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 (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:

inputFormat

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.

outputFormat

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:

样例

4
0 0
1 0
0 1
-1 0

1

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