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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡏⠀⣿⠀⠀⣾⡆⣿⠀⠀⠙⣧⡹⣷⣍⢷⣻⣆⠘⣿⡄⢿⣇⠀⠀⣿⡇⠀⢹⣿⠇⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢠⡇⠀⣿⡄⠒⡏⢹⣿⡄⠀⠀⠈⢻⣦⡉⢷⣿⣿⣦⠻⣷⢸⣿⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣸⣷⠀⢿⡇⢀⡇⢀⣻⣧⡀⠀⠀⠀⠙⣿⣶⣦⠿⣿⣛⣿⣦⣿⠀⠀⢸⣧⠀⢸⣿⣀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⡆⢿⣿⢾⣿⣟⣿⠿⣧⠀⠀⠀⠀⠈⢻⡇⠀⠀⠈⢿⣿⣿⠀⠀⢸⣿⡇⢸⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠉⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⢻⣼⣿⡞⣧⠀⠹⣦⣿⡆⠀⠀⠀⠀⠘⣯⠻⠄⠀⣸⣼⡿⠀⠀⣸⣿⡇⠘⣿⠀⠀⠀⠀⠀⢀⣤⠶⠛⢩⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⢻⣿⣧⠀⢹⣏⣷⡀⠀⠀⠀⠀⢿⣦⣀⣴⠋⢸⡇⠀⠀⣿⣿⠀⠀⢿⡀⠀⣀⣤⠖⠋⠁⠀⠀⠘⠳⣄⣀⡴⠟⠁⠀⣀⢀⠀⠀⠀⣀⠀⠀⢀⣀⣀⠀⢀⢀⡀⢀⡀⢀⡀⠀⢀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⣿⣧⡿⢻⣆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⣰⣿⣿⡀⠀⣨⡷⠞⠉⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⢀⢠⣾⢿⣿⡄⠀⢰⣿⣿⠿⠿⣿⣿⡶⠿⠿⢿⣿⡿⠿⠿⠾⣿⣿⡿⠷⢶⣾⣿⠿⠿⣿⡶⠾⠿⢿⣿⡿⠿⠿⢿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⢈⣿⣧⣤⣀⡀⠀⠀⠒⠀⢀⣠⣤⣶⣿⡿⠀⢘⣿⣿⣿⠷⠛⠉⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⣮⣿⣿⣠⣿⣿⣆⣾⣿⣿⠷⣾⣿⡟⠁⠀⣰⣾⣿⡇⠀⢀⡀⣾⣿⡧⡄⠈⣛⡛⠿⢿⣶⣦⠀⠀⢸⣿⣷⠀⠀⠀⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⢸⢻⣦⡈⢻⣿⣿⡟⠻⠿⣿⡵⠟⠛⣽⠁⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣴⠛⠁⠀⠀⠀⠀⠀⠀⠺⠿⣿⠙⠋⠙⠻⣿⣾⠿⣿⠂⠈⠻⠿⠦⠀⠘⠻⠿⠇⠀⠈⠻⢿⣿⢷⣶⠚⠿⠷⢶⣾⠿⠟⠈⠈⠐⠿⠿⠐⠀⠀⢿⡿⠿ 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⠀⠋⠛⠛⠛⠛⠙⠀⠀⠀⠋⠙⠀⠀⠀⠃⠛⠙⠀⠀⠛⠛⠊⠛⠘⠀⠀⠀⠋⠛⠀⠋⠛⠘⠀⠀⠛⠙⠀⠁⠋⠛⠛⠛⠉⠈⠀⠋⠛⠛⠛⠛⠈⠂⠛⠙⠀⠀⠋⠛⠀⠀⠀⠀⠀⠋⠛⡆⢻⠀⠀⠀⠀⠀⡄⢻⠈⡤⢀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⣿⣿⣏⣿⣿⢿⠀⠀⣿⣻⠿⠀⠀⣿⣿⣿⠻⠈⣿⣿⢼⣧⣿⠾⠶⠷⣿⣼⠉⡇⣿⣿⠻⠀⣿⣿⡽⣿⣿⣿⣽⣤⣷⣿⠘⣀⣹⣉⣯⣿⣿⠈⣄⣿⢿⠻⣿⣿⠆⠁⠉⠛⠛⣿⣿⠀⣇⢹⠀⠀⠀⠀⠀⣆⢹⠀⠂⠠⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣿⣿⣿⣿⣨⠀⠀⣿⣿⣀⢀⠀⣿⣿⣌⣿⢿⣿⣿⢀⠀⣧⣿⠛⣿⣼⣠⣀⡗⣿⣭⣯⢻⣿⣿⣼⣡⣉⣉⣀⢱⡟⣿⣽⣄⣬⣤⣧⣿⣿⣽⡿⣽⣠⣤⣯⣿⡛⣯⣿⣉⠀⣧⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⣿⣴⣄⣷⣶⣤⣶⣴⣷⣿⣿⣾⣰⣿⣿⣘⡀⣄⣿⣼⠀⠀⠀⣦⣿⣴⠀⠀⠀⣷⣿⢙⡈⣦⣿⣾⢀⣅⣭⣿⣿⣿⣾⣣⣞⣶⣾⣷⣿⣾⣷⣀⣄⣿⣷⣾⣶⣿⣸⣀⣿⣿⣾⣷⣿⣤⡇⣼⠀⠀⠀⠀⠀⡏⣼⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠈⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⢁⣉⠀⠃⠛⠛⡿⢰⠒⠖⡤⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠛⠙⠀⠀⠋⠛⠛⠛⠀⠀⠀⠇⣿⢠⠀⠀⠀⠀⠀⠁⠛⠞⠀⠛⠛⠐⠀⠃⠛⠛⠛⠛⠈⠀⠀⠃⠘⠀⠛⠛⠞⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣶⣽⣭⠉⢟⡼⣥⠿⣿⣴⠤⠷⢽⡦⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣧⣴⢠⣄⣿⠸⡟⣿⣄⣠⣶⢹⢀⠄⣿⣧⠹⠀⠀⠀⠀⠀⡇⣿⢻⠀⣯⣿⠼⠀⡇⣸⡄⢡⣿⢰⠀⠀⡇⢿⡿⣿⣸⡦⠄⣷⠼⠀⠀⠀⠀⠀⠀⠀⠁⠟⣶⣤⣤⣠⣀⣀⣀⣄⣤⣦⢶⣶⠶⣤⣀⣀⣤⠶⠛⠈⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡷⢡⠨⠀⣿⢿⣧⢻⠀⠀⠃⣹⣴⡿⢠⠀⣷⠙⠀⠀⠀⠇⡿⣺⣷⣿⣸⡄⢿⠈⡏⣼⣤⣤⢁⠀⠀⠀⡏⣿⣼⣿⢸⠀⠀⡟⣼⠀⠀⠀⠀⠃⠟⠟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠉⠛⠴⣠⠀⠀⠀⠀⠀⠀⠀⠉⠖⠠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⣶⣠⣄⣶⣴⣀⣤⠷⠶⣿⣤⣶⣴⠀⠀⡆⣷⠈⠀⠁⣧⣿⠀⣄⣾⢰⠀⣧⣸⣄⣶⡶⣾⣷⢏⠿⣶⣷⢲⣀⣿⣿⠾⣶⣠⠀⠀⠀⠀⠟⣿⡟⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠉⠞⡤⣀⠀⠀⠀⠀⠀⠀⠁⠋⠖⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢸⠀⠀⠀⠀⠀⠀⡟⣿⣿⢰⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠋⣿⠞⣤⢀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠁⠈⠀⠉⠀⠁⠉⠘⠀⠀⠉⠉⠘⠀⠀⠀⠀⠇⠓⠉⠀⠀⠀⠀⠉⠀⠁⠙⠀⠀⠛⠉⠀⠀⠀⠋⡇⣫⢙⠉⠉⠉⠀⠀⡇⣾⣿⣻⠘⠃⣏⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠾⣤⢀⠀⠀⠀⠀⠀⠀⠉⠚⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⠓⡟⢿⠀⣿⣾⣴⣷⢿⠾⡶⣰⣧⣿⠻⠈⠀⠀⡇⣿⣿⠀⠀⠀⠀⣿⣿⣧⣾⢷⠘⡇⣿⠸⠀⠇⣿⡹⣯⣿⣴⣤⣿⠺⠀⣿⢀⣷⢻⠛⡾⣤⣠⣤⠷⠘⠀⠀⠀⠀⠀⠀⠠⠄⠯⠛⠖⣤⢀⠀⠀⠀⠀⠀⠁⠋⠞⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⡶⣿⣿⡀⣿⠿⠿⡶⣾⠀⠀⠀⡆⡇⢻⢰⠀⠀⡅⣧⣿⠀⠀⠀⠀⣿⢸⡄⢠⡇⢸⡇⣿⢰⠀⡷⣿⣿⣯⣿⢿⡾⣷⢀⠀⣿⠀⣟⣾⣀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠉⠞⣤⣀⠀⠀⠁⠀⡄⣤⠷⠛⠟⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣿⢿⡟⣿⣼⣀⣧⡟⠉⣯⣿⣶⣷⠟⢫⡟⣴⠀⠀⠀⡄⡇⣾⠀⠀⠀⠀⣿⢻⡝⠿⣾⢠⡀⣿⠛⠛⡿⣿⣀⣇⣿⣹⡟⣿⡐⠀⣿⠀⡇⢹⠉⠀⠀⠀⠀⠉⡿⠀⠁⠋⠞⡤⣀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠃⣾⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⣀⣀⣄⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⡛⣟⠀⠀⠀⠀⡯⢸⡀⣠⠀⠀⠀⡀⣀⢀⠀⣀⠀⠀⠀⣤⣀⢠⠀⠀⣇⠘⡏⣰⠀⠀⠀⠀⠀⠂⣿⠾⣠⢀⠀⠀⠀⠀⠀⠀⠋⠟⣶⠲⠛⠞⣦⣽⣆⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠈⠁⠋⠖⠲⠛⠈⣯⠸⠀⠀⠀⠀⠁⠋⠞⣤⢀⠀⠀⠟⣿⢸⠀⣷⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠿⣠⢀⠀⠀⠋⣾⣠⢀⠀⠁⠛⠿⣼⢀⠋⠙⠈⠉⡿⣤⣧⢿⠈⣿⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡞⣤⣀⢦⠓⠚⡴⣀⠀⠁⠟⡶⣿⣴⣀⠀⠉⠀⠀⣇⣽⢿⠚⡗⣿⢸⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⡿⢿⠀⠀⠐⠿⠿⠐⠈⠈⠟⠿⣾⢶⠷⠿⠚⣶⢷⣿⢿⠻⠈⠀⠇⠿⠻⠘⠀⠦⠿⠻⠈⠂⣿⠿⣾⣿⠻⠙⠋⠙⣿⠿⠺⠀⠀⠀⠀⠀⠀⠁⠛⣴⢠⠀⠀⠀⠀⠀⠀⠀⠋⠟⣾⠀⠁⣽⠛⠟⡵⣿⠿⠻⡟⣿⣿⢻⡈⣦⢻⢸⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⠀⣷⣿⢸⠀⠀⣦⣶⢿⠿⡛⣛⠈⡄⡧⣿⣾⡀⢀⠀⡇⣿⣾⣰⠀⠁⡟⣿⣾⠷⣿⣿⣾⣆⣿⣿⣠⣿⣿⣮⠀⠀⠀⠀⠋⠞⡴⣠⠀⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣿⢘⠀⡿⣿⣶⣤⣠⢀⠀⠒⠀⠀⡀⣀⣤⣧⣿⢈⡇⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⣿⣿⢿⠿⠿⡿⣿⢿⠿⠾⡶⣿⠿⠿⣿⣾⢶⠷⡿⣿⣿⠾⠿⠿⡿⣿⢿⠿⠿⡶⣿⣿⠿⠿⣿⣿⢰⠀⡄⣿⢿⣾⢠⢀⠀⠋⠾⣴⢀⠀⠀⠀⠀⠀⠀⠉⠞⡷⣨⠀⡀⣿⣿⣰⠀⠇⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣆⢻⡿⣧⣿⠸⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⡀⢀⠀⡀⢀⡀⢀⡀⢀⢀⠀⣀⣀⢀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠁⠟⡴⣀⣄⠳⠘⠀⠀⠁⠋⠖⣤⣀⠀⡀⢿⠀⠀⣿⣿⠀⠀⡇⢸⠋⣴⣀⣦⢿⠀⠀⠀⠀⡀⣷⣏⢹⠀⣧⣿⢻⣿⣿⠘⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣴⢀⠀⠀⠀⠀⢩⠛⠶⣤⢀⠀⠀⠀⠀⠀⣿⠘⡇⣿⣸⠀⠀⡿⣼⣸⠀⠄⠻⣯⠘⠀⠀⠀⠀⡆⣿⣦⠹⠀⣧⡞⣿⣼⢻⣧⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⢻⠉⠉⠛⠞⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⢸⡇⣿⢸⠀⠀⣿⣿⢿⠈⠀⠀⡇⢻⠈⠀⠀⠀⠀⣧⠿⣿⣟⣿⢾⣿⢿⡆⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣾⣶⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣠⣀⣿⢸⠀⣧⢸⠀⠀⣿⣦⣿⣛⣿⠿⣦⣶⣿⠙⠀⠀⠀⡀⣧⣻⢀⡇⢀⡇⢿⠀⣷⣸⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⣿⢸⠀⡇⢿⠀⠀⣿⢸⣷⠻⣦⣿⣿⢷⡉⣦⢻⠈⠀⠀⡄⣿⢹⡏⠒⡄⣿⠀⡇⢠⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣶⢠⠀⣄⣶⣶⠀⠀⡀⣦⣷⣾⣶⣤⣶⣴⠀⡀⣤⣿⢠⠀⠀⠀⡄⣦⣴⢠⠀⠀⠀⠀⣦⣶⣶⣴⣴⣦⣶⣶⣷⣾⠀⣤⣶⢰⠀⠀⠀⡀⣦⣶⢠⠀⣤⣦⣴⠀⠀⠀⠀⣤⣦⣤⠀⠀⣄⣤⣶⣾⣦⣴⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀