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 {
  long double px, py;
};
long double norm(const Point& a) { return a.px * a.px + a.py * a.py; }
long double dot(const Point& a, const Point& b) {
  return a.px * b.px + a.py * b.py;
}
long double crs(const Point& a, const Point& b) {
  return a.px * b.py - a.py * b.px;
}
Point Minus(Point a, Point b) {
  a.px -= b.px;
  a.py -= b.py;
  return a;
}
int ccw(const Point& p0, const Point& p1, const Point& p2) {
  Point a = Minus(p1, p0), b = Minus(p2, p0);
  if (crs(a, b) > 1e-10) return 1;
  if (crs(a, b) < -1e-10) return -1;
  if (dot(a, b) < -1e-10) return 2;
  if (norm(a) < norm(b)) return -2;
  return 0;
}
bool is_convex(vector<Point> v) {
  if (v.size() < 3) return false;
  int s = -3;
  for (int i = 0; i < v.size(); i++) {
    int r = ccw(v[i], v[(i + v.size() - 1) % v.size()], v[(i + 1) % v.size()]);
    if (abs(r) == 1 && s == -3) s = r;
    if (s * r == -1) return false;
  }
  return true;
}
int n;
Point p[1000];
vector<Point> G;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> p[i].px >> p[i].py;
    G.push_back(p[i]);
  }
  cout << is_convex(G) << endl;
  return 0;
}
