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 task851b {

    void run() {
        Scanner sc = new Scanner(System.in);
        long ax = sc.nextInt();
        long ay = sc.nextInt();
        long bx = sc.nextInt();
        long by = sc.nextInt();
        long cx = sc.nextInt();
        long cy = sc.nextInt();
        long ab = (bx - ax) * (bx - ax) + (by - ay) * (by - ay);
        long bc = (bx - cx) * (bx - cx) + (by - cy) * (by - cy);

        if (ab == bc && (by - ay) * (cx - ax) != (cy - ay) * (bx - ax)) {
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }
    }

    public static void main(String[] args) {
        new task851b().run();
    }

}