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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Scanner;

public class B {

	public static void main(String[] args) {
		try (Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
				PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)))) {
			out.println(solve(in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt()));
		}
	}

	private static String solve(int x0, int y0, int x1, int y1, int x2, int y2) {
		if ((long) (y1 - y0) * (x2 - x1) == (long) (y2 - y1) * (x1 - x0)) {
			if (x2 == x0 && y2 == y0) {
				return "Yes";
			}
			return "No";
		}
		if ((long) (y1 - y0) * (y1 - y0) + (long) (x1 - x0) * (x1 - x0) == (long) (y2 - y1) * (y2 - y1)
				+ (long) (x2 - x1) * (x2 - x1)) {
			return "Yes";
		}
		return "No";
	}

}