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 xA, yA, xB, yB, xC, yC, temp;
int main() {
  cin >> xA >> yA >> xB >> yB >> xC >> yC;
  for (int i = 0; i < 4; ++i) {
    long long xD = xB - xA, yD = yB - yA;
    if (xD == 0 && yD == 0) {
      cout << "YES" << endl;
      return 0;
    }
    long long n1 = xC * xD + yC * yD;
    long long n2 = -yC * xD + xC * yD;
    long long n3 = xC * xC + yC * yC;
    if (n3 > 0 && n1 % n3 == 0 && n2 % n3 == 0) {
      cout << "YES" << endl;
      return 0;
    }
    temp = xA;
    xA = -yA;
    yA = temp;
  }
  cout << "NO" << endl;
}
