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(void) {
  long long x1, y1, x2, y2, x3, y3;
  cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
  for (int i = 0; i < 4; i++) {
    long long dx = x2 - x1;
    long long dy = y2 - y1;
    long long u = dx * x3 + dy * y3;
    long long v = dx * y3 - dy * x3;
    long long w = x3 * x3 + y3 * y3;
    if (dx == 0 && dy == 0) {
      cout << "YES" << endl;
      return 0;
    }
    if (w != 0 && u % w == 0 && v % w == 0) {
      cout << "YES" << endl;
      return 0;
    }
    x1 = -x1;
    swap(x1, y1);
  }
  cout << "NO" << endl;
  return 0;
}
