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 M = 300 + 10;
long long int Ax, Ay, Bx, By, Cx, Cy;
int main() {
  cin >> Ax >> Ay >> Bx >> By >> Cx >> Cy;
  bool ok = false;
  for (int i = 0; i < 4; i++) {
    long long int squ = (Cx * Cx + Cy * Cy);
    long long int xbma = Bx - Ax;
    long long int ybma = By - Ay;
    long long int r1 = -xbma * Cy + ybma * Cx;
    long long int r2 = xbma * Cx + ybma * Cy;
    if (squ != 0) {
      if (r1 % squ == 0 && r2 % squ == 0) {
        ok = true;
        break;
      }
    } else {
      if (xbma == 0 && ybma == 0) {
        ok = true;
        break;
      }
    }
    long long int nx = Ay;
    long long int ny = -Ax;
    Ax = nx;
    Ay = ny;
  }
  string ans = ok ? "YES" : "NO";
  cout << ans << endl;
  return 0;
}
