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;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {

	static Scanner in = new Scanner(System.in);
	static final double EPS = 1e-7;

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		Long xa = Long.valueOf(st.nextToken());
		long ya = Long.valueOf(st.nextToken());
		long xb = Long.valueOf(st.nextToken());
		long yb = Long.valueOf(st.nextToken());
		long xc = Long.valueOf(st.nextToken());
		long yc = Long.valueOf(st.nextToken());

		if(dis(xa, ya, xb, yb) == dis(xc, yc, xb, yb) && Math.abs((yb-ya)*(xc-xb)-(yc-yb)*(xb-xa))!=0)
			System.out.println("Yes");
		else
			System.out.println("No");
		
	}
	public static long dis(long x1, long y1, long x2, long y2){
		return (x1-x2)*(x1-x2) + (y1-y2) * (y1-y2);
	}
}