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 isSolvable(long long A, long long B, long long a, long long b) {
  long long delr = a * a + b * b;
  if (delr == 0) {
    return A == 0 && B == 0;
  }
  if (((A * b - B * a) % delr == 0) && ((b * B + a * A) % delr == 0))
    return true;
  else
    return false;
}
int main() {
  long long x, y, a, b, A, B;
  cin >> x >> y;
  cin >> A >> B;
  cin >> a >> b;
  bool a1 = isSolvable(A - x, B - y, a, b);
  bool a2 = isSolvable(A + y, B - x, a, b);
  bool a3 = isSolvable(A + x, B + y, a, b);
  bool a4 = isSolvable(A - y, B + x, a, b);
  if (a1 || a2 || a3 || a4)
    puts("YES");
  else
    puts("NO");
  return 0;
}
