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);
  long long x1, y1, x2, y2, x3, y3;
  cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
  long double dist1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  long double dist2 = (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3);
  long double dist3 = (x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2);
  if (!((double)(y1 - y2) / (x1 - x2) == (double)(y1 - y3) / (x1 - x3)) &&
      !(y1 == y2 && y1 == y3) && (dist1) == (dist3))
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}