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;
long long a, b, u, v, x, y, o;
bool check(long long a, long long b) {
  if (!o) return a == u && b == v;
  return ((u - a) * x + (v - b) * y) % o == 0 &&
         ((a - u) * y + (v - b) * x) % o == 0;
}
int main() {
  cin >> a >> b >> u >> v >> x >> y;
  o = x * x + y * y;
  puts((check(a, b) || check(b, -a) || check(-a, -b) || check(-b, a)) ? "YES"
                                                                      : "NO");
  return 0;
}
