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E. The Child and Polygon

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 (10^{9} + 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}| ≤ 10^{7}) — 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 (10^{9} + 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:

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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