⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣭⣿⣿⣆⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⣾⠟⢙⣿⠿⠛⠉⠉⠉⠀⠀⠀⠈⠉⠉⠙⠓⠲⢦⣄⡀⢀⣴⣖⣞⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⣿⣎⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⣥⣿⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢦⡀⠹⡷⣌⣿⣎⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⣥⣼⣻⡿⠃⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠙⣄⢼⠋⡙⣿⣯⢿⣦⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⠀⡞⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠘⣎⣷⡱⡘⢿⣧⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⠃⠀⣴⠏⣷⠀⠀⠀⠀⢸⣧⡀⠀⢀⠀⠘⣆⠀⠀⠀⠀⠀⠸⣼⣷⣧⠈⣿⣷⣿⡧⠀⠀ ⠀⠀⠀⠀⣸⣯⡆⠀⠀⠀⣿⠀⡼⠣⠤⢽⡄⡆⠀⠀⢸⠋⣷⡄⠸⣷⣄⠻⡆⠀⠀⠀⠀⠀⢿⣇⠿⣴⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⣿⣿⠇⠀⠀⢀⣿⣼⣁⣀⠀⠀⢷⣹⡀⠀⢸⠀⠘⠻⣟⣿⠛⣦⣹⡀⠀⠀⠀⠀⢸⣿⣾⣿⣿⢻⡆⠀⠀⠀ ⠀⠀⠀⢸⠇⢸⢰⠀⠀⢸⣿⠟⣿⣿⣿⣦⡺⣷⣧⠀⢸⡄⢀⡀⢈⣻⣆⣈⢿⡇⠀⠀⢠⠀⠈⣿⣿⢿⠁⠀⣇⠀⠀⠀ ⠀⠀⠀⣼⠀⢸⠸⡇⠀⣾⡿⠰⡟⢻⣿⣍⡷⠈⢿⣧⡘⡇⢩⣾⣿⣿⣿⡿⣷⣇⠀⠀⢸⡄⠀⣿⡇⠘⡄⠀⢻⠀⠀⠀ ⠀⠀⠀⡏⠀⣿⣰⣷⠀⢹⡟⠀⠻⣅⣈⡿⠁⠀⠀⠙⢷⣿⠈⣏⡹⢿⣤⡇⢸⡿⠀⠀⣸⣇⠀⢻⣷⠀⡇⠀⢸⡆⠀⠀ ⠀⠀⢸⠇⠀⡟⢱⡟⣇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠹⢤⣠⠟⠁⢉⡇⠀⢠⣿⣿⠳⢾⣾⠀⢇⠀⠘⡇⠀⠀ ⠀⠀⣼⠀⢰⠃⢸⠁⠘⣦⣿⣿⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣠⣿⣹⠇⠀⠀⢸⡀⢸⠀⠀⣧⠀⠀ ⠀⢀⡇⢰⠸⠀⣼⠀⠀⠈⠳⠙⣿⣯⣷⡶⢤⣄⣉⣛⣉⣀⣀⣀⣀⣤⠴⢚⣏⡴⠛⠛⠃⠀⠀⠀⢸⡇⢸⠀⠀⢻⠀⠀ ⠀⢸⠃⢸⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⠛⢣⣾⣷⣨⡿⣏⣩⡿⠛⢦⠀⠠⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡀⠀ ⠀⡿⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⢸⢶⣏⣉⣧⡰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⡇⠀ ⢰⡇⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⣸⠀⡇⠰⠘⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⡇⠀ ⢸⠁⠀⠘⡇⠀⡇⠀⠀⠀⢀⣴⣿⣿⣿⣟⣧⠀⣯⡄⡇⢰⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣿⠀ ⣾⡆⠀⠀⢻⠀⡇⠀⠀⠀⡼⢿⣿⣿⣿⠞⡜⢰⡏⢁⡇⠸⡄⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⢸⠀ ⢻⢳⠀⠀⠘⣇⣧⠀⠀⠀⠓⠒⠛⢉⣾⣦⡀⣰⣿⣿⣆⢀⣵⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⡀⠀⠸⡇ ⢸⡌⢇⠀⠀⢹⣿⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡼⠀⠀⠀⠀⠀⠀⢸⡟⠀⢰⡇⠀⠀⡇ ⠀⢻⡈⣧⡀⠀⢿⡆⠀⠀⠀⠀⠀⠈⠙⠻⡭⣭⣿⣟⣿⣯⠭⠽⢷⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⢏⡇⠀⢰⠇ ⠀⠀⠹⣾⣿⡢⣄⢳⡄⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⡏⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⠎⣼⠀⢠⡟⠀ ⠀⠀⠀⠈⠙⠿⣾⣥⣙⣆⠀⠀⠀⠀⠀⠀⢻⣿⣹⣻⡇⣷⣿⠶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⡴⠃⣰⢇⣴⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⣾⣿⣿⠃⢹⣽⣸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣽⡥⠴⠾⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀