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 T, class first>
inline bool checkbit(T a, first pos) {
  T t = 1;
  return ((a & (t << pos)) > 0);
}
template <class T, class first>
inline T setbit(T a, first pos) {
  T t = 1;
  return (a | (t << pos));
}
template <class T, class first>
inline T resetbit(T a, first pos) {
  T t = 1;
  return (a & (~(t << pos)));
}
template <class T, class first>
inline T togglebit(T a, first pos) {
  T t = 1;
  return (a ^ (t << pos));
}
template <typename T>
T POW(T B, T printf) {
  if (printf == 0) return 1;
  if (printf & 1)
    return B * POW(B, printf - 1);
  else
    return (POW(B, printf / 2) * POW(B, printf / 2));
}
template <typename T>
T Bigmod(T base, T power, T mod) {
  T ret = 1;
  while (power) {
    if (power & 1) ret = (ret * base) % mod;
    base = (base * base) % mod;
    power >>= 1;
  }
  return ret;
}
template <typename T>
T ModInverse(T number, T mod) {
  return Bigmod(number, mod - 2, mod);
}
template <typename T>
T GCD(T a, T b) {
  if (a < 0) return GCD(-a, b);
  if (b < 0) return GCD(a, -b);
  return (b == 0) ? a : GCD(b, a % b);
}
template <typename T>
T LCM(T a, T b) {
  if (a < 0) return LCM(-a, b);
  if (b < 0) return LCM(a, -b);
  return a * (b / GCD(a, b));
}
template <typename T>
T EUCLIDE(T a, T b, T &x, T &y) {
  if (a < 0) {
    T d = euclide(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = euclide(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = euclide(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <typename T>
T ABS(T a) {
  if (a < 0)
    return -a;
  else
    return a;
}
double DEG(double x) { return (180.0 * x) / ((2.0 * acos(0.0))); }
double RAD(double x) { return (x * (double)(2.0 * acos(0.0))) / (180.0); }
template <typename T>
T DIS(T x1, T y1, T x2, T y2) {
  return sqrt((double)((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)));
}
template <typename T>
T ANGLE(T x1, T y1, T x2, T y2) {
  return atan(double(y1 - y2) / double(x1 - x2));
}
template <typename T>
long long isLeft(T a, T b, T c) {
  return (c.x - a.x) * (b.y - a.y) - (b.x - a.x) * (c.y - a.y);
}
template <class T>
inline bool setmin(T &a, T b) {
  return a > b ? a = b, true : false;
}
template <class T>
inline bool setmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
void P_ARR(int *ar, int a, int b) {
  if (a > b) swap(a, b);
  if (a <= b) cout << ar[a];
  for (int i = a + 1; i <= b; i++) cout << " " << ar[i];
  cout << endl;
}
template <typename T>
T in() {
  char ch;
  T n = 0;
  bool ng = false;
  while (1) {
    ch = getchar();
    if (ch == '-') {
      ng = true;
      ch = getchar();
      break;
    }
    if (ch >= '0' && ch <= '9') break;
  }
  while (1) {
    n = n * 10 + (ch - '0');
    ch = getchar();
    if (ch < '0' || ch > '9') break;
  }
  return (ng ? -n : n);
}
long long dp[202][202];
struct data {
  long long x, y;
} ar[222];
long long call(int s, int e) {
  if (s == e) return 0;
  if (s + 1 == e) return 1;
  long long &ret = dp[s][e];
  if (ret != -1) return ret;
  ret = 0;
  for (int i = s + 1; i <= e - 1; i++) {
    if (isLeft(ar[s], ar[i], ar[e]) > 0)
      ret = (ret + (call(s, i) * call(i, e))) % 1000000007;
  }
  return ret;
}
int main() {
  int(n);
  scanf("%d", &n);
  double area = 0.0;
  ar[0].x = 0ll;
  ar[0].y = 0ll;
  for (int i = 1; i <= n; i++) {
    scanf("%lld%lld", &ar[i].x, &ar[i].y);
    area += isLeft(ar[0], ar[i - 1], ar[i]);
  }
  area += isLeft(ar[0], ar[n], ar[1]);
  if (area < 0) reverse(ar + 1, ar + 1 + n);
  memset(dp, -1, sizeof dp);
  printf("%lld\n", call(1, n));
  ;
  return 0;
}
