⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢰⠷⠓⠉⠁⠀⠀⢀⠁⠀⠀⠀⡀⠀⠂⠐⢄⠀⠁⠵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⡠⠊⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠔⠀⠀⠀⢰⡀⠀⠈⡄⠡⠢⠀⠤⣐⣶⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⠀⢀⢬⠎⢀⠀⣶⠘⣷⡀⠀⢹⡄⣧⠡⢼⠥⡙⢎⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⡈⢀⢠⡞⠁⡐⠀⠀⣲⡟⠀⣼⠀⣿⡄⣿⣧⠃⢸⣿⣻⣶⡏⣧⠙⣦⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣴⠀⠀⣸⢡⣶⣿⠁⣰⠁⠀⣼⣿⠁⣼⠻⣸⡏⢳⡏⢿⣾⣸⣿⠯⣿⣷⢸⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⣿⣿⡟⣰⣿⡇⣸⣿⣟⣼⠃⣠⡿⢄⣚⢇⠀⣿⣿⣿⢻⣿⣿⡌⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣼⣿⣿⣿⣧⣿⣿⣰⣿⣿⡿⠋⣡⣿⣏⠉⠃⠈⠀⡿⠋⠟⢸⡙⣿⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠄⠀⠈⠸⠿⠀⠀⠀⠀⠀⠈⠒⣿⡇⣸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠠⢬⣂⣄⡀⠀⠀⠀⠀⠀⠀⠐⡼⣓⡙⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠶⡪⠵⠤⠀⠀⠀⢀⡀⠄⣰⡟⠌⠡⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⣥⡂⠀⠀⠀⠀⠀⣰⢿⡜⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣟⢛⠷⠤⢤⣄⣀⣀⣀⣀⣰⣿⠰⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⡻⡻⢟⠝⠻⡳⠄⠀⠀⠹⠽⠥⠤⠶⣶⣬⣀⣀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣤⠃⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⠀⢹⣿⣿⣆⠈⠁⠂⡤⠂⢄⢀⣑⣄⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠉⠐⠂⠄⠀⠀⠀⠀⠀⠘⠈⢳⠀⠀⠀⢸⣿⣿⣿⠀⠀⢊⠄⠊⠀⠀⠀⢀⠡⡄⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠘⠀⢀⡆⠀⠀⢸⣿⣿⣿⠐⠑⠁⠀⠀⠀⡀⠔⠁⠀⡴⣆⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠃⢁⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠠⠊⠀⠀⠀⢸⠀⠘⢄⠀⠀⠀⠀⠀⠀⠈⢄⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡸⢀⣾⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⠉⠒⢄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⡴⣾⣿⣿⠿⢿⣿⣿⣧⣀⣀⡀⠤⠒⠉⠀⠀⠀⢸⠖⠒⡖⠒⠃⠤⠄⣀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣾⡟⢹⠈⢷⠈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠟⠀⢸⡆⠈⣧⠘⣿⣿⣿⡏⠒⠠⢄⡀⠀⠀⠀⢸⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⡇⠉⠙⠉⠉⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀?