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.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner scan=new Scanner(System.in);
		int x1=scan.nextInt();
		int y1=scan.nextInt();
		int x2=scan.nextInt();
		int y2=scan.nextInt();
		int x3=scan.nextInt();
		int y3=scan.nextInt();
		long d1=(long)(x2-x1)*(x2-x1)+(long)(y2-y1)*(y2-y1);
		long d2=(long)(x3-x2)*(x3-x2)+(long)(y3-y2)*(y3-y2);
		long m1=(long)(y3-y2)*(x2-x1);
		long m2=(long)(x3-x2)*(y2-y1);
         if(d1==d2 && m1!=m2) System.out.println("Yes");
		 else  System.out.println("No" );
        
	}
}