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>
#pragma comment(linker, "/STACK:16777216")
using namespace std;
inline long FastMax(long x, long y) {
  return (((y - x) >> (32 - 1)) & (x ^ y)) ^ y;
}
inline long FastMin(long x, long y) {
  return (((y - x) >> (32 - 1)) & (x ^ y)) ^ x;
}
long IR[] = {0, -1, 0, 1, -1, -1, 1, 1};
long IC[] = {1, 0, -1, 0, 1, -1, -1, 1};
struct POINT {
  long long x, y;
  long long Prev, Next;
};
vector<POINT> Poly;
bool operator==(POINT &a, POINT &b) { return a.x == b.x and a.y == b.y; }
bool operator!=(POINT &a, POINT &b) { return !(a == b); }
long long Area2(POINT a, POINT b, POINT c) {
  return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);
}
bool Collinear(POINT a, POINT b, POINT c) { return Area2(a, b, c) == 0; }
bool Left(POINT a, POINT b, POINT c) { return Area2(a, b, c) > 0; }
bool Between(POINT a, POINT b, POINT c) {
  if (!Collinear(a, b, c)) return false;
  return c.x >= min(a.x, b.x) && c.x <= max(a.x, b.x) && c.y >= min(a.y, b.y) &&
         c.y <= max(a.y, b.y);
}
bool Intersect(POINT a, POINT b, POINT c, POINT d) {
  if (!Collinear(a, b, c) && !Collinear(a, b, d) && !Collinear(c, d, a) &&
      !Collinear(c, d, b)) {
    return (!Left(a, b, c) ^ !Left(a, b, d)) &&
           (!Left(c, d, a) ^ !Left(c, d, b));
  }
  return Between(a, b, c) || Between(a, b, d) || Between(c, d, a) ||
         Between(c, d, b);
}
bool Diagonalie(POINT a, POINT b) {
  long long i;
  for (i = 0; i < Poly.size(); i++) {
    POINT c = Poly[i], c1 = Poly[(i + 1) % Poly.size()];
    if ((c != a) and (c1 != a) and (c != b) and (c1 != b) and
        Intersect(a, b, c, c1))
      return false;
  }
  return true;
}
bool InCone(POINT a, POINT b) {
  POINT a0, a1;
  a1 = Poly[a.Next];
  a0 = Poly[a.Prev];
  if (Area2(a, a1, a0) >= 0) {
    return Area2(a, b, a0) > 0 and Area2(b, a, a1) > 0;
  } else
    return !(Area2(a, b, a1) >= 0 and Area2(b, a, a0) >= 0);
}
bool Diagonal(POINT a, POINT b) {
  return InCone(a, b) and InCone(b, a) and Diagonalie(a, b);
}
long long N;
bool diag[207 + 7][207 + 7];
bool tria[207 + 7][207 + 7];
bool vi[207 + 7][207 + 7];
long long way[207 + 7][207 + 7];
long long TotalVer(long long i, long long j) {
  if (i < j)
    return j - i + 1;
  else
    return N - (i - j - 1);
}
long long FindWay(long long i, long long j) {
  if (vi[i][j]) return way[i][j];
  vi[i][j] = true;
  way[i][j] = 0;
  long long k;
  for (k = (i + 1) % N; k != j; k = (k + 1) % N) {
    if (!diag[i][k] or !diag[j][k]) continue;
    if (i < j and !(k > i and k < j)) continue;
    if (i > j and !(k > i or k < j)) continue;
    way[i][j] += FindWay(i, k) * FindWay(k, j);
    way[i][j] %= 1000000007;
  }
  return way[i][j];
}
int main(void) {
  long long i, j, x, y, Icase, k = 0;
  cin >> N;
  for (i = 0; i < N; i++) {
    cin >> x >> y;
    POINT pt = {x, y, (i - 1 + N) % N, (i + 1) % N};
    Poly.push_back(pt);
  }
  long long s = 0;
  for (i = 0; i < N; i++) {
    j = (i + 1) % N;
    s += (Poly[i].x + Poly[j].x) * (Poly[j].y - Poly[i].y);
  }
  if (s <= 0) {
    reverse(Poly.begin(), Poly.end());
    for (i = 0; i < N; i++) {
      Poly[i].Prev = (i - 1 + N) % N;
      Poly[i].Next = (i + 1) % N;
    }
  }
  for (i = 0; i < N; i++) {
    diag[i][(i + 1) % N] = diag[(i + 1) % N][i] = true;
    for (j = i + 1; j < N; j++) {
      if (!Diagonal(Poly[i], Poly[j])) continue;
      diag[i][j] = diag[j][i] = true;
    }
  }
  for (i = 0; i < N; i++) {
    vi[i][(i + 1) % N] = true;
    vi[i][(i + 2) % N] = true;
    way[i][(i + 1) % N] = 1;
    way[i][(i + 2) % N] = 1;
  }
  long long ans = FindWay(0, N - 1);
  cout << ans << endl;
  return 0;
}
