⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⢾⡇⢸⡷⠶⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠟⠋⠉⠁⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⠉⠙⠻⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢀⣀⠈⠉⠛⠛⠳⠶⣶⣶⠶⠞⠛⠛⠉⠁⣀⡀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣿⡟⠙⢷⣄⡀⢀⣠⡿⠋⠙⢿⣄⡀⢀⣠⡾⠋⢻⣿⣤⡀⠀⠀⠀
⠀⠀⠀⢿⣇⠙⠻⢶⣤⣝⣛⠛⠋⠀⠀⠀⠀⠙⠛⣛⣫⣤⡶⠟⠋⣸⡿⠀⠀⠀
⠀⠀⠀⠈⠛⠷⣦⣤⣀⡉⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⢉⣀⣤⣴⡾⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠶⠶⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⢾⡇⢸⡷⠶⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠟⠋⠉⠁⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⠉⠙⠻⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢀⣀⠈⠉⠛⠛⠳⠶⣶⣶⠶⠞⠛⠛⠉⠁⣀⡀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣿⡟⠙⢷⣄⡀⢀⣠⡿⠋⠙⢿⣄⡀⢀⣠⡾⠋⢻⣿⣤⡀⠀⠀⠀
⠀⠀⠀⢿⣇⠙⠻⢶⣤⣝⣛⠛⠋⠀⠀⠀⠀⠙⠛⣛⣫⣤⡶⠟⠋⣸⡿⠀⠀⠀
⠀⠀⠀⠈⠛⠷⣦⣤⣀⡉⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⢉⣀⣤⣴⡾⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠶⠶⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
