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 xa, ya, xb, yb, xc, yc;
  while (cin >> xa >> ya >> xb >> yb >> xc >> yc) {
    if ((xb - xa) * (xb - xa) + (yb - ya) * (yb - ya) ==
            (xc - xb) * (xc - xb) + (yc - yb) * (yc - yb) &&
        (xc - xb) * (yb - ya) != (yc - yb) * (xb - xa)) {
      printf("Yes\n");
    } else {
      printf("No\n");
    }
  }
  return 0;
}