⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣴⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠻⠿⠟⠋⠁⡰⠁⠀⠀⡇⢸⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠘⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠐⠒⠈⠀⠀⠀⢀⠁⡘⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣦⠇⠀⠀⠀
⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠝⠛⠉⠉⠀⠀⠀⠈⠻⢍⠉⠉⠙⠛⠲⢶⣾⣿⡿⠋⠁⠀⠀⠀⠀
⠀⠀⡰⠁⢠⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠉⠉⠙⢆⠀⠀⠀⠀⠀
⠀⡜⠀⢠⠃⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀
⡜⠀⢠⠃⠀⠀⠀⠀⡘⠀⠜⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀
⠁⢀⡆⠀⠀⠀⠀⠀⣷⡆⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⠀⠀⠈⢇⠀⠀
⠀⢻⠀⠀⠀⠀⠀⠀⠇⠇⠀⢠⠎⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⡇⠀⠀⠘⡄⠀
⠀⡆⠀⠀⠀⠀⠀⠀⡄⢰⡰⡡⠊⠀⠀⢣⠀⣀⣀⣠⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡆⡇⠀⠀⠀⢣⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⡱⠁⠀⢀⣤⠾⠟⡉⠭⠭⢝⣦⢱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠃⡇⠀⠀⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⠁⠤⢾⠋⠀⠀⡜⠀⠀⠄⢄⢹⣿⡵⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠀⠀⡇
⢂⠀⠀⠀⠀⠀⠀⠀⢰⢃⠀⠀⡗⠀⠀⢔⣃⠖⠈⠛⢚⡸⢸⠸⠱⡘⡀⠀⠀⢸⠀⣀⠤⣲⣯⠤⠶⣤⡂⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⢆⠀⠘⢄⠀⠀⠀⠑⠠⠤⠘⢁⡸⠀⠒⠩⠅⠒⠂⡇⡮⣴⡟⢋⡁⠪⡐⠊⢳⡆⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀
⠀⢇⠀⠀⠀⡆⠀⠀⠀⢡⠀⠳⡀⠀⢑⡆⠤⠤⠤⠤⠒⡁⠀⠠⠤⠤⠀⠀⢀⡄⣽⢝⡦⠧⠼⡀⡇⠀⠈⡇⠀⡇⢀⡇⠀⠀⡠⠄⠒⠈
⠀⠘⡢⡀⠀⢻⡄⠀⠀⠈⡆⠀⠈⢍⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢌⠆⣀⣀⠜⠁⠀⢠⠇⠀⢧⠃⡇⠀⡜⠀⠀⠀⠀
⠀⠀⠱⡈⠢⡸⠰⠀⠀⠀⠰⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠒⠤⣀⣀⣀⠔⠁⠀⣼⠃⡠⠗⠂⡇⠀⠀⠀⠀
⠀⠀⠀⠱⡀⠈⠁⡇⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠃⠀⠀⠀⠀⠀⠀⢠⢅⠀⡠⢪⢃⠊⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢷⡀⠀⢡⠀⠀⠀⠈⡆⠀⢀⠔⠊⠉⠁⠐⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠏⠀⡘⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠱⡄⢸⠀⠀⠀⠀⠘⣴⣿⣄⢀⡀⠤⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠘⢄⠀⠀⠀⠀⠀⢹⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣠⡀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡀⠈⠀⠀⠀⠀⠀⠀⡟⠦⣀⣀⠤⠤⠀⠀⠀⠤⠤⠄⣀⡀⠘⣿⠇⠀⠀⠀⠀⠀⢀⠜⠀⠀⠸⠀⠀⠀⠀⠀⡠⠊⠁⠀
⠀⠀⠀⠀⠀⠀⢡⢰⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⢀⡠⠊⠀⠀⢸⡇⠀⠀⣀⠠⠔⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⢸⡥⠐⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡰⢾⡒⠤⣀⡀⠀⠀⠀⢀⣀⣤⢰⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀