Problem: Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a, b, c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Input

The only line contains six integers ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 109). It's guaranteed that the points are distinct.

Output

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

Examples

Input

0 1 1 1 1 0


Output

Yes


Input

1 1 0 0 1000 1000


Output

No

Note

In the first sample test, rotate the page around (0.5, 0.5) by <image>.

In the second sample test, you can't find any solution.

Solution (in JAVA):

Solution:
import java.util.*;
public class C{
    public static void main(String []args){
        Scanner s=new Scanner(System.in);
        double a1=s.nextDouble();
        double a2=s.nextDouble();
        double b1=s.nextDouble();
        double b2=s.nextDouble();
        double c1=s.nextDouble();
        double c2=s.nextDouble();
        double m1=Math.abs(a2-b2)/Math.abs(a1-b1);
        double m2=Math.abs(a2-c2)/Math.abs(a1-c1);
        if(m1==m2)
        System.out.println("NO");
        else{
            long x=(long)Math.abs(b1-a1);
            long y=(long)Math.abs(b2-a2);
            long xy=x*x+y*y;
            long dis1=xy;
            
             x=(long)Math.abs(b1-c1);
             y=(long)Math.abs(b2-c2);
             xy=x*x+y*y;
             long dis2=xy;
             if(dis1==dis2)
             System.out.println("YES");
             else
             System.out.println("NO");
        }
    }
}