Celestia from MLP Emojis & Text

Copy & Paste Celestia from MLP Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠙⠢⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣴⠟⢠⣻⠀⢀⡤⠂⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠳⣿⡆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣾⠏⠀⣼⣇⡔⠋⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⢗⠀⠀⠀⠻⣧⠀⠘⢦⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⠤⣄⣲⡾⠊⢣⠤⢥⣤⣼⢾⠇⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⠛⣿⣦⠀⠀⠈⠃⠀⢻⢻⠈⢦⠀⠀⢀⣔⠟⠀⢫⢡⡏⣾⢂⣎⢸⡎⢣⢔⣃⢀⠝⢿⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⡀⠈⠛⢵⡄⠀⠀⠀⠀⠻⠀⠈⣆⣾⡝⢡⠀⠀⣸⠎⠀⠎⢸⣿⢲⡗⠯⢠⠞⠉⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⣄⠀⠀⠈⠀⠀⠀⣠⣀⠀⠀⡝⡱⡀⢸⣠⠞⡁⠀⠀⢀⣠⢽⠙⣒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⠉⠻⣷⡄⠀⠀⠀⠀⢻⠀⠳⣼⠸⡀⢓⣯⣼⡔⠒⢢⠉⠉⠈⠑⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠈⠙⠢⠀⠘⣏⠑⢧⠀⡞⠀⠉⠉⡏⡿⢷⣤⣀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣌⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠘⢆⠀⠀⢣⠀⠀⡴⠀⢷⣠⣿⡿⡇⠀⠉⠒⠢⣤⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠑⠟⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣲⠶⠶⠯⣍⠓⢤⠀⠻⣅⠃⠀⠸⡀⠀⠳⠷⠈⠻⢞⣸⠋⠀⠀⠀⣴⡏⡇⠀⠀⠀⠀⠀⠀⠙⡈⠉⠒⠤⡀⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠕⠊⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠈⠓⣄⠀⠳⡀⠀⡜⢄⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⢄⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⡔⠁⠈⠋⠀⡠⠚⠉⠀⠀⠈⠑⢞⠢⠀⠻⣄⠀⠀⠑⣄⢸⠀⠈⠓⢢⡀⡀⠀⠀⠟⡆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡎⠀⠃⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡞⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⣈⡳⣄⠀⠀⡑⠀⠀⠈⠻⡆⠀⠀⠀⠙⠓⠄⠒⠊⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡴⠁⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠘⢆⠑⠖⠕⠀⠀⠀⡞⣇⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡦⠊⠀⠀⠀⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠘⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣨⡞⠉⠦⡀⠀⢠⠁⠸⠀⠀⠀⠀⠀⢸⢡⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡤⠊⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢳⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢰⡟⢲⢴⠧⣠⠀⢸⠄⠀⢣⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢀⡆⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⡏⣿⣧⣰⡵⠆⠘⠀⢀⠀⠱⡄⠀⠀⡸⠀⢁⠀⠀⠀⢸⠀⡠⠋⠀⠀⠀⢀⣴⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠛⠉⠃⠀⠀⢷⠈⠂⠀⠈⠢⣠⠃⠀⡎⠀⠀⠀⠀⠟⠁⠀⠀⠀⡰⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⣀⡴⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠈⢧⡀⠀⠐⢀⣯⠠⣱⠃⠀⠐⠒⢢⠀⠀⠀⠀⣴⠁⢀⡜⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠁⠀⠞⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡿⣟⠢⣠⠀⠀⡱⡄⠀⢿⣿⢳⠃⠀⠀⠀⠀⢘⡆⠀⠀⠀⠘⣄⠉⠁⢙⡀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⢠⠖⠋⠀⢀⡾⢡⠟⠀⠸⠀⠀⠱⠌⠷⡄⡱⣏⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠟⠻⢦⣄⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠏⠀⢀⡴⠋⠀⠀⡷⠀⠀⠀⠀⢠⡆⠀⣸⠃⠀⠀⢹⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠙⢷⡄ ⠀⠀⠀⠀⠈⠻⣦⣀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠏⠀⠀⡾⠁⠀⠀⣴⢷⡀⡆⠀⠀⠀⣇⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠁⢢⠀⠀⠀⠀⢀⠆⠀⢰⠏⠀⠀⠀⠁⠀⣠⡾⠋⠘⡃⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⡎⠀⠀⠀⣴⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⠀⠀⠀⢀⠎⠀⢰⠏⠀⠀⠀⠀⠀⣰⢿⠖⡉⠙⠳⡆⠀⠀⠀⢿⠀⠀⠀⡀⣸⠁⠀⢀⠎⢸⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁ ⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⡠⠋⠀⠀⢀⠎⠀⢠⠏⠀⢀⡀⠀⠀⠀⢿⡈⠉⢹⡆⢸⠀⠀⠀⠀⡇⠀⠀⡜⢡⡏⠀⣔⠚⠀⠸⠀⠀⡠⠊⠀⠀⠀⣀⣤⡴⠶⠚⠋⠉⠀⠀⠀ ⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⢸⠀⢠⡟⠀⡠⠊⡇⢀⠇⠀⠈⠛⠛⠛⠀⡇⠀⠀⠀⠀⡇⡀⠈⠀⡾⣄⠀⡗⠁⠀⡆⢀⠞⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⢆⣾⠒⠺⠀⠀⠡⣼⠄⠀⠀⠀⠀⠀⠂⡏⠀⠀⠀⠀⣸⡰⡄⠀⠐⣄⠙⠚⠂⢠⡳⠃⠀⠀⣴⠏⠀⠀⠀⣠⣄⠶⠶⣤⡄⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠋⠀⠀⣠⣶⣿⠯⣭⣉⠛⡗⣟⡇⠇⠀⠀⢶⡺⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⢹⠱⣇⠀⠀⠈⠓⢤⣠⡾⠁⠀⠀⠀⣿⡀⠀⠀⣮⠭⢦⡄⠀⠀⢻⡄⠀⠀ ⢾⠁⠀⠀⠀⠀⠀⢢⡀⠀⢿⡥⣤⡿⠀⢹⡆⢣⠘⠃⠀⠀⠀⠔⣧⡤⠤⢤⣤⡴⠟⡏⠉⣤⠀⢰⠚⠃⠀⡹⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠷⣤⣀⣀⣠⣾⠃⠀⠀⣸⠇⠀⠀ ⠸⣧⡀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠀⢀⣼⠃⠘⢆⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⡇⣟⠀⠘⡡⠷⠀⢓⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣴⠏⠀⠀⠀ ⠀⠈⠛⠶⣦⣤⠀⣀⣀⡀⠀⣠⣴⠶⠛⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠒⠤⠬⠀⠀⠘⠋⡷⢦⣄⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢀⣀⠀⢀⣠⠃⠀⠉⠉⠛⠦⠶⢟⠶⠤⠤⠤⣖⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀

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