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 f(long long x, long long y, long long xc, long long yc) {
  if (!x && !y) return true;
  if (!xc && !yc) return false;
  if (!xc)
    if (x % yc || y % yc)
      return false;
    else
      return true;
  else if (!yc)
    if (x % xc || y % xc)
      return false;
    else
      return true;
  else {
    if ((y * yc + x * xc) % (yc * yc + xc * xc)) return false;
    long long a = (y * yc + x * xc) / (yc * yc + xc * xc);
    if ((x - a * xc) % yc)
      return false;
    else
      return true;
  }
}
int main() {
  long long xa, ya, xb, yb, xc, yc;
  cin >> xa >> ya >> xb >> yb >> xc >> yc;
  if (f(xb - xa, yb - ya, xc, yc) || f(xb + xa, yb + ya, xc, yc) ||
      f(xb - ya, yb + xa, xc, yc) || f(xb + ya, yb - xa, xc, yc))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
