⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⡿⣏⢯⣽⣿⣿⣿⣿⣿⣿⣿⡿⣛⠿⣹⢻⣝⡻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣻⣙⢶⣹⢾⣚⢯⣛⠽⣻⣿⣿⡿⣿⣟⡿⣷⡿⣚⣽⣦⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⣻⣶⣿⣿⣞⢶⣽⣶⣿⣿⣷⣿⣿⣟⡷⣯⣿⣽⢿⣷⣿⣻⣿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⢂⠄⣹⣯⣻⢫⢟⣿⢿⣽⣿⣿⣿⣿⣿⣟⠿⣾⣯⣘⣹⣯⢿⣻⣿⢏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣱⣞⠷⣼⣿⣏⠟⠩⢘⣷⣿⠟⠋⠀⠀⠀⠀⠹⣿⣝⣾⣿⣟⣯⣻⣽⡙⢞⡼⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⡟⡮⣼⣿⡟⣞⡽⣻⣿⣹⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⢿⣿⣿⡿⢽⣿⡞⡵⢹⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢿⡟⣹⣞⣵⡿⣿⣭⠿⣽⣿⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣷⣿⣟⣳⢸⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⣿⡧⡟⣼⣿⣽⢧⡿⣿⣽⣿⣁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡯⣿⣿⣿⣿⣿⣏⢿⡼⠒⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⣿⢧⣹⣯⣷⡟⣿⣿⡟⣽⣭⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣶⣾⣽⡈⢿⣿⣿⣿⣇⠡⣿⣟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢲⡽⣾⣿⢳⣿⣿⢿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⢔⢿⣿⣿⣿⡿⠻⣻⢿⣿⣻⣾⡐⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⢱⣿⣿⣿⣿⣿⢻⣾⣿⣛⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢩⡉⣹⠟⢁⣿⣸⣿⣿⣻⠄⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢶⣿⣿⠸⣿⣾⣿⡏⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢸⣿⣿⡿⣾⢿⠸⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⢺⣽⡟⣸⣿⡿⢿⡇⣿⣇⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣭⡛⡿⡇⢜⡸⡾⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣽⣿⣻⣿⣣⣿⣽⣷⣾⣿⠈⠻⣆⣰⣶⠷⣲⣄⣶⡦⣦⡀⠀⠀⠀⠀⣼⣿⣿⠿⣿⣿⠁⢎⡼⣷⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⢏⢿⣿⣿⣯⣿⣛⣷⣦⠭⠥⢛⣶⣿⠏⠴⠖⠕⠁⠀⠀⢀⣴⣿⡿⣿⣿⣿⣱⢜⡠⣛⣿⢯⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⢻⣿⠁⣎⣿⣿⣯⢻⣯⣷⣽⣷⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⢿⣽⣿⣮⡿⡇⢨⠔⣏⣿⡞⣟⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡏⣽⡇⢎⢸⣿⣿⣛⢯⢻⣺⣿⣿⠀⠈⠓⠦⣤⠤⡤⠴⠛⠀⣾⣿⣿⣿⢿⡟⣿⢹⠀⡾⠰⣍⢿⡿⣿⡦⡳⣄⠀ ⠀⠀⠀⠀⣰⣿⠱⣟⢼⡈⢲⣿⢿⣻⢀⠐⢿⣿⣿⣁⣸⣆⠀⠀⠀⠀⢀⢠⡏⣽⣿⠏⢾⣿⣿⣟⠻⢀⡏⠜⣧⢻⣿⢳⣷⡟⢮⡣ ⠀⠀⢀⣴⢿⡟⣺⣳⣻⡅⢛⣾⢿⣻⣟⣶⣺⣭⣶⣀⠉⣳⣄⠀⠄⣼⢶⡿⠛⢉⣙⠳⣾⣿⣿⡇⠆⢹⡇⣘⣧⣛⣿⡄⢣⣿⡊⢻ ⢀⣴⣋⣵⣿⢱⣯⢿⣟⠳⣾⣯⡟⣯⣿⢻⡟⢛⡛⠾⡙⢙⣿⡄⢠⣇⠈⣿⠚⠋⣹⢷⣿⣿⣷⣺⢀⣹⣷⠞⣷⡇⣿⣧⣤⣿⣿⡀ ⢰⡟⠋⣻⡏⣵⡾⣯⡿⣆⠈⢻⣯⣿⣧⡟⢸⣡⡼⠞⠋⣡⣴⡟⣿⣤⡙⠓⢦⣴⡧⠚⣿⣿⣿⣆⣾⠛⠀⣼⢿⡘⢾⠿⠃⢀⢿⣿ ⠈⠀⢠⣿⡱⣻⡽⣾⣹⣿⠀⠀⣿⡿⠿⠛⠉⢁⣠⡴⢛⢉⣽⠁⣿⠈⣻⠶⣄⡀⠉⠙⠿⢿⣿⣿⠃⠀⣼⣛⢻⣮⡃⠀⢄⠂⢸⣿ ⠀⠀⣸⡟⣴⣿⢳⣯⣿⡿⠀⠀⠀⠀⠀⡤⣶⢯⠽⣦⣁⡿⠃⠀⠻⣤⢻⣀⣤⣿⣷⣦⣀⠀⠀⠉⠀⠀⢿⣼⡿⣼⣷⣌⣈⠐⢸⣿ ⠀⠐⠛⠓⠛⠛⠛⠛⠛⠓⠒⠒⠒⠚⠒⠀⠐⠒⠒⠒⠛⠀⠒⠀⠀⠀⠐⠓⠒⠒⠂⠀⠐⠐⠂⠀⠀⠀⠘⠛⠛⠛⠚⠛⠛⠒⠚⠉