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.io.*;

public class B851 {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] tokens = br.readLine().split(" ");
        long ax = Integer.parseInt(tokens[0]);
        long ay = Integer.parseInt(tokens[1]);
        long bx = Integer.parseInt(tokens[2]);
        long by = Integer.parseInt(tokens[3]);
        long cx = Integer.parseInt(tokens[4]);
        long cy = Integer.parseInt(tokens[5]);

        long ab2 = (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
        long bc2 = (bx - cx) * (bx - cx) + (by - cy) * (by - cy);

        long slopeTop = (by - ay);
        long slopeBot = (bx - ax);
        long lhs = slopeBot * (cy - ay);
        long rhs = slopeTop * (cx - ax);
        if (lhs == rhs) {
            System.out.println("No");
        } else {
            String ans = "";
            if (ab2 == bc2) {
                ans = "Yes";
            } else {
                ans = "No";
            }
            System.out.println(ans);
        }
    }
}