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);
  cin.tie(NULL);
  long long n, m, i, x, y, j, k, l, x1, x2, y1, y2;
  string a, b = "";
  cin >> x >> y >> x1 >> y1 >> x2 >> y2;
  n = (x - x1) * (x - x1) + (y - y1) * (y - y1);
  m = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
  if (n == m) {
    i = (x + x2);
    j = (y + y2);
    if (x1 * 2 == i && y1 * 2 == j)
      cout << "No" << endl;
    else
      cout << "Yes" << endl;
  } else
    cout << "No" << endl;
  return 0;
}