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 ax, ay, bx, by, cx, cy;
bool f(long long P, long long Q) {
  if (cx == 0 && cy == 0) return P == 0 && Q == 0;
  long long r1 = (P * cx + Q * cy) % ((cx) * (cx) + (cy) * (cy));
  long long r2 = (P * cy - Q * cx) % ((cx) * (cx) + (cy) * (cy));
  return r1 == 0 && r2 == 0;
}
int main() {
  cout << setprecision(9);
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (f(bx - ax, by - ay) || f(bx - ay, by + ax) || f(bx + ax, by + ay) ||
      f(bx + ay, by - ax))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
