⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠲⠦⠉⠉⠉⠏⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⠃⢀⣤⠀⠀⠀⠲⠂⠀⠠⠆⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⢁⡴⠚⠉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠔⠒⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡆⢰⠆⠀⠋⣠⠔⠉⠁⣀⡠⠄⠒⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡜⠁⣠⠔⠋⢁⡔⠒⠒⠤⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣀⣤⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡆⡶⠀⠀⢀⡜⠁⢀⣀⢸⠀⠀⠀⠀⠈⢆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⢀⡀⣴⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⠀⡞⠁⠀⠉⢇⠀⣿⣄⠀⠈⡆⠀⠕⠒⠉⣉⡒⡄⠀⠀⠀⠀⢀⠤⠊⠁⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢇⠀⣤⡄⠈⢢⡈⠻⡖⢀⡞⣀⠔⠊⠁⠀⠀⠉⠐⠒⠠⢎⢁⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢂⠘⢿⣦⡇⠉⠓⢶⡫⠞⠁⣀⣤⣤⣤⣤⣤⣤⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠦⠭⡇⠀⡠⠊⠀⣠⣮⣬⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⡧⠊⠀⢀⡜⠁⠙⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣡⠎⠀⠀⢠⠊⠀⠀⠀⣸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣰⣧⣀⣀⡠⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣾⡿⠿⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠛⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡰⢤⣀⣀⡄⢠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⣾⡟⠉⠻⣦⣄⠄⠄⠄⠄⠄⣿
⣿⡀⠄⢀⣴⠞⠋⠄⠄⠄⠈⣷⠄⠄⠄⠄⠄⠄⣾⠁⠄⠄⠄⠙⠳⣦⡀⠄⠄⣿
⠸⣧⠾⠿⠷⠶⠶⠶⠶⠶⠶⢾⣷⠶⠶⠶⠶⣾⡷⠶⠶⠶⠶⠶⠶⠾⠿⠷⣼⠇
⠄⢻⣆⠄⠄⠄⠄⠄⠄⠄⠄⠄⢿⡄⠄⠄⢠⡿⠄⠄⠄⠄⠄⠄⠄⠄⠄⣰⡟⠄
⠄⠄⠻⣆⠄⠄⠄⠄⠄⠄⠄⠄⠘⣷⠄⠄⣾⠃⠄⠄⠄⠄⠄⠄⠄⠄⣰⠟⠄⠄
⠄⠄⠄⠙⢷⣄⠄⠄⠄⠄⠄⠄⠄⢹⣇⣸⡏⠄⠄⠄⠄⠄⠄⠄⣠⡾⠋⠄⠄⠄
⠄⠄⠄⠄⠄⠙⠳⣦⣄⡀⠄⠄⠄⠄⢿⡿⠄⠄⠄⠄⢀⣠⣴⠞⠋⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠉⠛⠳⠶⣦⣤⣼⣧⣤⣴⠶⠞⠛⠉⠄⠄⠄⠄⠄⠄⠄⠄