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>
long long a, b, c, d, e, f, i = 4, r, z, x, y;
int main() {
  std::cin >> a >> b >> c >> d >> e >> f;
  for (z = f * f + e * e; i--; x = c - a, y = d - (b = -b),
      r |= (!z && !x && !y) | (z && !((x * e + y * f) % z) &&
                               !((y * e - x * f) % z)))
    std::swap(a, b);
  puts(r ? "YES" : "NO");
}
