Knots

An even number of strands, $N$, are pushed through a wall. On one side of the wall, one person ties $N/2$ knots, each joining a pair of strands, so that every strand is used in exactly one knot. On the other side of the wall, a second person likewise ties $N/2$ knots between disjoint pairs of strands. Find the probability that the knots tie all of the strands into one single big loop.

For example, suppose $N = 4$ and the strands are numbered 1, 2, 3, 4. If the first person makes the knot pairs {(1, 4), (2, 3)}, then the second person has two ways to tie the knots: {(1, 2), (3, 4)} or {(1, 3), (2, 4)}.

The input consists of one or more lines. Each line contains a single positive even integer that is at most $100$, giving the number of strands, $N$, pushed through the wall. Input continues until end of file (EOF).

For each line of input, print exactly one line: the probability that the knotted strands form one single big loop for that number of strands. Print the probability rounded to $5$ decimal places.