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 Main {
    public static void main(String[] args) {
        Scanner bb = new Scanner(System.in);
        long a = bb.nextInt(); 
        long b = bb.nextInt(); 
        long c = bb.nextInt(); 
        long d = bb.nextInt(); 
        long e = bb.nextInt(); 
        long f = bb.nextInt();
        boolean ans = ((f-d)*(c-a) != (d-b)*(e-c)) && ((f-d)*(f-d) + (e-c)*(e-c) == (d-b)*(d-b) + (c-a)*(c-a));
        if(!ans)
            System.out.println("No");
        else
            System.out.println("Yes");
    }
}