⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠈⢻⣦⠀⢀⠀⠀⠀ ⠀⠀⡀⠀⠀⢸⣿⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢷⣄⠀⠀⢨⡟⠀⢹⣷⠀⠀ ⠀⢸⡇⠀⠀⢈⣿⣿⣏⣤⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⡾⠀⠀⢠⡏⠀⠀ ⠀⢸⣿⡀⣰⠟⠀⢈⣽⡿⠛⠉⠈⣿⣠⣾⣿⢿⣷⣄⠀⠀⢀⣾⡿⠛⠋⠁⢠⡌⣽⣿⣿⣿⣷⣤⣴⡿⠁⢠⣶ ⡀⠈⠻⣷⣯⣤⣴⣾⠋⠁⠀⠀⠀⣻⣿⣿⣟⣼⣿⣿⡄⢀⣾⡿⠁⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡁⠀⣸⡿ ⣇⠀⣰⠋⣼⡿⢻⡏⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⡾⠟⠁ ⠛⢳⡿⣾⡿⠃⣼⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⣀⣴⣿⣿⣿⣿⣿⡟⠉⠸⣿⢿⡇⢻⡄⠀ ⠀⢸⠇⣿⠀⠀⢿⠷⣶⣿⣟⣿⣿⣿⣿⣿⣿⡿⠛⠉⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠐⣿⢸⣧⠈⢳⠀ ⠀⢸⠀⡇⠀⠀⣸⣾⢿⣽⣾⣿⣿⡿⣿⡿⠋⠀⠀⠀⣿⣿⡿⣿⣿⣿⣟⣙⣿⡿⠃⠀⠀⠀⠈⣿⠀⣿⠀⠸⡇ ⠀⢸⡆⡇⠀⠀⠹⣇⣾⠏⠈⠙⢿⣦⣿⠁⠀⠀⠀⣠⡇⣾⣷⡿⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⡟⠀⣿⠀⢸⠇ ⠀⠘⣇⣿⡀⠀⠀⢻⣿⣄⠀⠀⣼⣿⣇⠀⠀⠀⣠⣿⣴⠇⣿⣷⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⣼⡇⢰⣿⠀⣾⠀ ⠀⠀⢿⠹⣿⣄⠀⠀⢻⣿⠷⣾⣿⣿⣿⡄⠀⣠⣿⡿⠋⠀⠘⣿⣿⣿⡛⣿⣿⣆⠀⠀⢀⣼⡟⠀⣾⡇⣸⠇⠀ ⠀⠀⠘⣧⠙⢿⣶⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣿⣧⣿⣿⣶⣿⢿⡽⠃⠀⠀ ⠀⠀⠀⠘⢷⡀⠈⠙⠛⣿⡿⠿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣻⡍⢀⡼⣅⣠⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣆⠀⢾⠏⢀⢶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⢈⣿⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣆⣠⡶⣞⠋⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡟⣛⡒⠞⠿⢿⣶⣶⣶⡿⢛⣉⡀⢀⣿⠀⠰⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⢻⣿⣄⣾⠿⣷⡀⢀⣠⣿⠛⢿⣿⡿⠟⠗⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⣴⡶⠿⠛⠛⠀⠿⣷⣾⣟⣉⠀⠈⠉⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠈⠉⠀⢀⣀⡀⠀⢿⣿⠏⠉⢿⣦⣼⣷⡶⠶⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⠶⠾⠿⣿⣿⠶⠿⠋⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢠⡿⢻⡇⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸⡇⣾⣧⠀⢸⡿⠀⠀⠀⠀⢀⣼⡿⢿⣶⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠸⣿⣼⣿⡀⠈⠿⠻⠟⠿⠿⢾⣯⣀⡀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣾⡗⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡏⠛⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⣿⣷⣿⠛⠋⠀⠀⠀⢠⣾⡿⠟⠻⠿⣷⣦⣄⡀⠀⠙⣿⢄⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⢻⣿⡿⠶⢆⣠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣷⣴⡿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣯⣀⣴⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀