⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠁⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢱⣟⣦⣄⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⡿⠟⢫⣧⣠⣴⢻⡞⠁⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⢸⣿⣧⢿⢹⡆⢠⣴⣟⣫⣿⣃⢭⠛⠁⢀⣼⢿⣏⡇⣼⣳⡇⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠈⣯⠉⠹⠏⢻⢸⡃⡽⡁⠉⠌⣆⣷⠀⠾⣷⣿⠻⠇⢉⣿⢁⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠀ ⠀⠀⠣⡀⠀⠉⠑⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⣳⠀⠀⢸⠀⠱⣝⣷⡦⠴⡿⣿⣀⣰⡿⡇⠀⠀⣯⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠂⠉⠉⣠⠇⠀ ⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠉⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣿⣤⣄⠈⠙⣿⣿⣷⠊⣽⣿⣠⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠉⠉⠀⠀⠀⢀⡠⠄⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠉⠓⠂⣴⠲⣦⣤⠝⣩⢞⡫⢻⣧⠴⠏⠛⠛⠛⢟⡝⢿⠛⠋⣿⣶⣺⣛⣷⠚⠉⠁⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⢹⣿⠿⠿⡇⡐⠋⠀⡜⠁⠘⠛⠶⠦⡄⠈⠉⠃⠰⠞⠀⢻⣿⡾⠃⠀⠀⠀⠀⣀⠠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣄⡴⠋⠀⠀⠀⠘⣷⣤⣾⣱⠀⢀⣀⠀⠀⠀⠀⣤⢤⢠⡞⣆⣀⣿⣿⣄⠤⠖⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢯⠀⠒⠒⠒⠠⠤⠤⣄⣀⣀⣀⠀⠀⣠⣴⣿⣿⣧⣴⣾⣿⣶⡾⢛⢉⣿⠿⠀⠀⠉⠛⠶⣤⢈⠇⠘⡆⣽⠟⠉⢈⣿⣿⣄⣀⣀⣀⣀⣀⠠⠤⠤⠤⠄⠒⠒⠒⠒⠒⠈⠉⡹⠃ ⠀⠀⠑⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠻⠿⠿⢿⣟⢻⣻⣟⢻⣿⣿⣷⣄⣀⠀⠀⠀⣤⣿⣞⣿⣿⣆⠀⢀⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠐⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⢤⣀⡀⠀⠀⠈⢦⠀⠀⠸⣷⣯⡻⠟⠧⠈⢻⠛⠛⢿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⠟⢿⣿⣿⣿⢿⣿⣠⠤⠤⠐⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠲⠷⡄⠀⠹⣏⡿⠤⣄⠀⠀⣷⢰⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠒⢺⠙⠋⠋⢾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠹⣯⡉⠙⠶⣿⣿⠛⠙⢧⣙⡿⠿⠿⠿⠿⠟⠻⣧⣿⡶⢾⣷⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢛⣣⣶⣻⣿⣵⡾⠋⠻⣄⣀⢠⡀⠙⠦⡀⠀⠀⠠⣖⡜⠉⢳⠟⠃⠀⠀⢸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠻⢼⣽⣵⣿⡟⢿⣦⠀⠀⠙⢿⣷⣬⣳⠁⠘⡄⠀⡸⡟⠉⣱⠇⢣⢸⣀⣀⣼⠀⠉⠑⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠸⡤⣿⠃⣴⡟⠀⠀⢳⣿⣿⣧⣀⡀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠈⠁⠀⠀⠀⠀⢀⣀⠤⠖⠊⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠆⢀⡈⣁⣼⡟⠀⠀⠀⠀⠙⣿⣿⡄⠉⠉⠀⠒⠢⠤⠄⢀⣀⡀⢀⣉⠵⠆⠀⠀ ⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠀⠀⢠⣼⡏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⠉⣡⣽⣿⡄⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀ ⠰⣞⡁⠀⠀⣀⡤⠄⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡾⢛⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⠠⣀⠀⠀⠀⠀⠀⠀⠀⡇⡀⣶⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⣓⠄⠀⠀⠀⢀⠴⠧⡇⠇⢀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⢀⡴⠙⡆⠀⡇⡆⠈⡆⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢻⠷⢯⢄⡜⠀⣴⠀⢻⠤⣜⣦⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡋⠉⠘⢦⣠⠈⢀⡼⡿⡀⠘⡆⠀⡸⠣⢬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⡼⠙⡲⠋⠀⢳⢱⠒⠓⡏⠀⢰⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠏⠀⠀⠐⢁⠞⠁⠀⠀⠈⣎⡆⠀⠃⠀⢸⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀