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⠀⠀⠀⠀⠀⠀⠀⠀⠾⣰⠋⡜⠀⠀⢠⠏⠀⡐⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠛⠙⠲⣤⣀⠀⠀⠈⠙⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣏⡁⢻⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡜⠀⠀⠀⣾⠀⢠⢁⡏⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⡞⠀⠀⠀⠀⠛⠛⠓⠒⠒⡞⣸⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠉⢀⣿⠏⠉⠛⣦⠀⠀⠹⡍⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⡸⠁⠀⠀⢀⡇⠀⢂⡼⠀⠀⠀⣀⣤⠖⠛⠉⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣤⣤⣶⣶⣿⣿⣿⠟⠁⠀⣴⡋⠉⣳⢦⣤⣿⣷⡄⠀⢿⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⢠⠇⠀⠀⠀⢸⡇⢀⢾⣣⣾⡿⠿⣿⣿⣦⣌⠛⠦⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢹⠀⣿⣿⣿⣿⣟⣡⡤⠴⣾⠏⠙⠲⣇⣤⠞⠉⠈⠙⢦⣜⣧⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⠀⢸⡇⢨⣾⡽⠋⠀⣼⣷⣾⣿⣿⣧⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⠓⠆⣸⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡴⣿⠉⠉⠉⠁⠀⣠⠞⠁⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠈⠛⣧⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠃⠀⠀⠀⠀⢸⡷⣿⣿⠁⠀⢸⡏⠀⠀⠀⠙⣯⡟⠀⠀⠀⠀⠀⣠⠄⠀⠀⣶⣿⣿⠿⣿⣧⣄⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠃⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⢟⣿⣷⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢸⡽⣿⣻⠀⠀⣏⡇⠀⢰⣵⢠⣿⠀⣀⣀⣠⠴⢺⠏⠀⣠⣾⡍⠛⠛⢿⣦⣿⠻⣷⣄⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⣞⣛⣧⣄⣂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣍⠁⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣴⠀⢸⡶⣄⠘⠆⠀⢿⡓⠀⠈⠙⠋⡟⠉⠉⠀⠀⢰⣏⡤⠞⠁⣞⠇⢠⡀⠀⠈⣿⡀⠈⢿⡿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡄⣟⢰⣛⣧⠀⠀⠀⠉⠉⠙⠛⣧⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⡇⠀⡞⣇⠈⠓⠃⣴⣤⠁⠚⠲⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣘⠀⣇⠇⠀⠀⣿⣷⠀⢸⣿⡀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡟⠀⣧⡿⠂⡉⠷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⠳⠶⠶⢤⣄⣀⠀⣿⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⢀⡞⠟⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⣇⠀⣿⢸⡀⠈⢰⡷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣏⣀⠀⠀⣀⣾⠏⠈⣧⣿⣿⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⣷⠀⢹⡷⠋⠙⢲⡌⠳⣤⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠉⠙⠓⠦⣤⣀⣀⢙⣦⠀⠀⠀⢀⡞⠀⠀⠀⠙⣦⠘⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡸⣜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡏⣽⠛⠋⠉⠀⠀⡴⠋⠉⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣸⠇⡼⠁⢹⡀⢸⣧⠀⠀⠀⢹⠆⢹⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣆⠀⠀⡾⠁⠀⠀⠀⠀⠈⢷⡈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠫⣷⢐⡷⠦⢴⣋⣤⡤⠴⢖⡿⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⡾⠁⠀⠀⢷⡟⠹⡄⠀⠀⣸⠀⣾⠀⠀⠀⠀⠀⠀⠀⣼⣴⡾⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣸⣃⠀⠀⠀⠀⠀⠀⠀⢷⡈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣞⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⣠⠴⠋⠀⠀⡤⠀⠀⠀⠀⢀⡴⠟⡏⠀⠀⠀⣀⠌⠻⣄⣷⠀⠀⣧⢀⡇⠀⠀⠀⠀⠀⠀⢰⣿⡽⠁⠀⢀⡴⢻⡄⢀⣀⡀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠟⣾⠏⠀⣠⠞⠻⣦⣀⠀⠀⠀⠸⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡠⢤⡶⠋⢁⣀⣤⢴⡾⠁⠀⠀⢠⣴⡏⠀⠀⣇⣠⣿⣋⣁⣤⡤⠈⠉⠀⢀⡟⢸⣷⣀⠀⠀⠀⠀⠀⣾⢻⠃⠀⠠⡏⠀⠀⣧⠀⠀⠈⡽⠒⠦⣄⡀⠈⣿⡍⠛⠒⠦⠤⣤⣀⣀⠀⣿⠉⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⡿⠃⡴⠃⢚⣿⣿⣦⣄⣀⣹⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣽⣶⣚⣛⠚⠋⠉⣰⣤⣛⣀⣀⣠⡤⣾⠏⢳⣀⡀⢻⢘⣾⡉⠛⢿⡟⠓⠲⠶⠤⣿⣦⣠⡟⠃⠀⠀⠀⢠⣿⣏⣀⣄⣀⣻⡀⠀⢹⡄⠀⠀⡇⠀⠀⠀⠈⠑⠺⣿⡖⠦⠤⠤⢤⣤⣭⣽⣿⣿⣶⡶⠦⣀ ⠀⠀⢀⡞⠳⣄⠀⣰⠏⢠⡾⢁⡾⠁⢀⣾⣿⣛⣿⣽⡿⠟⠛⠋⠻⣶⣦⣤⣤⣤⡤⠶⠖⠒⠛⠛⡉⣉⣹⣏⡙⠲⠒⠛⣻⠀⠁⠀⠀⠀⢰⡇⢀⡼⠻⣽⠙⡿⣧⣏⣳⣌⠑⠢⣄⠀⠀⠀⠀⣿⣠⣤⣤⡀⢀⣼⣿⡿⠛⠉⠉⢿⣷⡀⠚⣇⠀⢰⡃⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠉ ⠀⣠⢻⡇⠀⠈⠳⣏⣰⠏⠀⡞⠀⠀⡿⠏⠉⠀⠈⣧⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⡭⠖⢃⣠⡴⠚⠉⠁⠀⠙⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⡇⡼⠁⠀⠸⣿⡷⢸⡇⢈⣉⠛⢦⡈⢻⡦⢤⣴⣏⠳⠦⣼⣷⠿⠋⠁⠀⠀⠀⢀⡈⣏⠃⠀⣿⠀⡼⠙⠲⠦⣄⣀⡀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ ⡰⢡⣿⠷⣄⡀⢀⣼⡇⠀⢸⠁⠀⢸⠇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣸⣟⣭⠽⢖⣺⡿⠟⠃⠀⠀⠀⠀⠀⠀⠙⠦⣄⣰⡇⠀⣠⠀⠀⠰⣿⢹⠇⠀⠀⠀⠘⢦⠀⠓⠺⠭⣽⣛⣛⣓⣷⠶⠛⠁⠀⣰⡟⠁⠀⠀⢀⡴⡾⠛⠋⡴⠾⢦⡀⢸⡤⠃⠀⠀⠀⡟⠈⠉⠉⠛⠺⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ 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