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 Geometry {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in=new Scanner(System.in);
		long ax,ay,bx,by,cx,cy;
		ax=in.nextLong();
		ay=in.nextLong();
		bx=in.nextLong();
		by=in.nextLong();
		cx=in.nextLong();
		cy=in.nextLong();
		long ab=(bx-ax)*(bx-ax)+(by-ay)*(by-ay);
		long bc=(bx-cx)*(bx-cx)+(by-cy)*(by-cy);
		if((bx-ax)*(by-cy)!=(bx-cx)*(by-ay)&&ab==bc)
			System.out.print("YES");
		else
			System.out.print("NO");
		
	}

}