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.io.*;
import java.util.*;

public class B {
	
	static class Point{
		int x;
		int y;
		
		Point(int x, int y){
			this.x = x;
			this.y = y;
		}
	}
	
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

		StringTokenizer st = new StringTokenizer(in.readLine());
		long xa = Long.parseLong(st.nextToken());
		long ya = Long.parseLong(st.nextToken());
		long xb = Long.parseLong(st.nextToken());
		long yb = Long.parseLong(st.nextToken());
		long xc = Long.parseLong(st.nextToken());
		long yc = Long.parseLong(st.nextToken());
		
		if((xa-xb)*(xa-xb)+(ya-yb)*(ya-yb)==(xc-xb)*(xc-xb)+(yc-yb)*(yc-yb) && (xa-xc)*(yb-yc)!=(xb-xc)*(ya-yc))
			System.out.println("Yes");
		else
			System.out.println("No");
		
		in.close();
	}

}