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;
struct pnt {
  int x, y;
  long long dist() { return 1ll * x * x + 1ll * y * y; }
  pnt operator-(const pnt &a) const { return pnt{x - a.x, y - a.y}; }
  long long operator*(const pnt &a) const {
    return 1ll * x * a.y - 1ll * y * a.x;
  }
  void in() { scanf("%d%d", &x, &y); }
  void rot() {
    swap(x, y);
    x *= -1;
  }
  bool net(pnt a) {
    if (x == 0 && y == 0) return a.x == 0 && a.y == 0;
    return a.dist() % dist() == 0 && a * (*this) % dist() == 0;
  }
} A, B, C;
int main() {
  A.in(), B.in(), C.in();
  if (C.net(B - A)) {
    puts("YES");
    return 0;
  }
  A.rot();
  if (C.net(B - A)) {
    puts("YES");
    return 0;
  }
  A.rot();
  if (C.net(B - A)) {
    puts("YES");
    return 0;
  }
  A.rot();
  if (C.net(B - A)) {
    puts("YES");
    return 0;
  }
  puts("NO");
}
