲⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⣴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⠊⠉⢱⠀⠀⢰⠉⠁⠒⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⡠⣎⠀⠀⠀⢀⡜⠀⠀⠀⠣⣄⡀⣀⡽⢦⡀⠀⠀ ⠀⢀⠎⠀⠈⠑⠒⣾⡍⠀⠀⠀⠀⢠⣴⡀⢀⠔⠋⠑⡄⠀ ⠀⡞⠉⠉⠑⢄⠐⣀⠑⠑⠤⠤⠞⠉⢉⡡⢺⠀⠀⠀⢸⠀ ⢰⠀⠀⠀⠀⠘⡆⡜⠒⢢⠀⠀⢀⡠⠤⠤⢀⠓⠤⠐⠋⡇ ⠀⢦⡀⠀⢀⡼⠈⢧⠀⢰⠀⡴⠁⠀⠀⠀⠀⢱⠀⠀⡰⠁ ⠀⠀⠉⠁⠛⠒⠒⣶⣿⣳⣖⢓⡦⠤⣤⠄⠒⠚⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡿⣯⠋⣿⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡃⣟⠀⢸⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⣿⣿⠀⠈⠃⢹⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⡀⣤⣄⣼⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⢀⣤⣤⣤⣤⡄ ⣰⡟⠉⠀⠈⠙⢿⣦⠀⢀⣾⠟⠁⠀⠈⠹⣷⡀⠀⢸⣿⠉⠉⠉⠀ ⣿⠀⠀⠀⠀⠀⠘⣿⠀⢸⡿⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣀⣀⣀⠀ ⣿⠀⠀⠀⠀⠀⢠⣿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠉⠉⠉⠀ ⢹⣧⣀⠀⠀⣀⣾⠏⠀⠘⣿⣆⡀⠀⢀⣰⡿⠁⠀⢸⣿⠀⠀⠀⠀ ⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠳⡀⢀⠔⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢢⣯⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣫⡾⣳⠧⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣥⣾⣿⡿⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣳⢴⣿⣵⣿⣫⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡒⠕⢁⡠⣾⣕⣷⣻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⡳⣤⢐⠹⣮⣿⡟⠟⠉⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣅⣶⠞⡉⢻⢤⠀⣠⡾⣕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⡞⣵⡏⠻⠘⠢⣑⣥⠼⠛⢯⣑⢌⠓⢕⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠔⠁⣠⡾⠃⠈⠀⢹⡒⢺⡁⠀⠀⠀⠙⢗⢷⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⣠⠞⠋⣀⣴⡿⢙⡕⠀⠀⠀⢸⡇⠸⡅⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢦⣾⠟⢠⡱⠁⠀⠀⠀⠀⠸⠇⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⡉⠀⠐⠂⣠⠂⠐⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⢀⣴⣶⣄⣠⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣧⣿⣿⣿⣿⣿⣉⠘⠈⣻⠗⠂⠲⠦⡀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡏⠉⢙⣿⣿⣿⣬⣿⣿⣿⠋⣲⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣯⣿⣿⣿⣿⢿⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣟⢛⣿⣧⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡻⣿⣿⡽⠛⢷⡦⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣇⣡⣇⣿⣿⣷⣤⡄⠴⠿⠿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣃⣀⡀⢀⣈⢿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠈⣹⣿⡿⣫⠉⢹⣿⣷⠀⢀⠀⠀⠀ ⢟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⡿⣿⣟⣿⣿⣟⣂⣹⣿⣿⣤⣀⣀⣀⠐ ⠘⠋⠈⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⡟⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠻⣿⣿⣦⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣇⣤⣤⣀⣰⣦⣀ ⣿⣿⣿⣯⣀⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢁⣠⣶⣿⠿⣿⣶⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠟⠉⠀⣠⣴⣿⣷⡝⢿⡀⠙⠻⠿⣿⣿⣿⣿⣟⣩⡶⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣟⠛⣿⢠⡈⣙⣿⣿⣿⣿⣿⣿⣿⠋⢁⡀⠘⢻⣿⣿⣿⣿⣿⡇⠙⠻⣿⣧⠀⠀⠸⠻⣿⣿⣿⡇⠀⠁⢠⠔⢲⣾⣿⣿⣯⣛⣯⣴⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠛⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣁⣀⠶⣿⣿⣿⣿⣿⣿⣧⠀⠀⢌⠙⠷⣄⠀⢀⠺⠿⢟⠇⠀⠀⠀⣠⣿⡿⡏⢉⡽⣿⣭⣍⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣭ ⠉⠛⣫⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⠀⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠳⣄⠀⠀⠀⠀⠱⠦⣄⣈⣁⠀⠀⠀⠀⠀⠀⠸⣷⠏⢹⣿⣿⡟⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣸⣿⣿⣿⡿⠛⠁⠀⣼⣿⣿⣿⣿⣿⠀⠀⣀⣰⢾⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⡼⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠟⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⡀⠘⠛⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣈⡷⠦⣤⠖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⡟⠁⢀⣠⡴⠂⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠈⠉⣰⡾⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣵⣿ ⡿⢀⣴⣿⡏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠿⠁⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣟⣩⣽⣿⠿⢿⣿ ⣇⣿⣿⡟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⣸⠋⠉⠁⠀⠐⠒⠶⠤⢌⠉⠉⣹⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿ ⣿⣿⣿⡃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⣀⣀⠀⠀⠀⡸⠁⠀⠀⢀⣾⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡆⢀⠀⠀⠀⠀⠀⣯⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⠓⠚⠁⠀⠀⣠⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶ ⠀⠀⠉⠛⠻⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣼⡀⠀⠀⠀⠀⣿⠀⠘⢿⣷⣦⡀⠀⠀⠀⠀⠀⠐⠿⠟⠁⠀⠀⠀⣠⣾⣿⡟⢿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠓⢄⠀⠹⣿⡏⠸⣿⣿⣿⣿⡇⢸⢸⡏⢿⡀⠀⠀⠀⣿⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠘⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣝⠧⠀⠻⣿⣿⣿⡇⢸⣾⠀⢈⢷⠀⠀⢀⡏⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⢻⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠻⣿⣧⠸⡇⠀⠀⠘⣇⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⡆⢸⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠈⠙⠷⠛⠀⠀⠀⢻⣤⡟⠀⠀⠀⠀⠀⢀⡴⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣧⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⡴⠋⠀⠀⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⣶⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠓⠶⠤⣄⡚⠀⠀⠀⠀⠀⠎⠀⠀⠀⠰⠛⠁⠀⠈⣙⠛⠿⠿⠿⠿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣬⣿⣡⣾⣿⣿⡿⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⢤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⣦⡘⢆⠀⠀⠀⢀⡴⠛⣁⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿
⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣻⣿⠷⠿⠚⠛⠋⢋⠉⡉⠌⠉⠄⡉⠉⢍⣛⢛⠻⠾⢿⣽⣻⡿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠶⠛⡙⢀⠂⠄⡁⠂⠌⠠⢀⠄⠐⠈⣤⣶⣿⣿⣿⣿⣿⣶⣦⣠⢉⠛⡶⣭⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⡁⠄⡡⠐⠠⢈⠐⠀⡁⠂⢁⠠⠀⢸⣿⣿⣿⡿⠟⠛⠻⢷⣿⣻⢿⣷⣌⡰⠉⡝⢷⣿⡢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠟⡡⢊⠑⡈⠐⢀⠈⠄⢀⠈⠐⠠⠁⠂⠄⠂⠈⠿⠟⠋⠀⠄⢂⠠⠀⠉⠻⢿⣿⣿⣷⡅⡘⢄⠚⢿⣾⡳⣄⠀⠀⠀ ⠀⠀⠀⣴⢿⡿⢣⠘⡤⢁⢂⣤⣥⣦⣶⣶⣦⣮⣤⣔⡀⠁⡐⠈⠠⠀⠄⠂⡁⠂⢀⠂⠡⠐⠠⢈⠛⡿⠟⡡⠎⢠⠉⢆⡹⢷⣞⢦⡀⠀ ⠀⢀⣾⣷⠟⡢⢍⠒⡄⢃⢾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⡆⢁⠂⣁⠢⠐⠠⢁⠂⡄⡁⢆⠱⣈⠒⢄⠣⡐⡡⢊⠜⡠⠜⡱⣻⣮⢳⡀ ⣠⡾⣵⢏⠸⡑⢌⠢⡑⡌⢢⢎⡐⠄⠂⢀⠀⠀⠀⡉⢛⠟⡁⢢⢸⠀⠄⠁⠠⢀⠠⠐⡐⠌⠲⣄⢫⢄⠣⠔⣡⠊⡔⠡⢎⠰⡡⢟⣷⡃ ⣿⣽⢟⢪⢑⡘⠬⣡⢑⣾⢋⢆⣰⣼⠶⠷⠿⠷⣶⣦⣌⢒⡁⢆⣃⣬⡶⠾⠟⠻⢶⣶⣤⣉⡒⣌⢣⢎⢧⠩⣄⠣⠜⡡⢊⠱⢌⠣⣟⣧ ⢿⡟⣌⠲⢌⡌⠳⣄⣻⣿⣼⡞⢋⡁⢲⡜⣶⣿⣷⣶⣝⡻⣦⣼⠟⣁⠐⡢⢞⣽⣿⣷⣯⣝⡻⣶⣭⣚⢾⡇⢦⠙⡬⠑⣌⠃⣎⠱⣎⣿ ⣾⡗⣌⠣⢒⠬⡑⢦⣿⣿⡱⣌⢣⡜⣹⣾⣿⣿⣿⣿⣮⣕⣻⣏⠖⡌⢧⡹⣿⣿⣿⣿⣿⣿⡱⢢⣝⣻⣿⣿⢢⡙⠴⣉⠤⢋⡔⢣⡜⣻ ⣿⡇⢦⠙⡌⣒⢉⢾⣟⣿⣷⡹⢦⣝⡲⢻⣿⣿⣿⣿⣟⣶⠏⣿⣯⣜⣣⣓⠻⣿⣿⣿⣿⠟⣜⡳⣎⣷⣿⢻⡇⣌⠓⡬⡘⠦⡘⢥⢚⢷ ⣿⡏⠦⡙⣄⠣⢊⡒⢿⡞⣿⣽⡿⣼⣳⢏⡼⣩⣝⣶⣿⣫⠜⡴⣹⢷⣧⣏⡷⣥⢫⣍⢶⣹⢮⣽⣿⡟⣣⡟⠴⣈⠇⠦⢱⢡⡙⢆⡫⣞ ⣿⣏⠲⢡⢂⠝⢢⡙⡜⣻⣎⡻⢿⣷⣿⣯⣿⢷⢻⡭⡟⢥⢋⠴⡛⢿⣭⡻⢿⣾⣿⣾⣯⣿⣿⠟⣣⣼⠟⡬⢓⠬⣘⢡⢃⠦⡙⢆⡳⡽ ⣿⣏⠖⣌⠚⣐⠪⣅⢣⢋⠿⣷⣬⣽⣋⡛⣭⡜⢮⡑⡣⢜⡸⢄⠳⣌⠛⡷⢪⢭⢛⡛⢛⣋⣍⢶⠻⣍⠶⣡⠚⢤⠋⡜⢸⢠⠓⡜⣧⣳ ⣿⣏⠞⡠⢍⠤⠓⡤⢃⣎⠳⡜⡼⣡⠧⣙⠦⡸⠡⢎⡑⢊⠔⣉⠒⡌⠹⡰⢋⢬⠣⡝⣣⠞⡜⢎⡳⢜⠢⣅⢋⠆⣍⠲⢡⠎⡹⣜⡵⣯ ⣿⣯⠞⡱⢌⢪⡑⢆⡱⢈⠧⡙⠴⡑⢎⠰⡁⢆⡑⠢⠌⢂⠌⡠⠡⢌⠱⢠⠉⠆⡓⠬⡑⢎⡹⢌⡱⢊⡱⢌⡘⢆⠢⢍⠦⡙⡵⣎⣷⣻ ⣿⣿⣭⠓⣌⠲⣈⠆⡔⢃⠆⡑⢢⠑⠌⠂⠅⠂⠤⠁⠌⠂⠄⡁⠒⡈⠄⢃⡘⠄⡑⠢⠑⡌⠔⡊⠔⡡⢒⠰⣈⠦⡉⢆⠳⣍⠶⣽⣞⣿ ⢋⢿⣷⣋⠦⡓⠴⣈⠔⡨⢐⣡⢢⣜⡬⠕⠮⠱⠎⠱⠊⠗⠚⠒⠳⠸⠜⢢⠴⢬⡴⣁⣎⣄⠃⡜⢠⠑⡌⠒⢤⢒⡩⢎⠳⣜⢯⣷⣻⡿ ⠀⠘⣿⣽⣎⡝⠻⠟⡛⣓⠛⣭⣉⣆⢦⣉⢦⢣⡜⣤⢣⡜⣤⣉⢦⡡⢎⢤⡒⡄⢆⡩⢜⡙⡛⠿⠶⢧⣼⣱⣎⣶⡱⢎⡻⣼⣻⣾⣿⠁ ⠀⠀⠸⣿⣿⣾⣿⣷⢿⣼⣿⣶⣿⣾⣯⣿⣯⣷⣿⣞⣷⣻⣶⣻⣮⣽⣻⣮⣷⣻⣽⣞⣧⣿⣵⣫⣶⣲⣤⢦⡬⣥⣺⣭⣷⣿⢿⣷⠋⠀ ⠀⠀⠀⠙⣿⣿⣿⣻⣿⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣷⡿⣾⢿⣽⣷⡿⣷⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣳⣟⡾⣽⣳⣟⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⡿⣽⡾⡿⣽⡳⢿⡽⣯⢷⣻⣽⣿⣿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣽⣷⣻⣞⣷⣻⣞⣯⣟⡾⣯⢷⡿⣽⣾⣻⣞⡿⣽⣞⣷⣻⢗⣻⣽⡳⣟⣯⢿⣽⣻⣿⣿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣞⣷⣻⡾⣽⣻⡽⣯⣟⡷⣯⢷⣯⣟⣷⣻⢾⡽⣯⢷⣯⢿⣽⣾⣿⣻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣿⣟⣾⣿⣽⡿⣾⣽⣾⣽⣯⣿⣿⣿⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠿⠿⠿⢿⣿⣿⣿⣿⢿⠿⠿⠟⠛⡙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡶⠒⠒⠶⣄⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢱⠀⠀⢠⠉⢡⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠄⠀⢸⣦⣾⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⡴⠶⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇ ⠀⠀⠀⣀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⡛⠁⠀ ⠀⣠⢾⣭⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⣝⣷⡀ ⢠⡏⠘⠋⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠈⠛⠃⢻ ⠈⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡽⠟⠛⠿⣭⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠞ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣿⡟⠋⠉⠙⠟⠛⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣮⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏⠀⠀⢀⢀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡄⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢣⣶⡿⣿⠃⠀⣠⣾⠗⣡⡶⠾⣿⣿⣿⣿⣿⡟⢻⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠐⠒⠚⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣸⣿⢃⡾⠉⢀⡖⠀⣸⢟⣡⣾⡟⠀⡸⣷⡿⢱⠀⢹⠇⣸⣿⡇⠸⣿⣿⣏⠀⠈⣿⣿⣷⣷⡀⠙⢿⣽⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⣾⠁⣠⡞⠀⢰⡿⠟⠛⣿⠁⣰⠿⣿⢡⠆⣰⣿⣶⡿⣿⡇⠀⡏⠉⢻⣴⠀⣿⣿⣿⣿⣷⡀⢈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⢃⡔⡹⠃⢀⡏⠃⣠⣾⠁⢠⣿⢖⠏⣞⣠⣿⢿⢻⡇⢹⣿⢠⡇⠀⡜⣿⠀⣿⣿⣇⠈⣿⣿⡘⢧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣤⣰⣿⢸⣮⣾⡏⠀⣼⡴⠻⢠⣿⢟⠁⢸⢸⠁⢸⡏⠸⢸⡀⢁⣻⣤⣿⣿⣿⡀⠃⠹⣷⡸⡻⢾⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡟⡾⠟⣡⣧⠀⣿⢁⠇⣾⢇⡎⠀⣘⣿⠀⣼⠇⡆⢸⣿⣾⣿⣿⣿⣿⢸⣧⢰⠀⢹⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⣸⣿⠉⢿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣏⣘⠀⢃⣴⣿⠘⢰⠃⡾⠀⣿⡼⠀⢰⣿⡟⢰⣿⠀⣧⣿⣿⢿⣿⢸⣿⣿⠀⢿⢸⡀⠘⣿⣿⡤⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⢻⣿⣀⠘⠓⣢⣬⡿⠛⠋⢸⢿⣿⣻⣯⡆⣾⣻⣿⠈⣾⢰⠇⣦⣳⠃⠀⢸⢻⡇⢸⡟⠀⣿⣿⣿⢸⣿⣼⣿⣿⠀⠘⣿⡇⠀⢸⣿⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⢻⣿⣿⠾⠵⠏⠀⣠⠀⢰⣿⠏⠁⢿⣇⢻⣟⢻⠀⠋⢸⣰⣯⠋⠀⠀⣸⣸⣁⣾⣡⡴⢟⣿⣿⢸⣿⣿⡟⣿⠤⣤⣿⣧⣀⣸⢹⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⢀⣤ ⠖⠊⠉⠙⣧⣀⢀⠖⠉⢀⣠⡾⠁⠀⡀⣸⣿⠈⣿⠀⢸⢸⢸⣿⠽⣴⠖⠚⣟⢻⣹⣯⠇⠀⠀⣿⣿⢸⣿⣿⣇⣿⠀⢀⣿⡇⠀⢹⢻⡗⣼⡇⣿⡿⡿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠉ ⠀⠀⣠⠼⣿⡛⠻⣿⣻⣿⡟⢁⠔⠚⢁⣷⣿⠀⣿⡆⠘⢺⡏⢷⡄⠘⠄⢀⣯⣧⡟⡈⠀⠀⠀⣽⡿⢸⣿⣿⢻⡟⢀⡠⠼⠧⢄⡸⢸⣷⡏⣿⣿⣿⣷⣼⣿⣿⣿⠟⡃⠀⠀⣠⡄ ⣶⠞⠁⢠⣿⣯⣭⣭⣽⠫⠄⠐⣠⣫⡿⠚⣿⠀⣇⣷⣤⠀⡇⠀⢇⡴⠾⢍⣼⣃⣀⣀⣀⠀⠀⡟⡇⡾⢠⣿⣼⠡⠤⢤⡴⢒⣒⡣⠼⡽⠀⣟⣿⠇⢹⣿⣿⣟⡻⣿⡵⣀⠀⠈⠓ ⠋⠐⢶⣯⣿⡿⢻⣿⢿⡶⡶⢼⠣⠋⢀⡤⢻⣇⢸⡸⣿⠀⠁⢤⣳⣶⣮⣭⣽⣶⣶⣦⣤⡄⠀⠋⠀⠀⠀⠀⠁⣶⣿⣿⣿⣿⣿⣿⢿⣷⣤⣿⣿⡆⣸⡟⢿⣿⣝⣽⢿⠟⠃⠀⠀ ⠀⠀⢰⣿⡿⢀⢸⣿⡼⠹⣷⣼⠘⡄⠁⠀⠀⣿⣺⢳⡸⣦⣾⡿⠛⣻⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠀⠙⣿⣿⠟⠰⣿⡇⢘⣇⠘⣎⣿⠀⠀⠀⠀ ⡀⠀⡟⢻⡇⢸⡈⢿⡇⠀⠙⢿⣷⡹⣄⠀⠆⢹⣏⡎⣇⢻⡻⣄⣀⡖⡻⢻⣿⣟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠿⠿⠿⠿⠷⠖⢰⣻⣃⠔⢱⡇⣧⣼⣿⠀⢹⣿⠀⠀⠀⠀ ⠆⠀⢱⢸⠀⡾⡵⡌⣷⣀⠀⠀⢿⡟⢮⡛⠛⠲⢿⡿⣿⡈⣇⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⢸⡷⣻⣿⡟⠀⣼⡏⠀⠀⠀⠀ ⠀⠀⠈⢿⣧⡅⣷⡽⡜⣯⠳⢤⣸⣧⠘⠛⣿⣦⣼⣿⣼⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣀⣀⢞⣴⣿⣿⣷⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣼⣿⣿⣷⠙⢮⠳⣌⠹⣾⡴⢠⡟⣽⣿⣹⠜⣧⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣽⡌⢉⣡⣿⣿⡏⣹⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⡻⣧⡈⠳⣌⠻⣿⣿⡿⠁⣿⡟⣿⣧⣜⡇⢹⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣫⡿⣋⣴⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠭⣙⣿⣀⣠⡽⠋⣼⣷⣶⢏⠚⢉⡼⡽⡇⡾⣼⣧⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣿⠏⣾⡇⣿⣿⣿⣿⡯⡞⢋⡇⢸⡇⠀⠀⢀⣤⣤⣀⠤ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢲⣄⣀⣸⣿⣿⣟⠛⣻⠋⣠⣷⡇⣷⠿⢍⢻⣼⣿⡇⠙⣿⣦⣤⣀⣀⡀⢀⣀⣤⣾⣯⣲⣼⡳⣴⣻⠠⣿⠇⠀⢀⠀⣿⢸⡇⠘⡇⠀⠚⠋⠉⠁⠀⠀ ⠀⠀⠄⢐⡲⠭⣄⣂⣤⠤⠚⠛⢻⢿⣿⠟⡟⡞⠃⡼⠻⣿⡇⣿⣤⡀⠱⠟⠻⢧⣀⠈⠳⣮⡉⢉⡙⠻⣿⣿⣿⣿⣿⠟⠃⠈⣧⣤⣿⣄⠀⢸⠀⣿⡇⡇⠀⢿⠀⠀⠀⠀⠀⠀⢀ ⠀⢀⣴⣿⡶⠟⠛⠉⠀⠀⠀⠀⣾⣸⠃⢠⣿⠇⣴⠃⠀⢻⢯⣿⣿⣿⣯⣉⣉⡉⠉⣆⠀⠈⠙⠲⠥⡶⠛⡿⠉⠛⢫⣾⡀⠀⣿⡏⡿⠈⠙⣾⣤⣿⣧⢧⡀⠸⡆⠀⠀⠠⠴⠚⠛ ⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢸⣿⡿⠁⠀⢀⣼⣾⡘⣿⣬⣿⣋⣉⣉⠕⣻⠦⣀⠀⡠⢾⢏⠀⡄⢈⣴⢯⡖⠽⠴⣼⣿⡷⠚⠉⠀⠀⠀⠉⢿⣧⡀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⣴⡿⣿⢄⠀⠈⠁⣿⠃⠱⣌⠻⣿⣇⠀⢌⣠⣒⣉⠹⠛⠧⣼⣳⡼⣄⣿⢏⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠠⠀⢤⡹⣷⡄⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡴⢿⣟⣿⠃⠀⠀⠂⢸⠁⢰⠀⠈⠳⢼⡿⣤⣌⣿⣿⣿⣿⣍⣭⣀⣁⣤⣾⡟⠊⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢹⡹⣿⡀⢻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⡤⠋⡾⠃⠀⠀⠀⢀⣟⠀⠘⣇⠀⠀⠀⠙⢝⢻⣿⣿⣿⣯⣤⣴⣿⣿⣿⡿⡝⠀⠀⠀⢠⠇⡀⢰⢹⡇⠀⠀⠀⠀⢢⠀⠈⡇⢹⣷⠸⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣹⢏⣤⡞⣁⠀⠀⠀⠀⢸⣿⠀⡆⢿⡄⠀⠀⠀⠀⠑⠉⠻⣿⣿⣿⣿⣿⡿⠁⡾⠁⠀⠀⢀⠏⠀⡿⣸⢸⣱⠀⠀⠀⠀⡰⠀⠀⣧⣀⣿⠀⢻⡞⡆⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⢁⣼⠋⢻⣇⢇⠈⢧⡀⠀⠀⣿⣿⡄⠀⣾⠱⣄⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⡀⢀⠀⠀⠀⢀⡟⠀⣼⢁⡇⠈⡏⣆⠀⠀⡰⠃⠀⢠⠍⠉⣷⣇⠘⡄⢸⠀ ⠀⠀⠀⠀⠀⢀⡇⢠⢿⠇⠀⠘⢯⢿⣆⠀⠹⣆⡀⣿⣿⣇⠀⣿⠁⠈⠳⣄⢀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣦⢦⣀⢀⡞⠀⢸⢇⡞⠀⠀⡇⢿⠀⣰⢁⠀⣠⠏⠀⠀⣿⢿⣾⡇⢸⠤ ⠀⠀⠀⠀⠀⣾⣇⣏⠏⠀⠦⠀⠈⠳⣿⣆⠀⠹⣷⣹⣿⣿⣸⣿⠠⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠟⠀⢠⢯⣿⠃⠀⠀⡇⣾⠀⢉⣩⠼⣅⡀⠀⠀⣿⢰⠃⠷⢧⣄
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠉⠉⠛⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀ ⢐⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣠⣤⣤⣶⣶⠂⠀⠀⡂ ⢐⣀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣦⣀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀ ⠀⠈⠐⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣉⣽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠛⠛⠿⣷⠶⠶⠛⠛⠳⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⣴⠶⠶⠶⣶⣶⣆⣤⡾⠛⠉⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣸⠇⠀⠀⢀⣛⡛⠉⠁⠀⠀⠀⣀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣿⠀⠀⢘⣫⣭⣀⠀⠀⠀⢀⣠⠬⢽⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣸⣿⠀⢰⡿⠵⠶⢾⣷⡀⠀⡿⠷⠖⠲⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⡆⠀⠀⠀⣼⠃⠀⣷⣀⠀⢀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠙⠓⠖⠛⠁⠀⠀⢹⡏⠙⠉⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠟⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⣀⣰⡆⠀⢠⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣄⡀⠙⠶⣤⣀⣀⣀⣤⣤⣀⣠⣤⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡄⠈⠻⢿⣓⠚⠻⣿⣿⣿⢛⡟⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠙⠺⢿⣿⣿⡟⠀⠈⣿⣷⣤⣀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣄⠀⠀⣹⠏⠀⠀⢀⣿⣿⣿⣿⣷⡄ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⣶⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡏⠀⠀⣠⠀⣾⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣼⠃⣼⣿⣿⣿⣿⣿⣿⣿ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣿⣿⣦⣴⣿⣿⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣾⣿⠟⠛⠿⠇⠀⠙⠋⠀⠸⠿⠛⠻⢿⣷⣤⡀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣀⣀⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⠁⢀⣠⣄⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠈⢹⣿⡁⠀⢾⣿⣿⡷⠀⢈⣿⡏⠉⠁⠀⠀⠉⣿⣿ ⠻⣿⣶⡆⠀⠀⠀⠘⣿⣧⡀⠈⠙⠋⠁⢀⣼⣿⠃⠀⠀⠀⠀⣿⣿⠛ ⠠⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣶⣦⣴⣶⣿⠟⠁⠀⠀⠀⠀⡀⣰⣿⠆ ⠀⠛⠻⣿⡷⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⣿⡟⠉⠀ ⠀⠀⠐⣿⢷⣴⣶⡄⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣶⣦⠾⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⢼⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠂⠀⠉⠉⠉⠉⠉⠁⠒⠠⡤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡉⠓⢦⡀⠀⠀⠀ ⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡙⢦⡀⠀ ⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢱⡀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣷⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠄⠀⢠ ⢻⡀⠈⢷⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣎⡎⠀⠀⢨ ⠘⡇⠀⠸⡇⢆⠀⠠⠤⠤⠤⢀⡀⠀⠀⠀⠀⣀⠄⠀⠀⠈⠒⠤⢀⡃⡇⠀⠀⡄ ⠀⢹⡄⢸⡇⠀⠀⠀⠀⠸⠂⠀⠈⠀⠀⠀⠈⠁⠀⢀⣖⣠⣤⣄⣀⡀⠸⡀⠰⠁ ⠀⠈⣇⡸⠀⣴⣾⣿⣿⣿⣿⣷⣆⠀⠀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⢳⠁⠀ ⠀⠀⢹⠃⢸⣿⣿⣿⣿⣿⣿⣿⡿⠈⠀⡇⠑⠚⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡀⠀ ⢀⣤⠇⠀⠸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠓⡄ ⠘⡇⠀⠀⠀⠉⢛⡿⠟⠉⠁⠀⠀⠀⣼⢻⣇⠀⠀⠈⠙⠛⠻⡋⠉⠁⠀⠀⠀⡇ ⠀⢹⡀⠀⠀⢰⠊⠀⠀⠶⠂⠀⠀⣰⣿⣼⣿⡄⠀⠀⠰⠒⠀⠈⢢⠀⠀⢀⡰⠀ ⠀⠀⠉⢲⠒⠥⢀⣀⡀⠀⠀⠀⠀⣿⣿⢸⣿⡧⠀⠀⠀⠀⠀⣀⠤⠗⡆⠉⠀⠀ ⠀⠀⠀⠀⢃⠀⠘⡇⢹⠀⠀⠀⠀⡉⠉⢤⠉⠀⡀⡄⠀⢀⡎⡝⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠹⣌⣇⣸⣿⣐⣀⣀⣘⣈⣀⣇⣤⣌⣾⡝⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠙⢿⣿⢦⣸⣸⠉⡏⢘⣿⣆⡿⣿⣿⠁⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⡀⠀⠀⠘⠻⠾⢧⣯⣯⣏⣇⣥⠥⠚⠋⠁⠀⠀⡰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠠⠄⢀⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠔⠁⠀⠳⠤⠄⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣀⣀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣼⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠛⢻⠉⡉⠍⠁⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⢀⡼⡄⠃⠤⠀⠀⠀⠀⠀⡐⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣸⡎⣀⣷⣤⣶⣶⣶⣦⡀⠀⠈⠓⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣤⣯⣿⣿⣿⣿⣿⣿⣿⣭⣯⡆⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣿⣿⣼⠀⢹⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢘⣿⠙⠡⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⣯⠏⠀⢀⣿⣿⣿⣯⣠⡀⠀⠀⠀⢀⣾⡏⠒⢻⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢘⣏⣺⣤⣬⣭⣼⣿⣿⣯⡉⢻⣦⣌⣦⣾⣿⣿⡚⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⢿⡟⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣧⡞⣻⣩⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣇⣬⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡟⠻⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠓⠲⠤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢯⡁⠀⠀⠀⠉⠹⠶⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢀⠹⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢩⠀⢸⡄⢹⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⡄⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡀⣀⣰⣿⠀⠄⠹⣾⣿⣿⡿⣿⠀⢠⣤⣀⣴⣤⣤⡴⠶⠶⠿⠿⠛⠛⠋⠉⠉⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡱⠏⠉⡟⠃⠀⠀⠀⢸⣿⣿⠇⣿⡴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢋⣡⣶⣿⣂⡼⠁⠉⠙⠋⠙⠿⠟⣢⣄⢿⡟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀ ⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⣸⡿⠟⠀⠀⠀⠀⠀⠀⠲⣾⡛⣿⣬⡄⠀⠀⠁⠠⣤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡟⣿⡟⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠆⠀⠀⠀
⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠖⠛⠻⣷⣠⣶⠟⠉⠁⠀⠀⠈⠉⠛⠻⢿⣮⣙⣘⣙⢶⣄⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣀⣠⡾⠛⠛⠛⠛⠿⣿⣿⣿⡁⢀⣠⠤⣤⡀⠀⠀⠀⠀⠉⠻⣿⣝⢦⣝⣷⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠉⣋⣼⣿⡟⠃⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⡅⠀⠸⣯⠉⠉⠉⣉⣉⣛⣻⣿⣿⡌⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⢿⣿⣤⠤⠤⠤⠶⢶⣞⣻⠉⠉⠉⠉⠋⣿⣀⣠⣟⠙⠛⠛⠿⣯⠻⠿⣿⣿⣿⡷⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡿⠃⣼⡟⠉⠙⠒⠒⣾⣿⡿⠉⠀⠀⠀⠀⠀⣿⣇⡏⠹⣧⡀⠀⠀⠘⢧⡀⠀⢹⣿⣿⡀⢻⡟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢁⣾⣿⣷⠀⠀⠀⣼⣿⣿⠀⠀⡇⠀⠀⡄⠀⣼⣿⣇⠀⠘⣷⡄⠀⠀⠈⣷⣧⠐⢿⣿⣧⡀⡇⠘⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣠⡤⠀⠀ ⡇⢸⡏⢸⡟⢳⣤⣼⣻⡟⣯⠀⠀⣿⠀⠀⣷⣐⣿⡟⢻⣧⡀⢸⣿⡀⠀⢰⣿⣿⠀⠸⣿⣿⣿⣷⠖⠛⠛⠓⠒⠲⠥⢤⣤⣤⣤⣤⣤⣴⠺⡏⢛⡋⠁⠀⠀⠀⠀ ⡇⣿⠁⢸⣿⡀⢹⣏⣿⠀⣿⠀⠀⢻⣦⠀⠹⣿⣿⠀⠸⣿⣿⣦⣽⣧⢀⣼⣿⣿⡇⠀⣿⣟⠿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀ ⡿⡟⠀⣼⣿⡿⣾⣿⣯⠀⣿⣧⠀⢸⣿⣧⣰⢿⣿⣆⠀⣹⡏⢻⣾⣿⣿⣿⣿⣿⣿⢠⣿⡏⢀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⡇⢠⣿⣿⣿⣿⡿⣿⡀⣼⣿⣶⢸⣿⣿⠛⢿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣼⠀⠀⠀⠙⢿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢳⡌⢹⣿⣿⣿⣧⠉⣷⣿⣿⣿⣾⣿⡇⠀⢀⣸⣿⣿⡟⠁⣸⣿⣿⣿⣿⡿⣿⢻⣿⡟⢹⠛⡀⠀⣀⣠⣤⠿⠳⢬⣛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣼⣷⡿⢻⣿⣿⣿⡀⠻⣿⡟⠛⢻⣿⣯⣭⣉⠀⠘⣿⠇⠀⠁⠁⠀⣉⠽⠚⠁⣿⣿⣀⡟⠀⣹⣿⣿⠭⠀⢀⠒⠋⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⢻⡟⠀⣼⡋⣿⣿⣷⣧⣻⣇⣼⠿⣿⣿⣷⡏⠳⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣿⣿⠄⠀⣿⣽⡿⠷⠦⢬⣿⣦⣄⡀⠀⠀⠈⠳⡄⠉⠻⠷⣶⣤⣄⣀⡄⠀ ⡀⠈⠁⢾⣹⣇⣹⣿⣿⣿⣿⣿⡉⠳⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣄⢦⣿⠟⠀⠀⠀⠀⠈⠉⠙⠿⣤⣀⣀⣠⠤⠷⠶⠒⠚⠛⠛⢛⡅⠀ ⠀⠀⠀⢀⣿⠟⠉⠉⢙⣷⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠟⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢯⡄⠀⠀⠀⠀⠀⠀⠀⣼⠉⡆ ⠀⢀⣴⡿⠁⠀⢀⣴⠟⠉⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠚⠋⢠⡿⣽⠃⠀⠈⣿⡦⠷⠤⠤⣤⣤⣄⣠⠄⠀⠀⠈⠁⢻⡅⠀⠀⠀⠀⠀⢠⠇⢠⠃ ⠾⠿⢷⡀⣠⡴⠛⠀⠀⠀⠀⠹⡌⠻⣾⡟⡶⣤⣀⠀⠀⠘⠋⠉⠀⠀⢀⣴⠋⠀⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⠛⠋⢹⣿⣄⡀⠀⠀⠀⢻⡓⠲⢤⣤⣤⡾⠀⠘⠀ ⠀⠀⠈⠻⠿⣦⣀⡀⠀⠀⠀⠀⢻⡄⣿⠁⣽⠏⠉⠛⠲⠶⠶⠤⡤⠴⠛⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠁⣾⡁⠉⠙⠓⠂⠀⠈⣧⠀⢀⠈⢉⠇⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⠿⣽⣶⣶⣄⣈⣧⣿⣴⡏⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢻⣠⠏⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠙⣆⠙⢿⣿⣾⣿⠟⣀⣤⠴⠚⠛⠉⠁⠉⠙⠓⠒⠂⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡄⠀⠀⠀⠀⠀⢸⡏⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣧⠀⠀⠀⠀⠀⣾⠀⣠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣸⡟⣠⠟⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣿⠿⣶⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠀⠘⢿⣷⠟⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⡶⢦⣄⢀⣤⣿⠀⡄⣿⠀⠉⠉⠻⣏⣙⣛⣛⣿⡿⠷⣶⣦⣤⣀⣠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⢠⣿⠃⠀⣹⠀⠀⠀⠀⠀⠀ ⣤⠔⠛⠁⠀⠀⢀⣨⡿⣿⡏⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠈⢻⣦⢤⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠚⣿⠁⣠⡿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠤⠤⠤⠒⠒⠺⠿⣿⣗⢠⣾⣿⠛⢿⡇⠀⠀⠀⠀⠀⠀ ⡤⠶⠋⠁⠀⣰⢃⣴⡟⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⡀⣦⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⣸⡿⠋⠀⠀⠀⣼⠏⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡿⠀⠀⠀⠀⠀⠀⠀ ⣴⡿⠟⠉⠀⠀⠀⠀⣴⡏⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⣽⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣇⣤⣴⣶⣶⠶⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣠⣿⠃⠀⠀⠀⣤⡴⠖⠛⠁⠀⣀⣤⣶⡿⠟⠋⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠉⠀⠙⢷⣄⠀⠀⠀⠉⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⢀⣤⣴⠏⢀⣴⣿⠇⠀⠀⠐⠋⠁⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⠙⠛⠛⠲⠿⠟⣿⣿⣿⣿⣟⡭⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⣿⣿⠁⠀⠀⠀⢀⣠⡴⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠞⠋⣉⣰⣾⣿⠿⠿⠿⢿⠇⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡾⠃⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣿⣿⠟⠁⠀⠀⢀⡟⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⢦⣤⡴⠟⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣀⣀⣀⣐⣿⢀⣴⣿⣁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡟⣧⡈⠻⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠛⠿⢽⣿⣿⠿⠿⠟⠛⠋⠀⠀⠀⠈⠙⢶⣸⡇⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⠀⠀⠀⠈⠉⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠻⣆⠀⠀⠀⠀⡽⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠂⠀⠙⣷⠀⠀⠀⠀⠻⡄⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⠒⢒⡒⠢⠤⣀⠀⠀⢀⣊⡠⠤⢆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡲⠔⠉⠀⠀⠀⣬⠈⡆⠀⢀⠼⣾⠋⠁⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⢀⡴⡗⠉⠀⠀⠀⠀⠀⠀⡼⢄⣈⠖⡡⠊⠉⠉⢲⡄⠀⠀⢰⠁ ⠀⠀⠀⠀⠀⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡞⠁⠀⠐⢲⡞⠃⠀⢠⠏⠀ ⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⠀⠀⠀⢀⡤⠊⠀⡴⠁⠙⢢⣀⣀⣀⡗⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⠸⡀⢀⡠⠖⠁⢀⢤⡊⠀⣁⢀⠡⠀⠤⣯⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣆⢀⡠⠗⠃⢠⡒⠊⠱⠁⠀⠶⠄⠡⠀⠖⠀⠈⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡖⢋⠉⠁⠀⠀⠀⠈⢱⠀⢣⠀⠀⠀⠀⢠⣀⣀⠀⡠⡇⠀⠀⠀⠀⠀ ⣤⣄⠀⠀⣹⠋⠀⡠⠚⠐⣲⢲⣸⡇⠀⠑⠂⠀⠒⠡⠀⠠⠋⠀⠸⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⡇⠀⡖⡇⠀⠀⠻⠟⠻⠃⠀⠀⢾⣭⣥⣀⢭⣷⠀⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣾⣧⠑⠄⣀⡠⢄⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠠⢢⡇⠀⠀⠀⠀ ⣿⣿⣿⢻⣿⣿⣿⣿⣄⣀⣴⠶⡷⠖⠶⢢⡄⠀⠀⠀⠀⠀⠀⣠⣮⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣱⣶⣾⣭⢿⠠⠤⠤⣤⡶⠟⣽⣿⣯⣷⣦⣤⣤ ⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣶⠃⢹⡞⣾⡆⠀⢰⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⡿⠀⢸⡇⣿⡇⠉⣿⣿⠀⣿⢿⣿⣿⡟⢺⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⢺⢿⣿⡇⠀⣿⣿⠊⣿⡌⣿⣿⣧⡌⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣠⡤⠴⠶⠒⠒⠒⢒⣒⡶⠶⢾⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠏⢿⡙⢶⣄⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⢛⣁⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠈⠉⠓⠒⠾⠃⠀⠈⠻⣖⠒⠒ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠘⢷⡀ ⠀⣾⡿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢷ ⢸⡇⣉⠢⢄⡀⠀⠀⠲⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡀⠀⠀⠀⠀⣼ ⢸⡇⡿⠿⣶⣍⡑⠲⠤⠌⣑⣤⣉⠉⠀⠒⠒⠒⠒⠒⠒⠈⢻⣿⣧⠀⠀⠀⢀⣿ ⢸⡇⢠⠀⠀⢹⣿⣶⣄⡀⡄⡠⠀⣀⣠⣤⣤⣶⣶⣾⣿⣿⠘⣿⡏⠀⠀⠀⣼⠃ ⠀⢿⡀⠳⢄⡀⠙⠛⢋⠿⠇⠿⡛⠻⠿⠿⠟⠁⠀⢀⡜⠈⢠⠟⠁⢨⠆⣸⠏⠀ ⠀⠈⢷⡄⠀⠈⠉⠉⠀⠀⠀⠀⠙⠢⠤⠀⠠⠤⠒⠉⠀⠀⠀⢀⡤⢋⣴⠏⠀⠀ ⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠢⡀⠀⣨⣶⠟⠁⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⠉⡶⠒⠒⠲⡄⠀⠀⠀⠘⠁⠀⢀⣠⠖⢖⢿⡟⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠈⠳⠤⣤⠂⠀⠀⠰⢩⠉⠉⠉⠉⠉⠉⣰⠁⠀⠘⠈⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠇⢸⠀⣀⣴⣒⣀⣂⡇⠀⠀⠀⡇⠀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢘⣠⡟⠋⠀⠀⠀⠀⠐⠀⠀⠀⢀⡇⠀⠈⣷⡀⠀⠀⠀
⠀⠀⢷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠅⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠜⢸⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⡐⠀⡀⠀⠀⢀⠌⠀⡆⠀⠀⢀⠆⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠔⠁⠄⠠⠋⠀⢠⠀⠀⢄⠂⠀⠘⠀⠀⠀⠀⠀⠀ ⡀⡠⠀⠀⠀⠀⠀⡠⠁⡠⠊⢀⠊⠔⠁⠀⠀⠌⠀⡪⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠳⡤⠀⢰⠀⣤⣞⣵⣎⣠⣴⡁⠈⠀⠀⠀⠰⢐⠗⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⣂⠘⡀⠈⡰⠉⠍⢛⢻⣿⣿⡿⢷⣯⣴⣤⠗⠁⠀⠀⢀⡚⠀⠀⢀⡆⠀⠀⠀⠀ ⢢⡆⠀⢀⠃⡌⠀⠈⠺⡙⡯⠙⠓⣾⠋⢋⣠⣴⢋⣀⠜⡀⢀⢀⡞⡰⠀⠀⠀⠀ ⡇⠀⠀⡘⢠⠀⡀⠀⠀⣧⠇⠀⠀⠀⠀⠀⠀⠉⠋⠥⢎⣤⣧⣺⣵⣷⣦⣄⠀⠀ ⠶⡀⠀⡇⠞⠀⠁⠀⠀⠃⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣿⠋⠺⣆⡀ ⠻⢙⠀⠃⠀⠇⠀⠀⢰⢠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡾⠁⠈ ⣏⠙⣧⠢⠀⢰⠀⠀⢸⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠞⠀⠀⠀ ⠁⢂⠘⣧⢆⡈⡄⠀⡜⠀⣤⠇⠲⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀ ⠀⠘⣧⠸⡌⢷⡇⢀⠃⠀⡛⠀⠀⠑⢄⣀⡈⠕⠂⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀ ⠀⠀⢃⡄⡿⣄⡇⡀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⡠⠒⡆⠀⠀ ⠀⠀⠀⠸⡇⡟⣰⠁⠀⢀⣧⣀⠀⠀⠀⠀⢀⡀⠤⣲⡨⠧⢄⠴⠯⡴⠎⡀⠀⠀ ⠀⠀⠀⡠⡰⡰⢹⡘⠀⣌⣹⠇⢱⠢⣖⠼⠃⠀⡐⣵⠁⢀⠞⣀⠔⠃⠰⡅⠀⠀ ⠀⣴⣊⡠⠓⠣⡝⠓⠊⠁⠉⠉⠉⠈⠉⠐⠢⢔⢀⠃⠀⢸⠔⠁⠀⢀⢤⡇⠀⠀ ⠊⠀⠀⣆⠀⠀⡱⠐⠁⠀⠀⠀⢀⠠⠂⠀⠀⠀⠙⣄⠰⠀⠀⠀⡰⠁⡞⠀⠀⠀ ⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⣄⠀⢀⡬⠔⠊⠈⡡⠖⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡀⠔⠈⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⣠⣾⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⣗⡲⠶⠖⠋⣡⣯⡀⠀⠈⠉⠓⠒⠲⢶⣶⡖⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⡿⢯⠙⠛⠋⣹⡇⠙⠲⢤⣀⣀⡤⠖⢫⠏⠀⠀⠀⠀⠀ ⠈⠙⠓⠶⢤⣴⣋⢀⣰⠃⠈⣿⡛⠉⣽⠙⠲⢤⡤⠞⢻⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢯⡙⢳⡲⢴⣇⣙⣄⣇⡤⠚⠉⡇⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⣧⠀⣇⡼⢻⢿⡲⠤⣄⣧⠀⠸⡆⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⣠⣿⡊⠙⢦⡞⠀⠳⣴⠋⠉⢉⡷⠿⠤⣌⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢾⣋⠁⠀⠙⢦⢸⡟⠉⠉⠙⣆⢠⠏⣠⠖⠋⠉⠉⠉⠓⠲⠤⡄ ⠀⠀⣠⠖⠋⠁⠀⠈⠙⠦⡀⠈⣿⣠⠤⠴⠶⠾⢿⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡏⠀⠀⢀⣀⣀⣀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠚⠉⠉⠁⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠁⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢠⠇⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠛⠛⠓⠀⢀⡞⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⢤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢀⣠⣴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠾⠿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠂⠹⣄⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠔⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣴⣏⣳⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⣴⠛⠙⣦⣤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⠿⠟⠀⢀⣀⣠⢶⣶⣶⣋⣀⡀⢧⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢾⡖⠋⠓⡄⠀⠀⠈⢿⠉⢹⣿⣍⠀⠈⠙⠻⣾⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠈⢧⡀⢀⡝⠀⠀⠀⠀⠳⢿⣿⠛⠷⠀⠀⠀⠈⢧⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠈⠛⠤⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠉⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠔⠚⠉⠑⣶⠋⢛⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠐⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢰⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠢⡤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣽⣦⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⠛⠿⠿⠿⢿⢿⢿⢿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠳⣆⠀⠀⠀⠀⠀⢠⡤⣄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣼⠀⠀⠀⠀⢰⠃⠀⢸⡆⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠇⠀⠀⠀⠀⣿⠀⡀⣸⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⢁⣤⠤⠤⣄⠀⠘⠓⠚⠁⠀⢸⡇⠀⠀⠀⣠⣤⡀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⣼⠀⠀⢰⠚⣯⢼⣇⠀ ⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠉⠉⠋⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⣀⡀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢰⠛⣷⢄⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠙⠛⠚⠁ ⢸⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⢰⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⢹⡄⠀⠀⠀⠀⠀ ⠈⡇⠀⠸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠁⠀⠀⠀⠀⠀ ⠀⣧⠀⠀⠻⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣴⣇⠀⠀⠀⣠⣾⣇⣀⢀⣀⡴⠿⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠉⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣬⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣄⠀⠀⢶⣌⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⢶⣌⢿⣦⣄⢻⣷⣜⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠰⠶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡈⠹⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡿⠛⠛⠛⠛⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠙⢷⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢾⣿⣿⣧⡀⠀⠀⠀⡀⠀⠀⡀⠀⠰⣤⣀⠀⠀⠀⠉⠻⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣇⠀⠀⠀⠀⠀⠀ ⢀⠟⣼⣿⣿⣿⣷⣦⡀⠠⠀⠲⣄⠀⠲⣄⠀⢻⣷⣤⣦⣌⡷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡄⠀⠀⠀⠀⠀ ⡜⢠⣿⣿⣿⣏⣿⠘⣿⣆⠐⠀⢹⣷⡀⣟⠳⠄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠓⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣄⣯⠿⣆⠀⢸⡿⣿⣷⠐⣎⣷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢫⠀⡌⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⠹⠀⠘⣿⣾⣧⡼⢿⣿⣿⣿⣤⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣰⠋⣹⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⡄⡀⠀⠘⣿⡿⢺⡵⠿⣿⠟⢻⣿⠀⠻⣿⠻⡈⠛⠛⠛⠁⠇⡰⢃⣾⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⠻⣿⣿⣿⣿⣦⣄⠹⡇⠀⠁⠈⠁⠀⠀⢻⡄⠀⠹⡆⠀⠀⠀⠀⠀⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡻⡇⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⣾⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢱⣸⠉⠁⠹⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡿⠹⡏⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⡁⠀⠀⠃⠀⠈⠻⣿⣿⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⠀⢰⠃⠀⠀⠀⠀⣀⠠⠤⠙⠓⢲⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢖⠒⠂⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⡟⠀⢀⡤⠒⣉⣤⣴⣶⣾⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡅⠀⠀⠀⠀⣠⣴⣿⣿⡿⠁⠀⢀⣧⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⡠⠞⠉⠈⠻⣋⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣤⣤⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⣤⣤⣤⣴⣾⣿⣿⣿⣿⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠠⠾⢿⣿⣿⠟⠋⠁⠤⣬⣽⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⡄⠄⠄⢀⣽⣦⡎⠁⠒⠒⢻⣿⣿⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣧⡀⢀⣾⣿⣿⣧⣦⣴⣾⣿⣿⣿⣿⣧⠄⠄⣠⣴⣆⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⣿⣿⣿⣿⣧⢸⣿⣿⣿⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣝⣿⡟⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠸⣄⢺⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⢿⠄⡀⠄⣸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠸⡆⠄⣀⣛⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠇⠄⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠐⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠿⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢸⣿⣿⣿⡿⠟⠛⠉⠄⠄⠄⠄⠄⠄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡶⠶⠶⠶⠿⠿⠿⠿⠛⠛⠛⠻⠿⣿⣛⡛⠛⠛⠛⠛⠛⠛⠿⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⣋⣉⣉⣉⣉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣀⣈⡉⠒⠤⣀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠁⢀⡠⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⠒⠢⠤⠬⣉⠒⢤⡉⠲⢄⡀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠁⠀⠀⠀⢠⠚⠁⠀⠀⠀⠀⠸⡌⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⠳⣄⠉⠂⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡏⠀⠀⠀⠀⠁⠀⣀⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⣶⣶⣶⣶⣤⣄⠀⠁⠈⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀ ⠀⣴⡾⠋⣀⠤⠄⠤⠤⠰⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣾⠟⢁⣀⣤⣿⣿⣿⣿⣯⣽⣿⠄⠠⠤⠄⠀⠀⠤⢶⣶⣿⣷⣤⠀⠀ ⣾⠏⡴⢊⠤⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⠟⠋⠀⠀⠀⠈⠻⣿⠟⠋⠉⠀⠹⣦⣀⠀⠈⠁⠀⣁⣤⣶⡶⠶⠶⣶⣄⠀⠙⡝⣷⡄ ⣿⣾⠀⡇⠴⠟⠛⠛⢻⣶⣤⣴⡆⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠾⠛⠛⠉⠁⣰⡆⠀⠀⠻⣧⠀⢸⠈⣿ ⣿⣿⠀⢧⡀⠀⢀⣷⠀⠉⠉⠉⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠶⢶⣦⡰⢄⣀⣀⣀⠀⠀⠀⠀⣀⣤⣶⠿⠛⣿⣦⣤⡀⣿⠆⢸⠀⣸ ⠸⣿⡳⢤⣁⠀⣿⣿⣆⠀⠀⡠⠔⠛⠿⢿⣄⠀⠀⠀⠀⠴⠶⠶⣶⢀⣿⠇⠀⠀⢀⣀⣤⣴⣾⣿⠟⠉⠀⢀⣼⣿⠉⠉⢰⡿⠀⡌⢠⣿ ⠀⠹⣷⠀⠀⢸⣿⣿⢿⣷⣦⣀⡀⠀⠀⠀⠙⢿⡶⠗⠀⠀⠀⢀⣀⣨⣥⣴⣾⠿⠛⠋⠉⠀⣠⣿⣀⣤⣶⣿⡿⠃⠀⠀⠀⠴⠊⣠⡿⠃ ⠀⠀⣿⠀⠀⢸⣿⡇⢸⡏⠉⢻⡿⠿⠶⠶⣶⣶⠿⠶⠶⣿⠟⠛⠋⠉⠉⢹⣧⠀⣀⣤⣴⣾⣿⣿⠟⠉⣼⠟⠁⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⣿⠀⠀⢸⣿⣿⣿⣷⣤⣼⣧⣄⣀⣀⣼⣇⣀⣀⣀⣿⣄⣀⣀⣤⣤⣶⣿⣿⡿⠿⠛⠉⠸⣿⣠⡾⠋⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀ ⠀⠀⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢹⣇⠀⠀⠀⠀⣠⡿⠟⠁⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⢻⣿⣿⡝⣿⡟⠻⣿⡟⠛⠻⣿⠛⠋⠉⠉⣿⠁⠀⠀⠀⠀⠈⢿⣄⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠻⢿⣦⣼⣿⣀⣹⣷⡀⠀⣿⡆⠀⠀⠀⣿⣄⣀⣀⣠⣤⣶⠿⠟⠋⠁⣀⠤⠒⣀⠤⠒⣡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⡀⠀⢠⡀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⢀⡠⠤⠒⣉⡤⠐⢊⣡⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⢣⡀⠀⠙⠲⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠠⣤⣒⡋⠥⠄⠒⣉⣠⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡀⠀⠀⠈⠓⠤⣀⣀⣀⣀⣀⠀⠠⠤⠤⠤⠤⠔⠒⠒⠊⠉⠁⠀⢀⣠⣴⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⠾⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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