⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣴⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠀⠀⣼⠃⠀⠀⢸⠀⠀⠀⢸⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⣸⠃⠀⠀⠀⢸⣀⡆⠀⢸⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⣰⠏⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠉⠑⠒⠢⠤⠤⠤⠤⣷⠠⠶⠖⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠒⠒⠠⠤⠤⣀⣀⣀⣀⣀⣻⣄⣄⣿⣤⡤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⠠⠤⠀⠀⠹⣟⢶⣄⡹⣦⡀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⣟⠛⠛⠛⠿⡿⢿⣿⣿⣿⣿⣷⣶⠀⠀⢻⡄⠉⠛⢿⣿⣆⡀⢀⡾⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢿⠀⠀⠀⢠⡇⠀⠀⠀⠉⠉⠉⣧⠀⠀⠀⢿⡀⠀⠀⠈⠙⠻⢾⠇⠀⠀⠈⠛⡿⠛⠛⠛⠟⠟⠿⠿⡿⠿⠛⢻⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⣸⡿⣦⣜⣇⠀⠀⠈⡇⠀⠀⢾⣦⠀⠀⢸⠀⠀⠀⠈⢷⠀⠀⡾⣆⠀⡿⠀⠀⠀⠀⠀⡇⠀⠀⣠⡄⠀⠀⠀⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢷⣄⠰⣦⡿⠀⠈⣿⠛⠀⠀⠀⠙⣆⠀⠈⠉⠀⠀⣼⠀⠀⠀⠀⠈⢷⣀⡇⠘⣿⠇⠀⠀⠀⠀⠀⢳⡀⠀⠙⠃⠀⠀⢠⠃⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣦⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠻⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠄⠠⠔⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢽⡏⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡄⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⠁⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠈⠧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠀⣴⠋⠈⣢⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⣾⣻⡴⠟⢩⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿
⠀⢰⡟⠀⠀⠀⠀⠀⠀⢹⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⣿⣿
⠀⣼⣳⣷⠀⠀⠀⠀⠀⠈⣿⡇⢈⠛⣷⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢺⡟⣣⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣿⣿
⢠⡿⠃⢻⡀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠈⠀⣾⣿⣿⣿⣿⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣂⣀⣠⣤⡴⠶⢾⠟⠉⠉⠀⠀⣸⡇⢒⣀⠐⢀⠀⠀⠀⣀⣶⣿⣷⣿⣿⣿
⠞⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠲⠤⠤⢴⠊⠉⠉⠉⠉⠁⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⣿⢤⣿⣏⠿⠛⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⣶⣦⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡏⣻⣿⡘⣴⠀⣩⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣇⠄⠀⠀⠀⠀⠀⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢀⡴⠋⡀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⡇⠭⢤⢐⣽⣿⣯⣿⣿⣿⡿⢋⣡
⠀⠀⠀⠀⠀⢻⡆⢸⣿⠀⠀⠊⣿⣿⣧⠹⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣖⠀⠹⣆⠀⣾⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⣿⣻⢻⣿⣿⣴⢸⣾⣿⣿⣿⣿⣟⣡⣶⣿⣿