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 a1, a2, b1, b2, c1, c2;
bool check(long long x, long long y) {
  long long d = c1 * c1 + c2 * c2;
  if (d == 0) return x == 0 && y == 0;
  return (x * c1 + y * c2) % d == 0 && (y * c1 - x * c2) % d == 0;
}
int main() {
  cin >> a1 >> a2 >> b1 >> b2 >> c1 >> c2;
  cout << (check(a1 - b1, a2 - b2) || check(a1 + b1, a2 + b2) ||
                   check(a1 - b2, a2 + b1) || check(a1 + b2, a2 - b1)
               ? "YES"
               : "NO")
       << endl;
}
