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;
int main() {
  long long ar, ai, br, bi, cr, ci;
  cin >> ar >> ai >> br >> bi >> cr >> ci;
  complex<long long> a(ar, ai), b(br, bi), c(cr, ci);
  complex<long long> e(1, 0), i(0, 1);
  for (long long alpha = 0; alpha < 4; alpha++, e *= i) {
    complex<long long> n = b - e * a;
    if (norm(c) == 0) {
      if (norm(n) == 0) {
        cout << "YES\n";
        return 0;
      }
    } else {
      complex<long long> d = n / c;
      if (c * d == n) {
        cout << "YES\n";
        return 0;
      }
    }
  }
  cout << "NO\n";
  return 0;
}
