⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⢲⡖⠛⠒⠒⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠁⠀⠀⣀⢾⡷⣄⡀⠀⠀⠀⣸⠳⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠎⡸⣗⠒⠚⠉⠁⢸⡇⠀⠉⠉⠉⢩⡿⣄⠘⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣧⠞⠁⠸⡄⠀⠀⠀⣸⣇⠀⠀⠀⠀⡞⠀⠈⣱⣾⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⡿⢿⣷⣷⣤⠶⠚⢹⡏⠑⠲⣦⣾⣷⡿⠿⢿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠻⣷⣄⣸⣇⣠⣾⠟⠋⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠹⣿⣼⣧⣿⠋⠀⠀⠀⠀⢀⣿⣷⡇⠀⠀⠀⠀
⠀⠀⡶⣶⢦⡸⣿⣿⣄⠀⠀⠀⣀⣽⡏⣿⣧⡀⠀⠀⠀⣀⣾⡟⡞⣠⣶⢲⠀⠀
⢼⡙⢿⣌⠿⠓⠷⣽⠿⣿⣿⠿⠟⢻⠧⢾⡟⠿⠿⠿⣿⠟⢙⡾⠽⡷⣇⡞⣩⠇
⠀⠙⢦⣇⣀⠀⠀⠈⠳⢌⡙⢦⢀⣞⣀⣀⣣⡀⡠⠊⢁⡴⠋⠀⠀⢀⡸⣞⠁⠀
⠀⠀⣏⣰⠋⠉⠙⠲⢦⣀⡉⠑⠻⣯⠤⠤⣬⡽⠖⢊⢁⣠⠴⠚⠉⠉⢳⣸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⣿⣯⡶⠳⣿⢟⡇⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣾⣯⣀⣀⢿⡻⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣜⣇⡸⣷⠉⠉⣏⡇⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠶⢤⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢸⠉⠓⢶⣄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⢀⣾⠀⢠⠏⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠶⣯⡞⠀⢸⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠘⣷⣄⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣍⣉⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀