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 a, a1, b, b1, c, c1;
bool kiemtra() {
  long long n = b - a, n1 = b1 - a1, m = c - b, m1 = c1 - b1;
  if (n * m1 == n1 * m) return false;
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a >> a1 >> b >> b1 >> c >> c1;
  if ((b - a) * (b - a) + (b1 - a1) * (b1 - a1) ==
          (c - b) * (c - b) + (c1 - b1) * (c1 - b1) &&
      kiemtra())
    cout << "YES";
  else
    cout << "NO";
  return 0;
}