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
public class Main{
  public void run(java.io.InputStream in, java.io.PrintStream out){
    java.util.Scanner sc = new java.util.Scanner(in);
/*answer*/
    int n;
    double[] x, y;
    int i, j, s;
    double ax, ay, bx, by;

    n = sc.nextInt();
    x = new double[n];
    y = new double[n];

    for(i = 0;i < n;i++){
      x[i] = sc.nextDouble();
      y[i] = sc.nextDouble();
    }
    sc.close();

    s = 1;
    for(i = 0;i < n - 2;i++){
      ax = x[i + 1] - x[i];
      ay = y[i + 1] - y[i];
      bx = x[i + 2] - x[i];
      by = y[i + 2] - y[i];
      if(ax * by - ay * bx < 0){
        s = 0;
        break;
      }
    }

    if(s == 0){
      System.out.println("0");
    }else{
      System.out.println("1");
    }

  }
  public static void main(String[] args){
    (new Main()).run(System.in, System.out);
  }
}