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;
void method(long long x1, long long y1, long long x3, long long y3,
            long long x2, long long y2) {
  x3 -= x1;
  y3 -= y1;
  if (x2 == 0 && y2 == 0) {
    if (x3 == 0 && y3 == 0) {
      cout << "YES" << endl;
      exit(0);
    } else
      return;
  }
  if (x2 == 0) {
    swap(x2, y2);
  }
  if ((y3 * x2 - x3 * y2) % (x2 * x2 + y2 * y2) == 0) {
    long long y = (y3 * x2 - x3 * y2) / (x2 * x2 + y2 * y2);
    if ((x3 + y * y2) % x2 == 0) {
      long long x = (x3 + y * y2) % x2;
      cout << "YES" << endl;
      exit(0);
    }
  }
}
int main() {
  int x1, y1;
  int x2, y2;
  int x3, y3;
  cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
  method(x1, y1, x2, y2, x3, y3);
  method(-y1, x1, x2, y2, x3, y3);
  method(-x1, -y1, x2, y2, x3, y3);
  method(y1, -x1, x2, y2, x3, y3);
  cout << "NO" << endl;
  return 0;
}
