⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⣤⢠⡐⡖⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣠⣾⠀⠀⠀⠀⠀⠀⠀⡠⣄⢺⡏⣴⢺⢸⡇⡇⣧⠄⠀
⠀⠀⠀⠀⠀⢐⣴⠃⣸⣿⡇⠁⢀⠀⣀⢠⡆⣿⢱⡟⣾⢰⡇⣾⠸⢇⠁⡖⠀⠀
⠀⠀⠀⠀⠀⣾⣿⢀⣿⣿⠁⡢⢶⠀⡏⢸⡇⣿⢸⡇⡿⠜⡋⠀⣾⣿⠀⡇⠀⠀
⠀⠀⠀⠀⢰⣹⡇⣼⢸⣿⢸⡇⣿⢸⡇⣸⠀⠧⠘⡁⢰⣿⡇⢠⣿⣿⢀⢠⠀⠀
⠀⠀⠀⠀⡆⣿⣣⠇⣿⡇⣾⠡⡿⠼⠗⢋⣥⠾⣿⡟⢸⣿⠀⣼⢻⡇⢸⠀⠀⠀
⠀⠀⠀⢀⠃⣿⣿⠀⣿⡇⠿⢚⣁⡀⢠⣿⡇⠀⣿⡧⢸⣿⢀⡏⢸⡷⡇⠀⠀⠀
⠀⠀⠀⢸⠀⣿⡏⠀⣋⣥⠖⢻⣿⡇⣼⣿⠇⢸⣿⡇⣿⣿⢸⠃⣿⣿⠃⠀⠀⠀
⠀⠀⠀⡼⠀⠉⠀⠂⢹⣿⠀⢸⣿⡇⣿⣿⣀⡼⠟⠃⣿⣿⡏⠀⣿⠟⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⠀⣸⣿⠃⣿⣿⠉⢀⣰⢀⣿⣿⠁⠰⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⠀⣿⠿⠚⠁⠲⢸⠟⠁⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣴⣶⣦⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿⡇⠀⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⣹⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣀⣀⣠⣾⠋⠀⠾⣲⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠖⢻⡷⠊⣿⣡⡴⠒⢶⡎⠁⢀⠀⠻⠀⢠⡖⠋⠉⠓⠿⠋⠉⠳⡦
⠀⢀⡴⠁⠀⠀⢈⠀⢰⣿⡏⠀⡦⢠⡇⠐⠛⢀⡄⠀⣾⠁⣰⣶⠀⠀⠰⣶⡾⡁
⢀⣾⠄⠀⢀⣴⡟⠀⠀⠀⠀⠀⢤⡾⣇⠈⠻⠟⣁⠀⠻⠀⠙⠋⠀⠺⠆⠈⣷⠀
⠜⡏⠀⢀⣿⣿⡇⠀⢸⡄⠸⣦⣤⣴⠟⠷⠶⠞⠉⠳⠶⠛⠶⠞⠳⣤⣤⠾⠃⠀
⢸⡇⠀⠸⣿⣿⣧⠀⢸⣧⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢧⡀⠀⠉⠉⠁⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠶⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀