⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⡶⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡴⣫⣾⠛⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢠⡿⠁
⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠉⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⢀⡴⠋⣴⣿⠃⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣠⡿⠁⠀
⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀ ⠀⠀⣠⠟⠁⣼⣿⡟⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢃⣴⠏⠀⠀⠀
⠀⡞⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⠶⠶⠶⠶⣶⠿⠒⢒⣿⣿⡏⠁⠀⣠⣠⢆⣠⣤⣄⠀⠀⠀⢀⣀⣤⢤⣠⣠⠆⠀⠀⣀⣠⢤⣄⠀⠀⢨⣿⣿⡷⠋⠁⠀⠀⠀⠀
⢠⠇⠀⠀⠀⠀⠀⢠⣴⠟⠋⠁⠀⠀⠀⠀⠀⣰⠋⠀⠀⢸⣿⣿⠓⠀⣰⣿⣿⠞⠫⣿⣿⠀⠀⣠⣾⡿⠋⣼⣿⠟⠀⢀⣴⡿⠋⣸⣿⠆⢀⣾⣿⠟⠁⠀⢠⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢠⣿⣿⠃⠀⣰⣿⡿⠁⣰⣿⡿⠁⢀⣼⣿⡟⠀⣰⣿⠃⠀⣰⣿⡿⣡⡾⠿⠋⣠⣾⣿⠏⠀⠀⣠⠏⠀⠀⠀⠀
⠀⣇⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⣺⠟⢁⣠⣼⣿⡟⠓⢚⣯⠟⢀⡴⠋⣼⡛⠀⣴⣿⠃⣠⠞⢿⢿⠉⠀⢀⢠⠞⠱⣏⡟⠀⢀⡴⠁⠀⠀⠀⠀⠀
⠀⠘⣆⠀⠀⠀⠀⠑⠳⠤⠤⠴⠞⠋⠀⠸⠿⠷⢦⣚⡥⠞⠋⡼⠚⠊⠀⠀⠘⢾⡶⠋⠀⠀⠙⠵⠺⣷⠷⠚⠁⠀⠈⠫⠶⠔⠋⠀⠀⠀⠛⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠙⠶⡄⣀⠀⠀⠀⠀⠀⣠⠖⠀⠀⢀⣠⠴⢚⠛⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠉⠘⠛⠛⠛⠉⠁⠀⠀⣴⠏⠀⢠⢂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⠠⢔⣃⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀