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 a1, a2, b1, b2, c1, c2;
long long flag = 0;
long long check(long long x, long long y) {
  x -= b1, y -= b2;
  long long dis = c1 * c1 + c2 * c2;
  if (!dis) return !x && !y;
  return !((c1 * x + c2 * y) % dis) && !((c1 * y - c2 * x) % dis);
}
signed main() {
  cin >> a1 >> a2 >> b1 >> b2 >> c1 >> c2;
  flag |= check(a1, a2);
  flag |= check(-a1, -a2);
  flag |= check(a2, -a1);
  flag |= check(-a2, a1);
  if (flag)
    printf("YES");
  else
    printf("NO");
  return 0;
}
