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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀  ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀  ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀  ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀  ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀  ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀  ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀  ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀  ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀  ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀  ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠉⠉⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀    ⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣠⣶⠛⠛⠛⠛⠛⠛⠳⣦⡀⠀⠘⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢹⣿⣦⣀⣀⣀⣀⣀⣠⣼⡇⠀⠀⠸⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⣿ ⠀⠀           ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀                  ⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀  ⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣠⡶⠶⠿⠿⠿⠿⢷⣦⠀⠀⠀⠀⠀    ⣿⠀ ⠀⠀⣀⣀⣀⠀⣸⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀ ⣠⡿⠛⠛⠛⠛⠻⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀ ⠀⣿⠀ ⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⢀⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀  ⠀⣿⠀ ⠈⠙⢷⣶⣦⣤⣤⣤⣴⣶⣾⠿⠛⠁⢀⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀                                ⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠃⠀ ⠀                        ⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣾⣿⡿⠿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣰⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⣴⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣼⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀ ⠀⠀⢰⣿⣿⡿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠁⠀⠀ ⠀⠀⣿⣿⣿⠁⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⢰⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣷⣦⠀⠀⠀ ⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠉⠉⠻⣿⣿⡇⠀⠀ ⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⣿⣿⣇⣀⠀⣠⣾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠒⠲⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀ ⣶⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠉⠉⠉⠓⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠘⢷⣶⡾⠿⠭⣙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⡆⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⠀⠀⠀⠀⢀⠞⠁⠈⠑⠢⠤⣀⣀⡀⠀⠀⠀⠀⣀⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢳⠀⠀⠀⢠⣯⢴⣶⣖⣺⣿⢲⣦⡬⣍⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣈⢧⡀⠀⠸⣷⣾⣡⣿⣇⣼⣏⣨⡷⢛⣯⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⣓⠂⣼⡿⢷⣾⣉⣀⣉⠉⠳⠟⣿⠴⡿⢻⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣷⣶⠤⣄⠀⠉⠙⣲⢄⠀⠀⠻⣿⣿⣿⡜⣷⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠀⠀⠉⠲⣤⣼⣾⣷⡄⠀⠈⠁⢈⣇⣁⠀⠀⠀⠀⠀⠀⣰⠋⠈⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠻⣿⡿⣆⢀⣄⢀⣼⠿⣟⠛⠛⡄⠀⠀⣸⡏⣹⠀⠀⠀⠀⢀⡴⠁⠀⣰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣦⡙⠒⠻⣄⡽⡏⣻⡟⢻⣿⢻⣤⠻⣿⣾⣿⣿⢁⣿⡆⠀⠀⣠⡞⠁⢀⣾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠿⠶⣾⣤⣿⣧⣟⣎⣉⣉⢙⣶⣿⣿⡿⠹⣾⣿⣿⡆⠀⢻⠀⢠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠛⠛⠃⢰⠋⠀⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⡀⠀⠀⠀⣀⡼⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣽⡗⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠯⠭⣉⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠉⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⡇⡘⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⠀⠀⣈⠆⢹⣦⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠋⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⢠⣿⣢⣌⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠏⠉⡉⠁⠀⣸⢹⠇⠀⠀⠀⠀ ⠀⢠⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡇⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠤⠒⡎⢀⣠⠴⠯⣞⡀⠀⠀⠀⠀ ⠀⡾⠁⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⣠⠞⠁⡎⣰⣇⠀⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠛⠛⠓⠒⠦⣄⠙⠳⣄⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⠿⠋⠀⢠⠀⡿⠛⣛⣿⠿⣿⡖⠒⠒⠲⠦⠤⣀⡀⠀⠀⠙⢷⣤⣀⣀⣀⣤⣤⣤⣤⣀⠑⠀⠘⢦⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡜⠙⠾⡋⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠉⠒⠶⣦⣿⣿⣾⠛⠀⠀⠀⠀⠹⣟⡆⠀⠘⣧ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡶⢦⣴⠿⠆⠶⣿⡛⢿⡖⠦⣤⣀⡀⠀⠀⠀⠀⠈⠉⠛⠧⠄⣀⣀⠀⣀⣼⡟⠁⠀⠀⣿ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠟⠦⡀⠙⠳⠤⣀⠈⠛⠾⣷⡀⢧⡜⠛⢷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣿ ⠀⠀⠀⢹⣷⣦⣀⠀⠀⠀⠀⠀⠀⢠⠃⣼⣷⣶⡿⣶⠀⠀⢀⣷⡀⠀⠘⣿⣿⣧⠀⠈⠾⣏⠛⠻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿ ⠀⠀⠀⢸⣿⠀⠉⠛⠶⢤⣄⣀⢀⡇⣼⣋⠭⣿⢃⠙⡟⢉⣿⠀⢳⡀⢰⣿⠉⢿⠇⠀⣰⠙⣆⠀⠘⣮⠉⠛⠻⠶⢶⣶⣶⣾⠿⠟⠋⠀ ⠀⠀⠀⠀⠻⣦⣄⠀⠀⣀⢀⠝⢙⣧⣌⡉⠛⠛⠿⠴⠿⠿⠷⠆⣀⣷⣼⣇⣆⡈⣧⣴⣿⣃⣘⣆⠀⢸⠀⣠⠖⠊⠉⢱⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⠷⠋⢠⠞⣿⠁⠙⢦⡼⠛⠉⠑⠒⣶⢰⡖⠲⠴⠠⠔⠫⢭⡄⠀⣠⣠⡌⣷⢸⡀⡏⠀⠀⠀⠻⠼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣮⡥⠔⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠁⠀⠀⠀⠀⠀⠀⢳⢀⡇⠀⠻⣿⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢻⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⠦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣀⣠⣼⠇⠀⠘⣧⣄⣀⣀⣀⣠⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡷⠶⠒⠒⠒⠶⢶⣄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⠛⠛⢻⡆⠀⠀⠀⠀⠀ ⠀⢹⡷⠶⣤⣤⣤⣤⣤⡾⠃⠀⠀⠀⠀⢻⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡴⠟⠀⠀⠀⠀⢀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣤⠶⢾⡿ ⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀ ⠀⠀⠀⠈⠛⠶⠶⠶⣤⣀⠀⠀⠀⠀⢠⡶⠞⠛⠒⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣀⣤⣤⣤⣤⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⣸⠏⠉⠁⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡶⢶⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠁⠀⢸⡇⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⢹⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⣠⡤⠶⠶⠶⠤⣄⣀⠀⣀⣽⣄⡀⠀⠀⠀⠀⠀ ⠈⣿⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⢾⣩⡵⠖⠚⠛⠓⠲⢦⣍⠻⣧⡀⠀⠙⢶⡤⠤⣄⠀ ⠀⠈⠻⠶⢾⡇⠀⠀⠀⠀⢠⣤⣄⣀⣀⡤⠄⠀⣿⠀⠀⢠⡿⠿⢷⠶⠛⠋⢻⡀⠀⠀⠈⠳⡌⢷⡀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⡏⠀⠀⢹⣄⣠⠟⠀⠉⢳⡟⠀⠀⠀⠀⣠⠇⢸⠇⢀⣴⣀⣠⠾⠁ ⠀⠀⠀⠀⠀⢿⣄⡀⠀⣀⣼⠇⠀⠘⠷⣤⣤⣼⣃⡴⠖⠛⠉⠙⢧⣄⣀⣴⠧⠤⠴⠶⠛⣁⣴⣿⠶⢋⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠾⣅⣀⣀⣀⣀⣀⣠⣦⠈⠉⠛⠓⠒⠛⢛⣉⣥⠴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠳⠶⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣰⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⣴⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣼⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀ ⠀⠀⢰⣿⣿⡿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠁⠀⠀ ⠀⠀⣿⣿⣿⠁⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⢰⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣷⣦⠀⠀⠀ ⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠉⠉⠻⣿⣿⡇⠀⠀ ⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⣿⣿⣇⣀⠀⣠⣾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠋⠉⠉⠁⠀⠀ඞඞ ඞ ඞ
⠛⠋⠁⢀⣿⣶⣽⣿⣿⣿⣿⣿⣷⣴⣶⣾⣋⣯⣥⣬⣭⣿⡓⠶⢤⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀ ⠄⠒⠉⠀⠈⠙⠛⠛⠻⣿⣿⠟⡟⠙⢻⣷⣦⡀⠀⠀⠈⠹⣷⠀⠀⠈⢩⣳⣦⣤⣤⣭⣵⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⡿⠃⢸⠀⠀⠘⣿⣿⣷⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠉⠓⠲⢤⡀⢀⡀⠈⠭⠟⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⡼⠁⠀⠘⣆⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠿⠿⠿⣷⣍⠳⢤⡀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠋⠀⢸⠃⠀⠀⠀⠈⠳⢄⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡀⠀⠀⠀⠀⢀⣤⡶⠾⢿⣿⣿⣿⣶⣦⣤⣀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⢈⡟⠀⠀⠀⠀⠉⢧⠀⣦⣀⠀⠀⢀⠞⢁⡜⠁⠀⠀⣠⡼⠛⢇⠀⠀⠀⠛⠿⢿⡿⠿⠛⠛⢷⣦⡀⢸⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⢿⠀⠈⠉⠒⠛⠊⠁⠀⠀⢀⡾⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀ ⣀⣿⠀⠀⠀⠀⣾⣄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠤⠖⠚⠉⠀⢀⣾⡿⣿⣿⣶⣶⣤⣤⣤⣤⣤⡀ ⠉⣿⠀⠀⠀⢸⣿⣿⠗⢤⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣹⠃⣸⠛⢿⣯⣭⣉⠛⠛⠛⠃ ⢀⣿⠀⠀⠀⣿⣿⡃⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⠏⢀⡟⠀⠀⠙⠻⣿⣿⣶⡆⠀ ⠋⢻⠀⠀⠀⣿⣿⣿⣷⣤⣀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠈⠑⠲⠤⣀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⢠⡟⠀⣸⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠉⠑⠒⠤⠤⣤⣄⣀⣉⣭⡿⠟⠉⠀⠀⠀⠀⣠⠏⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⢹⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣦⣤⣤⠞⠁⠀⠀⠀⠀⣠⡶⠋⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⠀⠈⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⠋⠁⠀⠀⣀⣠⡴⠞⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣁⣀⣤⠴⠖⠛⠉⠁⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢠⣾ ⠀⠀⠀⠀⠹⣆⠀⠀⠙⠲⢤⣀⣀⣀⣀⠤⠞⠛⠿⣭⣍⠡⠤⠤⠤⠤⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⠀⠀⠀⠀⣰⠟⣿ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠂⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣿ ⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣩⣿⣿⣿⠛⠛⠉⠉⣁⣀⣀⣀⣤⡤⠤⠶⠚⠋⠁⠀⠀⢠⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠺⣿⠛⠋⠉⠉⠉⠈⣧⣾⣿⣿⡇⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣀⣤⣴⣿⣿⣿⣿⣿⡷⠚⠶⢤⡀⠉⠛⠶⢤⣤⣄⣀⣀⠀⠀⠀⠀⠘⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣦⣀⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠞⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣴⠞⠁⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⢠⠏⠀⠀⠠⢯⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⢀⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣼⠁⣷⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⣸⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⡏⠀⠀⢠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⡇⠀⠀⠀⢹⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁ ⢹⡀⠀⠀⢸⣿⣷⣶⣤⣀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀ ⠀⢧⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀ ⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠒⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣼⢿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡝⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠈⣿⣿⣮⣛⢿⣿⡿⠿⠿⢿⣿⣿⣿⢿⣿⣿⣿⢧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣹⣧⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡟⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡟⠁⠀⠀⠀⣤⣴⣶⣶⢸⣶⣶⣄⣘⣿⢳⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠇⠀⣠⣶⡾⢿⣿⣿⣿⠀⢺⣿⣿⡿⣿⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠙⠁⠀⠘⣿⣿⣦⣈⣼⣿⡿⠀⠀⠹⣤⣥⣿⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⣿⣿⣿⡿⠟⠁⠈⣲⠃⠘⢻⣿⠷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢰⣦⡈⠋⠁⠀⠀⠐⠊⠀⠈⠂⢀⠁⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠒⠓⠀⠀⠀⠀⠀⠀⠀⠶⠋⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿
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