⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠿⠛⠛⠛⠛⠻⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡿⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⢰⠹⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠁⠀⠈⠀⠄⠤⠤⠤⠀⠐⠁⠀⠀⠀⢀⠆⠀⢹⣷⠀⠀⠀⠀⠁⠀⢸⣿⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣆⠈⠁⠐⠐⠂⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⣰⣿⠟⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣦⣌⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠛⠿⣶⣤⣤⣤⣄⣀⣤⣤⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠸⣿⡟⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⢹⣿⡄⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣟⠛⠻⠷⣶⣦⣤⣤⣤⣤⣤⣀⣄⣤⣤⣤⣤⣤⣴⣶⠾⠿⣻⡿⠉⣿⡇⠀⠈⣿⣷⠀⠀⢿⣿⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⢸⣿⢿⣦⠀⠀⠀⠀⠀⠈⠉⢹⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⡟⠁⠀⣿⡇⠀⢠⣿⡏⠀⠀⢸⣿⣤⣾⣿⠟⠛⠋⠉⠙⠛⠻⢿⣷⣄⠀⠀ ⠀⢸⣿⠀⠻⣧⡀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⣿⡇⠀⣼⣿⠁⠇⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀ ⠀⢸⣿⡄⠀⢹⣷⣦⣤⣀⣀⡀⢸⡇⠀⠀⠀⣀⣀⣠⣴⡶⣿⡅⠀⠀⡀⠄⣿⡇⢠⣿⡏⠀⢀⣠⣿⡏⠀⠀⠀⠀⣠⣶⣿⠿⠀⠀⠀⠀⠘⣿⡇ ⠀⠸⣿⣇⠀⣾⡇⠀⠉⠉⠛⠛⢻⣿⠿⠟⠛⠛⠋⠉⠁⠀⠈⢿⣆⠀⠀⠀⣿⡇⢸⣿⣧⣶⣿⣿⣿⠁⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⢀⠀⠂⣿⡿ ⠀⠀⣿⣿⣠⡿⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⣀⣴⣶⠾⠿⠷⢶⣶⣿⡇⠘⣿⣟⠉⣽⣿⠃⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⢸⣿⡿⣷⣤⣀⠀⠀⠀⠀⠀⢹⣷⣀⣀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣦⣿⣿⣾⡿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣦⣄⣀⣠⣤⣾⡿⠋⠀ ⠀⠀⠸⣿⡇⠀⠉⠛⠻⢷⣶⣤⣤⣾⣿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠛⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢛⣿⡟⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣤⣤⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⣄⣀⣀⣀⣀⣴⣿⡇⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⣿⣿⣤⣀⡀⠀⠀⠀⣀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀