⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠿⠿⠛⠛⠛⠛⠻⠿⠷⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠟⠁⠉⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠖⢻⡿⠁⠀⠀⠀⠀⡀⠘⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⣀⣠⡤⠶⠞⠛⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠀⠈⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⣠⣴⣾⠛⠉⠁⠀⠀⠀⠀⠀⢀⣴⣶⠶⣦⣈⢿⡄⠀⠀⠁⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀ ⠀⠀⣼⡏⢀⣴⣾⡏⠉⠻⣷⣄⠀⠀⠀⢀⣤⡾⠟⠉⠁⠀⠈⠻⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⢀⢻⣧⣿⣿⣿⣿⣧⣄⠈⠛⠓⠀⠀⠛⠋⠀⣠⣤⣶⣶⣦⣤⡈⡛⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⠀⠈⢸⣿⣿⡁⢱⣿⣾⣿⣧⠀⠀⠀⠀⠀⣤⡾⢿⣏⡀⠀⠈⠙⢿⣯⡛⣷⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⢸⡏⣿⠻⣾⣍⡩⠟⠙⣧⠀⠀⣠⡾⠋⣦⠀⠿⠧⠀⣀⣴⡾⠟⠁⠼⠷⠶⣶⡆⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠸⣷⢿⣧⠀⠉⠛⠓⢾⣿⠷⠶⠿⠤⠤⠿⠿⠿⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⣿⡌⣿⡄⠀⠀⠀⠘⢿⣤⣤⠤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⣴⡟⠀⠀⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠘⢿⡄⠀⠀⠀⠈⠿⣿⣛⣛⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⠉⣹⠁⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠀⠈⢿⣆⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠀⠏⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣾⡏⠉⠀⠀⢰⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠙⢷⣄⡀⢠⠀⢀⣤⡶⣿⠏⠀⣿⠇⠀⠀⠀⠈⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⠀⡆⠀⠀⠀⠈⠛⠿⡿⠋⠁⢠⡟⠀⠀⣿⡀⠀⠀⢰⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡀⠰⠀⠀⠸⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠀⡇⠀⠀⠀⣠⣶⡿⢿⣿⡃⣀⣤⣶⠿⠗⠲⣶⣄⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡀⢰⣄⣀⣴⣿⣱⣷⣸⣿⡟⠉⠁⠀⠀⠀⠀⠉⢿⡀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⡅⠀⠙⣿⣿⣼⣿⠷⠶⣦⠀⡀⠀⠀⠀⢸⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⣿⡀⠀⠈⣻⡏⠀⠀⠀⠈⢿⡇⠀⠀⠀⠈⣧⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⡟⠶⠶⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⠁⠀⠀⣾⠁⠀⠀⠀⠀⣰⣿⡀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⠀⠀⢠⡏⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⣼⡇⠀⠀⠀⠀⢰⡏⢸⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠸⣿⣆⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣾⠃⠀⠀⠀⢀⣿⠀⠸⡇⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣆⠸⣟⢷⣄⡀⠀⠀⣸⣿⡇⠀⠀⣿⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⢸⢿⣦⡀⠀⠀⠀⠀⣀⣴⡆⠀⡀ ⠈⣿⣷⣽⣦⡉⠻⠶⠾⠛⣽⠃⠀⢀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢻⠀⠀⠀⣿⡀⠉⠛⠷⠶⠶⠛⣻⠟⢀⣼⡿ ⠀⠘⣷⡌⠛⠿⣤⠀⠀⠀⡟⠀⠀⣿⡇⠀⠀⠀⢾⡏⠀⠀⠀⢸⡇⠀⠀⢿⡇⠀⠀⠀⠀⣠⣾⣫⣴⠟⣿⠇ ⠀⠀⠈⢷⣄⠀⠀⠀⠀⢰⣇⣠⡷⠿⠃⠀⠀⠐⢿⣄⡀⠀⠘⣿⡇⠀⠀⢻⠀⠀⢀⣤⠾⠿⠛⠋⢀⣼⡏⠀ ⠀⠀⠀⠈⠻⣷⣄⠄⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⣸⡇⠀⠀⣾⡄⣀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⣿⠂⠈⠁⠀⢀⣤⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⣤⣤⣶⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢸⣿⠉⣿⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢿⣿⡆⢀⠉⠙⠛⠳⠶⠶⠶⠶⢿⡟⢛⣉⠁⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠘⠃⠘⠻⢦⣤⣄⡀⠀⠀⠀⣿⣧⣿⡿⠟⢻⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢙⣿⡇⠀⠀⠙⠉⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⡀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣻⢣⣿⣧⡀⠀⠀⠀⢸⣿⡇⠀⠰⠀⠀⠀⣼⣿⣿⣿⢿⡛⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⢿⣿⣿⣼⡿⣿⣧⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣿⣿⡞⣿⣌⢻⣌⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣯⣾⣿⢿⣿⣿⠟⢿⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠏⢳⣽⣟⢷⣽⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⠟⠁⠾⠛⠁⠀⠈⣿⣄⠀⠀⢸⣿⠀⠀⠀⠀⢰⡿⠀⠀⠙⠻⠦⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⣿⡀⠀⠸⣿⡀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠐⣿⡇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢻⡇⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻⡇⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⣿⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣇⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡨⣿⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⡇⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⢸⡇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣸⡇⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠞⢻⣷⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⠿⠛⠉⠀⠀⠀⠈⣿⠻⢦⡿⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠓⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀