⠀⠀⠀⠀⠒⣒⣲⡦⣄⡀⠀⠀⠀⠀⣤⣄⣠⢴⣶⠿⢭⣿⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠀⠀ ⠀⠀⠀⠀⣀⣀⡀⠈⠑⣝⡆⠀⠀⣀⣸⣿⡜⠏⡀⠀⢰⢻⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠃⠀⣹⠀⠀⢸⠻⣾⠿⠓⠒⠺⢍⠀⡇⠀⠸⠒⠒⠫⣷⣤⣤⣶⣶⣶⣶⣦⣤⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠁⠀⠠⣏⡼⠁⢀⡖⢲⡀⠀⢳⡇⠀⢠⠤⣄⠀⠈⡿⣟⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⠉⠳⡄⠀⠘⡇⠀⠸⡟⠈⡇⠀⢨⡇⠀⢸⠀⢸⠀⠀⣿⡏⢳⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⡀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⡿⣿⣿⣿⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠤⠚⠁⠀⣰⢳⡀⠀⠳⠴⠃⢀⡼⡇⠀⠸⠤⠟⠀⣰⣷⠇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⢀⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠐⣿⡦⠤⠤⢴⣯⠰⣝⣲⡤⠤⢴⣺⢿⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣮⡉⠀⠉⠁⢀⡴⠋⢯⣉⠉⠉⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢠⣶⣶⠶⠚⠉⠉⠉⠉⠀⠀⠀⠉⠛⠷⣶⣶⣿⠀⠀⠀⠈⠉⠛⢋⣡⣤⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢀⣴⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠈⠛⠋⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⢿⠿⠋⠀⠀⠀⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣶⣄⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠻⣿⣿⣿⠀⠀⠀⢸⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⠿⠋⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠸⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢀⣾⣿⣦⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣸⣿⣏⠀⠀⠀⠀⣀⣴⣿⡿⠿⠛⠉⠉⠉⠉⠉⠙⠛⠿⣿⣷⣦⣀⠈⠛⢿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣠⣴⣾⣿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠃⠀⠀⠀⢀⣴⣿⠿⢿⣿⣦⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡀⣠⣼⡿⠿⠿⠿⠿⠿⠿⠿⠟⠻⣿⣷⣤⡀ ⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠉⠻⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠙⢿⣿ ⠸⣿⣷⣦⣄⣀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⢰⣶⣶⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠉⠁⠀⠀⠀⠀⢸ ⠀⠀⠉⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⠃⠀⠀⠀⣤⣤⡄⠀⠀⠀⢻⣿⡆⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⢀⣾⠟⠀⠀⠀⠀⢀⣠⣶⠿⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⣿⣿⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⣾⡏⠀⠀⠀⢀⣤⣿⣿⡁⠀⠀⠈⢻⣿⣿⣦⠀⠀⠀⠀⠈ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⡜⠛⠛⠀⠀⠀⠀⠛⠛⠃⢸⣿⠀⠀⢀⣴⡿⠛⢿⣿⣷⡄⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠃⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣴⡿⠋⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⢸⣿⡿⠁⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡹⣶⣤⣀⡀⠀⣰⡇⠀⢀⣀⣤⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⢸⡿⠁⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⢿⣿⣿⡝⠓⠛⣿⠿⢿⣿⠓⠛⢻⡿⠿⠛⠋⢿⣿⣿⢿⣿⡶⡟⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢸⣿⣿⣨⡇⠀⠹⣧⣼⠇⠀⢸⢉⡷⠞⠲⢶⡚⠋⠋⣷⠿⢿⠷⢺⣍⡷⠚⠳⣦⡶⠟⠿⢫⡿⠛⠉⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⡇⡇⢳⠀⢹⡏⣸⠀⢸⡞⠀⣞⢳⠀⢹⡄⠘⡿⢠⠟⡆⢸⡏⢀⣉⣀⣸⡄⠘⠦⣜⡏⢹⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⡷⠇⠸⣷⠀⣰⠿⠀⠸⢧⡀⠻⠼⢀⡾⢹⡄⢀⡞⣠⠇⠸⢧⠀⠓⠚⢸⠉⠶⠄⢸⡷⢸⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠶⠒⢻⡗⢯⠶⠒⠒⠮⢙⠶⠶⠟⢁⡟⠷⣾⠃⡷⢶⠒⠊⠱⣶⠶⠵⠖⣶⠶⠿⠧⢀⡏⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠛⠛⠓⠒⠒⠒⠋⠑⠒⠒⠉⢀⠀⠙⢚⠁⠘⠓⠒⠒⠋⠓⠒⢚⠙⠒⠒⠒⠋⠀⠀