⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡄⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣦⠀⠈⠥⣂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⠊⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡄⠀⠀⠠⢑⠢⣈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⢌⡔⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢡⠀⠀⠀⠀⠑⠈⠑⠖⣄⣍⠒⡠⠤⢤⣴⢦⡖⢗⠮⠁⣩⠎⠈⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠑⠁⢼⢠⠑⢃⠂⡜⠀⡠⠂⠀⠀⢀⣀⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⡁⣆⡟⢇⠀⢠⢣⠊⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠆⠂⠀⡇⢱⠁⢸⣇⣴⣦⣄⢄⠤⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣴⣶⣦⣨⠀⠀⠀⠈⠂⠊⣿⣿⣿⣿⡎⢅⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠔⠃⣿⣿⣿⡿⡁⠀⠀⡀⠀⠈⠈⢍⠛⠉⡀⣀⠉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠉⢁⡴⠀⢀⣴⣾⣢⡀⠀⡠⡷⡃⠉⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠉⠀⣚⣃⡀⠸⣿⣿⣿⠏⠀⢂⣸⣍⣿⣟⡖⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⡲⣚⡭⣒⢥⣄⠀⣀⠬⣷⠤⠄⠔⢏⢖⡍⠫⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠞⡡⡪⠋⢮⣹⠀⠀⠈⠀⠀⠀⠀⠀⠸⠘⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡁⠜⡰⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⣆⠋⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠠⢄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⠄⠌⣂⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠈⠇⠀⠀⠈⠑⠲⣐⠀⠀⠀⠀⠀⠀⠠⠀⠀⢱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢆⢀⣠⠀⠀⠀⠀⠀⠄⠈⢳⢀⡀⠀⠀⠀⠀⠀⠁⢨⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠊⠀⠸⣂⠁⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠉⠑⠲⣤⣀⠈⠆⡂⠀⠀⠀⠀⠀⠀⠙⢄⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢙⡇⠀⠀⠀⠀⠀⠀⠐⣈⠗⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠱