⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣀⡤⠖⠒⠋⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠶⠋⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡿⢿⣧⣀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣀⠀⠀⠀⣴⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣧⣾⡟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣾⣿⣿⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣠⣾⡿⠁⢀⣠⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠤⣄⡀⠀⠀⢹⣿⣸⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡴⠁⠀⠀⡴⠿⢈⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠘⣿⢹⢆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡼⠁⠀⢀⠎⣠⠖⢹⡾⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⣜⠈⢦⠀⠀⠀⠹⡄⠀⠀⠀⠀
⠀⠀⠀⣼⢀⠀⢀⡾⠋⠀⠀⢀⠀⠀⡀⣸⠀⠀⠀⠀⡇⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠈⠳⣈⣇⠀⢠⡀⢣⠀⠀⠀⠀
⠀⠀⢰⠃⡼⠀⠀⠀⡀⠀⠀⡎⠀⢠⠃⡟⠀⠀⠀⢰⢡⠀⡆⠀⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⢾⠀⠘⡇⢸⠀⠀⠀⠀
⠀⠀⡏⢠⠃⠀⠀⢠⠃⠀⢸⠁⠀⣸⢀⠇⠀⠀⠀⣸⣸⢰⡇⠀⠀⠀⢸⢸⠃⠀⠃⠀⠀⠀⠠⠀⠀⢸⠀⠀⠀⢸⠁⠀⡇⠀⡇⠀⠀⠀
⠀⠀⠀⠸⠀⠀⠀⡜⠀⢀⡇⠀⢀⡇⢸⠀⠀⠀⠀⡇⡇⢸⡇⠀⠀⠀⣸⡸⠀⢸⠀⠀⠀⠀⢸⢰⠀⢸⠀⠀⠀⡇⠀⠀⢧⠀⡂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡗⠀⣼⠀⢀⣾⡇⢸⠀⠀⠀⢰⣷⡇⣾⡇⠀⠀⠀⡇⡇⠀⣼⢰⠀⠀⠀⣸⢸⠀⢸⠀⠀⠀⠇⠀⠀⢸⠀⡇⠀⠀⠀
⠀⠇⠀⠀⠀⠀⢸⠇⢰⡏⠀⡸⡟⣅⣬⣀⣀⣀⣻⣻⣇⡟⡇⠀⠀⢀⣿⠃⢀⣿⢸⠀⠀⠀⣿⡌⠀⢸⡀⡄⢰⠀⠀⠀⢸⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⢀⢿⠃⠀⣷⢃⠀⡏⠀⠀⠀⣹⡇⣿⠁⡇⠀⠀⢸⣹⠛⢻⢻⡻⠛⠓⠒⣿⣿⡀⢸⡇⡇⣿⠀⠀⠀⢸⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡾⢸⠀⢸⢹⠈⠁⡇⠀⣀⠀⣿⣿⢸⠀⡇⠀⠀⣼⡇⢀⡏⢸⡇⠀⠀⢰⣻⣿⠀⣸⣇⢿⡇⠀⠀⠀⡌⠀⡇⠀⠀⠀
⢸⠀⠀⠀⠀⠀⣯⠃⡎⠀⡎⡎⠀⡆⢇⠀⠀⠁⣿⣿⡆⠀⡇⠀⢠⣷⠁⡸⠁⢸⡇⠀⠀⢸⣿⢻⠀⣿⢻⢺⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀
⢸⠀⠀⠀⠀⠀⣿⠀⡇⢀⣇⡇⠀⠧⠼⣤⣴⣄⠟⠹⠃⠀⠉⠀⠈⠟⠠⢷⣶⣚⠧⠄⠀⣿⣹⢸⠀⡇⢸⣾⠀⠀⠀⢀⡇⠀⢸⡆⠀⠀
⢸⠀⢠⠀⠀⠀⣿⠀⠟⠛⠛⠻⠿⠿⠛⠛⠋⠁⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⣿⠾⣿⡿⠀⠀⡏⠀⠀⠀⢸⡇⠀⠈⢇⠀⠀
⢸⠀⠸⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢠⠇⠀⠀⠀⣾⡇⠀⠀⠸⡀⠀
⠘⡄⠀⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⢀⣯⡇⡆⠀⠀⢧⠀
⠀⡇⠀⢧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡼⠀⣇⠐⡄⠈⣆
⠀⡇⠀⢸⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⠞⠀⡟⡇⠀⣿⠀⠘⡄⠘
⠀⡇⠀⠸⡄⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠋⠉⠉⠉⠙⠓⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡜⠀⢰⠃⡇⠀⢿⡀⠀⢯⢆
⠀⠁⠀⠀⡇⠀⠀⢸⡞⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢰⠃⢀⡞⠀⣇⠀⢸⡇⠀⢸⡀
⠀⠈⠀⠀⢹⠀⠀⠘⡇⠸⣧⡀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢀⣠⣿⡇⢀⠇⢀⡾⡇⠀⢿⠀⠈⣿⡄⠀⣇
⠀⢀⠀⠀⠸⡆⠀⠀⢳⠀⣿⢸⡷⣄⡀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠖⠁⠀⠀⠀⠀⠀⣀⣴⡏⢸⡿⢀⡞⠀⡼⠀⣿⡀⠀⠀⠀⢹⣇⠀⠸
⠀⢸⠀⠀⠀⣧⠀⠀⠘⡄⢹⡄⣿⠀⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣿⣿⠀⢰⠃⡞⠀⢠⡇⠀⢸⢧⠀⠀⠀⠈⣿⡀⠀
⠀⢸⠀⠀⠀⡿⡇⠀⠀⢷⢸⡇⣿⠀⠘⣇⣿⣷⣦⣄⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⣰⠿⣿⠀⡏⡜⠀⢀⡿⡇⠀⠈⣏⢦⠀⠀⠀⠸⡇⠀
⠀⢸⠀⠀⢀⠇⢻⠀⠀⠘⣆⡇⣿⠀⠀⣿⣿⣿⣿⣿⣿⡶⢒⠖⠉⣀⣠⡤⠖⠋⠀⠀⢻⡾⡼⠁⠀⡞⠀⣷⠀⠀⠸⣌⢣⣀⣠⠤⡣⢤