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 Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		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();	
		double mx=(ax+cx)/2.0;
		double my=(ay+cy)/2.0;
		if(mx==bx && my==by)
			{
			System.out.println("No");
			}
		else if((bx-ax)*(bx-ax)+(by-ay)*(by-ay)==(bx-cx)*(bx-cx)+(by-cy)*(by-cy))System.out.println("Yes");
		else System.out.println("No");
		
	}

}