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 B {
  public static void main(String[] args) {
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    long ax = in.nextInt();
    long ay = in.nextInt();
    long bx = in.nextInt();
    long by = in.nextInt();
    long cx = in.nextInt();
    long cy = in.nextInt();
    if ((bx-ax)*(bx-ax) + (by-ay)*(by-ay) == (cx-bx)*(cx-bx) + (cy-by)*(cy-by) && !((bx - ax == cx - bx) && (by - ay) == (cy - by)))
      System.out.println("Yes");
    else
      System.out.println("No");
    in.close();
  }
}