⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠐⣒⣲⠶⠖⠒⠂⠉⠑⢦⠤⣀⣀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⣀⡀⠈⢦⠔⠚⠉⠉⠄⠀⠀⠀⠈⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠂⠁⠀⠀⢀⣴⣾⣅⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀⠈⢧⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣄⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⣴⣿⠿⠟⠛⠛⠷⠀⠈⠀⠀⣠⢾⣿⣿⣿⣆⠀⠀⠀⠳⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠹⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠻⣆⢀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠁⡎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡌⠙⣻⣿⣿⣿⠟⣿⣿⣿⣿⡟⠋⠀⠀⣸⠁⠔⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠠⠀⠀⠸⡆⠀⠀⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣡⣾⣿⣿⣿⠟⠀⢻⣿⣿⣿⣧⠀⠀⢀⢇⠎⠀⡠⠤⠔⢖⡶⡗⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⣄⡀⠀⠱⡀⠀⢻⡀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣆⠀⣸⠏⠀⠀⠀⣀⡴⠋⠀⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠙⢯⡓⢄⢡⠀⠈⣷⠀⠀⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⠿⣿⣿⡟⠀⢀⠀⡀⢿⣿⣿⣿⣿⠀⡏⢀⣠⣴⣚⡁⠀⡠⠀⢿⠀⠀⠀⢀⡆⠀⢸⠀⠀⢠⡇⠀⠀⠙⣦⠀⡇⠀⣿⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⣠⠏⠀⠀⠐⣀⡜⠀⠘⠿⠿⠛⠛⢰⣿⡿⣿⣿⣿⣿⣿⣷⣾⣼⡀⠀⢀⣾⠁⠀⠸⠀⠀⣼⣠⣠⣤⣤⣬⣷⣽⡀⣿⢠⠀⠀⠀⠈⢟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠿⣥⣤⡤⠶⣾⠋⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⡎⠉⣿⣿⣿⣿⣻⡿⣇⣠⠏⢸⠀⢀⡇⠀⣰⣿⣿⠿⣿⣿⠿⠿⣿⣧⣿⡼⠀⠀⠀⡀⠀⠑⢄⡀⠀⠀⠀
⠀⠀⠀⡘⠀⢠⠆⠀⢰⡇⢀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⡇⠀⣿⣿⣿⡇⠀⡇⠈⠉⠀⢸⡇⢸⢃⡴⡟⢻⣿⣿⡏⠙⡆⠀⠀⢹⣿⡇⠀⠀⠀⠧⠤⠤⠤⠝⠀⠀⠀
⠀⠀⢰⠁⠀⡼⠀⢀⡾⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⣿⣿⣿⡇⢀⠇⠀⠀⠀⠈⣇⣯⠞⠀⡇⢸⣿⣿⡇⠀⡇⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡠⠃⠐⡼⠁⠀⡾⠁⣠⣿⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢣⠀⠹⣿⠟⠀⡼⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇⢸⣿⣿⠃⢰⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⠁⣠⠞⢡⡄⠺⢷⠞⠁⣿⠀⡆⠀⠀⡇⠀⠀⡇⠀⠀⠀⠑⠦⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⠋⢠⠎⠀⠀⠀⠀⢹⡇⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢻⡁⠀⣸⠃⢀⡏⠀⡀⣿⠀⢧⠀⠀⢣⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠹⣿⠋⢀⠎⠀⢸⣇⢻⠀⠸⡆⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀
⡄⢢⠀⠘⢶⢁⣠⣶⣿⣿⢿⣇⠀⢿⡀⠈⣇⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⢄⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡜⣼⠁⢣⠀⠀⠀⠀⠀⠀⠀
⠘⣆⠁⡤⣈⢫⠈⠉⠁⣣⣤⣽⡄⢸⣷⡀⢹⡀⠀⣷⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏⣰⣷⠃⠑⢤⣳⣄⠀⠀⠀⠀⠀
⠀⠘⣆⡇⠀⠉⠣⠔⠋⣡⠃⢠⠟⠾⠀⠳⣄⡳⡄⠘⡆⠀⠀⠈⠙⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⠤⠤⠤⣤⠴⠶⡒⠚⠋⣽⣹⡿⣠⡟⢯⠉⠓⠒⠛⠉⠀⠀⠀⠀⠀