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.

<image>

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:

<image>

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

<image>
#include <bits/stdc++.h>
struct point_t {
  long long x, y;
  point_t(long long x = 0, long long y = 0) : x(x), y(y) {}
  friend point_t operator-(const point_t& a, const point_t& b) {
    return {a.x - b.x, a.y - b.y};
  }
  friend long long operator*(const point_t& a, const point_t& b) {
    return a.x * b.y - a.y * b.x;
  }
};
const long long mod_const = 1000000007LL;
point_t pt[201];
long long f[200][200];
char mark[200][200];
long long solve(int l, int r) {
  if (mark[l][r]) return f[l][r];
  mark[l][r] = 1;
  if (l + 1 == r) return f[l][r] = 1;
  long long& v = f[l][r];
  for (int i = l + 1; i < r; ++i) {
    if ((pt[r] - pt[l]) * (pt[r] - pt[i]) > 0)
      v = (v + solve(l, i) * solve(i, r)) % mod_const;
  }
  return v;
}
int main() {
  int n;
  std::scanf("%d", &n);
  for (int i = 0; i != n; ++i) std::scanf("%I64d %I64d", &pt[i].x, &pt[i].y);
  long long area = 0;
  pt[n] = pt[0];
  for (int i = 0; i < n; ++i) area += pt[i] * pt[i + 1];
  if (area < 0) std::reverse(pt + 1, pt + n);
  std::printf("%I64d", solve(0, n - 1));
  return 0;
}
