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;
static const double EPS = 1e-12;
static const double INF = 1e24;
using Point = complex<double>;
using Plane = vector<Point>;
using Polygon = vector<Point>;
bool operator<(const Point &a, const Point &b) {
  return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
}
double cross_prod(const Point &a, const Point &b) { return imag(conj(a) * b); }
double dot_prod(const Point &a, const Point &b) { return real(conj(a) * b); }
enum {
  ONLINE_FRONT = -2,
  CLOCKWISE,
  ON_SEGMENT,
  COUNTER_CLOCKWISE,
  ONLINE_BACK,
};
int ccwise(Point a, Point b, Point c) {
  b -= a;
  c -= a;
  if (cross_prod(b, c) > 0) {
    return COUNTER_CLOCKWISE;
  } else if (cross_prod(b, c) < 0) {
    return CLOCKWISE;
  } else if (dot_prod(b, c) < 0) {
    return ONLINE_BACK;
  } else if (norm(b) < norm(c)) {
    return ONLINE_FRONT;
  } else {
    return ON_SEGMENT;
  }
}
bool is_convex(Polygon g) {
  size_t V = g.size();
  for (size_t i = 0; i < V; ++i) {
    int state = ccwise(g[i], g[(i + 1) % V], g[(i + 2) % V]);
    if (!(state == ONLINE_FRONT || state == COUNTER_CLOCKWISE)) return false;
  }
  return true;
}
int main() {
  size_t n;
  scanf("%zu", &n);
  Polygon g(n);
  for (size_t i = 0; i < n; ++i) {
    double x, y;
    scanf("%lf %lf", &x, &y);
    g[i] = Point(x, y);
  }
  printf("%d\n", is_convex(g));
  return 0;
}
