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 ll = long long;
bool achievable(ll X, ll Y, ll xc, ll yc) {
  if (!(xc | yc)) return !(X | Y);
  ll vol = xc * xc + yc * yc;
  if ((X * xc + Y * yc) % vol) return 0;
  if ((X * yc - Y * xc) % vol) return 0;
  return 1;
}
int main() {
  ll xa, ya, xb, yb, xc, yc;
  scanf("%lld%lld%lld%lld%lld%lld", &xa, &ya, &xb, &yb, &xc, &yc);
  printf("%s\n", achievable(xb - xa, yb - ya, xc, yc) ||
                         achievable(xb - ya, yb + xa, xc, yc) ||
                         achievable(xb + xa, yb + ya, xc, yc) ||
                         achievable(xb + ya, yb - xa, xc, yc)
                     ? "YES"
                     : "NO");
}
