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;
import java.util.Arrays;
import java.lang.Math;
public class MarvoloRing {
    public static void main(String[] args) {
        Scanner kbd = new Scanner(System.in);
        String inp = kbd.nextLine();
        String[] input = inp.split(" ");
        long inpAx = Long.parseLong(input[0]) * 2;
        long inpAy = Long.parseLong(input[1]) * 2;
        long inpBx = Long.parseLong(input[2]) * 2;
        long inpBy = Long.parseLong(input[3]) * 2;
        long inpCx = Long.parseLong(input[4]) * 2;
        long inpCy = Long.parseLong(input[5]) * 2;
        
        long n = (Math.abs(inpAx - inpBx) * Math.abs(inpAx - inpBx)) + (Math.abs(inpAy - inpBy) * Math.abs(inpAy - inpBy));
        long m = (Math.abs(inpBx - inpCx) * Math.abs(inpBx - inpCx)) + (Math.abs(inpBy - inpCy) * Math.abs(inpBy - inpCy));
        long i = (inpAx + inpCx) / 2;
        long j = (inpAy + inpCy) / 2;
        
        if(n == m && !(i == inpBx && j == inpBy)){
        	System.out.println("YES");
        } else{
        	System.out.println("NO");
        }
    }
}