⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢤⣸⣶⣠⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡙⢿⣿⣿⣿⣿⣿⣷⣷⣷⣷⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⡿⠛⣉⣀⣈⠻⣿⣿⣿⣿⡿⠉⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢻⣿⣿⣿⡟⠀⣹⣿⡧⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⣀⣾⣷⣌⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⣿⣿⡿⢿⣷⣄⠀⠀⢠⣴⣾⣿⡿⠧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣾⠋⠈⡛⠾⠛⠀⠀⠀⠀⠘⠳⢴⠇⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⣾⣿⣿⣿⡀⠀⠀⢀⡀⡼⠀⠀⠀⡂⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠁⠀⠀⠀⠀⡐⠈⢿⣿⣿⣷⡀⠀⠸⠉⠛⠒⠒⠉⠀⠀⠀⠀⠐⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠐⠄⠀⠀⠀⢠⣾⠇⠜⠈⣿⡟⠛⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠊⡝⣹⡟⠁⣠⡴⠞⠈⠀⠀⠀⠀⠀⢠⡿⢿⡀⢂⢠⣿⠇⢰⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⢀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠹⢸⠁⠀⠉⠀⠀⠀⠠⠒⠀⠀⢠⠂⢀⣼⣿⣶⡟⣿⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢹⣧⠀⠀⠐⢌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠙⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⣶⣿⣿⣿⡿⠀⣿⡷⠀⠁⠀⠀⣀⣀⠀⣀⠀⠀⠀⣼⡇⠀⠀⢻⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⡇⡀⠀⠀⢸⣿⣿⠿⠋⠁⡠⠻⣷⠀⡄⠀⣆⠈⠙⠛⠁⠀⠀⢠⣿⣿⣦⣄⠸⡇⠀⠀⢤⣄⡅⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠈⡁⠀⠀⠀⠀⡉⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⣿⡟⠛⠉⠀⢀⡴⣹⡿⢿⣿⣿⣿⠇⠀⠀⠀⠙⠀⠀⡄⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⢇⠀⠀⠀⢰⡶⠋⠀⠠⠀⠀⠀⣿⠀⢸⣿⠙⠷⢤⣴⠾⠋⢀⠋⠀⠀⠀⠈⢹⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⡤⠚⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠂⠀⠀⠀⢡⠂⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠐⠃⠀⣸⠟⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠆⠀⠀⠀⢰⠁⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⢻⣿⡿⠋⠀⠐⠀⠹⠋⠁⠀⡜⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠁⠄⠢⠉⠒⢅⡀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠉⠀⠀⠀⢀⣤⣄⠀⢀⠌⠀⠀⠀⠀⠑⢀⢈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⡀⠀⠀⠀⠀
⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢀⠔⠀⠅⠀⢠⠈⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⠁⠀⠀⢀⠀⠠⠠⠠⠃⠀⠀⠀⠀⠀⠀⠀⢔⠎⠀⢀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀
⢀⠠⠂⠅⠠⠈⠀⠀⠠⠒⠃⣰⣷⡆⣼⣯⠲⠦⠀⠀⢠⠊⠈⠻⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⡑⡐⠁⠀⠀⠀⠀⠀⠄⠐⡒⡜⠀⠀⠈⢄⠀⠐⠀⠀⠀⠑⠀⠀⠀
⠕⠈⠀⢀⠲⠄⡀⠀⠐⣤⠔⢻⠟⣼⣿⣿⡷⠈⠀⢀⠃⠀⠀⡄⠀⣹⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠁⠐⠄⠀⠈⠳⠼⠀⠀⠀⠢⠀⠃⠀
⠀⠀⠀⠀⠀⠄⠨⠆⠀⣿⣸⡆⣼⣿⣿⡟⠉⠀⠀⢨⣷⣦⡀⣱⣾⡇⣼⡇⠀⠀⠈⠉⠁⠤⠤⠐⠂⠉⠁⢢⠀⠀⠈⠀⢍⠱⠀⠀⠀⠀⠀⠈⢂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀
⠀⠀⠀⠀⠀⠀⠈⠀⢂⢻⡏⢀⣿⡿⢋⡄⠉⠉⢠⣾⣿⣿⠇⣿⣿⣇⣿⡇⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⠀⠀⠂⠀⠀⠀⠀⠂⠀⠠⡉⠀⠀⠀⢀⣀⣀⣶⣠⡾⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠉⣾⣀⣿⣎⣀⣤⣾⢿⡀⣰⣿⣿⣿⣿⢸⣿⠟⠟⠟⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⡟⠃⠀⠀
⠀⠀⠀⠀⠀⣠⣀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⢻⣿⣿⡿⠋⣈⣥⣠⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠠⠰⣿⣷⣤⣀⣀⣄⣀⣠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠂⠀
⠀⠀⠀⠀⠞⠉⠁⠁⠀⣾⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣶⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠛⠙⠀⠀⢰⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀
⠀⣠⣄⢀⠀⠀⠠⣤⠎⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠅⠈⠀⢠⠑⠀⠀⢸⠣⢍⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠹⠀⢀⠀⠀⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢋⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⢀⣴⠏⠀⠀⠀⠸⣄⠀⠈⢷⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀