⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢋⣉⠀⠀⠀⠀⠀⠉⠻⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⢾⣿⡆⢠⣾⡿⢿⣦⢸⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠈⠉⠀⣾⡏⠀⠈⣿⡇⠀⠹⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣿⡇⠀⠀⢻⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣰⣿⠃⠀⠀⣸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⠀⠀⢀⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣾⠇⠀⠀⠀
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠘⠿⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⡿⣫⣿⣿⠟⠁⠀⣼⠁⠀⠈⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⢟⣩⣾⠿⠋⠁⠀⢠⣴⣧⣤⣤⣤⣿⡏⠈
⣿⣿⢿⣿⣿⡿⠟⠽⠛⠉⠀⠚⠉⠚⠋⠉⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⢀⡿⠉⠂
⣿⠏⢸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀
⡇⠀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣤⣀
⣩⣿⡿⠟⣿⣿⣿⣿⣿⣯⠙⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣯⠙⠻⢿
⠹⣿⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢈
⡀⠈⠂⡀⣙⢩⢿⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⣿⠃⠀⢀⡘
⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣶⠶⠟⠋⠙⢶⣤⣴⠄⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣮⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿