This is a simple but ancient game. You are supposed to write down the numbers
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, how many different ways can you connect the numbers into pairs? Life is harder, right?
Input contains an integer
1 ≤ n ≤ 32).
Print in a single line the number of ways to connect the
2n numbers into pairs.