⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠙⣟⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢋⠍⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠙⢼⠀⠀⢄⡌⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢋⣀⡡⠔⢀⡌⠨⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠡⠘⠷⡀⠰⣿⣦⣭⣿⡀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⣹⣵⣿⣏⠄⠀⠨⣦⠿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠠⡀⠀⠀⠀⡜⢻⣿⣿⣿⣄⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⢠⣿⣿⣿⣿⠃⠀⠐⠃⠇⢒⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣎⣿⠻⣿⣷⠂⠙⠂⠀⠀⣁⡚⠤⣠⣶⣄⣤⠐⠂⠀⠀⠀⠀⣿⣿⡏⠛⣿⠆⠀⠈⠀⠀⠁⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣀⠀⠀⠀⠘⢿⣿⣦⣿⣿⡧⠀⠈⠀⠁⠙⠉⠀⢻⡿⠿⠋⠁⠀⠀⠀⠀⣾⣿⣿⣇⣀⠃⠀⠀⠀⢰⡗⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣦⠘⠀⠀⢀⡈⢸⣿⣿⡿⠛⠁⢀⣬⣀⠀⠀⠀⣀⠀⠀⣀⢠⣤⣤⡘⠀⠀⠈⠛⣿⣿⣯⠄⣠⠀⠀⠈⢰⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⢠⣿⣷⣾⠛⠋⠁⢠⠘⠻⣿⣿⣿⣷⡀⢻⡀⡿⢁⣾⣿⣿⣿⡓⠀⠀⠀⠙⡻⠃⣾⣿⡷⠀⠀⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢻⣷⣤⣸⣿⣿⠃⠀⠡⣶⣶⣿⣿⣿⣿⣿⣿⣏⠀⠀⠃⣾⣿⣿⣿⣿⣿⣿⣧⣆⡠⠀⠀⠙⡿⢣⣶⣾⠟⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣶⠿⣿⣿⠏⠀⣢⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⢠⣿⣿⣧⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣦⣶⣾⠍⠀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⠛⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⣿⣿⣒⠠⢤⣿⣿⣿⣿⡿⠋⠉⠀⠉⠉⠘⢿⣿⡇⢤⣤⣷⠈⣿⣿⠟⠛⠛⠋⠛⠛⣿⣿⣿⣿⣷⣄⠀⣠⣿⣿⡿⠿⠧⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⡿⠛⣁⣾⣿⡿⠋⠉⠀⠆⢀⠀⢀⡧⠀⠀⠘⣿⠇⠰⠌⠉⠀⢿⠃⡀⠀⠀⣖⢀⠀⠀⠛⠿⢿⣿⣿⣷⣬⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣥⣶⣶⡿⠛⠉⢠⣆⡀⠀⠀⠈⠀⠈⢁⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠁⠀⠂⢉⣉⠀⠀⠙⠿⣿⣿⣶⣶⣭⣍⡛⠻⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⠿⢛⣿⣿⣿⠋⠀⣀⣼⣿⠟⠈⠀⠀⠀⠀⠀⠁⠀⣠⣾⣿⡄⡀⣤⡀⠀⣾⣷⣄⠀⠉⣡⣤⣀⠀⢷⣤⣬⠭⠢⠈⠛⢿⣿⣿⣿⣟⣒⠢⣀⠀⠀⠀
⠀⠀⠀⠀⠀