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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⢸⣿⡟⢰⣿⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠙⢿⣷⣀⢀⣠⣿⡿⠁⣼⡇⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠻⣿⣶⣶⡄⠀⠀⠀⣴⣾⣿⣧⣄⡀⣻⣿⣿⣿⣿⠇⣰⣿⢠⣾⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣷⡆⠀⠀⠀⠀⣸⣿⣴⣷⣠⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠇⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⣼⣿⣿⣟⣛⠻⢿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⠛⣿⣿⣿⣷⣿⡇⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⢠⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠈⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡍⢡⣿⣿⣧⣘⣿⡃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋⠁⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⡏⠻⠿⣟⠛⠇⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣠⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⡁⠈⣿⡟⢻⣿⣛⠛⠿⢿⣾⣿⣷⣦⣼⣿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⣿⠁⠀⠀⢘⣶⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢶⣬⡛⠿⠶⢶⣭⣩⣿⣾⣷⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⣀⣀⣴⠟⣭⣽⣯⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡿⢤⣀⠈⠙⠻⣦⣤⣬⣤⠀⢸⣿⡋⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣏⢀⣿⠟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣁⠀⠈⠛⠁⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⠷⢶⡀⠀⢙⣿⣁⣠⣾⢻⣿⣷⢿⣯⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣼⣯⣀⣿⣿⣧⣴⣿⣿⣿⣿⣻⡿⠟⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣸⡿⠿⢿⣧⣿⣿⣿⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣷⠛⢛⡀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠋⠉⢉⣭⣭⡉⣭⣿⠉⠙⠋⠉⠀⣰⠃⠀⣾⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣉⣿⣿⠛⠛⠀⠀⠙⣷⠀⢀⣠⡴⠦⠀⠀⠻⠛⠙⢷⡞⠉⠴⠶⢿⣿⣿⣿⠀⢀⣿⡿⣴⣿⣿⣿⣿⣿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⡉⠿⠏⠀⠀⠀⠀⠀⠀⢠⡾⠉⢣⣀⣀⠠⢿⢛⣷⠾⡇⠀⢀⣠⣿⣿⣿⣿⣶⣿⣧⣾⠿⣿⣿⣿⣿⠾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢫⣿⡟⠀⠀⠀⣠⣶⣶⣶⣶⡶⠀⢀⣤⣈⣉⣿⣷⣾⣿⡇⣠⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⣿⡇⠀⢰⣾⣿⣧⣾⡿⠃⠀⠀⣾⠋⢙⡏⠀⠀⢈⣭⣷⣿⣿⣿⣿⣿⣿⡀⠸⢿⣿⠟⢣⣀⢸⣯⡉⠉⠻⣧⡄⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⣿⣽⢷⡄⠘⢿⣿⡋⠉⠀⠀⠀⣶⢹⡇⠈⣁⣼⣿⣿⢿⣿⡿⣿⣿⣿⣿⢿⣧⣄⣀⢸⣇⠀⢿⡀⠉⠛⢦⡀⠈⠛⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢀⣼⣿⣎⣿⣦⣀⣿⣷⣄⠀⣰⣿⢣⡼⠃⢸⣿⣿⣿⣿⣾⠿⣤⡀⠛⢷⣄⠈⢻⡉⠹⣿⣏⠀⠈⠙⢦⡄⠈⠛⢷⡄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡶⠋⢩⣥⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣦⣤⣾⢿⣿⣿⣿⣿⡆⠸⢷⣄⠀⠘⣿⣿⣷⠶⠛⠛⠷⣶⣄⠈⣷⡀⠀⠀⢻⣆⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢩⣤⣠⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣾⠟⠛⢿⡄⠀⠀⠀⠙⢷⣴⣿⣿⣿⠀⠀⠀⠀⠈⢻⡆⠈⢻⡄⠀⠈⢿⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣼⡟⣿⡿⢿⣾⣿⡿⢉⣿⣿⣿⣷⣿⢻⣿⡿⢿⡇⠻⣧⡀⠈⠁⠀⠀⠀⠀⠈⠁⣀⠈⠙⢦⢠⡴⠶⣀⢈⣿⣦⣘⢧⡄⠀⠀⣻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⡟⢳⡟⠁⢠⣾⢋⣽⠋⣹⣿⣿⣿⠿⣿⣿⠁⠈⠀⠀⠹⠷⠀⠀⠀⢠⡀⠀⠀⠀⠛⠃⠀⣤⠀⢳⠀⠉⠀⠀⠀⠀⠀⣿⣦⣤⣟⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣴⣾⠀⠀⣿⠀⠘⠃⠘⠛⣷⣾⣿⣆⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠁⠀⠹⠇⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠉⠁⢨⡦⠀⠻⡇⠀⠀⠀⠠⣾⡏⠀⠀⠀⠀⢹⡇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⣀⣠⣾⣿⣶⣦⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⣀⡀⠀⠐⠂⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣾⡟⠀⠀⣠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣤⠀⠘⣆⠀⠀⠀⢻⣄⠀⠀⢸⣧⠀⠶⡄⠀⠀⠀⣸⣿⡿⠿⡟⠛⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢹⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠇⢠⡄⢹⣄⠀⠀⠀⠀⠀⣶⠀⠀⠀⠘⠇⠀⠘⣦⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⢀⣀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣥⣤⡟⠀⢰⣆⠀⠀⠀⠀⠘⠛⠀⢠⡀⠀⣸⡇⠀⠻⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⡀⠀⠈⣷⣄⠀⠀⠀⠀⣙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠉⠀⠀⠘⢻⣇⠀⠀⠀⠀⠀⠀⣼⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⣶⣆⠀⠀⠘⣣⠘⣷⣄⡀⠈⢻⣷⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢠⠀⠀⣦⢹⣇⠀⠀⠀⠀⣸⡿⠁⠀⢂⠀⠀⠀⠀⠈⣇⠈⡁⠀⢸⡇⠀⢸⣿⣇⠸⡆⣿⠛⣯⡈⢻⣆⠀⢻⣿⠻⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⢸⡇⠀⣿⣿⣿⣀⢀⣀⣴⡿⢿⣆⠀⡾⠀⣀⠀⠀⠀⣹⣿⠁⠀⢸⣧⣄⠀⢻⣿⡄⢿⣿⢧⣸⣷⣼⣿⣶⣾⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠿⣿⡟⢹⣿⣿⣿⣷⣼⣿⣿⣤⠀⣿⣿⣿⣿⡿⣿⡇⠀⣿⡇⢻⣆⠘⣿⣷⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣇⠻⣿⣿⣅⣀⠘⣿⣈⣿⣿⣼⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡟⢿⣷⡌⢻⣿⣿⣷⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣉⡛⠛⢧⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⠻⠿⠿⠿⠿⢾⣿⣿⣿⣿⣶⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣧⣴⠾⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣾⣿⣏⣹⣿⡏⣙⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡾⣿⠇⢹⣿⠿⣶⠆⢰⠾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣡⣾⠟⣷⣾⣿⣿⠏⣿⡟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣦⠛⠦⣬⣷⣦⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⣁⣠⣿⣿⣿⣇⣼⣯⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣯⣿⣿⣷⡆⠀⠈⠋⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡶⣾⣽⣿⣿⣿⣿⣿⣿⡏⢹⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⣿⣿⠻⢿⡉⠘⠃⢿⡀⠀⠀⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢁⣴⣿⡿⣿⣿⠛⠉⢩⣽⡇⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⣿⡆⠘⣿⠻⣦⣬⣿⣦⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⠿⣧⣤⣶⣿⣿⣽⣷⣿⣤⣤⣤⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣯⣿⣷⣦⡿⢀⣿⢡⣴⠉⢿⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⠿⣧⣽⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣿⡁⠙⣿⣷⣾⣷⣬⣿⣄⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠾⠿⠿⠛⣃⢼⣿⢶⣤⣿⡿⠟⠋⢻⣿⣿⣿⡿⠛⢷⣍⡉⠛⠁⠀⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣿⣿⣶⣿⣟⣿⢻⣿⡿⣿⣷⣀⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠿⣏⠀⠀⠀⠻⠋⠉⠁⣠⣿⠟⠁⢀⣰⠿⠿⣿⣶⣤⣦⢠⣍⡉⠀⠀⣒⢦⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠷⣮⣿⣿⣿⠋⠙⠻⠇⠀⢻⣿⡿⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣆⠙⢦⣤⣤⡶⠛⣠⣾⣿⣿⣀⣀⣠⡏⠀⠀⠉⣀⣉⡹⠆⢻⣿⢀⡀⢉⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣉⠙⠁⢀⣼⣿⠈⢿⣆⠀⠀⠀⠀⠀⢹⣿⣦⣤⡀⠙⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ 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