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;
inline double add(double a, double b) {
  return abs(a + b) < (1e-10) * (abs(a) + abs(b)) ? 0.0 : a + b;
}
struct vec {
  double x, y;
  vec operator-(vec b) { return (vec){add(x, -b.x), add(y, -b.y)}; }
  vec operator+(vec b) { return (vec){add(x, b.x), add(y, b.y)}; }
  vec operator*(double d) { return (vec){x * d, y * d}; }
  double dot(vec v) { return add(x * v.x, y * v.y); }
  double cross(vec v) { return add(x * v.y, -y * v.x); }
  double norm() { return sqrt(x * x + y * y); }
};
int ccw(vec& a, vec& b, vec& c) {
  vec ab = b - a, ac = c - a;
  double o = ab.cross(ac);
  if (o > 0) return 1;
  if (o < 0) return -1;
  if (ab.dot(ac) < 0) {
    return 2;
  } else {
    if (ab.dot(ab) < ac.dot(ac)) {
      return -2;
    } else {
      return 0;
    }
  }
}
bool isConvex(vector<vec>& g) {
  int n = g.size() - 2;
  for (int i = 0; i < n; i++) {
    switch (ccw(g[i], g[i + 1], g[i + 2])) {
      case 1:
      case -2:
        break;
      default:
        return false;
    }
  }
  return true;
}
int main() {
  int n;
  cin >> n;
  vector<vec> g;
  vec v;
  while (n--) {
    cin >> v.x >> v.y;
    g.push_back(v);
  }
  g.push_back(g[0]);
  g.push_back(g[1]);
  cout.precision(1);
  cout << fixed;
  cout << (isConvex(g) ? 1 : 0) << endl;
  return 0;
}
