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 check(long long Cx, long long Cy) {
  long long dx = Bx - Ax;
  long long dy = By - Ay;
  if (dx == 0 && dy == 0) return true;
  if (Cx == 0 && Cy == 0) return false;
  return (dx * Cx + dy * Cy) % (Cx * Cx + Cy * Cy) == 0;
}
bool judge() {
  for (int i = 0; i < 4; i++) {
    if (check(Cx, Cy) && check(-Cy, Cx)) return true;
    long long tmp = Ax;
    Ax = -Ay;
    Ay = tmp;
  }
  return false;
}
int main() {
  scanf("%lld%lld%lld%lld%lld%lld", &Ax, &Ay, &Bx, &By, &Cx, &Cy);
  printf("%s\n", judge() ? "YES" : "NO");
  return 0;
}
