⠀⠀⣠⣴⣾⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢂⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀
⢠⣾⡿⠛⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠑⠚⠃⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀
⣾⣿⠁⠀⠀⠀⠀⡐⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀
⡟⣿⡀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀
⠸⡜⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣄⣠⣾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠘⢆⠻⢿⡶⠤⢤⣤⠤⠤⠖⠁⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀
⠀⠀⠈⠳⣄⡙⠷⡢⢄⣀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣦⡈⠑⠦⣉⠙⠛⠋⠉⠁⠀⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠙⢲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠑⢍⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠑⢄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠡⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣶⣶⣾⠟⠁⠀⠀⠀⢀⣠⣤⠄⠀⠀⢡⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡠⠤⠀⠤⠄⡀⠀⠘⣧⠀⠀⠀⠀⢠⠇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠢⡀⠙⠳⠶⠶⠚⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⡰⣶⡄⠀⠌⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢣⠀⠀⠀⠀⠀⠐⠭⠐⠈⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⢟⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠑⠢⠤⢀⣀⡀⠤⠔⠂⢡⠞⣡⠏⡎⠰⣤⡄⠀⠀⠀⠀⠠⠔⠂⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣰⠃⢀⠀⠀⠉⠓⠂⠀⠀⠀⠱⠿⠇⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⡏⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣿⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⣿⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠐⠂⠠⠄⠐⠂⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⢀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀