⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣾⣿⣿⣿⣿⣳⣶⣶⡦⣤⣤⣤⣳⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢹⣿⠿⠛⠛⠘⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠈⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⢀⡆⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⣿⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠃⣰⡟⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡄⣿⢞⣆⡄⠀⢀⡀⠀⠀⢀⠀⠀⠱⣷⢳⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣤⣿⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣸⢣⠇⢸⢻⡇⠀⣸⠃⠀⠀⢸⡜⣦⡄⠙⣟⢇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⠁⣿⠏⠀⣰⠃⠀⠀⠀⠀⠀⣠⠇⢠⣏⡾⠀⠈⣯⡇⢀⡇⠀⠀⢸⢸⡇⠈⣞⣄⠘⣟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢸⡇⠀⢰⠇⠀⠀⠀⢀⣴⡿⠋⢀⣾⣾⣧⣽⡿⣿⡇⣼⠀⠀⠀⣼⣼⠀⠀⠘⣿⡄⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢸⡇⢀⠇⠀⣀⢴⣾⣿⠟⠁⢀⣾⣿⣿⣷⢾⣧⣼⢷⠃⠀⠀⣠⣯⠏⢀⣀⠀⢻⣷⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⡷⠾⣿⢿⣚⠯⠋⠁⠀⣠⡿⢿⣟⣿⡿⠀⠙⣿⡏⠀⠀⢰⣿⣿⣿⣿⣤⣄⡬⣿⡆⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢐⣛⣿⡅⢀⠜⣷⡤⠤⣤⡶⠟⠉⠀⠈⠓⠒⠠⠒⢰⡿⢀⠀⣰⣿⡿⢿⣿⣿⣿⠙⢿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢽⠟⡇⢼⡦⠘⢳⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⢡⠇⣰⣿⠛⢧⠈⠛⠛⣃⣠⠂⣾⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠿⣄⢤⡀⢰⡄⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣣⣏⣼⠟⠁⠀⠈⠑⠎⠉⠉⠀⢀⣿⡁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⢹⣧⡉⠛⠃⠸⠘⢦⡀⠀⠀⠀⠀⠀⠀⣸⣻⡿⠋⠀⠀⠀⢀⣶⠞⠁⠀⠀⠀⢸⢻⠁⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠙⠦⠤⣿⡶⡄⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡿⡸⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⡌⡇⠹⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣠⢤⣤⡤⠀⠀⠀⣼⣿⡇⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⣿⠀⠀⠀⡇⢹⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⡾⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣹⣿⣼⠀⢠⡇⡘⡆⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢹⣿⢟⡏⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⡄⢸⣇⣿⣷⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡶⣿⡗⣿⡇⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣿⣿⣯⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣄⣠⣴⣟⣯⣿⢧⢻⡦⣿⣧⣾⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣯⣿⡇⢸⣿⢻⣹⣇⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣹⡿⣿⣾⣾⠭⣿⡿⣿⣯⠭⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⢨⣿⡏⣿⡇⢸⡿⠸⣧⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠻⣿⣿⠉⣹⣧⣿⢿⣅⠈⣱⡄⠀⠀⠀⠀⠀ ⠀⠐⣿⡆⢚⣱⠸⣿⠀⢻⣽⣄⣀⣠⠤⠼⠶⠶⠶⠶⢶⡀⣼⠋⠁⠀⠀⠀⠹⣿⣀⣀⣿⣿⣼⡒⠐⣒⢛⣆⠀⠀⠀⠀ ⠀⠀⠉⣽⣦⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢿⣃⣷⡀⠀⠀⠀⠀⠘⢷⣤⢾⣿⣿⡄⢀⠀⠀⠘⢦⡀⠀⠀ ⠠⣴⣿⣿⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣿⣿⣿⣷⡀⠀⠀⠀⣀⡾⠉⢻⣧⣿⡧⠤⠤⠤⠤⠬⡷⣦⡀