⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄
⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘
⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊
⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢢⠀⠀⠀⠀⠀
⠀⠀⠀⡄⢄⢀⠔⠐⠂⢦⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠑⠢⡏⠀⠠⠀⠠⢴⠀⢰⠤⡐⡤
⠀⠀⠀⠀⠀⣈⠤⠀⠀⡞⠀⠀⠀⠀⠀⠀
⠀⠒⡔⠁⠈⠁⠀⠀⠈⠗⡀⠀⠀⠀⠀⠀
⠀⠀⡨⠀⠜⠤⠀⠀⠌⠑⠝⠀⠀⠀⠀⠀
⡀⣀⢣⣊⡔⣁⢜⣜⡠⠤⣄⡠⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀
⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀
⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀
⡞⠀⠀⠹⣆⢰⣒⠆⠀⠀⠓⠊⠙⠚⠁⠀⠸⠭⠇⣰⠇⠀⠀⢻⠀
⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁
⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

⠀⢰⢗⡀⠀⠀⠀⠀⠀⡔⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⡺⣗⠱⣄⣤⣤⣾⢡⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢘⢿⣻⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢽⣾⣟⣿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣃⠹⣾⣿⣯⡇⣀⣠⣶⣶⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⡸⡇⣷⣤⣿⣭⣿⣿⡿⣟⡾⣷⣿⣶⣄⠀⠀⠀
⠀⠀⢰⢱⣴⣯⢻⡟⣿⣿⣷⢻⣯⢻⣵⠋⣿⣽⣷⠀⠀
⣠⣤⣫⢧⣟⣿⣾⣿⣽⡿⣟⣿⢯⣞⡧⣛⣼⣵⣻⡵⣄
⡧⣟⡿⣿⣬⡳⣻⣜⣯⣝⣯⣝⣯⣟⣽⣿⣯⠿⠯⠿⠙