⠀ ⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⡁⢳⣿⣿⣿⣿⣿⣿⡜⣿⣿⣧⢀⢻⣷⠰⠈⢿⣿⣿⣧⢣⠉⠑⠪⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⢠⣼⢳⡢⠤⡀⠀⠀⠀⢀⣱⡇⡞⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⡄⣧⠹⡇⠧⠈⢻⣿⣿⡇⢧⢢⠀⠀⠑⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⡇⢸⣠⠽⡖⢹⠉⠀⠀⢸⣿⣇⢃⢿⣿⣿⣿⣿⣿⣷⣿⣿⠇⢃⣡⣤⡹⠐⣿⣀⢻⣿⣿⢸⡎⠳⡄⠀⠀⠀⠰⣄⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀ ⠀⠈⠙⢼⣀⣀⢽⡁⠀⠀⠈⣾⣿⣿⠘⡸⣿⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⢟⡷⠈⠋⠃⠎⢿⣿⡏⣿⠀⠘⢆⠀⠀⠀⠈⠣⣄⠀⠀⠙⠻⢦⢄⡀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⡐⢹⣿⣿⡐⢡⢹⣿⣿⣿⣿⡏⣿⢣⣿⣿⡑⠁⠔⠀⠉⠉⠢⡘⣿⡇⣿⡇⠀⡀⠡⡀⠀⠀⠀⡄⠣⡀⠀⠀⢤⠀⠀⠀⠉⠙⠲⢤
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣇⠇⢣⢻⣿⣿⣿⡇⢇⣾⣿⣿⡆⢸⣤⡀⠚⢂⠀⢡⢿⡇⣿⡇⠀⢿⠀⠀⠄⠙⡄⠑⠴⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠹⣿⣿⡘⣆⢣⠻⣿⣿⢈⣾⣿⣿⣿⣶⣸⣏⢀⣬⣋⡼⣠⢸⢹⣿⡇⢠⣼⠙⡄⠀⠀⠑⢄⠀⠱⡸⡀⠀⠀⠀⠻⢦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⢹⡇⠁⠹⣿⣇⠹⡃⠃⠙⡇⠘⢿⣿⣿⣿⣿⣿⣏⣓⣉⣭⣴⣿⠘⢸⣿⠁⠘⠋⠀⠹⠄⠀⠀⠀⠀⠁⠌⢗⠤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠈⢷⠀⠀⠈⢿⣇⠂⣷⠄⠐⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢸⡏⠀⢀⣠⣴⣾⣿⣶⣄⠀⠀⡇⠀⠀⢅⠀⠁⢉⠒⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠙⠆⠈⠢⠲⠥⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣸⠁⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠨⣗⣄⠀⢃⠀⠀⠀⠒⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢐⡮⠫⣐⢷⣆⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠹⣿⣿⡿⠫⠊⠀⠀⠀⣶⠀⢻⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠻⡦⢈⠙⢻⢆
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⢋⠀⠀⠀⠀⢀⣼⣿⡆⠈⣿⣿⣿⡟⣱⡷⠀⠀⠀⠦⠀⠀⠀⢙⠂⣑⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⡀⠨⣛⠿⠶⠄⢀⣠⣾⣿⣿⣷⠀⢹⣿⡟⣴⠈⢃⣶⠔⠀⠀⠱⠀⠀⠀⠂⠡⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⡿⠀⡀⣿⣷⠀⠀⠀⠀⠑⠠⡀⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢙⠻⣿⣿⢀⠙⠻⠿⣿⣿⣿⣿⣿⣿⡇⠁⣿⠟⡀⠈⣧⢰⣿⠆⠀⢦⡀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⠿⠴⠮⣥⠻⢧⣤⣄⣀⡉⢩⣭⣍⣃⣀⣩⠎⢀⣼⠉⣼⡯⠀⠀⠀⠀⠈⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠑⠁⣛⠓⢒⣒⣢⡭⢁⡈⠿⠿⠟⠹⠛⠁⠀⠀⠀⠰⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀