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 a, b;
bool check(long long x1, long long y1) {
  if (a == 0 && b == 0) return x1 == 0 && y1 == 0;
  return (a * y1 - b * x1) % (a * a + b * b) == 0 &&
         (a * x1 + b * y1) % (a * a + b * b) == 0;
}
int main() {
  int x1, y1, x2, y2, x3, y3;
  scanf("%I64d%I64d%I64d%I64d%I64d%I64d", &x1, &y1, &x2, &y2, &a, &b);
  if (check(x2 - x1, y2 - y1) || check(x2 - y1, y2 + x1) ||
      check(x2 + x1, y2 + y1) || check(x2 + y1, y2 - x1))
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
