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 numbers into pairs? Life is harder, right!
Each line of the input ﬁle will be a single positive number n, except
the last line, which is a number −1.
You may assume that 1 ≤ n ≤ 150.
For each n, print in a single line the number of ways to connect the 2n
numbers into pairs.
Note : Big num!