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{
	static long dist(long x1,long y1,long x2,long y2){
		return Math.abs(sq(x1-x2))+Math.abs(sq(y1-y2));
	}
	static long  sq(long x){
		return x*x;
	}
	public static void main(String [] args){
		Scanner sc=new Scanner(System.in);
		long ax=sc.nextLong();
		long ay=sc.nextLong();
		long bx=sc.nextLong();
		long by=sc.nextLong();
		long cx=sc.nextLong();
		long cy=sc.nextLong();

		if(dist(ax,ay,bx,by)==dist(bx,by,cx,cy)){//check if distance is same
			if(((by-ay)*(cx-bx))==((cy-by)*(bx-ax))){//if on same line
				System.out.println("No");
			}
			else{
				System.out.println("Yes");
			}
		}
		else{
			System.out.println("No");
		}
	}
}