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;
void check(long long axx, long long ayy) {
  int xx = bx - axx, yy = by - ayy;
  if (cx == 0 && cy == 0) {
    if (xx == 0 && yy == 0) {
      cout << "YES";
      exit(0);
    } else
      return;
  }
  if ((cx * (yy)-cy * (xx)) % (cx * cx + cy * cy) != 0 ||
      (cx * (xx) + cy * (yy)) % (cx * cx + cy * cy) != 0)
    return;
  cout << "YES";
  exit(0);
}
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  check(ax, ay);
  check(ay, -ax);
  check(-ax, -ay);
  check(-ay, ax);
  cout << "NO";
}
