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;
struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
};
double dot(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; }
double cross(const Point &a, const Point &b) { return a.x * b.y - b.x * a.y; }
double norm(const Point &p) { return dot(p, p); }
int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > 1e-10) return 1;
  if (cross(a, b) < -1e-10) return -1;
  if (dot(a, b) < -1e-10) return 2;
  if (norm(a) < norm(b)) return -2;
  return 0;
}
bool isConvex(const vector<Point> &p) {
  for (int i = 0; i < (int)p.size(); i++) {
    if (ccw((p[(i - 1 + p.size()) % p.size()]), (p[i % p.size()]),
            (p[(i + 1) % p.size()])) > 0) {
      return false;
    }
  }
  return true;
}
int main() {
  int N;
  cin >> N;
  vector<Point> p(N);
  for (int i = 0; i < N; i++) {
    cin >> p[i].x >> p[i].y;
  }
  cout << isConvex(p) << endl;
  return 0;
}
