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;
const double EPS = 1e-8;
const double INF = 1e12;
namespace std {
bool operator<(const complex<double>& a, const complex<double>& b) {
  return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
}
}  // namespace std
double cross(const complex<double>& a, const complex<double>& b) {
  return imag(conj(a) * b);
}
double dot(const complex<double>& a, const complex<double>& b) {
  return real(conj(a) * b);
}
int ccw(complex<double> a, complex<double> b, complex<double> c) {
  b -= a;
  c -= a;
  if (cross(b, c) > 0) return +1;
  if (cross(b, c) < 0) return -1;
  if (dot(b, c) < 0) return +2;
  if (norm(b) < norm(c)) return -2;
  return 0;
}
bool isconvex(const vector<complex<double> >& complex<double>) {
  for (int i = 0; i < complex<double>.size(); ++i)
    if (ccw(complex<double>[(i + complex<double>.size() - 1) %
                            complex<double>.size()],
            complex<double>[(i) % complex<double>.size()],
            complex<double>[(i + 1) % complex<double>.size()]) != 1)
      return false;
  return true;
}
int main() {
  vector<complex<double> > poly;
  complex<double> p;
  int n;
  double x, y;
  for (scanf("%d", &n); n--; poly.push_back(p))
    scanf("%lf%lf", &x, &y), p = complex<double>(x, y);
  printf("%d\n", isconvex(poly));
}
