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;
void rec(long long p, long long q) {
  long long mod = c1 * c1 + c2 * c2;
  if ((p * c1 + q * c2) % mod == 0 && (q * c1 - p * c2) % mod == 0) {
    puts("YES");
    exit(0);
  }
}
int main() {
  scanf("%I64d%I64d%I64d%I64d%I64d%I64d", &a1, &a2, &b1, &b2, &c1, &c2);
  if (c1 == 0 && c2 == 0) {
    if ((a1 == b1 && a2 == b2) || (a1 == -b1 && a2 == -b2) ||
        (a1 == b2 && a2 == -b1) || (a1 == -b2 && a2 == b1))
      puts("YES");
    else
      puts("NO");
    return 0;
  }
  rec(b1 - a1, b2 - a2);
  rec(b1 + a1, b2 + a2);
  rec(b1 + a2, b2 - a1);
  rec(b1 - a2, b2 + a1);
  puts("NO");
  return 0;
}
