⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢡⠞⣀⡵⢤⣶⠰⠦⣀⣀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡄⣾⣿⠿⠛⠛⠋⠿⣿⡛⢳⣷⣤⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠠⢄⣀⣀⡼⡏⣿⣯⡿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⢻⣁⡋⠁⢴⣶⣦⣶⠂⢈⣷⣠⢨⣷⣷⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡦⠀⠆⠀⢸⠚⡟⡟⠟⠙⠮⠿⠹⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡟⡇⠀⠀⠻⢿⡇⠀⠋⠉⠀⣠⣧⣿⠙⢎⡨⣿⣿⠚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠒⢇⣠⡾⡠⢻⡿⠀⠀⠀⠀⠀⢠⠀⠨⠙⡀⠒⠢⠤⢀⡠⠤⢜⣻⡿⣿⣿⣇⡀⠀⠐⠚⣇⣠⣴⣆⣦⣾⠟⠀⠀⠀⠀⠈⢿⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠈⠒⢲⣆⣀⣀⣄⣨⡄⠀⢀⣀⠌⠀⠀⠀⠈⡀⠀⢁⠉⠙⠙⠶⢷⠢⠤⢠⣧⣿⡿⢟⣛⡇⠀⠀⠀⠀⠀⢠⣼⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣇⢳⠀⢽⣀⠀⠀⠀⠉⠑⠂⠀⠁⠀⢪⠱⡄⠀⠀⠘⠈⠃⠀⠈⠘⠛⡟⠁⠀⠀⠀⠀⠀⠀⠈⡟⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣣⢸⣇⣕⣆⢀⣄⣠⠜⠉⠉⠑⢺⡷⢀⣔⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠙⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡹⣧⢾⠿⣏⣿⡀⠀⠀⢠⠞⠛⠢⢾⡁⠀⠉⠁⠀⠐⣦⣄⣆⠀⣀⡠⠤⠒⠉⠀⣀⣰⣎⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣙⡎⠿⠻⠦⣈⠉⠓⢦⠀⠘⣏⠉⠀⠀⠱⠀⠀⠀⠀⡸⠁⡝⠛⠛⠉⠀⠀⢀⣠⣾⣿⡟⠉⢉⠻⠙⣳⣌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠒⠤⠤⣤⣿⠀⠀⡄⡠⡇⡀⠀⠀⠀⢣⠀⢀⠎⠀⡞⠀⠀⠀⢀⣰⣾⣿⠿⢋⡥⢕⡠⠔⠊⠁⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠲⠤⣀⣬⣿⠀⠀⡃⠲⡇⠉⠀⠀⠀⠈⠆⠈⢠⢡⠀⠀⠀⣻⣿⢿⢟⣣⢔⣠⠖⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣔⣊⡼⡏⠁⡴⠇⠀⠰⢄⠀⠀⠀⠀⢰⠀⠂⠀⢐⡶⣾⣿⠁⡠⣪⢔⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣍⡀⠂⠀⢃⠀⠀⠀⠱⡀⠀⠀⠀⠣⡀⢰⣿⣿⠟⡱⡫⢚⡵⠋⠀⠀⠀⡐⠀⠀⠀⠀⠀⠄⠀⢀⠌⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⢳⡈⠙⠒⠾⣄⡀⠀⢀⣸⡀⠀⢰⢀⡱⣿⠟⣩⡾⢞⣵⠟⠁⠀⠀⠀⠘⢀⠐⠀⠐⠀⠀⠀⠒⢡⠂⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠻⠟⠲⠤⢀⣀⡬⡿⠛⠻⣧⣀⠔⠉⠀⠈⢿⣯⡾⠿⠷⠀⠀⠀⠀⡘⠔⠁⠀⠀⠀⠀⠀⠀⡰⠃⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠢⠀⠀⠀⠀⢴⠀⢀⠋⡅⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢀⡠⠆⠀⢀⠔⠀⡄⡠⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹⣯⣽