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;
bool ok(long long int c1, long long int c2, long long int a1,
        long long int a2) {
  long long int d = c1 * c1 + c2 * c2;
  if (d == 0LL) return a1 == 0LL && a2 == 0LL;
  return (a1 * c1 + a2 * c2) % d == 0LL && (a1 * c2 - a2 * c1) % d == 0LL;
}
int main() {
  int a1, a2, b1, b2, c1, c2;
  scanf("%d %d %d %d %d %d", &a1, &a2, &b1, &b2, &c1, &c2);
  if (ok(c1, c2, b1 - a1, b2 - a2) || ok(c1, c2, b1 - a2, b2 + a1) ||
      ok(c1, c2, b1 + a1, b2 + a2) || ok(c1, c2, b1 + a2, b2 - a1))
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
