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>
using namespace std;
int p, q;
int x, y;
bool possible(int x, int y) {
  long long bm = 1LL * p * p + 1LL * q * q;
  if (bm == 0) {
    if ((x || y))
      return false;
    else
      return true;
  } else if ((((-1LL * p * x - 1LL * q * y) % bm) ||
              ((-1LL * q * x + 1LL * p * y) % bm)))
    return false;
  else
    return true;
}
int main() {
  bool ans = false;
  int ax, ay;
  cin >> ax >> ay >> x >> y >> p >> q;
  int i;
  int tmp;
  for (i = 0; i < 4; ++i) {
    x -= ax;
    y -= ay;
    ans = ans || (possible(x, y) || possible(-y, x));
    x += ax;
    y += ay;
    tmp = ax;
    ax = ay;
    ay = -tmp;
  }
  if (ans)
    cout << "YES";
  else
    cout << "NO";
  return 0;
}
