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You are pairing couples for a very conservative formal ball. There are n men and m women, and you know the height and gender of

You are pairing couples for a very conservative formal ball. There are n men and m women, and you know the height and gender of each person there. Each dancing couple must be a man and a woman, and the man must be at least as tall as, but no more than 3 inches taller than, his partner. You wish to maximize the number of dancing couples given this constraint. Write an efficient algorithm to solve it and explain its complexity.

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