⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠺⣿⣿⡶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠸⢩⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠓⢲⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣾⠁⠀⠀⠀⠈⢷⡀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀
⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⠀⠀⠀⠀⠈⢧⡤⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣐⡀⠀⠀
⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠠⡇⠠⠀⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⠿⠃⠀⠀
⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⢹⡄⠀⢀⠀⠀⠀⠀⣾⠀⠀⠀⣴⣤⡄⠀⠀
⠀⠀⠀⠀⠈⢻⡖⠀⡄⠀⠀⣇⠀⠀⠀⢀⡞⠀⠀⠈⡇⠀⠀⣇⠀⠀⠀⣽⠀⠀⠘⢿⡴⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣄⠙⡆⠀⢹⠀⠀⠀⣸⠀⠀⠀⢀⡇⠀⠀⢸⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡆⠈⢧⡀⢠⠇⠀⠀⢀⡞⠀⠀⠀⢘⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠈⠃⢸⠀⠀⡠⠞⢁⣀⣠⡤⢾⡟⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠓⠦⣀⠘⣠⠴⠛⠉⠉⠀⠀⠀⢸⠁⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠸⣤⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀
⠀⠀⠀⢡⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⠲⢤⣀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀
⠀⣀⣀⣼⠏⠹⣦⣤⣀⣀⡀⠀⠀⠀⠀⠈⠳⣦⣄⠀⠈⠉⢹⠒⠦⠤⣀⣀⣀⣀⣤⡾⠁⠀⠀⠀
⠉⠛⠉⠙⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿⣄⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠁⠉⠑⢦⡀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣥⡄⠀⠀⢠⠀⠀⠀⠈⢧⠀⠀
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠠⣾⡧⠀⠀⠀⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀