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 xa, ya, xb, yb, xc, yc, dx, dy, a, b, c;
  cin >> xa >> ya;
  cin >> xb >> yb;
  cin >> xc >> yc;
  for (int i = 0; i < 4; i++) {
    dx = xb - xa, dy = yb - ya;
    a = dx * xc + dy * yc;
    b = dx * yc - dy * xc;
    c = xc * xc + yc * yc;
    if (dx == 0 && dy == 0) {
      puts("YES");
      return 0;
    }
    if (c != 0 && a % c == 0 && b % c == 0) {
      puts("YES");
      return 0;
    }
    xa = -xa;
    swap(xa, ya);
  }
  puts("NO");
  return 0;
}
