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 N = 100004;
long long xa, ya, xb, yb, xc, yc;
bool f(long long xa, long long ya, long long xb, long long yb) {
  xb -= xa;
  yb -= ya;
  if (xc == 0 && yc == 0) {
    return xb == 0 && yb == 0;
  }
  long long k1 = (xb * xc + yb * yc) / (xc * xc + yc * yc);
  long long k2 = (xc * yb - xb * yc) / (xc * xc + yc * yc);
  return k1 * xc - k2 * yc == xb && k1 * yc + k2 * xc == yb;
}
int main() {
  cin >> xa >> ya >> xb >> yb >> xc >> yc;
  puts(f(xa, ya, xb, yb) || f(-ya, xa, xb, yb) || f(-xa, -ya, xb, yb) ||
               f(ya, -xa, xb, yb)
           ? "YES"
           : "NO");
}
