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, d1, d2;
int main() {
  cin >> a1 >> a2 >> b1 >> b2 >> c1 >> c2;
  for (int q = 0; q < 4; q++) {
    if (q == 0) {
      d1 = b1 - (a1);
      d2 = b2 - (a2);
    }
    if (q == 1) {
      d1 = b1 - (-a1);
      d2 = b2 - (-a2);
    }
    if (q == 2) {
      d1 = b1 - (-a2);
      d2 = b2 - (a1);
    }
    if (q == 3) {
      d1 = b1 - (a2);
      d2 = b2 - (-a1);
    }
    long long k1 = d1 * c1 + d2 * c2;
    long long k2 = c1 * c1 + c2 * c2;
    long long k3 = c1 * d2 - c2 * d1;
    long long k4 = c1 * c1 + c2 * c2;
    if (k2 == 0) {
      if (d1 == 0 && d2 == 0) {
        cout << "YES";
        return 0;
      }
    } else if (k1 % k2 == 0 && k3 % k4 == 0) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
  return 0;
}
