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 collinear(long long x1, long long y1, long long x2, long long y2,
              long long x3, long long y3) {
  long long a = x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2);
  return a == 0 ? 1 : 0;
}
int main() {
  long long ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  long long ab = ax - bx;
  ab *= ab;
  ab += (ay - by) * (ay - by);
  long long cb = cx - bx;
  cb *= cb;
  cb += (cy - by) * (cy - by);
  if (ab == cb && !collinear(ax, ay, bx, by, cx, cy))
    cout << "Yes";
  else
    cout << "No";
}