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⠛⢿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣼⣛⣉⣉⣀⣀⣀⣀⣰⡇⠀⠀⠀⠀⠀⢀⣶⠿⠲⠤⢤⣄⣀⣀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣶⣶⣾⣿⣿⣿⢿⣿⣿⣿⣿⣟⣻⣿⣿⠿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⢿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⡀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠉⠙⣳⣤⣤⣶⡦⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⣙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣧⣆⡀⠀⠀⢀⣤⡴⠾⠿⠋⠉⠉⠁⠀⠀⠉⣹⠟⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣮⣍⡀⠀⠀⠀⠀⠀⠀⠀⠲⢶⡏⠀⠀⠀⠄⠈⠉⡟⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⢛⡅⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠀⠀⠀⠀⠙⠙⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣠⡿⠐⠀⠀⠐⠂⠀⣼⠁⠀⠀⠈⠻⡶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠙⠛⠓⠶⠶⠶⣶⣶⣾⡶⡶⢤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⠀⢀⣼⠃⠀⠀⡄⠀⠀⠷⡇⠀⢹⡿⢿⢳⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⡿⠋⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣶⠟⢹⠋⢙⠀⠷⣼⣿⠛⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣧⣴⣇⢠⡄⠀⣠⣀⣹⠀⢸⣷⠀⠀⢻⣄⠈⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⣀⡴⠞⠉⠀⠀⢠⡀⣤⣀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠈⣷⣤⣤⣶⣿⠏⢭⣙⣿⣷⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⣿⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣠⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⠁⠀⢴⣿⣽⠇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣼⠉⠙⢠⡟⠶⠾⢇⣰⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣾⠏⠀⢀⣾⣿⡿⠛⢉⣹⡿⠿⠿⢿⣄⠈⠙⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣻⣿⣿⡿⠷⢶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡇⠀⠀⠈⢿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⠂⠀⠀⠁⢻⣿⣿⣄⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢰⣇⣀⣀⣿⠿⠿⠖⣼⡿⢻⡟⢡⣿⣿⣿⣿⣿⣿⡟⠁⠀⣴⣿⠟⠁⠀⣰⡟⠁⠀⣀⣠⣤⣾⠳⣆⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⡇⢺⡇⠀⠀⠀⠀⢀⡟⣿⣿⣦⡀⠀⠀⠀⠘⠀⠀⠀⠀⠘⢿⣿⣉⣛⣹⣷⣶⣿⣷⣂⣧⣾⣿⣿⣿⣿⣿⣿⠃⠀⠘⠋⠁⢀⠤⠾⢿⡟⢷⣆⠈⢿⡋⠁⠀⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠃⠀⠀⠘⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣷⣾⡇⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣦⣄⠀⠀⠀⣷⣄⠀⠀⠈⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠸⣧⠀⠻⣷⣾⣿⣿⢿⣆⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣤⣤⣾⣶⣾⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⢠⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡙⣛⣿⠓⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⠀⠀⠶⠶⣾⣿⣄⠈⠁⠀⣹⣆⢻⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡿⢼⣷⠀⠛⠀⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣦⣿⠟⠛⠈⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣧⣄⣀⠙⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣁⠀⢀⣄⠀⠲⠶⠖⠒⠂⠈⠛⠛⠉⠂⡹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⣟⣉⣿⣿⣻⣿⠿⠟⠋⠉⠁⠀⠠⣬⠹⣧⣦⣤⣬⣉⠻⠿⢿⣯⡝⢷⣶⣶⣿ 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⢸⣆⢿⣿⣿⣾⣷⠻⠀⣧⠸⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢻⠈⠀⠀⣄⣷⠀⠀⠀⣄⣦⣿⣿⢿⠿⠿⠈⠀⠀⠀⠀⡇⣾⣷⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⠘⠀⠀⠃⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠘⠀⠁⡋⢿⠈⣆⢷⡟⢿⠾⠤⢀⠁⠋⠘⠀⠃⣿⣿⣿⣿⣿⣿⣾⣧⣂⣷⣿⣶⣷⣹⣛⣉⣿⢿⠘⠀⠀⠀⠀⠘⠀⠀⠀⡀⣦⣿⣿⡟⢀⠀⠀⠀⠀⡇⢺⡇⣿⣿⣿⣿⢿⠿⠿⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣿⣿⣸⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣆⠳⣾⣤⣠⣀⠀⠁⡟⣰⠀⠁⠟⣿⣴⠀⠁⡟⣿⣿⣿⣿⣿⣿⢡⡟⢻⡿⣼⠖⠿⠿⣿⣀⣀⣇⢰⠀⠀⠀⠏⢰⠀⠀⠀⠀⠀⣄⣿⣿⢻⠁⠀⠀⠂⣠⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⣿⣿⢿⠈⠀⠀⡇⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⢶⠷⡿⣿⣿⣻⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠙⠈⣄⢿⠿⠿⡿⣹⢉⠛⡿⣿⣾⢀⠀⠏⣾⣿⣿⣿⣿⣿⣿⣿⣼⣧⣿⣰⢇⠾⠶⡟⢠⠙⠉⣼⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠇⣽⣿⢴⠀⠁⠘⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣠⢀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡏⣿⣤⣀⣀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⣿⢼⡤⣤⣿⣿⣿⣶⣶⣶⣿⣿⠛⠉⠟⣴⠤⡯⣿⣿⣿⣿⣿⣿⢷⣿⣴⠀⡿⣡⡨⢀⠀⡀⣀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠟⣶⣿⣿⣿⣿⠉⠛⡿⢿⠙⠉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢻⠈⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣿⢻⠈⡄⣿⣿⣿⢾⠻⠛⠙⠉⣀⣀⢋⠸⠃⣿⣿⣿⣿⣤⣄⣧⡷⢻⠉⠋⣿⣿⢶⠛⠉⠈⠀⠉⠋⠛⣼⠀⠀⠀⠀⠆⣶⠿⣿⣾⣿⣿⣿⣿⢿⠘⣇⣾⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠇⠿⡿⣿⣿⢿⠀⠀⠀⡿⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣀⣉⠻⡟⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢻⣿⣷⣿⢉⠋⠟⣴⣠⢀⠋⡿⣼⠋⣿⣿⣿⣿⢠⠋⡞⣠⠀⠀⣀⣀⣧⣬⣦⠠⣀⣀⣤⣀⣀⣀⣄⠀⠀⠀⠀⠁⡿⣾⣴⠷⡟⣿⣿⣿⣠⠀⠋⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠛⠛⠙⠉⣈⣤⣦⣶⣿⠸⠀⠀⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⣿⣿⣿⣤⣤⢀⠀⠀⠟⣿⣼⣄⣠⡏⣿⣼⣿⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⠛⠒⠖⣤⣠⠀⠀⠀⣄⢷⣿⢰⠀⠏⣿⣿⣿⣌⣷⣿⠈⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠉⠀⣄⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣿⣿⣿⣿⣶⣿⠰⠀⠀⠉⡿⣿⣴⢀⠀⠃⣿⣼⠏⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡴⣤⣀⣀⠀⠀⠀⠀⠊⢀⠀⠁⠟⣿⣹⣤⡟⣿⣼⣿⣇⢿⠻⣧⢻⠈⠀⣿⣿⣿⣿⣿⣾⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠻⠙⣿⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢿⡿⣿⠁⣤⠊⠀⠇⣿⣿⣾⠀⠄⣤⡧⣿⢏⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠋⡿⣶⢰⣋⡿⣾⣲⣿⣿⣿⣿⣎⢻⣿⣿⣀⣧⣿⣀⣇⣾⣶⣠⠀⣿⣶⣶⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣿⣿⣿⢨⠀⠋⡿⣿⣾⢁⠚⡶⠀⣿⣼⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⠁⠀⠀⠀⠀⠀⠀⠁⠞⣵⠉⠋⠋⠖⣴⣤⢴⡤⣤⣤⣀⠀⠀⠀⠀⣄⢲⢒⡀⣦⣷⢿⡿⣿⠈⡀⢻⠀⠄⣶⣿⠚⠀⡟⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣼⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣿⣙⢭⠏⣿⣶⣤⣤⣷⠈⠀⡟⣿⣴⢀⠀⠀⠀⠀⠀⠁⠟⣴⣀⣀⣀⣀⣤⡀⢠⠀⠀⠉⠞⡴⣀⠋⡿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⢿⠈⣄⢻⠀⠀⣷⢸⠀⣹⣀⣠⠀⡄⢠⣇⣴⣧⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⡀⣽⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⠛⣿⣼⠷⠀⢙⠋⢹⠟⣶⢀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡴⣀⠀⠋⡿⣹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣄⢳⢿⡿⢹⠀⡇⠷⠀⠀⡄⠀⠀⠃⣼⢀⠀⡀⣀⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠈⠀⡗⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⢤⡶⡶⣾⣶⣶⠶⠶⠶⠓⠛⠙⠉⠟⡴⢀⠀⠀⠀⠀⠀⠀⠁⠛⡴⣀⠀⠀⠀⡿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠶⡶⠻⠈⠀⠀⠁⣼⠀⠂⠐⠀⠀⠐⡿⣠⣀⣀⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⡀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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