⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⣄⣠⣤⣀⡤⠒⣉⡀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠈⠙⠛⠻⣿⣏⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠉⠑⢲⣿⡇⣾⡿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠘⢿⡄⠀⠀⠄⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡘⠀⡠⣤⡦⠒⣾⡿⢨⡟⠁⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠐⡄⠀⠀⠀⠈⢿⡀⠀⠀⠈⠢⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠁⠀⢀⠞⠀⢰⣿⡇⡸⠀⠀⠀⠀⠀⠇⠀⢀⡎⠸⡀⠀⠀⠀⠀⠀⠇⠘⢆⠀⠀⢷⡀⠄⠀⠀⠘⣧⠀⠀⠀⠀⠈⢦⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡴⠀⠀⡜⠀⠀⢸⣿⣇⠃⠀⠀⠀⠀⢰⠀⠀⡜⠀⠀⢇⠀⠀⠀⠀⠸⠀⠀⠈⣢⠐⢸⠻⣼⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠳⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠇⠀⢰⠀⠀⠀⠘⣿⣯⢁⠀⠀⠀⠀⠈⡄⢠⠁⠒⠂⠈⢇⠀⠀⠀⡃⠀⠀⠀⠀⢣⢸⠀⠘⢇⠀⠀⣇⣏⢿⣆⠀⠀⠀⠀⠹⡄⢧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⡎⠀⠀⠀⠀⢸⡏⣾⢸⠀⠀⡆⠀⣇⡘⠀⠀⠀⠀⠀⠑⢄⡰⠁⠀⠀⠀⠀⣠⣽⠛⠀⢸⠀⢸⣿⢹⠀⠻⣦⠀⠀⠀⠀⠙⡌⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠰⠀⠀⠁⠀⠀⣸⣿⡏⡈⠀⠀⡇⠀⠋⠃⠘⠛⠲⠦⣤⣄⡀⠀⠀⠀⠀⢠⣾⣭⣤⣤⣀⢸⢀⣿⣿⣾⠀⠀⠹⣧⡀⠀⠀⠀⠙⡜⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡸⠀⢰⠀⡀⠀⠀⠀⣿⠁⡇⣿⠀⠀⣷⠰⡄⠀⠀⣀⣤⡴⠶⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⣸⣾⣿⣿⣿⠇⠀⠀⠙⣧⡀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⡆⠀⠁⠀⠀⠀⣿⠀⢣⣿⠀⠰⣿⡆⡇⠀⠀⠉⢁⡠⠤⠤⠤⠤⣀⡀⠀⠀⠀⢀⡠⠖⠈⠉⠉⠉⠛⢿⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢠⠁⠀⠀⠀⠀⢰⡏⠀⢸⢿⠀⣸⡙⣿⣽⡀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠉⠢⣄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⣇⠀⠀⠘⠀⣷⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠘⠀⠆⠀⠀⠀⣸⠃⠀⠈⢸⣰⣿⣷⣹⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠸⡆⠀⠀⠀⠸⡇⠀⠀⠀
⠀⠀⠀⠀⡇⢸⠠⠀⠀⠀⠀⣿⠀⠀⠀⠘⠛⣿⣿⠇⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡀⠀⠱⡀⠀⢠⠀⣇⠀⠀⠀
⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣿⠋⠀⡰⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⠀⠀⢃⠀⠈⡀⠸⡄⠀⠀
⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢠⣿⠀⢀⠀⠀⡌⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⣿⠀⠃⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡇⠀⡘⠀⠀⢣⡈⠳⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⡀⢀⠞⠀⠣⡀⠀⠀⠀⠆⠀⠀⢡⠀⢀⠀⢳⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣸⠇⠀⠃⠀⠀⢰⠀⠀⠘⢢⠔⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡻⠒⣔⣾⠟⡄⠀⠀⢸⠀⠀⠀⠂⠘⠀⠘⡆⠀
⠀⠀⠀⠀⣿⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⣿⠀⢰⣖⣲⡦⢴⣧⢐⣠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡦⠎⠀⠀⠀⢣⣠⣤⣵⣤⠀⠀⠄⠀⠀⢡⠀⠆⠀⡇⠀
⠀⠀⠀⠀⡿⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⡿⠀⣶⠀⢈⣭⣽⡇⠁⠀⠉⠁⠱⣰⣷⣄⠀⠀⠀⠀⠀⢰⣌⡀⣀⣠⣤⣤⣤⣿⣿⡿⢿⡆⠀⠂⠀⠀⠀⠆⠀⠀⢧⠀
⠀⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠘⣴⣿⡿⠿⡿⠿⣿⣶⣤⣤⣤⣾⡎⠱⢦⣄⣀⡴⠋⠀⠸⣟⢛⡉⠉⠉⠉⠙⢆⢃⢇⠀⠐⠀⠀⠀⠆⠀⠀⢸⠀
⠀⠀⠀⠀⡇⠀⣰⠁⠀⠀⠀⠃⠀⠀⠀⣿⡇⠀⠄⢹⠁⢀⠜⠁⠀⠀⠉⣻⡝⡭⠛⠀⠀⠀⡏⡄⠀⠀⠀⠀⠈⠛⢽⣦⡀⠀⠀⠀⠩⡜⡄⠀⠀⠀⠀⠸⣰⠀⢸⡄
⠀⠀⠀⢠⡇⢰⠃⠀⠀⠀⢈⠀⠀⠀⢠⣿⡇⠀⢠⡈⡠⠃⠀⠀⠀⢀⠼⡡⠊⠀⠀⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⢃⠀⠉⢻⣵⡤⣀⡀⣠⠇⠀⠀⠀⠀⠀⠇⠀⠘⡇
⠀⠀⠀⢸⢡⡏⠀⠀⠀⠀⡌⠀⠀⢀⣿⣿⡇⠀⣸⠟⠁⠀⠀⠀⡤⡫⠊⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢷⠀⠀⡇
⠀⠀⠀⢸⣾⠀⠀⠀⠀⠰⠁⠀⠀⣸⣿⣿⠀⠀⢋⢄⣀⣠⢔⠩⡎⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⠀⠱⠀⠀⢹⣿⣧⠀⠀⠀⠀⢸⠀⠀⠀⢸⡄⠀⡇
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠸⠀⠀⢰⣿⢣⣿⠀⠀⠈⠁⠒⠂⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⣿⣿⡆⠀⠀⠀⠈⠀⠀⠀⠈⡇⠀⡇