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 Main {

    public static void main(String[] args) {


        Scanner in = new Scanner(System.in);
        long ax = in.nextInt();
        long ay = in.nextInt();
        long bx = in.nextInt();
        long by = in.nextInt();
        long cx = in.nextInt();
        long cy = in.nextInt();

        long ab_sq = (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
        long bc_sq = (cx - bx) * (cx - bx) + (cy - by) * (cy - by);

        if (ab_sq == bc_sq) {
            if ((cy - ay) * (bx - ax) != (cx - ax) * (by - ay)) {
                p("YES");
                return;
            }
        }
        p("NO");
    }

    static void p(Object str) {
        System.out.println(str);
    }

    public static void pa(int[] objs) {
        String str = "";
        for (Object obj : objs) {
            str += obj.toString() + " ";
        }
        p(str);
    }

    public static void pi(Object[] objs) {
        String str = "";
        for (Object obj : objs) {
            str += obj.toString() + " ";
        }
        p(str);
    }

}