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

⠀⠀⠀⢰⣤⡀⠀
⠀⠀⠀⠈⣿⣿⣦
⠀⠀⠀⣀⡘⣿⣿⣷⡰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠁
⠀⠀⢻⣿⣿⣌⢿⣿⣷⣭⣤⣤⣤⣤⣄⣀⠀⠀⠀⣠⣶⣿⣿⡿⠃
⠀⠀⢸⣿⣿⣿⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠟⠉
⠀⠀⣸⠛⠉⢀⣿⣿⠋⣭⢿⣿⣿⣿⡿⠻⣿⣿⡿⠋
⢰⣿⣿⣶⡆⠻⠿⣿⣦⣤⣾⡿⣿⣧⠛⢀⣿⣿⡇
⠀⠻⣿⣿⣿⠀⢀⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⡇⣠⣤⣤⣤
⠀⠀⠈⠻⣿⣦⡻⣿⣿⣿⡇⠀⣰⣿⣿⣿⡏⠀⢀⣿⣿⣿⠟
⠀⠀⠀⠀⣿⣿⣿⣮⣛⠿⠷⣾⣿⣿⡿⠿⣣⣴⡿⠟⠋⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⡟
⠀⠀⠀⢼⡿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠺⠷

⠀⠀⠀⣠⣴⠶⠷⠶⣦⡀⠀⠀⠀⣀⣴⠶⠿⣶⣦⣀
⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠙⣦⢀⡼⠋⠀⣀⠀⠀⠙⠻⣦
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⢀⣿⣿⣇⠀⠀⢀⠙⠆
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢸⣿⣿⡿⢠⣾⣿⣷
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠸⣿⣿⠃⣿⣿⣿⡟
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟ ⠀⠿⠿⠟⣀⣀
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠙⣋⣤⣶⣾⣷⣦⠀⣠⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡈⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠛⣛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠉⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠳⣤⡀
⠀⠀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⡀⠀⠈⢻⣦
⠀⢸⠀⠀⠉⠉⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⢸⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⣴⠖⠄⡀⠀⠀⠀⠀⣿
⠀⠀⠀⢶⠀⠀⠀ ⠀⠀⠀⠰⠀⢰⠖⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠘⠀⠾⠛⠓⡄⢀⡀⠉⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠱⡁⣀⠟⠁⠛⣣⡤⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠉⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⡩⠗⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠟
⠀⠲⣤⡀⠀⢸⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠈⠻⣿⡎⠀⠀⡼⠀⢸⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠒⠤⢧⣀⡸⠤⠤⠃

⠀⠀⠀⠀⠀⣤⣶⣦⡀
⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣿⠿⡁
⠀⠀⡠⠛⠛⠉⠁⠀⢸⡀
⢀⠊⢀⠞⣆⢳⠀⠀⠈⡇
⠈⢄⠀⠀⠀⢳⣧⠀⠀⢷
⠀⠀⢂⣠⣀⣀⣡⣄⠀⠈⢦⡀⠀⠀⠀⣠⠞⠋⠛⢦
⠀⠀⡜⠈⢿⠋⠀⠈⡄⠀⠀⠉⢣⢌⡾⠁⠀⠀⠀⠠⡇
⠀⠀⠡⠀⠘⠀⠀⠀⠸⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⣦⣄⡐⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⣿⣿⣿⠘⢦⣤⣼⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⣿⣿⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⢠⠃
⠀⠀⣼⣿⡟⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢜
⠀⠀⢻⣿⠃⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠘⢄⠀⠀⡠
⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣼⣿⡄⠀⠀⠀⣾⣿⡀
⠀⠀⠸⠙⠿⠦⠀⠀⠇⠻⠷⠄⠀⠀