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;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long ax = scanner.nextLong();
        long ay = scanner.nextLong();
        long bx = scanner.nextLong();
        long by = scanner.nextLong();
        long cx = scanner.nextLong();
        long cy = scanner.nextLong();
        if (ax == bx && ax == cx && bx == cx) {
            System.out.println("No");
        }else{
            double k = ((double) (by - ay)) / ((double) (bx - ax));
            double b = ay - k * ax;
            long l_ab = (bx - ax) * (bx - ax) + (by - ay) * (by - ay);
            long l_bc = (cx - bx) * (cx - bx) + (cy - by) * (cy - by);
            if ((double) (cy) == k * cx + b) {
                System.out.println("No");
            } else {
                if (l_ab == l_bc) {
                    System.out.println("Yes");
                } else {
                    System.out.println("No");
                }
            }
        }
    }
}