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>
using namespace std;
const long long maxn = 200 + 5;
const long long mod = 1e9 + 7.5;
struct Point {
  long long first, second;
  Point(long long first = 0, long long second = 0)
      : first(first), second(second) {}
};
Point operator+(const Point& A, const Point& B) {
  return Point(A.first + B.first, A.second + B.second);
}
Point operator-(const Point& A, const Point& B) {
  return Point(A.first - B.first, A.second - B.second);
}
Point operator*(const Point& A, double p) {
  return Point(A.first * p, A.second * p);
}
Point operator/(const Point& A, double p) {
  return Point(A.first / p, A.second / p);
}
vector<Point> P;
long long n;
long long dp[maxn][maxn];
long long Cross(const Point& A, const Point& B) {
  return A.first * B.second - A.second * B.first;
}
long long PolygonArea(vector<Point> p) {
  long long area = 0;
  long long n = p.size();
  for (long long i = 1; i < n - 1; i++)
    area += Cross(p[i] - p[0], p[i + 1] - p[0]);
  return area / 2;
}
int main() {
  while (scanf("%I64d", &n) == 1) {
    P.clear();
    for (long long i = 0; i < n; i++) {
      long long first, second;
      scanf("%I64d%I64d", &first, &second);
      P.push_back(Point(first, second));
    }
    if (PolygonArea(P) < 0) reverse(P.begin(), P.end());
    memset(dp, 0, sizeof(dp));
    for (long long l = 0; l < n; l++)
      for (long long i = 0; i + l < n; i++) {
        long long j = i + l;
        if (l == 1) dp[i][j] = 1;
        for (long long k = i + 1; k < j; k++)
          if (Cross(P[k] - P[i], P[j] - P[i]) > 0)
            dp[i][j] = (dp[i][j] + dp[i][k] * dp[k][j]) % mod;
      }
    printf("%I64d\n", dp[0][n - 1]);
  }
  return 0;
}
