⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⣀⠀⢀⢀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⣀⣀⠀⣀⠀⣀⠀⣀⠀⣀⠀⣀⡀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⣿⡇⠀⢸⣿⡆⠀⠀⣾⣿⣿⡀⠀⣿⡇⢿⡏⢸⣿⢸⣿⠀⣿⠀⣿⡇⣿⡇⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⢠⣿⠇⠀⣼⣿⡇⠀⢸⣿⡿⣿⣧⠀⣿⡇⢺⡇⢸⡿⢸⣿⠀⣿⠀⣿⡇⣿⡇⢹⡇⢸⡿⠀⠀⠸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠘⣿⣼⣿⠀⠀⣿⢿⣧⠀⢸⡿⠀⢹⣿⠀⣿⡇⢸⡇⢸⡇⢸⣿⠀⣿⠀⣿⡇⢻⡇⢸⡇⢸⡇⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⣿⣿⡇⠀⢀⣿⢸⣿⠀⢸⡇⠀⢸⣿⠀⣿⡇⢸⡇⢸⡇⢸⡟⠀⣿⠀⣿⠁⢹⡇⢸⡇⢸⡇⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆ ⠀⢹⣿⠁⠀⢸⣿⠘⣿⠀⢸⡇⠀⢸⣿⠀⣿⡇⢸⡇⢸⡇⠈⡇⠀⣿⠀⢿⠀⢸⠃⢸⡇⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇ ⠀⢸⣿⠀⠀⢸⣿⣴⣿⡁⢸⣇⠀⢸⣿⠀⣿⡇⠘⠁⠈⠃⠀⠋⠀⠉⠀⠘⠀⠘⠁⠘⠁⠈⠃⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⢸⣿⠀⠀⣸⣿⣿⣿⡇⢸⣿⣤⣿⡿⠀⣿⡇⢰⡆⢰⣖⢰⣶⠀⣶⠀⣶⡆⣶⡆⢰⡆⢰⣶⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⣼⡇⠀ ⠀⢸⣿⠀⠀⣿⡏⠉⣿⣇⠘⣿⣿⣿⠇⠀⣿⡇⢸⡇⢸⣏⢸⣿⠀⣿⠀⣿⡇⣿⡇⢸⡇⢸⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⢸⡟⠁⠀⠀ ⠀⠘⠛⠀⠀⠛⠃⠀⠛⠛⠀⠘⠿⠋⠀⠀⠛⠃⠘⠃⠘⠛⠘⠛⠀⠛⠀⠛⠃⠛⠃⠘⠃⠘⠛⠀⠀⠀⠀⠀⣽⣿⠁⠀⠀⠉⠋⠁⠀⠀⡀⠀⠀⠀⠀⣾⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠛⠷⠶⠖⠋⠁⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠁⠋⠖⠶⠷⠛⠀⠀⠀⠁⠟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠅⣾⠀⠀⠀⠀⡀⠀⠀⠁⠋⠉⠀⠀⠁⣿⣽⠀⠀⠀⠀⠀⠛⠘⠃⠘⠃⠛⠃⠛⠀⠛⠀⠛⠘⠛⠘⠃⠘⠃⠛⠀⠀⠋⠿⠘⠀⠛⠛⠀⠃⠛⠀⠀⠛⠘⠀ ⠀⠀⠁⡟⢸⠀⠋⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣷⢸⡇⢸⡇⣿⡇⣿⠀⣿⠀⣿⢸⣏⢸⡇⢸⡇⣿⠀⠇⣿⣿⣿⠘⣇⣿⠉⡏⣿⠀⠀⣿⢸⠀ ⠀⡇⣼⠄⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠀⠀⠀⠀⠀⣶⢰⡆⢰⡆⣶⡆⣶⠀⣶⠀⣶⢰⣖⢰⡆⢰⡇⣿⠀⡿⣿⣤⣿⢸⡇⣿⣿⣿⣸⠀⠀⣿⢸⠀ ⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠃⠈⠁⠘⠁⠘⠀⠘⠀⠉⠀⠋⠀⠃⠈⠁⠘⡇⣿⠀⣿⢸⠀⣇⢸⡁⣿⣴⣿⢸⠀⠀⣿⢸⠀ ⣇⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⡇⢸⡇⢸⠃⢸⠀⢿⠀⣿⠀⡇⠈⡇⢸⡇⢸⡇⣿⠀⣿⢸⠀⡇⢸⠀⣿⠘⣿⢸⠀⠁⣿⢹⠀ ⡆⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢸⠀⠀⠀⠀⡇⢸⡇⢸⡇⢹⠁⣿⠀⣿⠀⡟⢸⡇⢸⡇⢸⡇⣿⠀⣿⢸⠀⡇⢸⠀⣿⢸⣿⢀⠀⡇⣿⣿⠀ ⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⡇⢸⡇⢸⡇⢻⡇⣿⠀⣿⠀⣿⢸⡇⢸⡇⢸⡇⣿⠀⣿⢹⠀⡿⢸⠀⣧⢿⣿⠀⠀⣿⣼⣿⠘ ⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⠸⠀⠀⡿⢸⡇⢹⡇⣿⡇⣿⠀⣿⠀⣿⢸⡿⢸⡇⢺⡇⣿⠀⣧⣿⡿⣿⢸⠀⡇⣿⣼⠀⠇⣿⢠⣿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣿⡇⣿⡇⣿⠀⣿⠀⣿⢸⣿⢸⡏⢿⡇⣿⠀⡀⣿⣿⣾⠀⠀⡆⣿⢸⠀⡇⣿⠀⣧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢀⡀⣀⠀⣀⠀⣀⠀⣀⠀⣀⠀⣀⣀⡀⣀⠀⠀⡀⣀⠀⠀⠀⠀⢀⢀⠀⣀⠀⠀⡀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⣶⣶⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⡆⣶⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀