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;
int ax, ay, bx, by, cx, cy;
inline bool isok(int ex, int ey) {
  if (cx == 0 && cy == 0) return ex == 0 && ey == 0;
  long long a = 1ll * ex * cx + 1ll * ey * cy,
            b = 1ll * ey * cx - 1ll * ex * cy,
            c = 1ll * cx * cx + 1ll * cy * cy;
  return a % c == 0 && b % c == 0;
}
int main() {
  scanf("%d%d%d%d%d%d", &ax, &ay, &bx, &by, &cx, &cy);
  if (isok(bx - ax, by - ay) || isok(bx + ay, by - ax) ||
      isok(bx + ax, by + ay) || isok(bx - ay, by + ax))
    printf("YES");
  else
    printf("NO");
}
