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>
int main() {
  long long x1, y1, x2, y2, x3, y3, tmp, i;
  scanf("%I64d %I64d", &x1, &y1);
  scanf("%I64d %I64d", &x2, &y2);
  scanf("%I64d %I64d", &x3, &y3);
  for (i = 0; i < 4; i++) {
    long long p = x3 * x3 + y3 * y3;
    if (p == 0) {
      if (x1 == x2 && y1 == y2) {
        puts("YES");
        return 0;
      }
    } else if ((x3 * (x2 - x1) + y3 * (y2 - y1)) % p == 0 &&
               (y3 * (x2 - x1) - x3 * (y2 - y1)) % p == 0) {
      puts("YES");
      return 0;
    }
    tmp = x1;
    x1 = y1;
    y1 = -tmp;
  }
  puts("NO");
  return 0;
}
