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;
long long size(long long ax, long long ay, long long bx, long long by) {
  return (bx - ax) * (bx - ax) + (by - ay) * (by - ay);
}
long long angl(long long ax, long long ay, long long bx, long long by,
               long long cx, long long cy) {
  return (ax - bx) * (cx - bx) + (ay - by) * (cy - by);
}
int main() {
  long long a[2], b[2], c[2];
  cin >> a[0] >> a[1];
  cin >> b[0] >> b[1];
  cin >> c[0] >> c[1];
  if (size(a[0], a[1], b[0], b[1]) == size(b[0], b[1], c[0], c[1]) &&
      angl(b[0], b[1], a[0], a[1], c[0], c[1]) ==
          angl(b[0], b[1], c[0], c[1], a[0], a[1]))
    if (abs(size(b[0], b[1], c[0], c[1])) ==
        abs(angl(a[0], a[1], b[0], b[1], c[0], c[1])))
      cout << "NO"
           << "\n";
    else
      cout << "YES"
           << "\n";
  else
    cout << "NO"
         << "\n";
}