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 maxn = 100000 + 10;
int n;
struct Point {
  int x, y;
  Point() {}
  Point(int _x, int _y) : x(_x), y(_y) {}
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  bool operator<(Point p) { return x == p.x ? y < p.y : x < p.x; }
  int cross(Point p) { return x * p.y - y * p.x; }
  int dot(Point p) { return x * p.x + y * p.y; }
  int norm() { return x * x + y * y; }
};
vector<Point> ps;
int ccw(Point p, Point p1, Point p2) {
  Point a = p1 - p;
  Point b = p2 - p;
  if (a.cross(b) < -(1E-10)) return -1;
  if (fabs(a.cross(b) < (1E-10))) return -1;
  if (a.cross(b) > (1E-10)) return 1;
  if (a.dot(b) < -(1E-10)) return -2;
  if (a.norm() < b.norm()) return 2;
  return 0;
}
vector<Point> convex_hull(vector<Point> ps) {
  vector<Point> u, l;
  if (ps.size() < 3) return ps;
  u.push_back(ps[0]);
  u.push_back(ps[1]);
  l.push_back(ps[ps.size() - 1]);
  l.push_back(ps[ps.size() - 2]);
  for (int i = 2; i < ps.size(); i++) {
    for (int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], ps[i]) != -1;
         n--) {
      u.pop_back();
    }
    u.push_back(ps[i]);
  }
  for (int i = ps.size() - 3; i >= 0; i--) {
    for (int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], ps[i]) != -1;
         n--) {
      l.pop_back();
    }
    l.push_back(ps[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; i--) l.push_back(u[i]);
  return l;
}
int main() {
  scanf("%d", &n);
  int x, y;
  for (int i = 0; i < n; i++) {
    scanf("%d%d", &x, &y);
    ps.push_back(Point(x, y));
  }
  vector<Point> qs = convex_hull(ps);
  if (qs.size() == n)
    printf("1\n");
  else
    printf("0\n");
  return 0;
}
