⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⠿⠻⠀⠀⠀⠀⠋⠟⠿⠶⠻⠓⠛⠉⠀⠁⠁⠁⠉⠈⠀⠀⠉⠛⠿⠷⠾⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣔⣠⢧⠀⠋⡶⣲⣖⣽⣷⡿⢿⡿⠾⣳⣶⠶⠾⣶⣶⠸⠀⣹⢿⡿⣦⣶⣭⣢⣶⢷⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡐⠀⠀⡞⢃⢰⠀⠛⠈⡀⢸⠀⡇⠀⡇⠸⣀⠃⢸⡀⢀⣿⠀⣿⣴⢀⠁⠈⠀⢣⠀⡆⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣼⣋⢠⠀⠀⠃⢰⡇⢶⠒⠉⣀⣄⢸⠀⠘⠀⡄⢠⠀⡇⣾⠀⠀⣿⠸⣇⠻⠙⡉⣉⣀⣆⠈⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣶⣀⣀⠀⠀⠀⠁⡴⠁⡌⠙⠈⡀⢁⠋⢠⠀⢸⠀⠇⠸⠀⡄⢤⠀⠀⣤⣧⠙⢷⠘⡀⣀⠀⠋⢹⠉⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡿⣠⠀⠀⠀⠁⠈⠔⢩⠞⣶⢳⡛⣽⣶⣿⣿⣿⢿⢻⠛⡟⢿⠿⠿⠛⠛⠻⠿⡛⣿⣿⣿⢿⠿⣿⣿⣿⣿⠳⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢠⠀⠀⠀⣿⣺⡠⣀⣀⠀⠼⠤⠤⣓⣮⣼⣂⣒⣖⣖⣭⣷⣯⣷⣭⣭⣭⣧⣽⣚⣒⣒⣒⣱⣼⣚⢴⠤⠤⣤⡿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⣄⡵⢸⠀⠀⠀⡇⣿⢸⠀⠀⠀⠁⣿⣧⠀⠀⠀⠀⡄⣟⢸⠀⠀⠀⠀⡄⣿⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠦⠓⠙⠉⠉⠚⠴⣀⠁⠟⠾⠘⠀⠀⡇⢸⠀⠀⠀⡏⣿⣿⠀⠀⠀⡇⣎⣸⠀⠀⠁⠀⠀⣇⠈⠀⠀⠈⠀⠀⡆⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢀⠀⠀⠃⣹⣿⣻⢰⠀⠀⠃⢸⠀⠀⠀⣶⣤⣤⠀⠀⠀⡇⠹⢸⠀⠀⡇⠸⠀⠀⠀⠀⠇⢿⠀⠀⠀⣇⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⡆⡟⣿⣴⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⡟⣯⠈⠀⠀⠀⡇⣙⢸⠀⠀⠀⣷⠹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⠀⠀⠀⠀⣿⣿⢿⠀⠀⠀⡄⣸⠀⠀⠀⡿⣹⢹⠀⠀⠀⡇⣯⡏⠈⠀⠀⠀⣷⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠳⠙⠈⠀⠀⠁⠋⠿⣿⣷⠀⠀⠀⠀⣿⣿⣸⠀⠀⠀⠆⢠⠀⠀⠀⣿⣿⡮⠀⠀⠀⡄⣿⢿⢛⠛⠟⠶⡶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⠿⣿⣿⣿⣿⠙⠉⠛⠉⠙⣏⣴⠲⠶⠴⠧⠿⠿⠿⠷⠾⠿⣻⣿⣿⣿⡿⣿⣿⣿⣿⢻⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠠⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠋⠿⣿⣶⣷⢿⣿⣿⣿⢿⡿⣿⢿⣿⣿⢾⣛⣟⣿⣻⣍⣧⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⣾⣧⣿⣿⣿⣾⣷⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣹⠀⠀⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠹⠀⡆⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠀⡿⣽⣷⣿⣿⣿⣿⣿⣿⡟⣟⣻⣻⣿⣛⣿⣿⣿⣿⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠘⠀⣿⣳⡿⣿⣿⣿⣿⣿⣿⣶⣠⡏⢉⡞⢁⣠⣤⣷⣶⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣽⡏⣿⣾⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠀⣤⡿⣿⣿⢼⠢⢻⠀⠀⠁⠟⣴⣥⢾⡿⠓⠒⡀⢰⡀⣀⣤⣷⣿⣴⣿⢿⡻⣿⢹⣿⣸⠀⠀⠀⠀ ⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⡟⣹⣭⣼⣣⣶⠁⠿⣺⠀⠃⣸⠀⡄⣿⢰⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⠀⠀⡇⣧⣿⠈⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⠻⣛⣭⣴⣤⣶⡿⣼⣲⠔⠤⣆⠀⠀⠀⢠⠀⠀⠀⠁⠛⣟⣷⣷⣿⣽⣿⠙⠀⡀⡦⣟⢰⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣻⠝⠙⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⣿⣶⣶⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣼⡁⢯⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠂⠄⠀⢁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠠⢀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀