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 inf = 1 << 28;
const double INF = 1e12, EPS = 1e-9;
bool _(long long x, long long y, long long a, long long b) {
  if (a == b && b == 0) return x == 0 && y == 0;
  return (a * y - b * x) % (a * a + b * b) == 0 &&
         (a * x + b * y) % (a * a + b * b) == 0;
}
void run() {
  int a1, a2, b1, b2, c1, c2;
  cin >> a1 >> a2 >> c1 >> c2 >> b1 >> b2;
  cout << (_(c1 - a1, c2 - a2, b1, b2) || _(c1 + a2, c2 - a1, b1, b2) ||
                   _(c1 + a1, c2 + a2, b1, b2) || _(c1 - a2, c2 + a1, b1, b2)
               ? "YES"
               : "NO")
       << endl;
}
int main() { run(); }
