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 X1, Y1;
long long A, B;
long long x, y;
int main() {
  while (cin >> X1 >> Y1) {
    cin >> A >> B >> x >> y;
    string res = "NO";
    for (int i = 0; i < 4; i++) {
      for (int j = 0; j < 4; j++) {
        if (x == 0 && y == 0) {
          if (X1 == A && Y1 == B) res = "YES";
        } else {
          bool good = true;
          long long c1 = A - X1;
          long long c2 = B - Y1;
          long long soor = c1 * x + c2 * y;
          long long makh = x * x + y * y;
          if (soor % makh) good = false;
          long long a = soor / makh;
          if (y == 0) {
            soor = c2;
            makh = -x;
          } else {
            soor = c1 - a * x;
            makh = y;
          }
          if (soor % makh) good = false;
          long long b = soor / makh;
          if (good) {
            res = "YES";
          }
        }
        swap(A, B);
        A *= -1;
      }
      swap(X1, Y1);
      X1 *= -1;
    }
    cout << res << endl;
  }
  return 0;
}
