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 can(long long x, long long y, long long m, long long n) {
  if (m == 0 && n == 0) return x == 0 && y == 0;
  return abs(x * m + y * n) % (m * m + n * n) == 0 &&
         abs(x * n - y * m) % (m * m + n * n) == 0;
}
int main() {
  int A[2], B[2], C[2];
  while (cin >> A[0] >> A[1] >> B[0] >> B[1] >> C[0] >> C[1]) {
    bool ok = 0;
    ok |= can(B[0] - A[0], B[1] - A[1], C[0], C[1]);
    ok |= can(B[0] + A[0], B[1] + A[1], C[0], C[1]);
    ok |= can(B[0] - A[1], B[1] + A[0], C[0], C[1]);
    ok |= can(B[0] + A[1], B[1] - A[0], C[0], C[1]);
    if (ok)
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}
