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.Collections;
import java.util.List;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Arrays;

public class Main {
  public static Scanner scanner = new Scanner(System.in);
  
  public static long distance(long x1, long x2, long y1, long y2) {
	return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
  }
  
  public static double slope(long x1, long x2, long y1, long y2) {
    return (x1-x2)*(y1-y2);
  }
  
  public static void main(String[] args) {
    
    long x1,y1,x2,y2,x3,y3,k1,k2,d1,d2;
    while(scanner.hasNext()) {
      x1 = scanner.nextInt();
      y1 = scanner.nextInt();
      x2 = scanner.nextInt();
      y2 = scanner.nextInt();
      x3 = scanner.nextInt();
      y3 = scanner.nextInt();
      if(distance(x1, x2, y1, y2)!=distance(x2, x3, y2, y3)) System.out.println("NO");
      else if(slope(x2, x3, y1, y2)==slope(x1, x2, y2, y3)){
        System.out.println("NO");
      }
      else System.out.println("YES");
    }
  }
}