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 (109+7) for him.

Input The first line contains one integer n (3 \le n \le 200) - the number of vertices of the polygon. Then follow n lines, each line containing two integers. The i-th line contains xi,yi (|xi|,|yi| \le 107) - the i-th vertex of the polygon in clockwise or counterclockwise order.It's guaranteed that the polygon is simple.

Output Output the number of ways modulo 1000000007 (109+7).

In the first sample, there are two possible splittings: In the second sample, there are only one possible splitting: