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 MyClass {
    public static void main(String args[]) {
        Scanner kbd = new Scanner(System.in);
        long ax = kbd.nextLong();
        long ay = kbd.nextLong();
        long bx = kbd.nextLong();
        long by = kbd.nextLong();
        long cx = kbd.nextLong();
        long cy = kbd.nextLong();
        
        long dx=bx-ax;
        long dy=by-ay;
        long ex=cx-ax;
        long ey=cy-ay;
        long fx=cx-bx;
        long fy=cy-by;
        
        if (dx*ey==ex*dy){
            System.out.println("NO");
            System.exit(0);
        }
        if  (dx*dx+dy*dy!=fx*fx+fy*fy){
             System.out.println("NO");
            System.exit(0);
        }
        System.out.println("YES");
    }
}