⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠴⠒⠛⠓⠶⠶⣤⣶⣦⣴⣦⣤⣤⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣼⣧⣀⣀⣠⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢹⣿⣿⣏⣛⣓⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠉⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠉⠉⠉⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣽⣆⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢠⡆⠀⠀⢸⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡆⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠰⣽⠇⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢸⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠸⣿⣿⣁⠀⠀⠀⠀⡀⣠⣾⣿⠛⠁⠹⣿⣦⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⣠⣾⣿⣿⣾⣦⠀⠀⠀⠀⠉⠻⢦⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⡇⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⢸⣿⠁⠀⣰⣿⣿⣿⣦⣨⣾⡿⠀⢰⣆⣀⣤⣤⣾⣻⠻⣷⣄⠀⠀⠀⠀⠀⠀⣄⠺⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢸⡏⠀⠀⢻⡿⢻⣿⣿⣷⣿⡀⠀⠈⢿⣿⣿⣿⣿⣻⠏⠙⢿⣷⣦⡀⠀⠀⠀⠙⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣼⣇⠀⡀⣸⣧⣞⢛⣿⣿⣿⣇⣀⠀⠈⠳⠏⠙⠋⠉⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢰⡆
⠀⢀⠜⢘⣧⣼⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢻⡇⠀⢱⣿⣿⣿⠀⠀⠛⢉⡟⠛⢻⡀⢀⡇⠀⠀⠀⠀⢠⡿⠁⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠇
⣚⣥⣶⣥⣿⠿⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠸⣧⠀⠈⢿⣿⣿⡆⠀⠀⢀⡀⠀⢀⣀⡜⠀⠀⠀⠀⢀⣿⠇⠀⣼⣿⡃⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢿⠀⢂⠈⠻⣿⣿⠀⠀⠈⢹⣶⠋⠀⠀⠀⠀⠀⠀⢿⠟⠘⣵⣿⣿⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠘⣷⣾⣄⣸⣿⣿⣷⠀⢘⣟⠿⠛⠛⢳⡶⠄⠀⠀⠀⢀⣼⣿⣿⣿⣿⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⣿⣷⡄⠉⠙⠛⠋⠉⠁⠀⢠⣤⠶⠛⠁⣹⣿⣿⣿⣿⣶⣶⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠙⡇⠀⠀⢸⠀⠀⠀⢀⣤⠞⠋⠀⣠⠾⠋⠘⣿⡟⢿⣦⣀⠀⠀⢀⣤⣴⠟⠁⠀⠀⢰⣿⣻⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⢸⠁⠀⠀⣸⣤⣶⡿⠋⠀⠀⠴⠞⠁⠀⠀⠀⠈⢻⣄⠉⢻⣿⣿⣿⠿⠃⠀⠀⠀⠀⣼⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⢸⡅⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣞⢻⣿⡿⠀⠀⠀⠀⠀⣸⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠠⠾⠃⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣯⣀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠹⠶⣤⣀⣀⣰⡏⣸⠿⢿⣿⣿⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀