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>
int main(int argc, char const *argv[]) {
  long long a1, a2, b1, b2, c1, c2;
  std::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);
  long long s11 = (a1 - b1);
  long long s12 = (a2 - b2);
  long long s21 = (c1 - b1);
  long long s22 = (c2 - b2);
  if (d1 == d2 && s11 * s22 != s12 * s21)
    std::cout << "Yes" << std::endl;
  else
    std::cout << "No" << std::endl;
  return 0;
}