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;
template <class C>
void mini(C& a4, C b4) {
  a4 = min(a4, b4);
}
template <class C>
void maxi(C& a4, C b4) {
  a4 = max(a4, b4);
}
template <class T1, class T2>
ostream& operator<<(ostream& out, pair<T1, T2> pair) {
  return out << "(" << pair.first << ", " << pair.second << ")";
}
const int N = 1e3 + 5;
const long long M = 1e9 + 7;
long long dp[N][N];
long long is_in[N][N];
struct Point {
  long long y, x;
  Point(long long x_, long long y_) : x(x_), y(y_){};
  Point(){};
};
Point vers[N];
long long cross(Point& a, Point& b, Point& c) {
  return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}
int odc(int a, int b, int c, int d) {
  if (a > b) {
    swap(a, b);
  }
  if (c > d) {
    swap(c, d);
  }
  return !((b < c) || (d < a));
}
int main() {
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(10);
  double beg = 1.0 * clock() / CLOCKS_PER_SEC;
  int n;
  cin >> n;
  ;
  for (int i = (1); i <= (n); ++i) {
    int y, x;
    cin >> y >> x;
    ;
    vers[i] = Point(y, x);
  }
  for (int i = (1); i <= (n); ++i) {
    for (int j = (1); j <= (n); ++j) {
      is_in[i][j] = true;
      if (abs(i - j) == 1 || abs(i - j) == (n - 1)) {
        continue;
      }
      for (int k = (1); k <= (n); ++k) {
        if (k == i || k == j) {
          continue;
        }
        int kk = 1 + k % n;
        if (kk == i || kk == j) {
          continue;
        }
        long long cr1 = cross(vers[i], vers[j], vers[k]);
        long long cr2 = cross(vers[i], vers[j], vers[kk]);
        bool first_inter = false;
        bool second_inter = false;
        if (cr1 == 0 && cr2 == 0) {
          first_inter = false;
          ;
        } else {
          if ((cr1 <= 0 && cr2 >= 0) || (cr1 >= 0 && cr2 <= 0)) {
            first_inter = true;
          }
        }
        cr1 = cross(vers[k], vers[kk], vers[i]);
        cr2 = cross(vers[k], vers[kk], vers[j]);
        if (cr1 == 0 && cr2 == 0) {
          first_inter = false;
        } else {
          if ((cr1 <= 0 && cr2 >= 0) || (cr1 >= 0 && cr2 <= 0)) {
            second_inter = true;
          }
        }
        if (first_inter && second_inter) {
          is_in[i][j] = false;
        }
      }
      int ii = 1 + i % n;
      long long abs_area = 0;
      long long area_left = 0;
      long long area_right = 0;
      bool passed = false;
      while (ii != i) {
        if (ii == j) {
          passed = true;
        }
        long long tr_area = cross(vers[i], vers[ii], vers[1 + ii % n]);
        if (passed) {
          area_right += tr_area;
        } else {
          area_left += tr_area;
        }
        ii = 1 + ii % n;
      }
      if ((area_left >= 0 && area_right <= 0) ||
          (area_left <= 0 && area_right >= 0)) {
        if (is_in[i][j]) {
        }
        is_in[i][j] = false;
      }
    }
  }
  for (int i = (1); i <= (n); ++i) {
    for (int j = (1); j <= (n); ++j) {
      cerr << is_in[i][j];
    }
    cerr << "\n";
  }
  for (int i = 1; i <= n; i++) {
    int ii = 1 + i % n;
    dp[i][ii] = 1;
  }
  for (int dl = 2; dl <= n - 1; dl++) {
    for (int i = 1; i <= n; i++) {
      int ii = 1 + (i + dl - 1) % n;
      int mid = 1 + i % n;
      while (mid != ii) {
        if (is_in[i][mid] && is_in[mid][ii]) {
          dp[i][ii] = (dp[i][ii] + dp[i][mid] * dp[mid][ii]) % M;
        }
        mid = 1 + mid % n;
      }
      if (is_in[i][ii] == 0) {
        dp[i][ii] = 0;
      }
    }
  }
  assert(dp[2][1] == dp[1][n]);
  for (int i = (1); i <= (n); ++i) {
    for (int j = (1); j <= (n); ++j) {
      assert(is_in[i][j] == is_in[j][i]);
    }
  }
  cout << dp[2][1] << endl;
  return 0;
}
