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This is a small but ancient game. You are supposed to write down the
numbers 1, 2, 3, . . . , 2n - 1, 2n consecutively in clockwise order on
the ground to form a circle, and then, to draw some straight line
segments to connect them into number pairs. Every number must be
connected to exactly one another.
And, no two segments are allowed to intersect.
It's still a simple game, isn't it? But after you've written down the 2n
numbers, can you tell me in how many different ways can you connect the
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