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 Ax, Ay, Bx, By, dx, dy, d;
bool check(long long x, long long y) {
  return !d && !x && !y ||
         d && (dx * y - dy * x) % d == 0 && (dx * x + dy * y) % d == 0;
}
int main() {
  scanf("%I64d%I64d%I64d%I64d%I64d%I64d", &Ax, &Ay, &Bx, &By, &dx, &dy);
  long long bx[] = {Bx, -By, -Bx, By}, by[] = {By, Bx, -By, -Bx};
  d = dx * dx + dy * dy;
  for (int j = 0; j < 4; ++j)
    if (check(bx[j] - Ax, by[j] - Ay)) return puts("YES"), 0;
  puts("NO");
  return 0;
}
