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 is_generated(long long a, long long b, long long x, long long y) {
  long long norm = x * x + y * y;
  if (norm == 0) return (a == 0 && b == 0);
  return ((a * x + b * y) % norm == 0) && ((b * x - a * y) % norm == 0);
}
int main() {
  cin >> Ax >> Ay >> Bx >> By >> Cx >> Cy;
  bool yes = (is_generated(Ax - Bx, Ay - By, Cx, Cy) ||
              is_generated(-Ay - Bx, Ax - By, Cx, Cy) ||
              is_generated(-Ax - Bx, -Ay - By, Cx, Cy) ||
              is_generated(Ay - Bx, -Ax - By, Cx, Cy));
  cout << (yes ? "YES\n" : "NO\n");
}
