⢠⠒⢀⢠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢷⢄⠘⡀⠃⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠈⡉⠉⠁⣢⡶⠦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠱⣴⠰⡀⠀⠀⠀⠀⠀⣼⠗⢁⠔⢲⣨⠑⠄⠑⣵⠀⠘⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢣⠑⠀⠀⠀⠀⡸⢯⣻⣧⠀⠈⣅⢄⡘⡖⠈⣧⠀⠰⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠱⠑⠀⠀⠰⢹⢀⠏⠚⠁⠀⠀⠛⠘⢠⢠⢿⡄⠄⢡⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢱⣶⣿⣧⡀⢎⣄⠀⢠⢄⠀⠀⠀⣸⣞⠚⢳⠀⠀⢧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢓⣪⡭⡤⣴⡾⠖⡅⠀⢸⠀⠀⠸⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠛⠻⢿⠧⣰⠟⣧⠞⡆⢨⢄⠀⠀⢸⠀⠀⠠⡘⡀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⢸⣌⡎⢰⣈⠶⢊⣾⣿⡇⠀⢸⠀⠀⠀⠁⢣⠀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣠⠈⣢⢀⡌⡅⡂⣸⣿⣿⣿⠀⣸⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢪⢿⣿⣿⣿⣎⣤⣼⣿⣿⣿⣧⠯⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠑⠯⣛⡟⠛⣻⠹⡻⢿⣻⢹⡇⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⡆⡄⠆⠀⠀⢰⢸⣿⣿⡿⣦⣿⣿⠀⠀⠋⣇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣅⠣⢇⠔⠃⢸⣿⣿⡇⣿⣿⣿⠀⠀⠀⠡⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠀⠀⠈⣿⣿⣧⣿⣿⡿⠀⠀⠀⠀⠁⠅⠀⢀⠜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠃⠿⠟⠁⠀⠀⠀⠀⠀⠸⠔⠋⠀⠀

⢠⠒⢀⢠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⢄⠘⡀⠃⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠈⡉⠉⠁⣢⡶⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠱⣴⠰⡀⠀⠀⠀⠀⠀⣼⠗⢁⠔⢲⣨⠑⠄⠑⣵⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢣⠑⠀⠀⠀⠀⡸⢯⣻⣧⠀⠈⣅⢄⡘⡖⠈⣧⠀⠰⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⠑⠀⠀⠰⢹⢀⠏⠚⠁⠀⠀⠛⠘⢠⢠⢿⡄⠄⢡⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⣶⣿⣧⡀⢎⣄⠀⢠⢄⠀⠀⠀⣸⣞⠚⢳⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢓⣪⡭⡤⣴⡾⠖⡅⠀⢸⠀⠀⠸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠛⠻⢿⠧⣰⠟⣧⠞⡆⢨⢄⠀⠀⢸⠀⠀⠠⡘⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⢸⣌⡎⢰⣈⠶⢊⣾⣿⡇⠀⢸⠀⠀⠀⠁⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣠⠈⣢⢀⡌⡅⡂⣸⣿⣿⣿⠀⣸⠀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢪⢿⣿⣿⣿⣎⣤⣼⣿⣿⣿⣧⠯⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠑⠯⣛⡟⠛⣻⠹⡻⢿⣻⢹⡇⠀⠀⠀⠀⠰⡄ ⠀⠀⠀⠀⠀⠀⠀⡆⡄⠆⠀⠀⢰⢸⣿⣿⡿⣦⣿⣿⠀⠀⠋⣇⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⢻⣅⠣⢇⠔⠃⢸⣿⣿⡇⣿⣿⣿⠀⠀⠀⠡⠂⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠀⠀⠈⣿⣿⣧⣿⣿⡿⠀⠀⠀⠀⠁⠅⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠃⠿⠟⠁⠀⠀⠀⠀⠀⠸⠔⠋⠀⠀