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;
long long int x2, y2, x3, y3;
bool check(long long int x, long long int y) {
  long long int xx = x3 * x3 + y3 * y3, tx = x2 + x, ty = y2 + y;
  if (xx == 0) return x == x2 && y == y2;
  long long int ret1 = tx * x3 + ty * y3, ret2 = tx * y3 - ty * x3;
  if (ret1 % xx != 0 || ret2 % xx != 0) return false;
  return true;
}
int main() {
  long long int x1, y1;
  cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
  if (check(x1, y1) || check(-x1, -y1) || check(-y1, x1) || check(y1, -x1))
    cout << "YES\n";
  else
    cout << "NO\n";
}
