⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣸⠃⣴⠥⠋⣴⠁⡿⢀⡞⢹⡇⢸⠇⢹⢀⡖⢱⡆⣴⠂⣦⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠈⠀⠁⠙⠀⠓⠈⠓⠙⠂⡾⠒⠋⠈⠃⠚⠁⠓⠔⠃⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡲⣖⡲⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⡝⣾⣿⣿⣮⢷⡹⢮⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣤⡐⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣭⢳⣿⣿⡿⠿⣿⣾⡹⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢣⣛⣾⣷⣿⣿⡿⣭⢧⣿⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠠⣁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡝⣮⢳⢎⡟⣯⢳⡝⣮⣛⢮⢿⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠹⣞⢧⡻⣜⢧⡻⣼⡱⣎⡟⡞⠁⠀⠀⠀⠀⠀⢀⣼⢿⣻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠷⣝⣮⢳⡝⡶⣹⣚⠀⠄⠀⠀⠀⠀⠀⢀⣾⣟⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢷⡀⠀⠀⠀⠀⠀⡄⢻⡽⣞⡿⣾⢷⣧⣯⠌⠀⠀⠀⠀⢀⣠⣿⣯⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⢐⣵⣁⣛⣯⣿⣿⢾⣿⣿⣀⠀⠀⢀⢶⣶⣯⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣆⠀⢀⡼⣗⢿⣻⣛⢿⣻⣟⣿⡻⣇⡶⣣⢤⣤⡤⢖⣫⣉⣁⣀⣀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡮⡛⠁⢀⡟⣮⢻⡔⢋⡚⢧⡻⣼⣗⢯⣾⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠠⣀⣤⢶⣾⠋⢂⡀⣠⢤⢛⠄⣠⣐⢦⣻⣈⣙⠯⣿⠿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⡿⣿⣷⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⡿⣿⠾⣿⡹⣎⢷⡹⣎⢳⡥⣚⢶⡽⣞⡷⣯⡿⣱⣾⣿⣿⡿⢿⣿⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⡖⠀⠀ ⠀⠀⠀⣾⣿⣿⣽⣣⣴⣎⢷⡹⣎⢷⡹⣎⢷⣽⠿⣝⣯⢿⣝⣾⣽⣿⢟⣧⣛⣷⣿⣯⣿⣿⣽⣿⣿⣷⣿⣿⣿⠇⠀⠀ ⠀⠀⢀⣿⣿⡿⣿⣏⢷⣎⢷⡹⣎⡿⣱⣏⡿⣾⢿⣿⣹⢿⣿⣿⣿⢏⡾⣶⢹⣿⣾⣿⣷⣿⣿⢿⣿⣿⣿⣿⡿⠀⠀⠀ ⢠⣶⣿⣿⣷⣻⣿⣿⣿⢮⡷⣛⣾⣳⢯⣿⣽⣾⣻⣞⣳⢯⣿⣿⣟⢮⣳⢭⡻⣽⣹⢾⣿⣟⣾⣿⢿⣿⣿⡟⠀⠀⠀⠀ ⢸⣿⢳⣝⣾⣷⣶⣭⣩⣭⡽⣻⢞⡙⡛⠛⠙⠛⠒⠉⠛⢻⢿⡻⡿⣿⣿⣾⣷⡳⣝⡞⣶⣛⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀ ⢸⣮⢟⣾⣟⣾⡿⣎⡗⣮⢳⡝⣮⣛⡵⣫⢞⡵⣫⠽⣭⣛⢮⡳⣽⡱⣞⡽⣿⣿⣮⡝⣶⣹⢮⣿⢿⣟⠁⠀⠀⠀⠀⠀ ⢸⣎⢿⣛⢾⡛⣷⡹⢞⣵⢫⡞⡵⣎⢷⡹⣎⠷⣭⣛⢶⡹⣎⢷⣣⢟⡼⣳⠝⣷⣿⣿⣧⢟⡞⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠰⣍⡞⣬⢏⡿⣜⢷⣫⣜⢣⡝⡳⡝⢮⡳⣝⢾⡱⣮⢳⡽⣎⡷⣎⠿⣜⢧⡻⣖⣧⠿⣷⣫⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠘⠂⠙⠈⠋⠘⠈⠃⠓⠊⠓⠊⠑⠙⠒⠑⠊⠒⠙⠈⠓⠙⠘⠓⠉⠛⠘⠃⠛⠘⠊⠓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀