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;
bool Check(long long A, long long B, long long T1, long long T2) {
  if (!A && !B) return !T1 && !T2;
  return !((T1 * A + T2 * B) % (A * A + B * B)) &&
         !((T2 * A - T1 * B) % (A * A + B * B));
}
int main() {
  long long X0, Y0, X1, Y1, X2, Y2;
  cin >> X0 >> Y0 >> X1 >> Y1 >> X2 >> Y2;
  cout << ((Check(X2, Y2, X1 - X0, Y1 - Y0) ||
            Check(X2, Y2, Y1 - X0, -X1 - Y0) ||
            Check(X2, Y2, -X1 - X0, -Y1 - Y0) ||
            Check(X2, Y2, -Y1 - X0, X1 - Y0))
               ? "YES"
               : "NO")
       << endl;
  return 0;
}
