⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⠤⠤⢠⠤⠒⠒⠒⠤⣀⡠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡔⣠⠯⠔⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢺⡟⠁⠀⠀⡈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠃⠀⠀⢀⣀⣧⣷⣷⡤⣤⡀⠐⡄⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣯⣤⡶⠞⠉⠉⠁⠘⠇⠀⠀⠙⢷⠈⠄⡄⠀⠀⠀⠀⠀⠀⠀⡰⠊⠳⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡞⣽⡿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣧⠀⢠⠀⠀⠀⢀⡀⠀⢜⢠⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀
⣸⢧⡟⣇⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⡄⡎⣆⠀⡶⢁⡔⠀⡟⢸⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⠀⣽⡟⠒⢦⠀⠀⢀⣀⣀⣀⣡⣤⠀⠀⠈⣿⡟⠻⣿⡇⡿⡇⢠⣧⢸⠀⡘⠀⠀⠀⠲⡀⠀⠀⠀
⣿⢀⣿⣧⣼⣿⣿⡄⠻⣿⣿⣿⣿⡿⡟⠛⠲⡿⡇⠀⠙⣿⣧⣷⡮⡽⠸⠠⠁⠀⠀⠀⠀⠱⠀⠀⠀
⣿⢸⣿⣯⣿⣿⣿⠀⠀⠀⠙⠛⠛⠋⠉⠀⣸⣷⠃⠀⠀⠹⡟⡐⠋⠑⡄⡅⢌⡀⠀⢀⠊⢀⡇⠀⠀
⢸⡌⣿⣿⠛⠋⣹⠀⠀⠀⠀⠀⠀⡄⠀⠀⢹⡗⠀⣀⢤⣾⣿⢣⠀⠁⣸⣃⣵⠇⠠⠉⣠⡾⠁⠀⠀
⠀⣣⣿⣿⣆⠀⡼⠀⠀⠀⢀⣁⠂⢥⠀⠀⣼⠻⣄⡰⠛⠢⡾⢷⡽⠿⠟⠀⠀⣀⡤⡲⠋⠀⠀⠀⠀
⠀⣷⠞⣿⣿⠀⢸⣶⣶⣿⣋⣡⣤⠜⣤⣤⣿⠀⣻⠟⡀⠀⠐⠃⠀⢠⣴⡶⢚⡏⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣸⣿⣿⣤⣿⣿⣿⣵⡶⢶⢛⣻⠟⠁⠹⣠⡟⣤⣷⣩⣤⡴⠟⡿⡋⠙⣆⢬⠕⢠⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⣿⣿⣿⡿⠷⠯⠔⣊⠁⠀⢀⣚⣿⡰⢺⡀⠉⠥⠒⠈⠉⠉⠉⠁⠑⢾⡙⢆⠀⠀⠀⠀
⠀⠀⢿⣿⣿⠋⢹⣿⡿⠿⠛⠋⠁⢀⣴⣞⣿⣿⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡤⠈⠂⠀
⠀⠀⠀⠈⠁⠀⠀⢻⣷⣠⣣⡄⣾⣿⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⠛⠓⠐⠒⠀⠠⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠛⣿⠇⠈⠁⠂⠀⡀