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 xa, xb, ya, yb, za, zb;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> xa >> xb >> ya >> yb >> za >> zb;
  long long x1 = (xa - ya) * (xa - ya) + (xb - yb) * (xb - yb);
  long long x2 = (ya - za) * (ya - za) + (yb - zb) * (yb - zb);
  long long y2 = (xa - za) * (xa - za) + (xb - zb) * (xb - zb);
  ;
  if (x1 == x2 && (za - ya != ya - xa || zb - yb != yb - xb))
    cout << "Yes";
  else
    cout << "No";
  return 0;
}