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[] arr = br.readLine().split(" ");
		long ax = Integer.parseInt(arr[0]);
		long ay = Integer.parseInt(arr[1]);
		long bx = Integer.parseInt(arr[2]);
		long by = Integer.parseInt(arr[3]);
		long cx = Integer.parseInt(arr[4]);
		long cy = Integer.parseInt(arr[5]);
		long distAB = (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
		long distBC = (bx - cx) * (bx - cx) + (by - cy) * (by - cy);
		if (distAB != distBC) {
			System.out.println("No");
		} else {
			long dxab = bx - ax;
			long dyab = by - ay;
			long dxbc = cx - bx;
			long dybc = cy - by;
			if (dxab == dxbc && dyab == dybc) {
				System.out.println("No");
			} else {
				System.out.println("Yes");
			}
		}
		br.close();
	}

}