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.Scanner;

/**
 * Created by igarus on 17.10.2016.
 */
public class CF_432_B {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long ax = scanner.nextInt();
        long ay = scanner.nextInt();
        long bx = scanner.nextInt();
        long by = scanner.nextInt();
        long cx = scanner.nextInt();
        long cy = scanner.nextInt();

        long ab = (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
        long bc = (bx - cx) * (bx - cx) + (by - cy) * (by - cy);
//        long ca = (cx - ax) * (cx - ax) + (cy - ay) * (cy - ay);

        long A = ay - cy;
        long B = cx - ax;
        long C = ax * cy - cx * ay;

        if (ab == bc && A * bx + B * by + C != 0)
            System.out.println("Yes");
        else
            System.out.println("No");


    }

}