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 b {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long ax = in.nextLong();
		long ay = in.nextLong();
		long bx = in.nextLong();
		long by = in.nextLong();
		long cx = in.nextLong();
		long cy = in.nextLong();
		long dx1 = bx - ax, dy1 = by - ay;
		long dx2 = cx - bx, dy2 = cy - by;
		long d1 = dx1 * dx1 + dy1 * dy1;
		long d2 = dx2 * dx2 + dy2 * dy2;
		long cross = dx1 * dy2 - dy1 * dx2;
		System.out.println(d1 == d2 && cross != 0 ? "Yes" : "No");
	}
}