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.io.*;
public class Maximus {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int ax = Integer.parseInt(st.nextToken());
        int ay = Integer.parseInt(st.nextToken());
        int bx = Integer.parseInt(st.nextToken());
        int by = Integer.parseInt(st.nextToken());
        int cx = Integer.parseInt(st.nextToken());
        int cy = Integer.parseInt(st.nextToken());

        if((ax - bx)*1L*(ax - bx) + (ay - by)*1L*(ay - by) != (bx - cx)*1L*(bx - cx) + (by - cy)*1L*(by - cy) ||
                (ax - cx)*1L*(by - ay)  == (ax - bx)*1L*(cy - ay)){
            System.out.println("No");
            return;
        }
        System.out.println("Yes");
    }
}