⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⢿⣿⣅⡘⠛⢻⣿⠟⠉⠉⣽⡟⢛⣿⡿⠛⣿⡿⠛⠛⠛⠛⣿⡿⠛⠛⠻⠿⢿⣿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⢀⣹⣿⠇⣠⣿⠋⠀⣠⣾⣿⣿⡛⠉⢹⣿⠟⠛⠛⠹⢿⣿⠟⠛⠛⠁⠀⣠⣾⠋
⠀⣀⣠⣤⣶⠾⠟⠋⠁⣰⡿⠁⠀⠠⠞⠁⠀⠹⣷⣤⣿⡿⠾⠟⣻⣶⣿⡷⠶⠟⠒⠀⣰⡟⠁
⠀⠈⠉⠁⠀⠀⣀⠀⠀⠉⢀⠀⠀⢠⡆⢀⣦⠀⣤⠉⠀⠀⢀⠀⠈⠉⣀⠀⠀⠀⢀⠀⠉⠀⠀⢀⣀⡀
⠀⠀⠀⢀⣴⣿⣿⠃⢠⣾⣿⠃⣴⡿⣡⣿⢋⣴⣿⣄⣠⣶⡿⠁⣠⣾⣿⠃⢀⣴⠟⠀⠀⣴⣿⣛⠉⠁
⠀⣀⣴⣿⣯⣿⠷⣶⡿⢻⣿⣾⠟⣰⡿⣣⡾⠋⠿⢟⣿⣟⣠⣾⣯⣿⡧⣶⡿⠋⠀⠀⠀⠀⢙⣿⡗
⠠⠾⠋⠀⣸⡏⣴⡟⠁⠸⠿⠋⣼⡟⠱⠛⠁⠀⢀⡾⠫⠿⠋⠁⣼⣏⣼⣿⣥⣤⣤⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠻⠞⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠛⠙⠋⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢰⣆⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⣾⢿⠧⢤⣄⣿⣿⡄⠀⣰⣿⣇⠀⢀⣾⣷⠀⢀⣤⡀⠀⠀
⠐⣶⠒⣲⡆⠀⣿⣿⣷⡄⣼⣡⣤⣄⠀⠘⣧⣼⣿⢰⡿⠙⣿⢠⡿⢿⣿⠀⣼⡿⢃⣴⡆
⠀⢿⡾⣿⣥⣀⠿⠀⠘⠃⣿⣿⠠⠽⣶⡄⠸⢤⣈⢻⣿⣄⡀⠈⠁⠀⠛⢰⡿⠀⣸⠟⠁
⠀⠘⣿⠀⠉⠛⠀⠀⠀⠀⠈⢻⣧⢂⣉⢻⣦⣀⡉⠑⠻⢿⣿⡆⠀⠀⠀⠀⠀⠘⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⢛⣉⣙⣧⡜⠑⠀⠂⣤⢭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣾⡇⢃⣼⡟⠀⢀⣤⣫⡉⢊⣀⠏⠳⢤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣴⡟⠀⣠⣞⢧⢹⡛⢼⠿⡿⡟⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⠀⡜⣷⢌⡷⠋⢹⣸⠲⡇⠹⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⡖⠛⢻⣬⠷⠀⠀⠸⡿⣄⣻⡳⠮⠽⠆⠀⠀⠀⠀

⠀⠀⠀⠀⣿⠙⣦⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⢻⠀⠈⠳⠀⠀⣀⣴⡾⠛⠁⣠⠂⢠⠇
⠀⠀⠀⠀⠈⢀⣀⠤⢤⡶⠟⠁⢀⣴⣟⠀⠀⣾
⠀⠀⠀⠠⠞⠉⢁⠀⠉⠀⢀⣠⣾⣿⣏⠀⢠⡇
⠀⠀⡰⠋⠀⢰⠃⠀⠀⠉⠛⠿⠿⠏⠁⠀⣸⠁
⠀⠀⣄⠀⠀⠏⣤⣤⣀⡀⠀⠀⠀⠀⠀⠾⢯⣀
⠀⠀⣻⠃⠀⣰⡿⠛⠁⠀⠀⠀⢤⣀⡀⠀⠺⣿⡟⠛⠁
⠀⡠⠋⡤⠠⠋⠀⠀⢀⠐⠁⠀⠈⣙⢯⡃⠀⢈⡻⣦
⢰⣷⠇⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠈⠻⢯⡄⠀⢻⣿⣷
⠀⠉⠲⣶⣶⢾⣉⣐⡚⠋⠀⠀⠀⠀⠀⠘⠀⠀⡎⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡄⠀⠀⢠⣿⣴⠀⠀⣿⣿⣿⣧
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠀⢠⠟⣿⠏⢀⣾⠟⢸⣿⡇
⠀⠀⢠⣿⣿⣿⣿⠟⠘⠁⢠⠜⢉⣐⡥⠞⠋⢁⣴⣿⣿⠃
⠀⠀⣾⢻⣿⣿⠃⠀⠀⡀⢀⡄⠁⠀⠀⢠⡾
⠀⠀⠃⢸⣿⡇⠀⢠⣾⡇⢸⡇⠀⠀⠀⡞
⠀⠀⠀⠈⢿⡇⡰⠋⠈⠙⠂⠙⠢
⠀⠀⠀⠀⠈⢧