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 a[2], b[2], c[2];
long long line(long long x1, long long y1, long long x2, long long y2) {
  return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}
bool tr() {
  if (a[0] - b[0] == 0 && a[0] - c[0] == 0) return false;
  if (a[0] - b[0] == 0 || a[0] - c[0] == 0) return true;
  if (((double)a[1] - b[1]) / (a[0] - b[0]) ==
      ((double)a[1] - c[1]) / (a[0] - c[0]))
    return false;
  return true;
}
int main() {
  std::cin >> a[0] >> a[1] >> b[0] >> b[1] >> c[0] >> c[1];
  std::cout << (tr() && line(a[0], a[1], b[0], b[1]) ==
                            line(b[0], b[1], c[0], c[1])
                    ? "Yes"
                    : "No");
}