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;
double EPS = 1e-10;
const double PI = acos(-1);
double add(double a, double b) {
  if (abs(a + b) < EPS * (abs(a) + abs(b))) return 0;
  return a + b;
}
struct point {
  double x, y;
  point() {}
  point(double x, double y) : x(x), y(y) {}
  point operator+(point p) { return point(add(x, p.x), add(y, p.y)); }
  point operator-(point p) { return point(add(x, -p.x), add(y, -p.y)); }
  point operator*(double d) { return point(x * d, y * d); }
};
double dot(point a, point b) { return (a.x * b.x + a.y * b.y); }
double cross(point a, point b) { return (a.x * b.y - a.y * b.x); }
double norm(point a) { return sqrt(dot(a, a)); }
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;
int ccw(point p0, point p1, point p2) {
  point a = p1 - p0;
  point b = p2 - p0;
  if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS) return CLOCKWISE;
  if (dot(a, b) < -EPS) return ONLINE_BACK;
  if (norm(a) < norm(b)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
bool is_convex(vector<point> pol) {
  for (int i = 0; i < pol.size(); i++)
    if (ccw(pol[(i + pol.size() - 1) % pol.size()], pol[(i) % pol.size()],
            pol[(i + 1) % pol.size()]) < 0)
      return false;
  return true;
}
int main(void) {
  int n;
  cin >> n;
  vector<point> pol(n);
  for (int i = 0; i < n; i++) cin >> pol[i].x >> pol[i].y;
  if (is_convex(pol))
    cout << 1 << endl;
  else
    cout << 0 << endl;
  return 0;
}
