⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢤⠤⣔⠲⠒⠒⠒⠒⠒⠒⠒⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡤⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ マキマ
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢂⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀
⠀⠀⠀⢀⠎⠔⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⠁⠐⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⠈⡄⠀⠀⡀⠀⠈⢆⠀⠀⠀
⠀⠀⠀⣍⠎⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠸⢀⠁⠀⠀⠀⠀⡖⠁⠀⠀⠊⠠⠁⠀⡀⠀⢠⡇⠀⠀⢸⠀⠁⠀⠀⢁⠀⠀⠈⡆⠀⠀
⠀⠀⢼⠂⠀⠀⠀⠀⢀⣾⠃⠠⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⢠⠁⠠⠁⣰⠁⠀⠰⡇⠀⢸⠃⠰⠀⡸⠀⠀⠀⠀⠘⠀⠀⡄⣿⡀⠀
⠀⢀⠏⠀⠀⠀⠀⠀⣼⡏⠔⠀⠀⠀⣀⠔⠁⡆⡆⠀⠀⠀⠀⣆⠊⢠⢁⠊⢘⠂⠠⠉⠇⢠⣇⠀⡄⢠⠁⠀⠘⠀⢰⠀⠀⠄⢁⣿⡇⠀
⠀⡘⠀⠀⠀⠀⠀⢸⡟⢈⣀⣤⠖⠋⠀⠀⢀⠇⠀⠀⠀⠀⢠⠎⢀⠞⠁⠀⢎⢔⣁⠀⡀⠃⢸⠠⠀⠀⠀⠀⡇⡇⢈⢰⠀⠀⣾⣿⣿⠀
⠂⠇⠀⠀⠀⠀⠠⢋⡉⠛⢿⣶⣶⣶⡿⠛⠋⠸⠀⠀⠀⠀⠘⢀⠤⠤⢦⣤⡥⠤⣄⡈⠂⠀⢈⠂⠁⠀⢀⠐⢀⡇⠸⣤⠀⡀⣿⣿⣿⠀
⢸⠀⠀⠀⡇⠠⠁⠠⠈⠂⠀⠛⠛⠓⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠠⠉⠋⠛⠀⠈⠳⡂⠀⠀⠀⠀⠀⠘⠁⠁⢇⠎⢹⠀⢇⣿⣿⡏⠀
⢸⠀⠀⠀⡇⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠑⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡂⢀⡎⠈⡸⣿⡿⠁⠀
⡈⠀⢀⠀⣧⠐⡀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⡆⠙⣿⣧⣴⡿⠟⠀⠀⠀
⢀⠀⢸⡀⢸⣰⠐⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⢃⢸⣿⣿⣿⠁⠀⠀⠀⠀
⢸⡀⠸⣇⠀⢿⠀⡈⠂⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀
⠀⢳⡀⢻⡄⠘⡇⣇⠀⣿⣿⠐⡀⠀⠀⠀⠀⠃⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⢻⣮⣿⣦⣻⣿⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠌⣿⢇⡏⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠜⠁⢉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣿⡾⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠁⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣿⡇⠀⢠⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠈⠁⠀⠀⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡆⢀⡻⠙⠁⠀⠀⠈⠁⠐⠠⠄⡀⠀⡄⢸⠀⢸⠀⠀⠀⠈⠐⠂⡤⣀⣀⠀⣀⡠⠊⠁⠀⠀⠀⢀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀
⢀⡠⢒⠊⠉⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀
⣎⣈⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⠀⠀⠢⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠁⠁⠄⠁⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠑⠄⢠⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠀⠀⠁⠁⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠈⢀⢀⡈⠲⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⣷⣶⣶⣷⣥⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠠⡄⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢈⠀⢀⠀⠀⢁⠰⢁⠌⠘⢿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⡸⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢀⡀⠜⠑⠆⠀⢀⡙⣿⣿⣿⣿⣷⡈⠒⢦⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠉⢿⣿⣿⣿⣧⠀⠀⠈⠢⢆⢧⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠙⢿⣿⣿⣶⣄⠀⣀⠰⠊⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠻⣿⣿⡿⠧⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡆⠀⡇⠀⠀⠀⠄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⡇⢀⠁⠀⠀⠄⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠁⠸⠀⢀⠌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀