E. The Child and Polygontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis 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.InputThe 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 xi, yi (|xi|, |yi| ≤ 107) — the i-th vertex of the polygon in clockwise or counterclockwise order.It's guaranteed that the polygon is simple.OutputOutput the number of ways modulo 1000000007 (109  +  7).ExamplesInput40 00 11 11 0Output2Input40 01 00 1-1 0Output1Input50 01 01 10 1-2 -1Output3NoteIn the first sample, there are two possible splittings:  In the second sample, there are only one possible splitting:  
Input40 00 11 11 0
Output2
['dp', 'geometry', '*2500']