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 <iostream>
#include <vector>
#include <complex>
using namespace std;
 
#define X real()
#define Y imag()
#define EPS (1e-10)
 
typedef complex<double> P;
typedef P Vec;
 
double dot(Vec v1, Vec v2) {
  return (v1*conj(v2)).X;
}
 
double cross(Vec v1, Vec v2) {
  return (v1*conj(v2)).Y;
}
 
enum { COUNTER_CLOCKWISE, CLOCKWISE, ONLINE_FRONT, ONLINE_BACK, ON_SEGMENT };
 
int ccw(P p0, P p1, P p2) {
  Vec a = p1 - p0;
  Vec b = p2 - p0;
  if(cross(a, b) > EPS) return CLOCKWISE;
  if(cross(a, b) < -EPS) return COUNTER_CLOCKWISE;
  if(dot(a, b) < -EPS) return ONLINE_BACK;
  if(norm(a) < norm(b)) return ONLINE_FRONT;
  return ON_SEGMENT;
}

typedef vector<P> Polygon;

#define prev(G, i) ((G)[((i)-1+(G).size())%(G).size()])
#define curr(G, i) ((G)[(i)%(G).size()])
#define next(G, i) ((G)[((i)+1+(G).size())%(G).size()])

int main() {
  double x, y;
  Polygon g;
  
  int n;
  cin >> n;
  for(int i=0; i<n; i++) {
    cin >> x >> y;
    g.push_back(P(x, y));
  }
  
  for(int i=0; i<n; i++) {
    if( ccw(prev(g, i), curr(g, i), next(g, i)) == CLOCKWISE ) {
      cout << 0 << endl;
      return 0;
    }
  }
  
  cout << 1 << endl;
  
  return 0;
}