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;
const int mod = 1000000007;
long long a, b, c, d, e, f, k;
bool check(long long x, long long y) {
  if (k == 0) {
    return x == c && y == d;
  }
  return ((c - x) * e + (d - y) * f) % k == 0 &&
         (e * (d - y) + f * (x - c)) % k == 0;
}
int main() {
  while (cin >> a >> b >> c >> d >> e >> f) {
    k = e * e + f * f;
    if (check(a, b) || check(-a, -b) || check(b, -a) || check(-b, a)) {
      cout << "YES" << endl;
    } else
      cout << "NO" << endl;
  }
  return 0;
}
