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E. The Child and Polygon
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 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.

Output

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

Examples
Input
4
0 0
0 1
1 1
1 0
Output
2
Input
4
0 0
1 0
0 1
-1 0
Output
1
Input
5
0 0
1 0
1 1
0 1
-2 -1
Output
3
Note

In the first sample, there are two possible splittings:

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