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 ax, ay, bx, by, cx, cy;
bool estimate(long long vx, long long vy) {
  long long r = cx * cx + cy * cy;
  if (r == 0) return (vx == 0 and vy == 0);
  return (vx * cx + vy * cy) % r == 0 and (cx * vy - cy * vx) % r == 0;
}
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (estimate(bx - ax, by - ay) or estimate(bx + ax, by + ay) or
      estimate(bx + ay, by - ax) or estimate(bx - ay, by + ax))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
