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;
int ddx[] = {1, 0, -1, 0};
int ddy[] = {0, -1, 0, 1};
int main() {
  int ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  bool ok = false;
  for (int i = 0; !ok && i < 4; i++) {
    long long dx = bx - (ddx[i] * ax + ddy[i] * ay);
    long long dy = by - (ddx[(i + 3) % 4] * ax + ddy[(i + 3) % 4] * ay);
    if (cx == 0 && cy == 0) {
      ok = dx == 0 && dy == 0;
      continue;
    }
    long long det = 1ll * cx * cx + 1ll * cy * cy;
    ok = (dx * cx + dy * cy) % det == 0 && (dx * cy - dy * cx) % det == 0;
  }
  cout << (ok ? "YES" : "NO") << endl;
}
