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;
inline void setmin(int &x, int y) {
  if (y < x) x = y;
}
inline void setmax(int &x, int y) {
  if (y > x) x = y;
}
inline void setmin(long long &x, long long y) {
  if (y < x) x = y;
}
inline void setmax(long long &x, long long y) {
  if (y > x) x = y;
}
const int N = 100000;
const int inf = (int)1e9 + 1;
const long long big = (long long)1e18 + 1;
const int P = 239;
const int MOD = (int)1e9 + 7;
const int MOD1 = (int)1e9 + 9;
const double eps = 1e-9;
const double pi = atan2(0, -1);
const int ABC = 26;
struct Point {
  long long x, y;
  Point() {}
  Point(long long x, long long y) : x(x), y(y) {}
  long long len() { return x * x + y * y; }
};
bool operator==(Point p1, Point p2) { return p1.x == p2.x && p1.y == p2.y; }
bool operator!=(Point p1, Point p2) { return p1.x != p2.x || p1.y != p2.y; }
Point operator+(Point p1, Point p2) { return Point(p1.x + p2.x, p1.y + p2.y); }
Point operator-(Point p1, Point p2) { return Point(p1.x - p2.x, p1.y - p2.y); }
long long operator*(Point p1, Point p2) { return p1.x * p2.x + p1.y * p2.y; }
long long operator%(Point p1, Point p2) { return p1.x * p2.y - p1.y * p2.x; }
bool point_in_segment(Point a, Point b, Point p) {
  if ((b - a) % (p - a) != 0) return false;
  return ((b - a) * (p - a) >= 0 && (a - b) * (p - b) >= 0);
}
bool SIS(Point a, Point b, Point c, Point d) {
  if ((b - a) % (d - c) == 0) {
    if (point_in_segment(a, b, c)) return true;
    if (point_in_segment(a, b, d)) return true;
    if (point_in_segment(c, d, a)) return true;
    if (point_in_segment(c, d, b)) return true;
    return false;
  } else {
    long long v1 = (b - a) % (c - a), v2 = (b - a) % (d - a);
    if (v1 < 0 && v2 < 0 || v1 > 0 && v2 > 0) return false;
    v1 = (d - c) % (a - c);
    v2 = (d - c) % (b - c);
    if (v1 < 0 && v2 < 0 || v1 > 0 && v2 > 0) return false;
    return true;
  }
}
long long get_area2(vector<Point> &a, bool absolute) {
  int n = (int)a.size();
  long long res = 0;
  for (int i = 0; i < n; i++) res += a[i] % a[(i + 1) % n];
  if (absolute) res = abs(res);
  return res;
}
bool check_counter_clockwise(vector<Point> &a) {
  return get_area2(a, false) > 0;
}
bool check_segment_in_polygon(vector<Point> &a, int i, int j) {
  int n = (int)a.size();
  if ((i + 1) % n == j || (j + 1) % n == i) return false;
  for (int k = 0; k < n; k++)
    if (k != i && k != j && point_in_segment(a[i], a[j], a[k])) return false;
  for (int k = 0; k < n; k++)
    if (k != i && (k + 1) % n != i && k != j && (k + 1) % n != j)
      if (SIS(a[i], a[j], a[k], a[(k + 1) % n])) return false;
  vector<Point> b, c;
  for (int k = i;; k = (k + 1) % n) {
    b.push_back(a[k]);
    if (k == j) break;
  }
  for (int k = j;; k = (k + 1) % n) {
    c.push_back(a[k]);
    if (k == i) break;
  }
  if (get_area2(b, true) + get_area2(c, true) != get_area2(a, true))
    return false;
  return true;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.precision(20);
  cout << fixed;
  int n;
  cin >> n;
  vector<Point> a(n);
  for (int i = 0; i < n; i++) cin >> a[i].x >> a[i].y;
  if (!check_counter_clockwise(a)) reverse(a.begin(), a.end());
  int dp[n][n];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) dp[i][j] = 0;
  for (int len = 2; len < n; len++)
    for (int i = 0; i < n; i++) {
      int j = (i + len) % n;
      if (len + 1 != n && !check_segment_in_polygon(a, i, j)) continue;
      for (int k = (i + 1) % n; k != j; k = (k + 1) % n) {
        long long v = 1;
        if (k != (i + 1) % n) v = v * dp[(k - i + n) % n][i] % MOD;
        if ((k + 1) % n != j) v = v * dp[(j - k + n) % n][k] % MOD;
        dp[len][i] += v;
        if (dp[len][i] >= MOD) dp[len][i] -= MOD;
      }
    }
  cout << dp[n - 1][0] << "\n";
  return 0;
}
