⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠟⠛⠛⠙⠛⠛⠛⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠶⠶⠶⠶⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⢠⣿⡆⠀⠀⠀ ⢀⣤⡀⠀⢀⣀⣠⣶⣶⡶⠟⠛⠉⠀⠀⠀⠀⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢠⣿⣿⡇⠀⠀⠀ ⣿⣿⡇⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⠃⠀⠹⣿⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀ ⠟⠁⠀⠀⣸⠏⠛⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠱⣄⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⣀⣿⣤⡀⠀⠀⢀⣤⠤⣴⣧⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⠃⠀⠀⠿⠦⣤⣤⣹⡆⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⢻⣦⡄⠀ ⡶⠶⠟⠛⠉⢿⡀⠠⣄⢠⣾⣁⠀⠉⠻⡄⠀⠈⣿⢻⣄⠀⠀⠀⠀⠀⠈⠙⣦⡀⢺⣿⣦⣴⡗⠀⡰⠀⠀⠀⠀⠀⠹⡏⠀⣶⣼⣿⡇⠀ ⣤⣤⣤⠶⠀⢸⠃⠀⣹⡟⠉⠛⢿⣄⠀⢻⡄⠀⢹⣇⠙⣷⣄⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿⣿⡃⢀⡇⠀⠀⢰⣶⣦⣤⣿⡄⠙⢿⣿⡇⠀ ⠀⢸⡟⠀⠀⡾⠀⠹⣿⠀⠀⠀⠀⠹⣦⠀⠹⣆⠈⣿⣿⣾⣿⠿⣦⡀⠀⠀⠀⠀⠈⠻⣏⡀⢳⣼⠁⠀⠀⠀⢻⣿⣻⣿⠿⡄⠈⠹⣷⡀ ⠀⢸⣧⠀⢸⡇⠀⢰⡇⠀⠀⣠⣴⣤⣬⣧⠀⠙⢧⡸⣿⠛⠁⠀⠀⠙⠳⣦⣄⡀⠀⠀⠈⠙⢲⡟⠀⠀⠀⡄⠀⠹⠟⠉⢆⣀⣤⡄⠈⠻ ⠀⠀⢿⣆⣾⠀⠀⢸⠃⠀⢰⣿⡟⣏⣟⣿⡆⠀⠈⠻⣿⣄⠀⢀⣾⣿⣿⣶⣬⡙⠳⠶⣦⣤⣼⠁⠀⠀⢰⡇⠀⠀⢀⠀⢺⣿⣿⡇⠀⠀ ⠀⠀⠈⣿⡏⠀⠀⣸⡄⠀⢿⣿⢀⠈⠀⠈⣷⠀⠀⠘⡇⠉⠀⣿⡟⠣⠧⠙⢻⣷⠀⠀⠘⣿⡏⠀⠀⠀⣸⣷⠴⠞⢻⣧⠀⠈⠛⠢⢄⠀ ⠀⠀⠀⣹⡇⠀⠀⣿⣷⠀⠘⢿⣯⣦⢤⣼⣿⠀⠀⠀⡇⠀⠀⢿⣟⢆⠀⢀⣼⣿⠁⠀⠀⣿⠁⠀⠀⠀⣾⣠⠾⢻⡇⣿⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⣿⠁⠀⠀⣿⣿⢿⠦⣌⣻⣿⡿⠿⠿⠀⠀⠀⢹⡀⠀⠈⢿⣿⣷⣾⣿⠟⠀⠀⢠⡏⠀⠀⠀⢠⣿⣿⡄⢻⢁⡿⠀⠀⢀⠀⠀⠀ ⠀⠀⣠⡿⠀⠀⢠⣿⡷⣡⢞⣝⡽⣿⡄⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠈⠉⠉⠁⠀⠀⣀⣾⠁⠀⠀⠀⣸⣷⠟⡁⢆⣼⠇⠀⠀⠀⠉⠓⢶ ⣠⡾⠋⠀⠀⠀⠀⣿⣿⡵⠹⢪⠞⠹⣧⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⣤⣴⣾⣿⡟⠀⠀⠀⠀⣿⢁⣢⣼⠟⠉⠢⡀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠜⡱⢻⢟⢾⣿⠇⠀⠀⠀⢸⣟⣿⣻⡅⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⢞⡵⡱⠫⣿⠟⠀⠀⠀⠀⣾⡿⢚⡵⣿⠀⠀⠀⠀⠈⣇⠀⠀⡀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣈⣠⣤⣾⡟⠀⠀⠀⠀⠘⣿⢖⣫⣞⡟⠀⠀⠀⠀⠀⢸⠀⢰⣿ ⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣣⢞⡽⣿⣿⣯⣤⣄⣀⣤⣴⣶⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⣯⣟⣽⠇⠀⠀⠀⠀⠀⢰⠆⣾⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⡥⣯⢾⢟⡵⣫⢾⣿⣿⣿⣟⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⣼⣾⠏⣾ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⣼⡿⠃⠈⠛