For a given polygon g, print "1" if g is a convex polygon, "0" otherwise. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of the polygon. The line segment connecting pn and p1 is also a side of the polygon.

Constraints

* 3 ≤ n ≤ 100
* -10000 ≤ xi, yi ≤ 10000
* No point of the polygon will occur more than once.
* Two sides of the polygon can intersect only at a common endpoint.

Input

g is given by coordinates of the points p1,..., pn in the following format:


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them.

Output

Print "1" or "0" in a line.

Examples

Input

4
0 0
3 1
2 3
0 3


Output

1


Input

5
0 0
2 0
1 1
2 2
0 2


Output

0
#include <bits/stdc++.h>
using namespace std;
template <class T>
void readVal(vector<T>& vec, int idx) {
  T input;
  std::cin >> input;
  vec[idx] = input;
}
int main() {
  char ans = '1';
  int size;
  cin >> size;
  vector<int> x(size);
  vector<int> y(size);
  int dir(0), vecx(0), vecy(0);
  for (int i = 0; i < size; i++) {
    readVal(x, i);
    readVal(y, i);
  }
  for (int i = 0; i <= size; i++) {
    int new_vecx = x[(i + 1) % size] - x[i % size];
    int new_vecy = y[(i + 1) % size] - y[i % size];
    int cross_prod = (vecx * new_vecy - vecy * new_vecx);
    if (cross_prod != 0) {
      if (cross_prod * dir >= 0) {
        dir = cross_prod > 0 ? 1 : -1;
      } else {
        ans = '0';
        break;
      }
    }
    vecx = new_vecx;
    vecy = new_vecy;
  }
  cout << ans;
  return 0;
}
