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() {
  long long n, k, t, a1, a2, b1, b2, c1, c2;
  cin >> a1 >> a2 >> b1 >> b2 >> c1 >> c2;
  long long d1 = (a1 - b1) * (a1 - b1) + (a2 - b2) * (a2 - b2);
  long long d2 = (c1 - b1) * (c1 - b1) + (c2 - b2) * (c2 - b2);
  if (d1 == d2) {
    if (((a1 - b1) == (b1 - c1)) && ((a2 - b2) == (b2 - c2)))
      cout << "No";
    else
      cout << "Yes";
  } else
    cout << "No";
}