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 input = new Scanner(System.in);
		long ax = input.nextInt();
		long ay = input.nextInt();

		long bx = input.nextInt();
		long by = input.nextInt();

		long cx = input.nextInt();
		long cy = input.nextInt();

		if (((ax - bx) * (ax - bx) + (ay - by) * (ay - by) != (cx - bx)
				* (cx - bx) + (cy - by) * (cy - by))
				|| ((ax + cx) / 2.0 == bx && (ay + cy) / 2.0 == by))
			System.out.println("No");
		else
			System.out.println("Yes");
	}

}