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;
long long o;
bool check(long long xa, long long ya) {
  if (!o) return xa == xb && ya == yb;
  return ((xb - xa) * xc + (yb - ya) * yc) % o == 0 &&
         ((xb - xa) * yc - (yb - ya) * xc) % o == 0;
}
int main() {
  scanf("%I64d %I64d %I64d %I64d %I64d %I64d", &xa, &ya, &xb, &yb, &xc, &yc);
  o = xc * xc + yc * yc;
  bool flag =
      check(xa, ya) || check(ya, -xa) || check(-ya, xa) || check(-xa, -ya);
  if (flag)
    printf("YES\n");
  else
    printf("NO\n");
}
