⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣦⡀⠀⠀⠀⣿⡟⣆⢿⡄⠀⠀⠀⠀⠀⣠⣴⠟⠋⢿⠟⠋⣡⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠛⢿⡄⠀⠀⢸⣿⣟⣮⢿⣄⣀⣤⠶⠛⠉⠁⢀⣠⡴⠖⠛⠉⠀⣀⣬⣽⣷⣤⣀⣀⠀⠀⠀⠀⣀⣤⡴⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡶⣌⣷⣄⠀⠼⣿⣿⣿⣿⣿⠋⠀⠀⢀⣴⠞⠋⠁⠀⢀⣠⣴⠾⠋⠁⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣷⣟⡶⢿⣦⣀⣼⣿⣿⡾⣿⣦⡀⠈⠉⠀⠀⣠⡴⠾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣯⣟⡷⣽⣿⡏⠀⢿⣿⡽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠤⠊⣩⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣮⣿⡿⠿⠿⠿⣅⣀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⣀⡠⠘⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣇⠀⢰⡀⠀⠀⠀⠙⠛⠒⢿⣿⡛⣀⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀⢀⣀⡀⠹⠏⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⡄⠀⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠛⠶⣤⡀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⢷⣌⣷⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠳⠶⣤⣄⣀⡀⢀⠀⠀⠀⠀⠈⢻⣆⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣯⢿⣾⣿⡷⣦⣀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠒⠒⠛⢷⣾⣏⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣶⣿⡏⠀⢀⡿⢷⣤⣀⠀⠀⠈⠙⠷⣶⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⢶⣶⣾⡿⠿⠟⢹⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣇⠀⣼⣿⢟⣫⣭⣷⣦⣤⣄⣀⠀⠙⠻⠷⣷⣾⣧⡿⢿⢿⣿⣟⠉⠀⠀⠀⠈⢿⣇⠙⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⣿⠃⣿⣿⣿⣨⣿⡟⠈⢹⡿⠛⠛⠂⣴⣾⣯⠀⢘⢸⡿⠛⠷⣤⣀⠀⠀⠀⠙⢶⣾⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠁⠀⠛⠛⠻⢷⣶⠿⠁⠀⣠⡾⠋⣠⠟⠀⣠⡿⠃⠀⠀⠉⠙⢷⣶⣶⣦⣤⣬⣉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣤⣾⡍⠀⣴⠀⢰⣿⡟⠀⣼⢱⡆⠀⠀⠀⢹⣦⠀⠀⠉⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣡⡴⠞⠋⠉⠷⣤⣛⡶⣿⡟⠀⣤⢁⣿⠁⢳⡀⢦⠀⠛⢷⣦⣤⣀⣈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⢷⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣜⠛⣻⣟⣡⡾⣃⠚⠁⠀⠀⠱⡈⣧⠀⠀⠸⣇⠉⠻⢯⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢀⠘⠀⠀⠀⡍⠲⡄⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⢀⣠⣴⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡈⠃⠀⠀⠀⣟⠀⠙⣦⡀⠀⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣤⣶⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣷⣄⠀⠀⠀⠙⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢿⡿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣏⣿⡿⣦⠀⠀⠀⠀⡆⠀⠀⠙⣿⠓⠛⠛⠋⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡾⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢷⡆⠀⠉⢹⣟⠉⠷⠶⠶⣤⣤⣤⣤⠶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⣄⣤⡾⢫⣿⣿⣿⣿⡿⢿⡟⠋⠉⠀⢸⣿⣿⣷⡟⢻⠛⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀