Number of triangulations P45584

You are given a polygon with $n$ sides without self-intersections. In how many ways can you triangulate it?

Input

Input consists of several cases with only integer numbers. Each case begins with $n$, followed by the $n$ coordinates $x$ $y$ of the vertices given in counterclockwise order. Assume $3 \le n \le 200$ and $\vert x \vert, \vert y \vert \le 10^6$. The given polygons are such that no triangulation contains a degenerate triangle.

Output

For every case, print the number of triangulations modulo $10^9 + 7$.