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⠀⠀⠀⠀⢀⣿⣄⣀⣀⣀⣀⣿⣟⠀⠀⣼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⣄⠘⢿⣀⣇⣦⣀⣸⣄⣠⣼⣯⣼⣧⣤⣧⣤⣼⣶⣼⣾⠾⢿⠿⠷⠿⠶⠶⢾⡷⠶⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠉⢻⣟⡀⢰⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣤⣻⡄⠀⠀⠈⢷⣹⣦⣈⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠊⠻⠿⠿⠿⠿⠷⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠙⠿⠻⠝⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣼⣿⣰⣤⣦⣀⣿⣿⣇⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢻⡿⣿⡇⢻⣦⣀⣀⣻⣿⣿⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢚⡛⠛⠿⣿⠼⠟⠉⠉⠉⠉⠙⠉⠉⣽⡇⣦⠀⡄⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠒⠾⣿⡿⡖⠒⠲⠶⠶⠷⡒⣷⢺⡇⢸⣷⠉⠉⠉⠀⠹⡆⠀⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⣧⢽⣇⣇⣘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⡀⣀⣤⡤⣤⣄⣿⣰⣇⣼⠹⠀⠀⠀⠀⠀⢿⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣷⠾⣿⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⣽⡏⠨⣿⡏⠈⢿⣷⣷⣹⡄⠀⠀⠀⠀⠀⠘⣇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡴⠖⠒⣲⠶⢾⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡌⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣤⣬⢥⣼⣵⣿⢸⣇⠀⠀⠀⠀⠀⠀⣸⠓⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⢸⡀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠋⠀⠀⠀⠀⠈⠙⣿⢸⡃⠀⠀⠀⠀⠀⣠⡟⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⠳⣼⣧⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⡞⠻⣿⣿⣷⣤⣤⣬⣟⣼⣟⣤⣬⣯⡴⠾⠛⢶⣶⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣦⣥⣶⡿⢿⣿⠿⠛⠀⠀⠀⠀⠁⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⣿⡿⠃⠀⠉⠛⠲⠶⡶⠶⣶⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⣧⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⡀⣀⠀⠀⠀⣿⠂⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⢀⣾⡇⡿⣄⡀⢸⡏⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟⢸⡆⡇⠈⣷⠘⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠇⢸⢠⡇⠀⠸⣶⣿⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⢸⡜⡇⠀⠀⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣻⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠚⠛⠛⠳⢦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢉⣀⡤⠤⠤⢤⣀⡀⠀⠀⠈⢿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⣴⠞⠓⠈⠁⠀⠀⠉⠒⠪⢵⣲⣤⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⠃⠀⠀⠀⠀⣠⠼⠛⠛⠀⠤⣜⠛⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠛⠀⠳⠤⠤⡤⠄⠋⣀⣠⠤⣤⣄⡀⠈⠑⠠⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⢁⣠⣤⣴⡦⡤⣤⣤⣀⠀⠀⠸⣿⣦⡀⠀⠘⢻⣦⡄⠀⠈⠙⢷⡄ ⠀⠀⠀⠀⡜⢁⣼⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⠛⢿⣦⡀⠈⢿⡛⡄⠀⠀⠨⣿ ⠀⠀⠀⢰⠃⣼⢇⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠈⣿⣧⠀⠈⢿⣄⠑⣤⣴⠟ ⠀⠀⠀⠘⡆⢿⠈⡆⢿⣅⣄⠀⠀⠀⠀⠀⠀⡀⣤⠀⢹⠀⢹⣿⡆⠀⠀⠀⠉⠉⠀⠀ ⠀⠀⠀⠀⢰⡸⡇⠈⠒⠭⠭⠃⡠⠀⢪⡙⠟⠟⣣⠞⡼⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣧⡀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⢀⡼⠁⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣌⠛⠶⠠⣀⣀⣀⣀⣀⣠⠴⠴⢋⢀⣌⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⣹⡷⠶⡤⠤⣀⣄⣀⣤⡤⠶⠿⢻⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣶⠿⠋⠀⣶⡀⠀⠀⠀⠀⢠⠂⠀⢰⠈⣿⣿⣷⣶⡤⢄⡀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⡿⠁⢀⣴⣾⣿⣃⠀⠀⠀⡠⠃⠀⢠⠏⠀⢘⣿⡟⠋⠀⠀⠨⠓⢦⡄⠀⠀ ⢠⡞⢻⡧⠱⠤⠾⠏⠋⠛⠳⢶⡖⠉⣀⣤⠾⠁⠀⠀⡴⠋⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀ ⠿⠤⢺⣇⠀⠀⠀⠀⠀⠀⠀⠫⡤⠾⠛⠉⠙⠓⢶⣿⣇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠙⠛⢢⣤⣾⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠷⢦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠘⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢲⣤⣤⡄⠀⠀⠀⠀⠀⡇⢠⠀⠀⢰⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠤⣼⣿⢶⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀

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