⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡴⠞⠉⠁⠉⠙⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⡞⠋⠑⠀⠀⣀⣠⡴⠚⠻⠿⢛⣹⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣯⠉⠓⠦⣴⣞⣻⣧⣶⣿⡶⠾⠋⠁⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣏⠀⠠⠀⣿⣿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠓⠦⣤⣿⣿⣿⣿⣀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠿⣿⡉⠘⠶⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⣤⣬⣽⣷⣦⣄⡀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⣀⣤⠶⠛⣉⡈⢉⣡⠾⠛⠓⠦⣄⡀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⣷⠦⣄⡀⠀⠠⣄⡈⠙⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣀⣤⣿⠀ ⠀⠀⠀⠀⢰⠛⢻⣿⣿⡇⠀⢹⣿⣿⣿⡀⠈⠙⠳⢦⣄⡀⠀⣿⣿⣿⣿⠷⢤⣀⠀⣀⣤⠶⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⢸⣤⡀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠒⠦⣀⠀⠈⠉⠳⠿⣿⣿⣿⠄⠀⡈⢻⣉⣤⣾⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⢸⡏⡟⠀⠀⣀⡀⠀⠻⢥⣀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠈⠙⠻⣧⣄⡉⣿⣿⣿⡿⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⡇⠀⠀⠀⠈⠛⠢⣤⡀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⣸⣿⣿⡟⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠉⠁⠘⠛⠛⠃⠀⠘⠛⠛⠿⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠓⠦⣄⣀⣤⠶⠿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣀⠸⠘⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⣠⣾⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⣅⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣿⣷⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠳⢤⣈⠁⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣈⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣉⠛⠲⢤⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣈⠛⠶⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀