⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠒⠒⠒⠒⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠈⢣⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌⠀⠀⡆⠀⠀⠀⢀⠀⠐⠀⠀⢀⠀⠀⠀⠀⢳⡀⠀⠀⠐⡀⠀⠀⢱⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⡘⠀⡀⠀⡇⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠇⠀⡄⠀⠗⡀⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠀⡃⠀⢃⠀⢀⠀⢸⠀⠘⡀⠀⠀⡄⠀⡀⠀⣌⢸⠀⢀⠀⢠⠀⡇⠀⢸⢃⢀⢠⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⡄⠀⣇⢸⠑⢦⡈⣎⠢⣦⠄⢵⠀⠠⡧⢊⡇⣠⢃⣸⠀⣸⠀⡇⠀⡇⠀⠀⡘⠀⢠⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡀⠀⠑⣶⣿⣶⣷⣷⣿⣾⣷⠾⠖⠚⠓⠶⠿⢿⣿⣿⣿⣿⣿⠟⠛⡇⠀⡇⠀⠀⡇⠀⣃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣿⠀⣿⣿⡟⢿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠹⣿⣿⡇⠀⡇⢠⠁⡇⠀⣿⠀⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡇⢀⠀⣿⠀⢻⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣿⣿⠃⢰⠁⠸⠀⠀⢸⢹⡇⠘⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠁⠸⡀⢃⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⡎⠀⠇⢸⠀⣼⣼⣹⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢸⠀⣧⢈⡄⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠢⣼⠀⡜⢀⣿⣾⣿⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢇⡇⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠇⣸⣿⢿⡻⢿⢸⢣⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠸⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠀⠀⠀⣀⣀⣠⡤⣖⡻⠁⡼⢀⠃⠀⠀⡗⢜⡌⠘⡎⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢧⣻⠀⣨⠉⠉⢰⠒⣒⠶⢲⣶⣶⡶⠾⢿⣿⣿⣟⠁⠀⠘⡗⠊⠉⢹⢄⠀⢀⡇⠈⡇⠀⠐⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡰⢁⡠⠤⠚⢹⢰⢀⣸⠏⠙⢿⣶⣟⣋⣈⣹⣿⡄⡠⢳⠀⠀⡸⠘⡆⢸⠱⡀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠤⠒⠈⠈⠻⣿⣄⣀⣀⠤⡖⠚⠉⡏⠉⠁⢸⣿⡿⠀⠀⠀⠘⣷⢁⠜⣆⢠⠇⠀⢰⠎⠀⠇⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⣲⣶⣂⡞⢋⠉⠉⡇⡜⠀⢱⢀⠎⡅⣸⡀⠸⠿⠧⠤⢠⠀⣀⣿⡆⠀⢡⢪⠀⠀⠎⢠⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠘⠀⠀⠸⠃⠀⠀⠏⠀⠃⠸⠀⠀⠀⠀⠀⢸⠀⠀⣇⢧⠀⠘⡄⠀⡇⠀⠸⠀⠀⡇⠀⠀⢸⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠃⠀⢸⢃⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠘⣦⣄⣇⢠⣇⠀⢀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢯⣯⣭⣶⠆⠀⠀⠀⢀⣿⡏⠀⢸⠀⢠⠢⠀⠀⠀⠀⠊⡆⠀⠸⡄⢹⠛⠻⣈⣿⣷⠘⠠⠹⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⠀⠀⠀⢸⠽⢿⣶⠞⡀⠘⢰⠀⠀⠀⠀⡆⠰⠀⢀⢧⠎⠀⠀⢟⠋⡤⠀⠀⡄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⢢⡖⠁⠀⠈⠃⢼⣀⣠⡤⢤⣰⠄⠃⠁⠀⠹⣄⣠⣷⠎⠀⠀⢀⠃⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣷⠀⠀⠀⠀⢠⠏⢇⣀⠀⠀⣸⣵⣟⣉⣠⢭⣆⠀⢀⣀⡸⡅⠈⣿⣀⣀⣀⡼⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣶⡦⢴⢖⢎⣢⠇⠘⣳⡺⠡⠑⣀⠌⠈⢄⡸⠓⣿⠉⢄⣱⣦⡰⠌⢃⢨⠇⣰⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⡿⡟⢄⠌⢸⠿⠛⢻⣿⢧⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡻⣿⠋⠙⠻⡇⠈⣽⣾⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠐⢛⠉⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣃⣀⣀⣀⣰⣶⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀