⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠈⠓⢾⡉⠉⠙⠒⠒⠒⠦⣄⡀⠀⠀⠀
⡤⠖⠒⠒⠋⠉⠉⠉⢩⠏⠁⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀⠀⠈⢳⠀
⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⢀⡼
⡆⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠛⠦⡆⡀⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣄⡖⠖⠂⠀⠀⠀⠀⠀⠀⠘⡌⠀⠀⠀⠀⣀⠖⠃⠀
⢳⡀⠀⠀⠀⡞⠀⠀⣀⣠⡤⣤⠤⣄⡀⠘⢀⢸⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣠⠖⠃⠀⠀⠀⠀
⠀⠘⠲⣄⠀⡇⡴⠋⠀⠀⠙⡆⢧⠀⠉⠧⡈⣸⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠂⠀⠀⣠⢖⣾⡟⠉⠓⢦⡀⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⡇⠇⠀⠀⠀⠀⢸⠀⡇⠀⠀⣹⡼⠯⠤⠤⠤⠤⠤⠤⢿⣦⠀⡼⠁⠀⠀⡏⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠲⣄⣀⣀⣫⣞⣁⣀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠸⣄⢳⡀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡴⠃⠠⣄⣀⠀⠀⣠⠄⠏⠀⠀⠀⣀⡤⠖⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠈⢯⢉⡓⠚⠛⠉⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣤⠤⣤⣤⡀⠙⠂⠀⠀⠀⠀⢩⡀⠉⠓⠒⠋⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⢨⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠧⣁⣤⠀⣴⣽⡾⠀⠀⠀⠀⠀⢀⠀⢳⡀⠀⠀⠢⡀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⢷⠀⠀⢠⢃⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⢧⠀⠀⠀⠙⠆⠀⢣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⢻⠀⣰⠃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧⠀⠀⠀⡗⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⡄⠀⠁⡇⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡇⠀⢀⡌⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣆⠀⠓⡦⣤⡀⠀⠉⠉⠓⠒⡖⠉⠉⠀⠀⠀⠀⠀⠈⠓⣲⠒⠒⠋⠁⣠⠖⠋⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠦⣄⡉⠙⠧⠲⠆⠀⠀⠀⠓⠲⠤⠴⠤⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⡰⢃⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠙⠒⠦⣄⡀⠈⠛⠻⠁⠀⣀⣀⡠⠟⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀