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 CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  double a[2], b[2], c[2];
  scanf("%lf %lf %lf %lf %lf %lf", &a[0], &a[1], &b[0], &b[1], &c[0], &c[1]);
  if ((a[0] * (b[1] - c[1])) - (a[1] * (b[0] - c[0])) +
          ((b[0] * c[1]) - (b[1] * c[0])) ==
      0)
    printf("No\n");
  else if (pow(a[0] - b[0], 2) + pow(a[1] - b[1], 2) !=
           pow(b[0] - c[0], 2) + pow(b[1] - c[1], 2))
    printf("No\n");
  else
    printf("Yes\n");
  return 0;
}