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;
//http://codeforces.com/contest/851/problem/B

public class Geometery {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int x1 = s.nextInt();
		int y1 = s.nextInt();
		int x2 = s.nextInt();
		int y2 = s.nextInt();
		int x3 = s.nextInt();
		int y3 = s.nextInt();
		s.close();
		// dist from point 1 to 2 squared'
		long x12 = (x1-x2);
		long y12 = (y1-y2);
		long d12 = x12*x12 + y12*y12;
		// dist from point 2 to 3 squared
		long x23 = (x2-x3);
		long y23 = (y2-y3);
		long d23 = x23*x23 + y23*y23;
		if (d12 == d23) {
			// test for collinearity (parallel vector cross product=0)
			long temp1 =((long)x1 - x2) * (y2 - y3);
			long temp2 =((long)y1 - y2) * (x2 - x3);
			if (temp1==temp2) {
				System.out.println("NO");
			} else {
				System.out.println("YES");
			}
		} else {
			System.out.println("NO");
		}
	}
}