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 int N = 205, MOD = 1000000007;
int n;
int x[N], y[N];
int cross(int x1, int y1, int x2, int y2) {
  long long t = (long long)x1 * y2 - (long long)x2 * y1;
  if (t < 0) {
    return -1;
  } else if (t == 0) {
    return 0;
  } else {
    return 1;
  }
}
bool intersect(int x0, int y0, int x1, int y1, int x2, int y2, int x3, int y3) {
  if (cross(x2 - x0, y2 - y0, x1 - x0, y1 - y0) *
              cross(x3 - x0, y3 - y0, x1 - x0, y1 - y0) ==
          -1 &&
      cross(x1 - x2, y1 - y2, x3 - x2, y3 - y2) *
              cross(x0 - x2, y0 - y2, x3 - x2, y3 - y2) ==
          -1) {
    return true;
  }
  return false;
}
bool g[N][N];
bool vis[N][N];
int f[N][N];
int dp(int i, int j) {
  if (vis[i][j]) {
    return f[i][j];
  }
  vis[i][j] = true;
  if (i < j) {
    if (i + 1 == j) {
      f[i][j] = 1;
    } else {
      for (int k = i + 1; k < j; ++k) {
        if (g[i][k] && g[j][k]) {
          (f[i][j] += (long long)dp(i, k) * dp(k, j) % MOD) %= MOD;
        }
      }
    }
  } else {
    if (i + 1 == j + n) {
      f[i][j] = 1;
    } else {
      for (int kp = i + 1; kp < j + n; ++kp) {
        int k = kp % n;
        if (g[i][k] && g[j][k]) {
          (f[i][j] += (long long)dp(i, k) * dp(k, j) % MOD) %= MOD;
        }
      }
    }
  }
  return f[i][j];
}
int inv(int a) {
  return a == 1 ? 1 : (long long)(MOD - MOD / a) * inv(MOD % a) % MOD;
}
int dot(int x, int y, int x1, int y1) {
  int t = x * x1 + y * y1;
  if (t < 0) {
    return -1;
  } else if (t == 0) {
    return 0;
  } else {
    return 1;
  }
}
bool online(int x, int y, int x0, int y0, int x1, int y1) {
  int dx = x1 - x0, dy = y1 - y0;
  if (cross(x - x0, y - y0, dx, dy) != 0) {
    return false;
  }
  return dot(x - x0, y - y0, x - x1, y - y1) == -1;
}
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  double Length() { return sqrt(x * x + y * y); }
};
Point operator-(Point a, Point b) { return Point(a.x - b.x, a.y - b.y); }
int Sign(double x, double eps = 1e-9) { return x < -eps ? -1 : x > eps; }
double Det(Point a, Point b) { return a.x * b.y - a.y * b.x; }
double Dist(Point a, Point b, Point c) {
  return abs(Det(a - c, b - c) / (a - b).Length());
}
double Dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
bool In_The_Seg(Point a, Point b, Point c) {
  if (Sign(Dist(a, b, c))) {
    return 0;
  }
  return Sign(Dot(a - c, b - c)) <= 0;
}
bool contain(double x, double y) {
  Point A, B, P = Point(x, y);
  int res = 0;
  for (int i = 0; i < n; ++i) {
    A = Point(::x[i], ::y[i]), B = Point(::x[i + 1], ::y[i + 1]);
    if (In_The_Seg(A, B, P)) {
      return 1;
    }
    if (Sign(A.y - B.y) <= 0) {
      swap(A, B);
    }
    if (Sign(P.y - A.y) > 0) {
      continue;
    }
    if (Sign(P.y - B.y) <= 0) {
      continue;
    }
    res += Sign(Det(B - P, A - P)) > 0;
  }
  return res & 1;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d%d", x + i, y + i);
  }
  x[n] = x[0], y[n] = y[0];
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j) {
      if (j == i + 1 || i == 0 && j == n - 1) {
        g[i][j] = g[j][i] = true;
        continue;
      }
      bool flag = true;
      for (int k = 0; k < n; ++k) {
        if (intersect(x[i], y[i], x[j], y[j], x[k], y[k], x[k + 1], y[k + 1])) {
          flag = false;
        }
        if (k != i && k != j && online(x[k], y[k], x[i], y[i], x[j], y[j])) {
          flag = false;
        }
      }
      if (flag) {
        double xx = (double)(x[i] + x[j]) / 2, yy = (double)(y[i] + y[j]) / 2;
        if (contain(xx, yy)) {
          g[j][i] = g[i][j] = true;
        }
      }
    }
  }
  memset(vis, 0, sizeof(vis));
  int ans = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j) {
      if (!g[i][j]) {
        continue;
      }
      for (int k = j + 1; k < n; ++k) {
        if (!g[i][k] || !g[j][k]) {
          continue;
        }
        (ans += (long long)dp(i, j) * dp(j, k) % MOD * dp(k, i) % MOD) %= MOD;
      }
    }
  }
  printf("%d\n", (int)((long long)ans * inv(n - 2) % MOD));
  return 0;
}
