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⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣾⣿⠟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⠟⠋⠀⠀⠀⠀⠀⠘⣧⢫⠹⣇⠲⢸⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣄⠀⠀⠀⠀⠀⠀⠀ ⠴⠴⠒⠚⠛⠛⠛⠉⠉⠉⠛⠛⠻⠿⠷⢦⣤⣀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣯⣾⣿⣿⠃⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣰⡿⠂⠇⣆⠻⣶⠼⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠉⠻⢶⣤⣀⣴⡾⠁⠀⣰⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣩⣾⡿⢸⡏⠀⠀⠀⠀⠀⠉⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⢿⣴⣜⡯⣿⣿⣿⣿⣿⡿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠘⢦⡀⠈⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⡀⢄⡴⠶⠶⢿⡿⡟⣛⣛⡛⠛⠛⠿⢶⣶⣤⣀⠈⢻⡏⠀⢠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠃⢸⣷⣆⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⠤⠶⠛⠉⠀⠀⠀⠀⠈⡀⣺⡥⣤⢟⣿⣿⣿⣿⣿⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠳⠀⠀⢻⣇⡀⠀⠀⠀ ⠴⠛⢁⡡⠒⠯⠽⠛⠋⠉⠉⠉⠉⠉⠛⠻⢶⣦⣈⠉⣳⠏⠀⣰⠟⠙⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣸⣧⡉⠓⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱⣿⠃⣻⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠻⡇⠀⠀⠀ ⠲⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⣰⠋⠄⠀⡜⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⠐⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡿⠉⣢⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏⠀⢰⠏⠄⠀⣸⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣭⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⡴⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢀⡾⠌⠁⣰⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠲⠖⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⢧⡇ 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⣬⣵⣮⣵⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢀⡾⣯⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⣿⣿⣿⣿⣿⣦⡹⣆⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢠⣟⣼⣿⣿⣿⡇⢻⣿⣿⣇⠸⣿⣿⣿⣿⣸⣿⣿⣿⣿⠿⡟⠁⢾⠟⠉⣿⣿⡿⣿⡏⣿⣿⡜⣦⡀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⡏⣾⣿⣿⣿⣿⣿⠀⢻⣿⢻⣆⠛⢉⣆⡟⠀⡒⠉⠀⣰⡿⠒⠀⣾⡆⢀⣼⡿⠁⣿⣿⣿⣿⣿⣎⢣⡀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣽⣿⣿⣧⡿⣿⣿⡀⠀⠹⣧⣉⠳⣄⠉⠁⠀⠁⠠⣴⣿⣷⣸⡂⡏⢁⣏⠀⢀⡤⠿⢿⣿⣿⣿⡟⣦⢷⡀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠞⠉⣩⣕⣾⣯⣿⠓⢦⡀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⣿⣿⣿⠉⠛⠀⠈⣛⣮⡄⢶⣿⣿⣷⣬⣛⠛⠛⢀⡀⣟⣡⣧⣿⠷⢿⣿⣿⣵⣿⣱⣐⢾⣋⣼⣿⣷⣿⡏⡧⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣤⡾⠿⠻⠟⠃⠀⠀⠈⢻⣥⣹⣿⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢸⣿⣿⣿⡀⣴⡇⠐⣿⣿⣿⣮⡻⣿⣿⣿⣿⣧⣦⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣸⣿⣿⣿⠏⣤⢿⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠀⣠⠞⠋⠉⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⠈⣄⢦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡋⢩⡟⣙⣯⣾⣿⣾⡆⠀⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁⡀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡉⣿⣿⣷⣏⣹⣷⡶⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⢸⠛⢿⣿⣿⣿⢧⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⡀⠀⠀⣾⣤⣤⠤⣀⠀⠀⣿⡟⠀⣰⠃⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⡇⢿⣿⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣄⣼⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⡇⠀⢠⣿⣿⣧⢀⡿⡇⠀⢺⠁⣼⠃⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠇⠀⣟⡉⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣷⠀⣾⢻⣿⣿⠘⣿⣿⠀⣿⣸⡏⠀⠀⠀⠀⢀⠀⣾⠁⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⣿⢣⡿⠻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⠿⣿⡃⢠⣄⣴⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⣿⡄⢿⣼⣟⢻⡆⣿⣿⠀⣿⡏⠀⠀⠀⠀⠀⢸⠆⣿⣶⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡿⣣⣿⡇⣼⣿⢿⣿⣿⣿⣿⣿⡿⣋⣿⣿⣭⣰⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣹⣿⣷⠸⣿⣇⢾⣅⣿⡿⣸⣿⣿⠀⠀⠀⠀⠀⠘⠀⣿⣿⠿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣿⣿⣿⣿⡟⡆⠻⣾⣿⢿⣿⣿⣡⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣻⣿⣿⣿⣿⡷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠐ ⣷⢹⣿⣿⣆⢻⣿⣾⣿⣿⣷⡿⢸⣿⠀⠀⠀⠀⣀⠀⠀⣿⣿⢈⠉⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⢱⣾⣿⣏⣾⣿⣽⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣷⣿⠿⣿⣿⣿⣿⣿⣿⣟⠿⠿⡿⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡎⡐⠀⠀⠀⠀⠌ ⢻⣆⢻⣿⣿⣿⣮⠻⢿⣿⣿⣇⠠⢿⡀⠀⠀⠀⠈⢛⠀⢹⣿⡁⠀⠀⠻⣽⣿⣿⣧⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣼⣿⣿⡿⣿⣿⡟⢻⣿⡿⣶⣿⣿⣿⣭⣿⣿⣽⣿⣿⣿⣿⣯⣛⢿⣿⣿⣏⣿⣦⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠆ ⢸⡇⠨⡍⢿⣿⠛⠀⢠⣿⣿⣿⣄⠈⠧⠀⠀⠀⠀⠨⠀⢸⣿⡅⠀⠀⠀⡙⢾⣿⣮⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⡿⠀⠀⢻⣿⣷⣽⣿⣿⣿⣿⣿⣿⢿⡜⢿⣾⣿⣿⣷⣽⣿⣿⣻⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⡟⢠⠀⠀⠀⠀⠀⠀⠐⠂ ⢸⡆⠀⠙⠂⠶⣞⣤⣿⢿⡿⠀⠻⣷⣄⣰⢶⡃⠀⠀⠀⢸⣿⡟⠀⠀⠀⠑⣄⠻⣾⣇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷⣿⣿⣳⠂⠀⠈⠻⣿⣿⣿⣿⣿⣍⣽⢾⡟⣴⣿⣿⠻⣿⣿⣿⣿⣿⡋⢽⣷⢛⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⢈⡇⠀⠶⠶⠟⠋⠾⢋⠈⣷⣼⠀⠙⠻⠿⠿⠋⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠘⣇⢻⣽⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢟⣿⣯⣿⣿⠛⣗⢻⣿⣿⡅⣄⠀⠀⠙⠛⢿⣿⣿⣿⠿⣷⣼⣿⣿⣿⠀⣿⣿⣿⠿⣿⡇⢸⣿⣾⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⢘⡇⠀⠀⠀⠀⠀⠀⢸⡄⠸⣾⣀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣿⣿⣆⠀⠀⠀⠀⢀⠘⢷⡙⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡿⢹⣿⢰⣿⣦⣝⢿⣿⣮⡀⠀⠀⢀⣾⣿⠉⠙⠂⠹⣿⣻⣿⡟⢸⣿⣿⣿⣷⣜⢷⣈⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣿⣿⡇⠀⠀⠀⠈⠄⠘⣷⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⡅⢸⣿⢸⣏⣿⣽⣷⣯⡛⣿⣷⣶⣾⣿⣡⣄⣳⣦⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠋⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣰ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿⠏⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠐⠀⣿⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡽⣸⡟⢸⣿⣾⠻⣿⣿⣿⣮⣩⣽⡭⠉⢠⡍⢉⠻⣷⣶⡎⢿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣿ ⠾⠀⠀⠀⠀⠀⠀⢀⡾⠋⡀⠀⣼⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⢀⠰⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⣿⠇⢹⡏⣿⣧⠹⣮⣿⣿⣿⣿⡀⠀⠘⣿⢸⣇⣠⣿⢡⣿⣿⠏⣷⡘⠻⢿⣼⣿⠈⠉⣿⣿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣾⡿ ⠀⠀⠀⠀⠀⠀⣠⣿⠀⠘⠀⣼⣿⠈⣿⣿⣬⠛⣦⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠘⣆⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣋⣴⣿⠀⣿⠀⣿⣿⣦⡘⣿⣿⣿⣿⣇⠀⢸⣿⢸⣷⢻⣥⣿⣿⣿⣷⣿⣿⡄⠐⣿⣿⠀⢀⡘⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⠋⣁ ⠀⠀⡀⠀⠀⢰⡿⠁⠀⠀⢠⣿⣿⠀⢸⣿⣻⣷⡀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⢻⣆⢳⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⡏⠀⠃⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⠀⣼⡁⠀⢈⣿⣞⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢰⠷⠟⠋ ⠀⠀⠁⠀⢠⡿⠁⠀⠀⠀⢸⣿⣿⣀⠀⢿⣷⠻⣿⡀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⢻⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⢠⡿⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⡿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣻⣿⣇⢹⡇⣾⢈⣿⣿⡞⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣠⠇⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢸⣿⡇⢻⡄⢸⢿⡆⢹⣇⠀⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠀⠀⣰⣿⢿⣾⣿⣿⣿⣿⣿⣿⣟⢠⣿⣿⣿⢿⣿⣿⣿⣿⠃⣽⣿⣿⡄⢰⣿⣼⣿⣿⣇⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣏⠆⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⣷⡀⠈⣗⠀⠙⠀⠀⠀⢠⡿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⡿⠛⣴⠀⠀⠀⠀⢠⣿⡟⢻⡏⢿⣿⣿⣿⡏⣿⡿⠞⢻⣿⡏⣿⣿⣿⣿⠟⠿⠿⠿⣿⣧⣼⣿⡅⢻⣿⣿⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣾⠏⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠀⢻⡀⠀⠈⠁⢠⣿⣷⡈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠇⢾⡇⠀⠀⠀⠀⣸⡿⠀⠀⡗⣾⠁⢹⣿⣿⣽⣧⠀⢨⣿⣿⣿⣿⣿⣿⣰⠟⠛⢷⠈⢿⣿⣿⣿⡈⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢠⣾⡟⣔⠂⠀⠀⡀ ⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢸⡇⠀⠀⠀⡿⠘⣿⣷⡄⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠘⣧⣤⠀⣸⠀⣏⠀⠀⢰⣿⢹⣿⡞⣿⣿⣿⣯⣽⡿⣿⣿⣿⠿⢸⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⣧⣸⣇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣴⠟⠀⢠⣿⡿⣼⡇⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣻⣿⣿⣦⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⠹⣿⢰⡇⢸⡇⠀⠀⠸⢷⣴⣻⡷⠾⣿⣷⠿⢻⣾⣿⡿⣿⣶⣈⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⣾⠃⠀⣴⣿⡿⣹⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡌⣿⣿⡿⠏⢳⡌⢿⣿⣧⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⣠⣦⣴⢿⡄⢻⣿⡇⢸⣧⠀⠀⠀⢸⣿⡿⠷⡾⠻⣿⣄⡾⣇⠽⠛⢉⡷⠟⠁⠀⠀⠀⣼⢿⣿⢾⣿⣿⣿⣟⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣠⡾⠃⢠⣞⠁⠉⣴⣿⠑⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⡼⣛⣿⣇⠀⣰⣿⣦⡙⢿⣤⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠻⣿⣯⡾⣿⡄⢻⣯⢼⣿⡏⠷⣦⣼⠿⠇⠀⠀⠀⢿⡏⠛⠋⡀⢀⡀⠀⣤⣤⠾⠶⢾⣫⣿⣿⣸⣿⣿⣿⣾⣫⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⣾⠏⠀⣰⡏⢹⡇⠀⠈⠓⠀⠀⠀⠀⠀⠀ ⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠈⣿⣯⣿⣿⡧⢰⣿⡏⠈⠻⣆⠹⣿⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⣿⡇⠘⣿⠸⣿⡇⣤⡈⣹⡇⠀⢀⠐⡄⠘⠿⠒⣿⡟⣯⠟⠨⢿⡆⠀⣈⣾⣿⣿⣹⣿⣿⢿⡿⢱⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣠⡾⠃⢀⣼⣏⡷⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⣿⣿⣧⠈⢿⣿⡿⠀⡾⢻⡇⠔⣿⣿⢷⡜⢿⣦⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⣿⣿⠁⢸⣿⣄⢻⠀⣿⣿⣿⣿⢹⣷⡄⠁⠀⣠⣥⣠⢇⣿⡇⢹⠠⠄⣾⣧⠀⣿⣿⡿⣱⣿⡿⣡⣿⠁⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⣾⠟⠀⣠⣿⣿⣿⡆⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠞⠁⢀⣼⣿⢿⣿⣿⣾⡤⢿⡇⠀⠁⠘⠇⣷⣿⣿⣆⣿⣦⠙⢷⣄⠀⠀⣿⡄⠀⠀⠀⠀⢸⢻⣇⠀⠸⣿⢹⣦⣦⠹⣿⣼⣿⣻⣿⣷⡆⣰⣿⣿⣿⢺⣿⣿⣿⣟⣴⣿⡷⢠⣿⡟⣱⣿⣭⠟⠋⠳⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣴⡿⠁⢀⣼⣿⣿⣟⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠘⢧⣄⠀⠀⠀⠀⠀⠀⡀⠴⠛⠁⢀⣰⣿⣿⠃⣸⣏⠣⣹⣿⡈⢿⡀⠀⠀⢂⠸⣿⣿⣷⡙⣿⣷⣌⠻⣦⡄⢸⣷⠀⠀⠀⠀⠈⢸⣧⠀⠈⣷⡹⢽⣿⣿⣬⡉⢻⣿⣿⣿⣿⢿⣿⣿⣽⢾⣿⣿⣿⣿⣿⣿⣯⣿⣿⠟⠋⣽⠛⢦⡀⠐⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣼⣯⡾⠋⠀⣰⣿⣿⣿⡿⡻⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠟⠂⠀⠈⠙⠛⠊⠁⠀⠀⠀⠀⣠⣴⣿⢿⣾⠇⣰⣿⣿⡄⠀⢻⣧⠈⣷⠀⠀⠀⠀⠹⣿⣿⣷⡈⣿⣿⣦⡈⠻⣶⣿⡆⠀⠀⢂⡀⢹⣟⠀⠀⠈⢿⣿⡿⠛⠛⣻⣶⣥⣈⠻⠟⠸⠿⠋⠛⠷⠿⣿⣿⣿⡿⣿⡛⣻⣵⣿⠆⡿⠀⠀⣿⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⣠⣾⣿⣿⣿⣿⠗⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣀⣤⣤⣤⣀⣠⣤⣤⣴⣾⣿⣿⣟⣵⡿⠁⣴⣿⣿⡁⣷⠀⠘⣿⠀⢸⣆⠀⠀⠀⠀⠠⠙⣿⣧⠈⠿⣿⣿⣄⠘⢻⣷⡄⠀⠋⣷⠘⣿⠀⠀⢀⠋⠉⢀⣴⣾⡿⠋⠙⠻⠿⣷⣶⣶⣿⣶⣦⣤⣈⣨⣭⣿⣾⡿⠿⢿⣿⢸⣧⣀⣀⢸⢀⣿⣿⠇⠀⠀⠀⠀⠀⣠⣿⡟⠁⣠⣾⢫⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⣽ ⠆⠀⣸⣿⡟⠋⠋⠉⢡⣐⣿⠿⠋⣼⠏⢠⣾⣿⠿⣿⡇⣿⠀⠀⢻⡇⠸⣿⡆⠀⠀⠀⠀⠀⠘⠿⣆⠀⠹⣿⣿⣷⣄⠙⣿⣦⠀⣻⣧⢹⣇⠀⢨⠀⢠⡿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣯⢉⣽⣿⡏⠉⠀⠀⠀⢸⣿⡟⣿⣿⣯⠉⢸⣿⠏⠀⠀⠀⠀⣠⣾⣿⠋⣠⣾⡿⢡⣿⡿⠳⠁⠀⠀⠀⠀⠀⠀⢘⡅⠀⠀⠀⠀⠀⠀⠀⡌⣼ ⠀⠀⣿⣿⣷⣄⣤⣶⠟⠋⢁⡠⠘⢀⣴⠏⣾⡟⠀⢸⡇⡿⠀⠀⢾⡇⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⣿⣿⣿⣷⣹⡟⢿⣾⣿⡆⠹⣦⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣠⣼⢀⣬⣿⣿⡼⣼⠋⠀⠀⠀⢠⣾⡿⣩⣿⣾⡿⠋⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡇⢾ ⣤⣄⣨⣿⠿⠋⠉⠀⠀⠀⠉⢀⣴⣿⠋⣸⣿⡇⠀⢸⡇⣿⠀⠀⣾⡧⠀⢹⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀⠙⢿⣿⡄⡈⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠋⢼⣿⡟⠉⣀⠖⢀⣴⠟⠁⣰⣿⣿⡟⠁⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⠖⠀⠀⢠⠀⠀⠀⠀⠀⢇⢺ ⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⡃⠀⣿⣿⡆⢀⣿⢸⡇⠀⠀⣿⡇⠀⠸⢻⡟⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⢿⣿⣿⣆⠈⢿⡇⠻⡃⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣿⡿⠀⣼⠋⣰⠟⢁⣴⢞⣿⣿⠋⣴⢿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⢸⡳ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⢟⠭⣿⠀⢰⣿⣿⣿⣿⣧⡿⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠈⠙⠷⣆⢀⡀⠀⠀⠀⠀⠀⠀⠈⢳⡟⢿⣿⣶⣶⣦⡀⠸⣦⣻⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣡⡾⢃⡶⣫⠶⢋⣡⣾⡿⠁⣠⠶⠋⠀⠀⠀⠀⣀⡠⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠈⣿ ⠀⠀⣀⣀⣛⣋⣉⡙⠀⠋⠀⠠⡟⠀⢸⣿⣷⣿⣟⡿⠁⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⣤⠀⠀⠀⠀⠙⢷⣯⣿⣿⣿⣿⣷⣬⣿⣻⣦⣰⡎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢏⣴⣟⣴⣿⡟⠋⣀⣽⣟⣉⣀⣈⠁⠀⣀⣀⠀⢀⣩⣉⣽⣻⡿⡋⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠘
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