⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⣿⣿⣿⣿⣟⠘⠛⠻⠿⣿⣿⣿⣿⣤⣤⣿⠿⠟⠃⠀⠀
⠤⢤⣀⣀⣀⣀⣀⣤⣾⡿⠻⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠛⠻⣿⣿⣤⡀⠛⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⣀⣴⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣤⣤⣀⣤⣤⣶⣶⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠉⠛⠟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠁⠌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣾⠟⠛⠉⠀⠀⠠⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⢻⣿⣿⡿⠿⣿⣿⡏⠉⠻⢿⣿⣷⠀⠀⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡛⠁⠀⠀⠻⣿⣿⣶⣿⣿⠁⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣤⣀⣀⣀⡉⠉⠉⣀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠙⠿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣶⣶⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠉⠉⠠⣿⣍⣽⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠒⠿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠋⣻⣿⣿⣿⣷⣶⣤⣤⣠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣤⣀⠀⡀⠀⠀⠈⣛⣉⣩⣶⣾⠟⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠿⠿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀