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>
int xa, xb, xc, ya, yb, yc;
bool judge() {
  long long x = xc, y = yc, u = xb - xa, v = yb - ya;
  if (!u && !v) return 1;
  long long f = x * u + y * v, g = x * x + y * y;
  if (g == 0 || f % g != 0) return 0;
  long long a = f / g;
  if (x)
    f = v - a * y, g = x;
  else
    f = u, g = -y;
  if (f % g != 0) return 0;
  return 1;
}
int main() {
  scanf("%d%d%d%d%d%d", &xa, &ya, &xb, &yb, &xc, &yc);
  bool flag = 0;
  flag |= judge();
  std::swap(xb, yb), xb *= -1;
  flag |= judge();
  std::swap(xb, yb), xb *= -1;
  flag |= judge();
  std::swap(xb, yb), xb *= -1;
  flag |= judge();
  printf("%s\n", flag ? "YES" : "NO");
  return 0;
}
