At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector А:

  * Turn the vector by 90 degrees clockwise.
  * Add to the vector a certain vector C.



Operations could be performed in any order any number of times.

Can Gerald cope with the task?

Input

The first line contains integers x1 и y1 — the coordinates of the vector A ( - 108 ≤ x1, y1 ≤ 108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).

Output

Print "YES" (without the quotes) if it is possible to get vector B using the given operations. Otherwise print "NO" (without the quotes).

Examples

Input

0 0
1 1
0 1


Output

YES


Input

0 0
1 1
1 1


Output

YES


Input

0 0
1 1
2 2


Output

NO
#include <bits/stdc++.h>
int main() {
  std::ios_base::sync_with_stdio(false);
  int64_t a1, a2, b1, b2, c1, c2, D, m[4], n[4];
  std::cin >> a1 >> a2 >> b1 >> b2 >> c1 >> c2;
  if (c1 == 0 && c2 == 0) {
    if ((a1 == b1 && a2 == b2) || (a1 == -b1 && a2 == -b2) ||
        (a1 == b2 && a2 == -b1) || (a1 == -b2 && a2 == b1))
      std::cout << "YES" << std::endl;
    else
      std::cout << "NO" << std::endl;
    return 0;
  }
  D = c1 * c1 + c2 * c2;
  m[0] = (b1 + a1) * c1 + (b2 + a2) * c2;
  n[0] = (b1 + a1) * c2 - (b2 + a2) * c1;
  m[1] = (b1 - a1) * c1 + (b2 - a2) * c2;
  n[1] = (b1 - a1) * c2 - (b2 - a2) * c1;
  m[2] = (b1 - a2) * c1 + (b2 + a1) * c2;
  n[2] = (b1 - a2) * c2 - (b2 + a1) * c1;
  m[3] = (b1 + a2) * c1 + (b2 - a1) * c2;
  n[3] = (b1 + a2) * c2 - (b2 - a1) * c1;
  bool ok = false;
  for (int i = 0; i != 4; ++i) ok |= !((m[i] % D) || (n[i] % D));
  std::cout << (ok ? "YES" : "NO") << std::endl;
  return 0;
}
