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.StringTokenizer;

public class B {
	public static void main(String[] args) throws IOException{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(in.readLine());
		
		final long ax = Long.parseLong(st.nextToken());
		final long ay = Long.parseLong(st.nextToken());
		final long bx = Long.parseLong(st.nextToken());
		final long by = Long.parseLong(st.nextToken());
		final long cx = Long.parseLong(st.nextToken());
		final long cy = Long.parseLong(st.nextToken());
		
		double D = 2*(ax*(by-cy) + bx*(cy-ay) + cx*(ay-by));
		if(D == 0){
			System.out.println("NO");
			System.exit(0);
		}
		double ox = ((ax*ax+ay*ay)*(by-cy) + (bx*bx+by*by)*(cy-ay) + (cx*cx+cy*cy)*(ay-by))/D;
		double oy = ((ax*ax+ay*ay)*(cx-bx) + (bx*bx+by*by)*(ax-cx) + (cx*cx+cy*cy)*(bx-ax))/D;
		
		double angle1 = (ax-ox)*(bx-ox) + (ay-oy)*(by-oy);
		double angle2 = (bx-ox)*(cx-ox) + (by-oy)*(cy-oy);
		
		//System.out.println(ox + " " + oy);
		//System.out.println(angle1 + "  " + angle2);
		
		if(Math.abs(angle1-angle2) < 1e-3) System.out.println("Yes");
		else System.out.println("No");

	}
}