⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠉⣀⣀⣀⣀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⣀⣀⡀⠉⠒⠁⢀⡴⠋⠁⠀⠀⠈⠙⢢⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⡴⠚⠉⠀⠀⠈⠙⢦⣰⠏⠀⠀⡰⢢⠀⠀⠀⠀⠹⣦⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠟⠁⠀⡄⠀⠀⠀⠀⠀⠹⣆⣀⣶⡇⢸⣶⣄⠀⠀⠀⠸⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⣣⠘⣿⣿⣦⡀⠀⠙⣾⣿⣧⣾⣿⣿⡄⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢸⠀⠀⠀⠐⣿⣧⣼⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣠⠊⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⢸⡻⠿⠿⠟⠃⠀⠀⠀⢠⡟⣦⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡼⠁⠀⠹⡄⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠳⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡼⠀⠀⠀⠀⠽⠒⠒⠒⠦⡀⠀⠀⠀⣀⡾⠥⣀⣀⣀⣀⣠⠴⣾⠁⠀⠀⠀⠀⠙⡄⠈⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡶⠿⠗⠒⠒⠒⠤⠤⣄⣀⠞⠁⠀⠀⠀⠀⠀⠀⠙⡄⠘⣆⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⣀⣀⣀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣀⣰⣄⣀⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣀⣀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠐⠦⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠤⠆⠀⠀⠀⠀⠀⠀⢏⠁⠘⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡟⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⢀⡴⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠉⠉⠛⠉⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠲⡄⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡇⠀⢀⣀⣀⠤⡀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠁⠀⠉⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡰⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠉⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⠀⢳⡀⠀⠀⠀⡗⢲⡖⠚⠛⢯⡟⠁⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⢤⣀⡸⠁⠘⣧⣄⡰⠎⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⡀⠤⣄⣈⢉⣀⡠⠊⠀⠀⠀⠀