CF437E.The Child and Polygon

普及/提高-

通过率：0%

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题目描述

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 $1000000007$ $(10^{9}+7)$ for him.

输入格式

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.

输出格式

Output the number of ways modulo $1000000007$ $(10^{9}+7)$ .

输入输出样例

输入#1
```
4
0 0
0 1
1 1
1 0
```
输出#1
```
2
```
输入#2
```
4
0 0
1 0
0 1
-1 0
```
输出#2
```
1
```
输入#3
```
5
0 0
1 0
1 1
0 1
-2 -1
```
输出#3
```
3
```

说明/提示

In the first sample, there are two possible splittings:

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

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