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 int MAX_N = 100005;
double add(double a, double b) {
  if (abs(a + b) < 1e-10 * (abs(a) + abs(b))) {
    return 0;
  }
  return a + b;
}
struct P {
  double x, y;
  P() {}
  P(double x, double y) : x(x), y(y) {}
  P operator+(P p) { return P(add(x, p.x), add(y, p.y)); }
  P operator-(P p) { return P(add(x, -p.x), add(y, -p.y)); }
  P operator*(double d) { return P(x * d, y * d); }
  double dot(P p) { return add(x * p.x, y * p.y); }
  double det(P p) { return add(x * p.y, -y * p.x); }
};
int n;
P ps[MAX_N];
bool cmp_x(const P& p, const P& q) {
  if (p.x != q.x) {
    return p.x < q.x;
  }
  return p.y < q.y;
}
vector<P> convex_hull(P* ps, int n) {
  sort(ps, ps + n, cmp_x);
  int k = 0;
  vector<P> qs(n * 2);
  for (int i = 0; i < n; ++i) {
    while (k > 1 && (qs[k - 1] - qs[k - 2]).det(ps[i] - qs[k - 1]) < 0) {
      k--;
    }
    qs[k++] = ps[i];
  }
  for (int i = n - 2, t = k; i >= 0; i--) {
    while (k > t && (qs[k - 1] - qs[k - 2]).det(ps[i] - qs[k - 1]) < 0) {
      k--;
    }
    qs[k++] = ps[i];
  }
  qs.resize(k - 1);
  return qs;
}
double dist(P p, P q) { return (p - q).dot(p - q); }
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    ps[i] = P(a, b);
  }
  vector<P> qs = convex_hull(ps, n);
  if (n == qs.size()) {
    cout << "1\n";
  } else {
    cout << "0\n";
  }
  return 0;
}
