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() {
  pair<unsigned long long, unsigned long long> a, b, c;
  cin >> a.first >> a.second;
  cin >> b.first >> b.second;
  cin >> c.first >> c.second;
  if (a != b && b != c && a != c) {
    if ((b.second - a.second) * (b.second - a.second) +
                (b.first - a.first) * (b.first - a.first) ==
            (b.second - c.second) * (b.second - c.second) +
                (b.first - c.first) * (b.first - c.first) &&
        (2 * b.first != a.first + c.first ||
         2 * b.second != a.second + c.second))
      cout << "YES";
    else
      cout << "NO";
  } else
    cout << "NO";
  return 0;
}