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 B {
  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int ax = s.nextInt();
    int ay = s.nextInt();
    int bx = s.nextInt();
    int by = s.nextInt();
    int cx = s.nextInt();
    int cy = s.nextInt();

    long v1 = (long)(by - ay) * (cx - bx);
    long v2 = (long)(cy - by) * (bx - ax);
    if (v1 == v2) {
      System.out.println("NO");
      return;
    }

    long dab = (long)(by - ay)*(by - ay) + (long)(bx - ax)*(bx - ax);
    long dbc = (long)(cy - by)*(cy - by) + (long)(cx - bx)*(cx - bx);
    System.out.println((dab == dbc) ? "YES" : "NO");
  }

}