Sex Dot Art

Copy & Paste Sex Dot Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⠃⠈⢻⣿⣦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠘⣿⣿⣿⡏⣴⣿⣷⣝⢿⣷⢀⠀⢀⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⢿⣿⣿⡇⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⡟⠙⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⡇⠀⠀⠀⠉⠛⣽⣿⣇⣀⣀⣀⠀ ⠙⠻⠿⠿⠿⠿⠿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣤⣤⡸⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣴⣿⣿⣿⣿⣷⠈⠙⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⢿⣿⣿⡿⢿⣿⣇⠀⠀⠀⠀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣿⣿⣿⣞⣋⣁⣀⣿⣿⣿⣦⡀⠀⣾⣿⣿⣿⡆ ⠀⣀⣀⣀⣀⣀⣀⣴⣾⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⡏ ⠐⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠛⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠤⠒⠒⠒⠙⠒⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⢹⡄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⠿⠀⠀⠀⠈⠷⠤⣄⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡇⠀⠀⠀⣠⠊⢠⡀⠉⠲⡄⠀⠀⠀⠀⠀⠀ ⠘⢯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣒⣦⣄⠀⠈⢦⡀⠀⠀⠀⠀⣇⢰⠇⠀⠀⡜⠁⣴⣿⣿⣶⡄⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⣿⣿⣿⣿⣦⡀⠳⡀⠀⠀⠀⣿⡟⠀⠀⠀⠸⡀⠙⢻⣿⡿⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡷⠖⠀⠀⠀⠀⠀⢚⠻⣿⣿⡿⣿⠏⠘⢷⣶⣷⡄⠀⢸⡟⠁⠀⠀⠀⠀⠱⡀⠈⠛⠀⠀⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠙⣏⢀⣤⣾⡴⢻⠂⠀⠀⠀⠈⠉⠒⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣻⡉⠉⣽⠃⠀⠀⠀⠲⠀⣀⣠⡄⠀⠤⠤⠄⠈⣡⣾⠟⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠹⣤⡧⠤⠶⢾⣍⣉⠍⠀⣰⠧⣤⣤⡤⣶⠿⢋⣡⣄⡞⢁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⠑⢢⣤⡤⠤⣖⣠⡜⠁⠀⢻⣧⣍⣉⣉⣭⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠉⠉⠁⠺⢿⣿⣁⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠟⠉⠉⠁⠒⣒⠤⢄⣀⠀⠀⠀⠀⠀⣠⣴⡶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⡀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠑⠢⢄⠀⠀⠋⣹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣆⠀⠙⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣧⡀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠤⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠶⠼⢿⣷⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⡇⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⣤⣀⣀⣀⣀⣀⣀⣤⣾⣿⠛⣧⡉⠓⢶⣤⣤⢤⡴⣶⡎⠁⠀⢴⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⢦⡈⠙⠛⢻⠉⠀⣼⠟⠀⡇⠈⠓⠤⣀⠀⠀⢣⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠉⠉⢁⣧⠀⠀⠀⠀⠀⠙⢦⡀⠸⠀⣸⣇⠈⠀⡇⠀⠀⠀⠈⠑⠦⣈⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠞⠁⠘⡆⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠈⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀
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pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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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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