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:
/* package whatever; // don't place package name! */

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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	  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();
		     System.out.println(((bx - ax) * (cy - ay) == (cx - ax) * (by - ay)) || ((ax - bx) * (ax - bx) + (ay - by) * (ay - by) != (cx - bx) * (cx - bx) + (cy - by) * (cy - by)) ? "No" : "Yes");  
	}
}