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>
using namespace std;
int main() {
  long long a1, b1, a2, b2, a3, b3;
  cin >> a1 >> b1 >> a2 >> b2 >> a3 >> b3;
  if ((b2 - b1) * (a3 - a2) == (b3 - b2) * (a2 - a1))
    cout << "NO";
  else {
    if (((a2 - a1) * (a2 - a1) + (b2 - b1) * (b2 - b1)) ==
        ((a3 - a2) * (a3 - a2) + (b3 - b2) * (b3 - b2)))
      cout << "YES";
    else
      cout << "NO";
  }
  return 0;
}