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;
class Point {
 public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double k) { return Point(x * k, y * k); }
  Point operator/(double k) { return Point(x / k, y / k); }
  double norm() { return x * x + y * y; }
  double abs() { return sqrt(norm()); }
  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }
};
double norm(Point a) { return a.x * a.x + a.y * a.y; }
double abs(Point a) { return sqrt(norm(a)); }
Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }
double getDistance(Point a, Point b) { return abs(a - b); }
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; }
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) > (1e-10)) return COUNTER_CLOCKWISE;
  if (cross(a, b) < (1e-10)) return CLOCKWISE;
  if (dot(a, b) < -(1e-10)) return ONLINE_BACK;
  if (norm(a) < norm(b)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
bool isConvex(const vector<Point> &Poly) {
  for (int i = 0; i < Poly.size(); i++) {
    if (ccw((Poly[i % Poly.size()]), (Poly[(i + 1) % Poly.size()]),
            (Poly[(i + 2) % Poly.size()])) != COUNTER_CLOCKWISE)
      return false;
  }
  return true;
}
int main() {
  int n;
  cin >> n;
  vector<Point> Poly;
  for (int i = 0; i < n; i++) {
    int x, y;
    cin >> x >> y;
    Poly.push_back(Point(x, y));
  }
  cout << isConvex(Poly) << endl;
  return 0;
}
