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