The Child and Polygon

2000ms

262144K

Description:

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.

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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 ≤ 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| ≤ 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).

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Note:

In the first sample, there are two possible splittings:

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

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Informação

Provedor Codeforces

Código CF437E