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 time{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long a1 = sc.nextInt();
		long a2 = sc.nextInt();
		long b1 = sc.nextInt();
		long b2 = sc.nextInt();
		long c1 = sc.nextInt();
		long c2 = sc.nextInt();
		long sqr = (b2 - a2) * (b2 - a2) + (b1 - a1)*(b1 - a1);
		long sqr1 =  (c2 - b2) * (c2 - b2) + (c1 - b1)*(c1 - b1);
		if(sqr == sqr1  && ((b2 - a2) * (c1 - b1) !=  (c2 - b2) * (b1 - a1) ) ){
				System.out.println("Yes");
			}
	
		
		else
			System.out.println("No");
		


	}
}