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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long a, b, c, d, e, f;
  cin >> a >> b >> c >> d >> e >> f;
  long long int d1, d2, d3;
  d1 = (a - c) * (a - c) + (b - d) * (b - d);
  d2 = (a - e) * (a - e) + (b - f) * (b - f);
  d3 = (c - e) * (c - e) + (d - f) * (d - f);
  if ((d1 != d3) || ((d - b) * (e - c) == (f - d) * (c - a))) {
    cout << "No";
  } else {
    cout << "Yes";
  }
  return 0;
}