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, x2, x3, y1, y2, y3;
  scanf("%I64d %I64d\n%I64d %I64d\n%I64d %I64d", &x1, &y1, &x2, &y2, &x3, &y3);
  long long z = x3 * x3 + y3 * y3;
  for (int i = 0; i < 4; ++i) {
    x1 ^= y1;
    y1 ^= x1;
    x1 ^= y1;
    y1 = -y1;
    long long difx = x2 - x1, dify = y2 - y1;
    if (!z && !difx && !dify) {
      printf("YES\n");
      return 0;
    }
    if (z && !((difx * x3 + dify * y3) % z) && !((dify * x3 - difx * y3) % z)) {
      printf("YES\n");
      return 0;
    }
  }
  printf("NO\n");
  return 0;
}
