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;
using lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... U> void assign(V<T>& v, int n, const U&... u) { v.resize(n); for (auto&& i : v) assign(i, u...); }

const double eps = 1e-10;
const double inf = 1e+10;
const double pi = acos(-1.0);
int sgn(double a) { return a < -eps ? -1 : a > eps; }
using P = complex<double>;
istream& operator>>(istream& i, P& p) { double x, y; i >> x >> y; p = P(x, y); return i; }
ostream& operator<<(ostream& o, const P& p) { o << real(p) << ' ' << imag(p); return o; }
bool operator<(const P& p, const P& q) { return sgn(real(p) - real(q)) ? sgn(real(p) - real(q)) < 0 : sgn(imag(p) - imag(q)) < 0; }
bool operator>(const P& p, const P& q) { return q < p; }
bool operator<=(const P& p, const P& q) { return !(p > q); }
bool operator>=(const P& p, const P& q) { return !(p < q); }
bool eq(const P& p, const P& q) { return !(p < q) and !(p > q); }
double dot(const P& p, const P& q) { return real(conj(p) * q); }
double cross(const P& p, const P& q) { return imag(conj(p) * q); }

int ccw(P p0, P p1, P p2) {
  p1 -= p0, p2 -= p0;                         //             (1)
  if (sgn(cross(p1, p2)) > 0) return 1;       //
  if (sgn(cross(p1, p2)) < 0) return -1;      // (-2)---p0---(0)---p1---(2)
  if (sgn(dot(p1, p2) < 0)) return -2;        //
  if (sgn(norm(p1) - norm(p2)) < 0) return 2; //             (-1)
  return 0;
}

bool convex(V<P>& ps) {
  int n = ps.size();
  for (int i = 0; i < n; i++) if (ccw(ps[i], ps[(i + 1) % n], ps[(i + 2) % n]) == -1) return false;
  return true;
}

int main() {
  cin.tie(NULL); ios::sync_with_stdio(false);
  int n; cin >> n;
  V<P> ps(n); for (int i = 0; i < n; i++) cin >> ps[i];
  cout << convex(ps) << '\n';
}
