A9529 | The Child and Polygon

This time our child has a simple polygon. He has to find the number of ways to split the polygon into non-degenerate triangles, each way must satisfy the following requirements:

- each vertex of each triangle is one of the polygon vertex;
- each side of the polygon must be the side of exactly one triangle;
- the area of intersection of every two triangles equals to zero, and the sum of all areas of triangles equals to the area of the polygon;
- each triangle must be completely inside the polygon;
- each side of each triangle must contain exactly two vertices of the polygon.

The picture below depicts an example of a correct splitting.

Please, help the child. Calculate the described number of ways modulo $1000000007$ $(10^{9}+7)$ for him.

The first line contains one integer $n$ $(3<=n<=200)$ — the number of vertices of the polygon. Then follow $n$ lines, each line containing two integers. The $i$ -th line contains $x_{i},y_{i}$ $(|x_{i}|,|y_{i}|<=10^{7})$ — the $i$ -th vertex of the polygon in clockwise or counterclockwise order.

It's guaranteed that the polygon is simple.

Output the number of ways modulo $1000000007$ $(10^{9}+7)$ .