⠐⠲⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀⠀
⠀⠀⠀⠈⠲⣧⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣷⣤⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⣽⣿⠿⢷⣄⣀⠀⢀⣸⣿⣿⣿⣿⣿⠿⢶⡦⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⢸⣿⢦⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠖⠂
⠀⠀⠀⠀⠀⠀⠠⠀⢀⣴⣶⣶⣦⣉⡀⠙⠿⣾⣿⣿⣿⣿⡏⠉⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠟⠛⢿⣿⣿⣦⣄⠀⠛⣹⣿⡿⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⣀⣴⡿⠿⠟⠁⠀⠀⠀⠙⣿⣿⣿⣿⣶⣿⣿⣧⠀⠀⠀⠀⠙⣷⡀
⠀⢀⣤⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⠿⠿⠃⠀⠀⠀⠀⠀⠜⠉⠲⠀

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾
⠀⠀⠀⠀⠀⡐⢕⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢳
⠀⠀⠀⠀⢰⢕⡇⠀⢀⡞⠙⢆⠀⠀⢀⣀⣀⣠⠶⠛⠉⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢸⢕⡇⠀⣸⠀⠀⠀⠉⠒⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢸⢕⠗⠉⠏⠀⢀⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠃
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠈⠁⠤⣆⠪⠸⠀⠒⠂⠜⠒⠀⠀⣠⠞⢷
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠚⠲⠶⡤⡤⠔⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⡾
⠀⠀⠀⠀⠀⠙⠛⠉⠑⠒⠢⠤⣾⡷⠓⢾⡷⠈⢾⣷⠒⠒⢾⣷⠊⠉⠉⠉⠉\