⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠉⣀⣀⣀⣀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⣀⣀⡀⠉⠒⠁⢀⡴⠋⠁⠀⠀⠈⠙⢢⡄⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⡴⠚⠉⠀⠀⠈⠙⢦⣰⠏⠀⠀⡰⢢⠀⠀⠀⠀⠹⣦⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠟⠁⠀⡄⠀⠀⠀⠀⠀⠹⣆⣀⣶⡇⢸⣶⣄⠀⠀⠀⠸⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⣣⠘⣿⣿⣦⡀⠀⠙⣾⣿⣧⣾⣿⣿⡄⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢸⠀⠀⠀⠐⣿⣧⣼⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⡇⠀⢧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣠⠊⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⢸⡻⠿⠿⠟⠃⠀⠀⠀⢠⡟⣦⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡼⠁⠀⠹⡄⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠳⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡼⠀⠀⠀⠀⠽⠒⠒⠒⠦⡀⠀⠀⠀⣀⡾⠥⣀⣀⣀⣀⣠⠴⣾⠁⠀⠀⠀⠀⠙⡄⠈⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡶⠿⠗⠒⠒⠒⠤⠤⣄⣀⠞⠁⠀⠀⠀⠀⠀⠀⠙⡄⠘⣆⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⣀⣀⣀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣀⣰⣄⣀⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣀⣀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠐⠦⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠤⠆⠀⠀⠀⠀⠀⠀⢏⠁⠘⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡟⠀⡸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⢀⡴⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠉⠉⠛⠉⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠲⡄⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡇⠀⢀⣀⣀⠤⡀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠁⠀⠉⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡰⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠉⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⠀⢳⡀⠀⠀⠀⡗⢲⡖⠚⠛⢯⡟⠁⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⢤⣀⡸⠁⠘⣧⣄⡰⠎⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⡀⠤⣄⣈⢉⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀