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 ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  long long abs = cx * cx + cy * cy;
  for (int i = 0; i < (4); i++) {
    long long dx = ax - bx, dy = ay - by;
    if (dx == 0 && dy == 0) {
      cout << "YES";
      return 0;
    }
    if (abs != 0) {
      if (((dx * cx + dy * cy) % abs == 0) &&
          ((-dx * cy + dy * cx) % abs == 0)) {
        cout << "YES";
        return 0;
      }
    }
    ay = -ay;
    swap(ax, ay);
  }
  cout << "NO";
  return 0;
}
