⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⢀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠶⠤⠤⠤⣶⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠐⠀⠀⢀⡠⠂⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢘⠢⠀⢤⠀⣀⠀⠀⠀⣀⠠⠚⠀⢀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠒⠒⠛⠛⢻⠛⢛⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢀⡀⠀⠀⡠⠀⠀⠀⠀
⠤⠀⠤⢘⠑⠼⠘⠔⠏⠤⠀⠒⠧⠽⠐⠸⠉⠐⠃⠈⠀⠁⢈⠁⠒⠈⠓⠊⢈⠁⠈⠊⠐⠉⠠⠊⠰⠶⠤⢤⣀⠀⣰⠀⠤⠄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡄⠀⣀⡰⠠⣀⡘⢄⢼⠄⢺⠀⠢⠄⢚⠯⣔⠁⠈⠀⠀⣀⠀⠌⠀⠀⢀⣴⡇⣀⢲⠠⢠⢤⠹⢧⠒⢵⠈⠢⠌⠂⠔⠀⡧⠔⢸⠡
⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠁⠂⠀⠈⢆⡀⠀⠀⡀⠀⢀⠀⠀⠁⢀⠊⠉⠑⠚⠑⠌⠒⠈⠆⠀⢢⠤⢀⣀⣀⣀⣠⣤⠴⠴⠄⠄⠒⠒⠚⠓⠩⠥⠶⣄⣐⣨⡅⠈⠁⠈⡀⠀⠀⠀⠀⠀⠀⡔⠊⠉⢉⣙⠛⠋⠛⢙⠟⠉⠉⠉⠐⠧⡀⠁⠄⡠⣀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⠢⠌⠷⠘⢗⣦⠀⠠⠀⠠⡄⠀⠀⢀⠁⢄⠈⠁⠠⡀⠀⠉⠑⣄⠀⠐⢈⠐⠊⢠⣀⣁⣦⠴⠻⠥⠤⠴⠚⠛⠒⠒⠂⠒⠹⠷⠶⠶⠦⠵⠖⢂⣈⡁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠚⢓⣲⣤⣼⡀⠁⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⣾⡇⠂⠈⢐⡦⠤⣸⢄⠖⡿⠐⠂⡉⠶⠤⠄⠀
⠤⣖⣰⠁⢰⡄⠑⡖⠒⠚⠒⢃⠁⠚⠉⠑⠒⠬⠋⠈⠑⠒⠒⠒⢥⠥⢤⣸⡖⠓⠾⡛⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠐⢀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠚⠻⡚⠒⠒⠒⠒⠂⠰⠤⠤⠤⠤⠤⠥⣠⠔⠂⠉⠉⠁⠀⠀⠀⠉⠉⠉⠛⠛⠶⠾⠿⠿⠟⠶⠒⠒⠒⠛⠋⠉⠉⠙⠓⠢⡤⠈⠈⢀⠀⢀⣒⣄⠀⠀⡀⣀
⠀⠁⠸⢷⡜⡌⠉⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠀⠢⠀⠙⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⡎⢠⡞⣠⠇⣶⡀⠘⣭⣿⠦⡿⠛
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠘⡆⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⣀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⠔⠁⣠⠟⠁⠙⠋⠷⡏⠉⠲⢼⡈⠀⠀⠀
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⡄⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⡀⠊⠁⠀⠀⠀⡀⠠⢌⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠤⣀⡗⠮⢸⡼⣿⣀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⠊⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⡀⠂⠀⠀⠀⠀⠀⠀⣲⣄⠒⠓⠄⠘⠀⠂⠀⠉⠀⢌⣑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠞⠋⡴⠂⢀⡔⣲⠂⠔⡜⢵⠀⠲⡤⣉⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠥⠤⠬⠥⠤⠑⠂⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠉⠁⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠠⠤⠤⠆⢄⡀⠀⠀⢈⠢⠄⠠⠔⠁⢀⣸⡤⢾⢀⣷⠁⣆⢠⢧⡀⢣⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⠭⢤⣀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣄⠀⠀⠀⠀⠀⠠⢄⠀⡐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⣤⣤⡴⡞⠉⠀⢀⣹⠎⢸⣼⠻⠏⠒⠋⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢸⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⢄⡀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⠁⠀⠀⠸⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢦⣀⣀⢀⣀⣀⣀⣀⣈⣁⣒⣀⣀⡐⠂⠁⠒⠒⣈⠤⠄⠂⠸⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢠⡇⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⢀⠀⡀⠀⢀⢀⠀⠈⢉⡉⠑⠫⠀⠀⠀⠀⠀⠀⠀⠈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣔⡁⠀⠀⢠⠀⠀⠀⠀⠡⡀⠀⠀⠢⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠂⠤⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣿⡿⢿⠶⢶⡴⣤⠶⡴⣤⢷⣶⡶⣶⣾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⠈⠁⢄⠀⠀⠀⠀⠀⢠⢿⠆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠸⡏⠓⠻⠦⢷⡬⠓⠛⠉⠉⠁⠉⠉⣻⡀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⠂⠀⠠⠀⠐⠀⠀⢀⠄⠂⡞⡇⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠊⠄⠐⠈⠑⢀⠇⠒⠠⠀⡀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠉⠛⠤⠵⢀⠤⠤⢤⣤⣔⡀⠒⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢠⠈⠊⠀⠀⢀⡷⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠈⠁⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠌⠉⠓⠒⠦⢄⣀⠈⠐⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠠⠃⠀⠀⣠⣾⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠄⣀⢉⡻⠛⠋⠉⡩⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠊⠀⢘⡶⢮⣵⡿⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠑⠠⢀⢀⡠⠤⠐⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠂⠄⣀⠀⠤⠀⠀⠂⠀⠠⠤⠀⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢆⡤⠤⠤⠤⠤⠤⠤⠶⢭⠯⡁⢉⢄⠀⠉⠐⠦⣀⠀⠀⠀⠁⢄⠀⠀⠀⠀⡠⠤⠄⠒⠚⠒⠂⠈⠉⠉⠉⠉⠉⠉⠉⠐⠒⠚⠂⠠⠤⠤⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠌⠒⠒⠀⠈⠁⠉⠀⠐⠒⠂⠤⢀⣀⣀⣠⣄⣤⣤⣤⣤⡤⣤⢲⡼⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠚⠧⣦⢛⠂⣦⣄⠦⠍⣢⣄⡀⠀⠐⠠⡀⣾⡇⠀⠀⠂⠀⠀⠤⠄⠀⠀⠤⡠⢤⠄⠀⢀⠀⠀⡀⠀⠀⠀⠄⠀⢈⡖⠒⠈⠉⠉⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠉⠙⠫⠽⣌⣳⡘⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠙⠶⠃⠀⠉⠀⠀⠀⠈⠉⠉⠐⠚⠤⣧⣀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⢆⠂⠁⠀⠀⢱⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⢠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⣤⣤⣤⣤⣄⣀⣀⢀⣀⣈⣦⣀⣀⣀⣼⣵⣤⣤⣤⣴⡏⢁⠀⠀⠀⠀⠄⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⢰⠈⢻⣿⡿⢟⣟⡻⢟⣻⠻⣭⣹⠭⠛⠉⠁⣈⡉⠉⠉⠈⢀⣃⡠⣔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠴⡀⢀⡀⡤
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⣯⠜⣣⡮⠓⠛⠁⠉⠉⠁⠀⠀⠀⠎⠀⠀⠉⠈⠉⠀⠀⠀⠐⠨⢄⣀⡤⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠠⡴⠍⣯⠐⢌⡀⠗⠁⠰⠕
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡿⡼⠣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡶⠋⠉⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠊⣀⠰⠾⠉⠉⢉⠡⠀⠀⠀⠀⠐⢠⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠐⠄⠀⠀⠀⠀⠀⣳⡅⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠠⠉⠉⠉⠉⠉⠉⠀⠀⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠀⠀⠀⠀⠀⠒⠒⠒⠂⠠⠮⠤⠤⠴⠬⢤⠀⣠⢶⠈⣉⠀⣗⡈⠙⢷⠦⠴⠶⠤⢄
⠀⠀⠀⠀⠀⠘⢄⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠁⠀⠀⢀⢲⣏⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⢂⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠛⠉⠙⠻⠃⠉⠉⠛⠀⡀⠄⠀⠀
⠀⠀⠀⠀⠰⠀⠀⠉⠀⠣⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠂⣠⣾⢇⠳⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠪⠀⠠⠤⠤⠼⠄⠀⣀⣀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠈⠌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠔⠊⠙⢿⡌⣳⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠠⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠙⢆⢇⠀⠀⠁⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠂⠄⠀⠀⠀⠀⢀⡀⠰⢸⠈⠢⡠⠀⠀⠀⠀⠀⢀⠇⠀⠠⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠊⠠⠁⠀⠀⠀⠀⠀⠀⠀
⢣⣏⣤⣀⠠⠤⠤⠬⠥⠶⢢⣴⣛⣦⠄⠠⠤⠄⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡞⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠡⠤⠤⠤⠤⠤⠶⠤⠤⠦⠥⠠⠀⣬⣷⣦⣥⣄⣀⣀⣠⣮⣥⣴⣊⣡⣴⣿⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠷⣄⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⢀⠔⠂⡠⠂⣾⣳⣀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⠛⠉⠓⠯⣞⡽⠛⠁⠀⠈⠉⠁⠒⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠉⠁⠀⠀⠀⠈⠉⠒⠀⠠⠤⢄⣀⣀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠖⠦⠤⠄⢀⣈⠢⢀⠀⠀⠀⠀⡆⠀⠀⠀⡰⡿⠱⡶⡿⠥⡼⠦⠀⠠⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡆⠀⠉⠉⠀⢀⠀⠀⡄⠤⠄⠠⠀⠂⠲⡈⠁⠠⠃⠀⠀⢀⡇⢈⠁⠐⠤⢀⣒⡲⠒⠋⠉⠀⠀⠈⠉⠁⠐⠠⢀⡀⠈⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡡⠀⠀⠀⠀⠉⠉⠚⠤⣂⡐⠀⠀⣠⢞⣱⡇⠊⣀⣀⡘⠉⣉⣱⣦⣤⠤⠤⠉⠂⠀⡰⠤⠀⠀⠣⢀⡈⢷⢦⣄⡀⠈⠤⠂⠀⠀⠂⠀⠀⠀⠀⣀⣴⣁⣠⡤⢶⣾⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⢽⡝⣋⣦⣏⡤⠧⠴⠦⠽⠷⠶⠴⣗⣻⣞⣤⣀⣀⣀⠌⠀⠀⠀⠀⠀⠀⠀⡎⠳⣭⢻⢿|⣿|⠿⡿⢿⢻⣛⣟⣻⡻⠿⠯⠽⠦⠽⠶⠃⠀⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠀⠀⠀⠀⢸⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠠⡄⠀⠀⠡⡀⠀⠉⠚⢦⠟⠼⠓⠋⠉⢀⠠⠐⠂⠠⠀⢀⠀⣠⠎⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣂⡤⢤⠤⠤⠴⠾⠿⠦⠤⠤⠶⠦⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢱⠀⠀⠀⠀⠑⢀⡀⠀⣀⡀⠠⠄⠊⠀⠀⠀⠀⠀⠀⢼⠊⡅⠂⠨⢂⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡡⠔⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡐⠂⢠⣠⠤⠤⠒⠋⠉⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠑⣄⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠢⣀⠈⠁⠂⠠⠄⡀⠀⠀⢀⡠⠊⡀⠔⠈⠀⠀⠀⠀⠠⠀⠀⠀
⣀⠀⠀⠀⡀⠀⠀⠀⠀⠑⢀⣀⡴⠓⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⢄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠒⠂⠀⠈⠁⠈⠉⠙⠃⠈⢄⡢⢀⡀⠔⠈⠉⠀⠀⠀
⣌⢧⡹⢼⣵⣄⠀⠀⠀⠀⢰⢣⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡆⠀⠀⡀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠠⠤⠌⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠂⠠⠄⠀⠀
⠉⠉⠉⠉⠉⠉⠛⠋⠛⠙⠛⠳⠧⣀⡀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣄⠀⠡⣠⣾⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢁⠔⠓⠒⠈⠂⠠⠤⠤⠐⡑⢄⠀⠀⠀⠀⠀⣴⣿⣶⣄⠀⣶⡄⠑⣄⠀⠀⠀⠀⠀⢠⠀⢸⣎⠿⠯⠿⠿⢳⣤⣦⣤⣶⣿⣿⣿⣷⣀⣊⠐⢄⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠈⣻⣿⣿⣿⣿⣿⠀⠀⠀⠁⠤⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠈⠉⡆⠀⠉⠉⠉⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣧⡀⠁⠒⢒⣁⣵⡀⠒⠂⠀⠀⡔⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠛⠋⠁⠀⠀⠂⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠙⠿⣿⣄⡀⠀⠈⠙⢧⠀⠀⠀⡘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣴⡇⠇⠀⠀⠀⠀⠀⡘⣏⠀⠤⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠰⡄⠀⠀⠘⠄⢊⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⣿⣦⣀⠀⠈⢟⠶⣶⣷⣶⣦⣼⣿⡿⠿⣿⣿⣿⣿⣟⣯⣿⣿⣯⣻⠼⠧⢈⠠⢀⣀⡀⣐⣠⣯⠳⡤⢴⣶⠶⢦⣤⣭⣶⡶⠾⠷⠤⠤⠤⠤⠤⠷⠺⣰⣒⡶⠤⠶⠬⠏⠲⠉⠡⠗⠶⠢⠔⢺⠥⢔⣲⠆⣀⡠⢤⠶⣩⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢃⠔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣤⣬⣿⣐⣓⣺⣥⣫⣝⣽⣿⣿⣿⣿⣿⣯⣄⣿⣿⡧⢀⣀⣀⣀⣙⣦⣔⣚⣋⣉⣍⣀⣤⣢⡴⠤⠀⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡲⠚⠀⢠⠀⣠⣠⢀⡒⠤⠰⣄⣀⣩⠭⠷⢿⡞⣵⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⢿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠛⢻⡿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣰⣎⣼⢁⡽⠖⠛⠓⠷⠖⠦⠼⠄⠀⠀⠄⡀⠀⠀⠀
⠀⠀⠀⠀⢋⠁⠀⠒⠠⡀⠀⠀⠑⠀⠀⡈⣦⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠐⠉⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠤⠐⣀⠹⠭⠘⠛⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠔⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⡄⠀⠀⠗⠁⠀⢸⣦⣀⣀⠘⠤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠁⠒⣸⣿⡰⢌⡳⠦⠤⣄⣀⣈⣐⣠⣀⢀⣠⠔⠀⠂⠉⠀⠓⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢊⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡀⢠⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠖⣹⣿⢲⠋⠀⠀⠐⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡦⣸⢧⡸⡑⣄⢀⠞⡆⢀⣀⡀⠈⠓⠚⠛⢿⣞⡄⠀⠀⢡⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠤⠄⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠈⠈⠉⠃⠈⠃⠀⠋⠁⣠⠯⣄⡀⡗⠢⣈⢿⣵⣀⡀⠈⠀⠀⠐⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⡐⠢⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡠⠤⠤⠤⠤⣀⡘⠀⠂⠀⠀⠀⠀⠉⢣⠙⠀⠋⠈⠁⠴⠥⢄⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⢤⠐⠁⠀⠀⠇⠀⠈⠀⢠⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢀⠔⠁⡆⠀⠀⠐⠀⠠⠄⣄⡀⠀⠀⠀⠀⢀⡔⠅⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⢀⠌⠀⠀⣤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠤⠠⢆
⠀⠀⠀⠀⠀⠀⠈⠉⠒⢯⡂⠐⠀⣦⣄⡑⠀⣆⢠⡈⢷⣀⣻⣍⠊⢀⠀⠀⠀⠀⠀⠁⠊⢆⠀⠉⠢⢄⠀⡠⠂⢀⠔⠁⠂⠄⡀⠁⢄⣠⣾⣿⣿⣿⠟⢿⣿⣿⣿⠋⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀⠀⠉⠑⠒⡤⠉⠄⠡⠦⠄⠀⠀⣠⣚⣀⠀⠀⠀⠀⡠⠐⠀⠉⠠⣀⣼⠔⠸⣦⢀⠠⠐⠀⠁⠀⠀⠀⣱⠼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢹⣖⠢⢼⠈⠉⠛⠈⠢⡟⠾⠀⠀⠈⠑⠢⡀⠠⡀⠀⠀⠀⠀⠀⠁⠀⡀⠠⠙⡅⠐⢁⠀⠀⠀⠀⠈⢂⣾⣿⣿⠟⠋⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⡀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠒⠒⠒⠚⠛⠛⠓⠤⠄⣈⣷⠦⣄⣠⢤⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢣⡀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠉⠁⠠⡀⠀⢔⠀⠀⠀⢡⠀⠀⠈⠀⠠⣀⣴⣿⠿⢏⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢷⠇⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⣇⠃⠀⠀⢄⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠸⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠑⠂⠤⣻⣿⣿⣧⡀⠀⠀⠀⠀⢠⠤⣀⠀⠀⠀⠀⢀⠎⠒⠂⠀⠀⠀⠀⠀⠀⡀⠐⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢸⠀⠀⠀⠀⠀⠴⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠄⠂⠡⠀⠀⢻⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠐⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠳⡘⢤⢙⠢⣤⠔⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠂⠁⠀⠀⠀⡜⠀⠀⠀⢀⠊⠀⢁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⡧⠐⠘⡑⢆⠀⠀⠀⠀⠈⠀⠒⠂⠀⠀⠤⢀⡀⠙⣦⢉⢖⡒⢦⡼⡎⢒⠢⢄⡀⠀⣧⠀⠈⢻⣿⣿⣦⠀⠀⠀⠀⢀⡠⡔⠚⢿⣿⣷⠒⣒⠢⠴⢺⢢⡉⠖⣣⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⡁⠀⠀⠀⡇⠀⡠⡾⠁⠀⠀⠀⡈⠀⠀⣄⡀⠀⠀⡞⢄⠀⢀⡠⢤⠆
⡀⠀⢠⣄⠀⢰⠉⠛⣄⡌⣇⡠⠄⣿⠈⢧⠀⠀⠀⢐⡦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣾⠳⣾⠀⣧⢧⡎⣆⢩⡘⣿⣵⣦⣤⣹⣿⣿⣧⣤⣖⣊⣧⠕⠚⠋⠉⠹⣿⣟⠳⣭⣮⣵⣢⡙⣼⡘⢦⡀⢀⡠⢎⠭⢭⡙⢦⣿⢀⣀⣀⣀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣰⢣⡇⠀⡄⠠⠈⠀⡄⢤⣘⡌⠙⠢⡇⠘⡖⠉⢠⠟⠊
⣎⠙⠺⡄⠙⠞⠀⠀⠻⠀⠁⠀⠼⠒⢉⡹⢇⣰⣔⣸⢣⠀⣁⠀⠤⢀⠀⣀⠤⠀⣈⣧⣡⣬⠾⢥⠮⠭⠿⠏⠉⠉⠉⢀⣀⠈⠉⢿⣿⡄⠉⠙⠋⠐⠂⠒⠂⠐⠻⣿⣷⣖⡉⠁⢀⠩⣙⢻⠶⢿⣡⣝⣌⣚⡴⠛⠉⠁⠀⠀⠀⢀⠳⣤⡈⠀⣀⣀⠀⠀⠀⣀⠀⡤⣰⢾⡖⣒⢫⣱⡾⣀⢰⠙⣀⡠⡤⠽⠦⠀⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⢀⠀⠐⠢⡀⠁⠂⠀⠀⠀⠉⠉⠉⠛⠣⣉⠘⠋⡼⢲⣖⠒⠒⠚⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣎⠀⠀⠉⠉⠀⠀⠈⢂⠼⠋⠀⠀⠀⠀⡠⠄⠐⠊⠀⠘⣿⢯⣐⡘⣿⢤⣀⡏⠻⢳⣡⢻⣳⢼⣢⡭⠧⡀⠙⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠤
⠀⠀⠐⢠⢤⣱⡀⠁⠘⠶⢄⣉⠦⣑⠠⡀⠢⣤⠤⠤⠽⠄⠀⠠⠄⠐⠛⠉⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠈⠉⠓⠂⠀⢻⣤⣦⢷⣖⣂⠁⣀⣀⣴⣂⣤⣴⢿⡄⠙⣏⠺⢆⠙⠇⠀⠈⠃⠘⠁⠛⠁⠀⠀⠀⠀⡀⠀⡀⠀⡠⠤⡐⢀⣀⡀⠀⠀⠀⠀⢀⠀⡀
⡖⣀⡀⠀⠀⠁⠉⠓⠀⢆⠀⠁⠀⠢⡈⠸⢦⢌⣳⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢿⣿⡿⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠐⠯⠀⠈⠉⠛⠋⠛⣩⣗⠊⠉⠉⠉⠉⠉⠀⠀⠐⠀⠀⠀⢀⣐⣀⣀⣈⣁⡀⠐⠘⠻⠺⠐⠊⣠⢀⡠⣍⢧⣠⢆⣠⢆⣴⣚⢶⡹
⣝⡲⢤⢆⡀⣄⢈⡟⣦⣈⡗⠦⠾⠽⣳⣄⣀⣳⢀⠉⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣄⠀⠉⠈⢩⡗⣀⡠⢴⠚⠁⢀⠤⠒⠚⠉⠉⠀⠀⠀⠀⠀⠉⠙⢲⣞⡷⣞⡯⠷⣭⣳⢻⣯⣞⣽⣎⡟⣦⣛⢮⣳
⡞⣿⣗⢮⣳⢎⡷⡋⠁⠈⠃⠀⠀⠀⠀⠀⠉⠛⠮⣀⠀⠘⠀⠀⡠⠃⠀⠀⠀⠈⠠⠤⠀⠀⠀⠀⠐⠂⠤⠤⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢴⢀⣀⡗⢤⠇⠑⠞⠎⠉⠁⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠂⠉Q⠀⠘⣗⡛⠻⡄⠈⠋⠘⠋⠀⠾⠚⠛⠡⠉⠾⢵
⡽⣾⡙⣾⣿⡻⢓⠇⠁⠒⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠒⣤⡀⡀⠀⠀⠀⢀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⣐⢠⡦⠔⠚⠛⠚⠓⠋⠵⡄⠀⢀⢀⠀⠀⠀⡑⠄⠈⣠⡗⠄⠀⠰⠀⠄⠂⢉⣼⢀⠀⣠⠤⠔⠒⠚⠳⢧⡄⢀⠀⣠⠆⠂⠀⠀⠠⠀⠀⣀⣙⡾
⠃⠈⠃⠙⠏⠀⣎⡠⡤⠀⢤⣄⡀⠀⢹⢢⣆⢵⠃⠐⠒⣀⣹⠤⠥⠼⢤⣀⠃⢘⠠⠠⠀⢀⡀⠀⠀⠠⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠑⠒⠢⠀⠤⠤⢒⣒⠒⠂⠂⠉⡀⠀⠉⠦⠀⠄⠀⢸⣥⡄⠤⢀⠀⡠⠀⠀⣠⠘⣶⣼⣄⡀⣀⡀⣄⢞⣼⡣⠿⠄⠒⠠⢤⣻⠢⠌⣸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⣬⡅⣀⢀⡶⣤⠴⣤⣀⣬⢻⡼
⠀⠀⠀⠀⢀⠈⠀⠼⢲⠦⠤⣬⢦⠑⢾⡈⢁⡧⢲⣿⠋⠁⠠⠀⠀⢀⣀⡈⠹⣶⣄⡃⠩⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠒⠛⠻⠾⠿⠻⠿⠷⠽⢾⠋⠁⠀⠀⠀⣀⠠⠊⠻⣦⡾⠋⠉⠐⠀⢀⠠⠐⣧⡀⠀⠀⠈⢷⣻⡿⣝⡾⢳⣿⠷⣿⣯⣷⣹
⡖⣬⠰⣖⣡⣄⠠⠄⢀⣀⠊⢉⣩⠭⠶⡄⠈⣤⠿⠧⢤⡠⣼⡤⠤⢤⠤⣿⣱⡉⠛⠉⠉⠙⢓⡶⡞⠀⣀⡴⠀⠀⠀⠐⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠙⣓⠲⠾⠥⡤⠤⡤⢤⣴⣿⣅⣀⣀⣤⢄⣸⡖⠢⡼⠹⠳⠔⠷⠏⠙⠀⠉⠀⠈⠄⠊⡁⢀⠋⣍
⣽⡲⣛⣼⢒⡦⢣⣒⣄⡀⢏⠛⠲⠦⢧⡴⢤⣀⡠⣄⢦⡤⣤⢀⣤⠤⢀⠀⠈⠉⠛⠃⢲⡦⢼⠑⣤⠊⣜⠅⣒⣺⣟⣉⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠤⣀⠤⡴⠴⠚⠃⢌⠉⣈⠁⠀⠠⣀⠤⢀⣀⣰⠔⣂⢈⠤⣙⡜⢫⡝⣣⢬⣳⣝⣫⡟⣴
thank you for the game man, I will play it and let you know my thoughs afterward
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