⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣿⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣾⠃⠀⢿⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠘⢷⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠠⣼⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⣧⡀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡏⢿⡆⠀⠀⢠⡟⠳⣄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡆⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣸⣷⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠀⠀⠀
⠀⠀⠀⢠⡟⠀⠈⣷⠀⠀⣾⠁⠀⠈⠳⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢿⡀⠀⠀⠀⠀⠀⣾⠃⠀⣀⣠⠶⠋⠁⢹⡆⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄⠀⠀
⠀⠀⢀⣾⠀⠀⠀⢹⡆⢸⡏⠀⠀⠀⠀⠀⢹⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⣧⠀⠀⠀⠀⣼⣧⠶⠟⠉⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⡇⠀⠀
⠀⠀⣼⠃⠀⠀⠀⠀⢷⣿⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣜⢷⡀⠐⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣴⣆⠀⠀⣿⡇⠀⠀⠀⠀⣇⠀⠀
⠀⢰⣷⣤⣤⣀⣀⣀⠈⠏⠀⠀⠀⠤⢀⣀⣀⣈⣷⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⢿⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠟⠁⢿⡄⢸⡟⣷⠀⠀⠀⠀⣿⠀⠀
⢀⣿⠛⠛⠿⠿⢿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣈⣉⣿⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡟⠿⣆⠀⠀⠀⠒⠒⠒⠄⠤⠀⠀⠉⠁⠀⠀⠘⣇⣾⠁⢹⣇⠀⠀⠀⣿⠀⠀
⣸⡇⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠛⠛⠿⠿⠿⢿⣿⠿⣦⡇⠀⠀⠀⠀⠀⢀⣴⢿⠀⠀⠈⠓⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣿⣶⡆⠀⣿⠀⠀
⣿⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣼⠃⠀⠀⠀⢀⣴⠟⠁⢸⡇⠀⠀⠀⠉⠉⠉⠉⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⢻⡟⠃⠀⡿⠀⠀
⡟⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⢀⣴⡟⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣧⠀⢰⡇⠀⠀
⢷⣹⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣠⡾⠛⠉⠛⢦⣄⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣸⠇⠀⠀
⠈⠻⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠙⠳⣤⡈⣧⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⣿⠀⠀⠀
⠛⠶⣬⣷⣤⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⣇⡏⠀⠀⠀
⠀⠀⣾⠋⠉⠉⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⢸⣿⠃⠀⠀⠀
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⣀⣠⡤⠞⠃⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀
⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀
⣧⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀
⢻⡀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀
⠘⣧⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠴⠶⠛⠛⠉⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀