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⣛⣿⣶⣶⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣏⣀⣹⠟⠛⠛⠋⣉⣀⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠿⠿⠟⡛⢿⣄⣬⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢿⡟⢁⡴⠖⠋⠈⠻⡟⠉⠛⣿⡷⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⡏⣿⣿⣗⣻⣿⣿⣿⢟⣽⠿⣃⣀⣴⠞⢛⣯⡀⠀⠀⠀⣀⣽⠆⠀⠈⠁⠀⢀⣿⣿⡰⢀⠼⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⠋ ⠟⢛⡋⢭⣶⣿⣿⣿⣿⣿⣿⣷⡟⠁⠀⣠⠌⠻⣶⠟⠈⠙⢦⡴⢟⡉⠁⠀⠀⢠⡟⢀⡤⠿⣷⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⢀⣀ ⢶⣶⣾⣿⣸⣿⣿⣿⣿⣿⣇⠈⡇⢀⣼⡋⠀⠀⣰⡖⠃⠀⠀⣷⠀⠙⠶⣄⣀⠈⢠⣶⠀⣴⣿⠇⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠰⣿⣄⣾⣿ ⠇⠛⢛⣿⣷⣿⣿⣿⣿⣿⣿⡼⠻⣿⠈⠳⣤⡼⢿⣿⣶⠦⠶⠶⣄⡀⣠⠿⠷⠶⠿⣿⡞⢿⣇⠀⣀⡀⣀⣠⣯⣀⣤⣤⣤⣤⣤⣾⣿⣿⡿ ⣯⣥⢰⣯⢻⣿⣿⣿⣿⣿⠟⠰⣴⣃⡶⢚⣋⣥⣤⠤⠤⠤⣤⣀⣸⡟⠁⠀⠀⠀⠀⠈⠙⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀ ⢿⣿⠟⢿⣾⣿⣿⣿⣿⠃⠀⠀⣈⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⡟⠉⢿⡻⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⣠ ⢠⣿⣇⣾⣿⣿⣿⣿⡏⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣿⣄⠀⠀⠀⠀⢀⡾⠁⠀⠀⠙⠻⣿⣴⠶⠛⠉⠁⠀⠀⠀⠀⢀⣴⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⠁⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠛⠛⠿⣷⣦⣄⣠⡿⠁⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⣀⣴⠿⣿⣿ ⠈⠙⢿⣿⣿⣿⣿⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠠⣌⣍⣉⡞⠀⠀⠀⠀⢀⣀⠀⣿⠀⠀⠀⢀⣴⣾⢿⡃⠀⠘⢿ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⢠⡶⠛⠳⣿⡧⠤⣤⣀⠀⠀⠀⢈⣿⣿⣿⣶⣶⣶⠾⠛⠁⣰⠏⣀⣤⣶⣿⣿⡿⠶⠛⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⠋⣿⡇⠀⢀⣤⡀⠀⠈⢧⠀⣴⢿⣿⠀⠀⢛⣧⣴⣾⣿⠿⠿⠿⢿⣁⠀⠀⠀⠰⣿⣿⣿⣿⣿⢃⡻⣿⣤⠀⢀⣀⣀ ⠲⠀⠀⠀⠀⣿⣿⣷⣰⡿⠃⠀⣼⠉⠻⣦⠀⢸⡟⢁⣼⣿⣇⣴⣿⠿⠋⣉⡀⠀⠀⠀⠀⠉⠛⣶⠀⠘⠿⢿⠿⠿⣥⣼⡷⠈⠻⢷⡶⠹⠛ ⡄⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⣘⣿⣤⣤⣼⢧⣈⣹⣿⠛⠋⠙⢋⣴⡞⠛⣿⡇⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠈⢻⣄⣀⠀⠀⠀⠀⠉ ⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡿⠿⠿⣧⡀⠀⠀⣴⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣶⢾⡗⠀⣸⣿⣿⡷⠀⠀⠀⠀ ⠉⠀⢹⣿⠋⢹⠿⢿⣿⣿⣦⠸⣿⣿⠋⢰⣄⢀⡾⠁⢠⣾⣿⡟⢉⣠⣼⣿⡇⠀⠀⢀⡀⠀⢸⣿⣿⣿⣿⡇⠉⣵⣾⡿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠉⣠⠻⠀⠀⡉⠛⠻⣿⣿⣿⠀⠈⢹⣿⡃⣰⣟⣽⣿⣿⣿⣿⣿⠟⠁⠀⢠⡾⠃⠀⢸⣿⣿⣿⣿⣇⣠⣿⡿⢹⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡄⠀⠀⠙⢦⡀⠘⢿⡛⠀⢸⣿⣿⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⣠⣾⠿⣳⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣶⣄⠀⠀⠙⠷⣤⡙⢻⣿⣿⣿⡀⠀⠀⠀⠀⣀⣀⣤⣤⣾⠏⢈⡳⣿⣤⡴⠋⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠈⢳⣽⣆⠀⠀⠀⠛⠻⢿⣿⡏⠈⢻⣄⠀⠰⣿⡛⠉⠀⠘⠁⠀⠊⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠋⢀⡽⣿⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠈⢳⡄⢻⣹⣆⠀⠀⠀⠀⢨⡟⠀⠀⠀⢹⣷⣄⠈⢻⡟⠦⣄⠘⢦⡄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡶⢋⣴⣿⡄⠀⠀⠀⢸ ⠀⠙⠋⠉⠀⠀⡇⢸⣿⣿⠀⠀⠀⠀⣾⠁⣠⡴⣦⡀⢻⡝⣆⢸⣧⠀⠈⠳⠀⠹⣆⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣿⣫⡾⠃⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⠀⠀⠀⠀⠙⠛⠁⠀⠀⠹⣆⢻⡜⣦⠻⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡜⠛⢷⡄⠀⠀⠀⣿ ⠀⠀⢐⣦⣤⣼⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠹⣾⣆⡉⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣭⣿⣿⣶⠘⠃⠀⠀⠀⠘ ⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠹⣏⣷⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⢁⣀⣾⠋⠀⠀⠀⠀⠀⠀

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