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 main() {
  long long x, y, ax, ay, bx, by, cx, cy, dx, dy, Cx, Cy;
  int i, j, k, m, n;
  while (cin >> ax >> ay >> bx >> by >> cx >> cy) {
    for (i = 0; i < 4; i++) {
      x = ay;
      y = -ax;
      ax = x;
      ay = y;
      dx = bx - ax;
      dy = by - ay;
      Cx = cy;
      Cy = -cx;
      if (cx || cy) {
        if ((dx * cy - dy * cx) % (Cx * cy - Cy * cx) == 0 &&
            (dx * Cy - dy * Cx) % (cx * Cy - cy * Cx) == 0) {
          puts("YES");
          break;
        }
      } else {
        if (!dx && !dy) {
          puts("YES");
          break;
        }
      }
    }
    if (i == 4) puts("NO");
  }
}
