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 long dist(long[] A, long[] B) {
        return ((long) Math.pow(A[0] - B[0], 2)) + ((long) Math.pow(A[1] - B[1], 2));
    }
    public static void main(String args[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        String[] axaybxbycxcy = br.readLine().split(" ");
        long[] A = new long[]{Long.parseLong(axaybxbycxcy[0]), Long.parseLong(axaybxbycxcy[1])};
        long[] B = new long[]{Long.parseLong(axaybxbycxcy[2]), Long.parseLong(axaybxbycxcy[3])};
        long[] C = new long[]{Long.parseLong(axaybxbycxcy[4]), Long.parseLong(axaybxbycxcy[5])};
        long x1 = A[0], y1 = A[1], x2 = B[0], y2 = B[1], x3 = C[0], y3 = C[1];
        if(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2) == 0) {
            System.out.println("No");
        } else {
            System.out.println(dist(A, B) == dist(B, C) ? "Yes" : "No");
        }
    }
}