⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣴⣦⣶⣤⣤⣤⣤⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣻⣿⣭⠽⠻⠿⠽⣿⣭⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠶⠒⠛⠛⠛⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⣤⣤⣀⣀⣤⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣶⣄⣀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠿⠿⢿⡟⠉⠹⡆⠀⠀⠀⠀⢠⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣼⠿⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢦⠀⠀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⣄⠚⢠⡆⢀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠲⠄⢹⡴⢻⡀⡞⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⢹⣿⢸⡏⢹⣿⡛⢷⣴⣦⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⢀⣀⣀⡀⠀⠀⣰⣶⣾⡿⣿⣿⣾⣿⣿⣧⣿⡟⣷⣠⡌⠻⠷⣿⣿⡷⠾⠷⠶⣶⣤⣶⡇⠀⠀⠀⠀⣸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⡿⢋⣷⣤⣴⣿⣿⣿⠃⠀⣾⣿⡏⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣷⣶⣾⣿⣿⡇⠀⠀⠀⠌⣹⣿⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣵⣿⣿⣧⣿⣿⣿⣿⣤⣼⣿⣿⠗⢿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣵⣿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⠈⡿⣿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⡀⢸⣿⡀⠀⠀⠀⣾⡇⡄⠀⠀⠀⠀⠐⡏⠀⠈⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⢹⣿⣿⣿⣿⡛⠛⣛⣨⣟⣒⡦⠈⠉⠉⠉⠉⠁⠴⣖⣦⣼⣿⣿⣧⣭⣀⣿⡇⠀⢠⠇⢸⡟⡇⠀⠀⠀⢿⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣷⠛⣿⣷⣿⡟⢻⠋⣿⣿⣧⠀⠀⠀⠀⠀⠀⠛⢹⣇⣽⣿⡏⠙⣿⣿⡇⢰⣿⠀⢸⣧⣷⠀⠀⠀⠈⣦⣇⠀⢠⡀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣧⢻⣿⣧⠙⠘⣿⡿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣻⠇⠘⢩⣿⣀⣾⡿⠀⣼⣿⣿⡆⠀⠀⠀⠘⣿⠀⠀⠱⣄⠹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣮⣿⣿⡇⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⣠⣿⣽⠋⣧⠀⠀⠀⠀⠘⡆⠀⠀⠈⢳⣳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣸⣿⣿⡏⠀⢹⡆⠀⠀⠀⠀⠹⣆⠀⠀⠀⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠟⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⣿⣷⣿⣷⣿⣿⣿⣧⠀⠈⣷⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣼⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⠶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⢀⣠⡴⠖⠋⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣶⣶⠚⠉⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⡄⠈⣿⣿⣿⣿⠿⠛⠀⠀⠤⠤⠔⠚⠉⣼⡿⢫⣼⣿⢿⡟⠛⠻⠿⣦⣀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⡟⠛⢿⣿⣴⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⣾⠁⠀⠀⠀⠀⠙⢷⡿⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣶⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣸⠏⠀⠀⢸⣿⢿⣿⠱⠦⣄⣀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣾⣿⡿⢠⡟⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡏⠀⠀⠀⢸⣿⣾⡏⠀⠀⠀⠉⠙⠂⠀⠠⠖⠋⠁⠀⢠⣿⡟⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠇⠀⠀⢰⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⡟⠀⢠⠄⠀⠀⠀⠀⠀⠀⣿⡀⠀⢳⡄⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⠀⠀⠀⢘⣯⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⡇⠀⣸⠇⢠⡞⠀⠀⠀⠀⠀⠀⠀⣿⣷⡤⠒⠛⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⢸⠀⠀⠀⣼⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⠀⢀⡟⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣿⢻⣼⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⢿⠿⠟⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⣿⡄⠀⢸⣿⣟⣴⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣸⣿⢿⠀⣸⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠘⣟⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⡼⣹⡁⢠⣯⡟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣿⢀⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⢻⣾⡆⠀⠀⠀⠀⠀⠀