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