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⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠉⣭⠷⢾⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⡽⢶⣄⠘⣿⣿⣿⣿⠏⠀⠀⠘ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⠀⣏⠀⠀⢹⡏⠹⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣐⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢹⣏⠀⠀⣹⢶⣿⢿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣧⣿⣧⡝⣷⠒⠋⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠙⣶⣶⣿⣿⣿⣾⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣍⠙⠻⠷⣦⣄⣀⣀⣀⣈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⢶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣀⣀⣀⣠⣴⠾⠟⠋⢠⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠯⣿⠀⠙⢦⣄⡀⠀⠈⠉⠉⠉⠛⠛⠻⢿⣦⣤⣤⣤⣴⣶⣶⣤⣴⣤⣼⣿⠭⠭⠭⠭⠭⣽⣿⣧⣤⣤⣤⣴⣶⣶⣤⣶⣤⣶⠿⠟⠛⠛⠉⠉⠉⠉⠀⢀⣠⠴⠋⠘⣿⢹⣧⠀⠀⠀ ⡀⠀⠀⠀⢸⣿⢸⢿⣦⣀⠀⠈⠙⠳⠶⣤⣄⣀⡀⠀⠀⠀⠈⠛⢶⣤⣤⣾⣽⣯⣿⣿⣿⢛⣷⣶⣶⣷⣾⣿⡋⢩⣭⣿⣯⣷⣭⣤⡷⠿⠛⠁⠀⠀⠀⢀⣀⣠⡤⡶⢞⡋⠁⠀⣀⣠⢽⣇⣿⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⠏⠀⣿⡉⡛⠛⠛⠛⠓⣷⡾⠿⠿⢿⣿⡛⠻⠷⡾⣿⣶⣶⣶⡾⢿⠿⡿⢿⡿⣿⣿⡿⣿⢿⡿⢿⠿⡿⣷⣶⡶⣶⠞⠶⠛⠛⢛⣿⣿⡿⠿⠿⠟⠟⠛⠛⠛⠛⢋⡿⠀⢻⣿⠀⠀⢀ ⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⠓⠓⠚⠚⠓⠚⠓⠒⠶⠾⠿⠿⢿⣟⢻⡟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢻⡟⢻⣿⠿⠿⠶⠶⠒⠒⠚⠚⠓⠛⠛⠛⠛⠁⠀⢀⣿⠀⠀⢨ ⠀⠀⠀⠀⠐⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⣷⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⢡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⣆⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣻⢫⡟⠀⠀⠀⢰⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣄⣤⣠⣤⣤⣄⣀⣠⣤⣤⣤⣤⣻⣮⣽⣯⣭⣭⣭⣭⣯⣽⣭⣿⣽⣯⣿⣽⣯⣭⣭⣯⣟⣫⣽⣟⣀⣠⣤⣄⣈⣿⣋⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⢛⠛⡛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠻⠷⢤⣀⠀⠀⠀⠀⠐⠆⠀⠀⢀⣾⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡍⢷⣄⡀⡀⠀⠀⠀⣰⡞⠉⠀⠀⠀⢠⣼⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠠⠀⠤⠀⠄⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⣀⣤⡾⠿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⠋⠁⣰⡝⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣏⡇⢺⠰⠇⢠⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡤⠸⡋⡁⠄⠥⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⡇⠤⢰⠒⡅⢰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠠⠄⠄⠂⠦⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣷⡃⠠⠈⠂⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢂⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠻⣿⣾⣤⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣦⣶⣿⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⣾⣿⣿⡆⣿⡿⢿⣿⣆⡻⣶⡙⣧⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣽⣯⣶⡿⣹⣿⡿⢻⣷⠀⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣟⢹⣷⣿⣿⣿⡿⢿⣟⣾⣙⣾⣷⡈⠿⣦⣀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⢟⣽⣿⣿⣫⣿⣿⡿⢿⣿⣾⣿⣼⡏⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⢻⣟⣿⣿⣟⣏⠀⠀⢸⣿⣬⣿⢿⣿⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣮⣿⣿⣿⣿⣿⣏⠀⠀⣼⣿⣿⣾⣿⡟⣿⠀⠀⢀ ⠀⠀⠀⠀⢰⣿⣠⣿⡇⠹⣿⣿⣷⣶⣿⢿⣿⣻⣧⣿⣿⡄⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢰⣿⣿⣼⣿⣿⠟⣯⣿⣿⣿⣿⠇⢸⠿⣇⣿⠀⠀⠘ ⠀⠀⠀⠀⢸⣿⣿⢰⣇⠀⠈⠻⠿⣟⣛⣿⣿⣿⣿⡧⠾⠟⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠺⢷⠿⣿⣿⣿⣿⣻⣿⠿⠛⠁⠀⣸⢆⣟⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣻⡞⣿⣄⠀⠀⠀⠀⠈⠉⠛⣿⣶⠶⢶⣦⠤⠤⣤⣄⣠⣤⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣤⣤⠤⠤⣶⡾⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⣿⢹⡏⣿⠀⠀⢠ ⠀⠀⠀⠀⠈⣿⣿⡇⢻⣿⠶⠦⠤⣤⣀⣀⣀⣿⣽⡇⠀⠙⣧⠀⠀⠀⠀⣽⠉⠉⠉⠉⠉⠉⠉⠉⠋⠙⠉⠉⠉⠉⠉⠉⠉⠙⣿⡀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⢤⣤⡧⢸⢗⡏⠀⠀⢸ ⠀⠀⠀⠀⠀⢻⡇⣿⠸⣿⣇⣦⣤⣤⣶⣭⣭⠿⣛⡓⠶⣤⣘⢷⣤⣄⣀⣽⠀⠀⠂⠀⠐⠠⡀⢴⠲⡖⢦⠲⡔⢦⠠⠀⠦⠴⣿⣅⣠⣤⡾⢁⣠⠴⣶⣾⡟⢯⣭⣥⣤⣴⣤⣾⣿⡇⣿⣾⠇⠀⠀⠐ ⠀⠀⠀⠀⠀⠘⣿⢻⡀⠻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣶⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠟⢠⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣇⠻⠦⠿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠀⣼⣿⣿⣿⣿⣿⢿⣧⣈⣿⣿⠿⠯⠴⠟⢡⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠙⠃⠠⠍⠻⠛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠍⠄⠸⠗⠚⠛⠋⠉⠉⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⣰⣿⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⡇⠙⣿⡶⠖⡶⣶⣞⣻⣖⣶⣲⣶⣶⣶⣾⣶⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣾⣷⣾⣷⣲⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⢛⣗⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⡇⡅⠈⠛⠟⢛⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⠟⠁⠘⡯⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⡗⣷⢶⡀⡄⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠠⡤⣤⡶⠷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣇⠞⠠⠙⠁⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠱⠀⠀⠀⠀⢛⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢯⣿⣴⣦⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣢⣆⣀⣻⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀