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 MexicanWave {

	void solve()
	{
		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();

        if ((ax * (by - cy) + (bx * (cy - ay)) + (cx * (ay - by))) == 0) {
            System.out.println("No");
            return;
        }

        long value1 = (bx - ax) * (bx - ax) + ((by - ay) * (by - ay));
        long value2 = (bx - cx) * (bx - cx) + ((by - cy) * (by - cy));

        if (value1 == value2)
            System.out.println("Yes");
        else
            System.out.println("No");
			
	}
	
	
	public static void main(String[] args) {
		new MexicanWave().solve();

	}

}