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;
const int MAXN = 100000 + 50;
const int INF = 1 << 30;
long long a[2], b[2], c[2];
int main() {
  cin >> a[0] >> a[1] >> b[0] >> b[1] >> c[0] >> c[1];
  double m0 = (a[0] + c[0]) / 2.0, m1 = (a[1] + c[1]) / 2.0;
  double dis1 = (a[1] - c[1]) * (a[1] - c[1]) + (a[0] - c[0]) * (a[0] - c[0]);
  dis1 /= 4;
  double dis2 = (b[0] - m0) * (b[0] - m0) + (b[1] - m1) * (b[1] - m1);
  double ab = (a[1] - b[1]) * (a[1] - b[1]) + (a[0] - b[0]) * (a[0] - b[0]);
  double bc = (b[1] - c[1]) * (b[1] - c[1]) + (b[0] - c[0]) * (b[0] - c[0]);
  if (ab == bc &&
      (c[1] - a[1]) * (b[0] - a[0]) != (c[0] - a[0]) * (b[1] - a[1]))
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}