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:
/*
ID: andrew42
LANG: JAVA
TASK: 
PROG: 
*/

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

public class arpageo {
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		long ax = input.nextLong(); long ay = input.nextLong(); long bx = input.nextLong(); long by = input.nextLong(); long cx = input.nextLong(); long cy = input.nextLong();
		long numer = cy-by; long denom = cx-bx;
		long num = numer; long den = denom;
		boolean line = false;
		if (den == 0 || num == 0){
			if (den == 0){
				line = ax == bx;
			} else {
				line = ay == by;
			}
		} else {
			while (num%den != 0){
				long n = den;
				den = num%den;
				num = n;
			}
			numer /= den; denom /= den;
			line = -numer*ax+denom*ay == -numer*bx + denom*by;
		}
		System.out.println((bx-ax)*(bx-ax)+(by-ay)*(by-ay) == (bx-cx)*(bx-cx)+(by-cy)*(by-cy) && !line ? "Yes" : "No");
	}
}