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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class B {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));		
		String[] line = br.readLine().split(" ");
		
		long ax = Long.parseLong(line[0]);
		long ay = Long.parseLong(line[1]);
		long bx = Long.parseLong(line[2]);
		long by = Long.parseLong(line[3]);
		long cx = Long.parseLong(line[4]);
		long cy = Long.parseLong(line[5]);
		
		long d1 = (bx-ax)*(bx-ax) + (by-ay)*(by-ay);
		long d2 = (cx-bx)*(cx-bx) + (cy-by)*(cy-by);
		long det = ax*(by-cy) + bx*(cy-ay) + cx*(ay-by);
		
		if(d1 == d2 && det != 0) {
			System.out.println("Yes");
		}else {
			System.out.println("No");
		}
	}
}