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 PI = acos(-1.0);
const int MAX = 1e1;
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  if (x < 0)
    return -1;
  else
    return 1;
}
struct Point {
  double x, y;
  Point() {}
  Point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }
  double operator^(const Point &b) const { return x * b.y - y * b.x; }
  double operator*(const Point &b) const { return x * b.x - y * b.y; }
  void transXY(double B) {
    double tx = x, ty = y;
    x = tx * cos(B) - ty * sin(B);
    y = tx * sin(B) + ty * cos(B);
  }
};
double CalcArea(Point p[], int n) {
  double res = 0;
  for (int i = 0; i < n; i++) {
    res += (p[i] ^ p[(i + 1) % n]) / 2;
  }
  return fabs(res);
}
bool isconvex(Point poly[], int n) {
  bool s[3];
  memset(s, false, sizeof(s));
  for (int i = 0; i < n; i++) {
    s[sgn((poly[(i + 1) % n] - poly[i]) ^ (poly[(i + 2) % n] - poly[i])) + 1] =
        true;
    if (s[0] && s[2]) return false;
  }
  return true;
}
Point p[MAX];
int main(void) {
  int n;
  scanf("%d\n", &n);
  for (int i = 0; i < n; i++) {
    scanf("%lf%lf\n", &p[i].x, &p[i].y);
  }
  printf("%d\n", isconvex(p, n) ? 1 : 0);
  return 0;
}
