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 angle {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long x1 = in.nextInt();
		long y1 = in.nextInt();
		long x2 = in.nextInt();
		long y2 = in.nextInt();
		long x3 = in.nextInt();
		long y3 = in.nextInt();
		long d1 = ((x2-x1)*(x2-x1) + (y2-y1)*(y2-y1));
		long d2 = ((x2-x3)*(x2-x3) + (y2-y3)*(y2-y3));
		if((d1 == d2) && ((y2-y1)*(x3-x2) != (y3-y2)*(x2-x1)) )
	 	{
			System.out.println("Yes");
		}
		else
		{
			System.out.println("No");
		}
		in.close();
	}

}