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, x, y, p, q, d;
long long c(long long a, long long b) {
  d = p * p + q * q;
  if (d == 0) return a == 0 && b == 0;
  return (a * p + b * q) % d == 0 && (b * p - a * q) % d == 0;
}
int main() {
  std::cin >> a >> b >> x >> y >> p >> q;
  puts(c(a - x, b - y) || c(a + x, b + y) || c(a - y, b + x) || c(a + y, b - x)
           ? "YES"
           : "NO");
}
