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;
const int mod = 1e9 + 7;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int Ax, Ay, Bx, By, Cx, Cy;
  cin >> Ax >> Ay >> Bx >> By >> Cx >> Cy;
  for (int i = 0; i < 4; i++) {
    int tx = -Ay, ty = Ax;
    Ax = tx;
    Ay = ty;
    if (Ax == Bx && Ay == By) {
      cout << "YES\n";
      return 0;
    }
    double Dx = Bx - Ax;
    double Dy = By - Ay;
    double X = Cx;
    double Y = Cy;
    auto T = complex<double>(Dx, Dy) / complex<double>(X, Y);
    if (abs(T.real() - round(T.real())) < 1e-12)
      if (abs(T.imag() - round(T.imag())) < 1e-12) {
        cout << "YES\n";
        return 0;
      }
  }
  cout << "NO\n";
}
