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 bx, by, cx, cy;
long long det(long long a, long long b, long long c, long long d) {
  return a * d - b * c;
}
bool solve(long long ax, long long ay) {
  long long dx = bx - ax;
  long long dy = by - ay;
  long long d = det(cx, cy, cy, -cx);
  if (d == 0) {
    return ((cx != 0 || cy != 0) && cy * dx == cx * dy &&
            cy * dy == -cx * dx) ||
           (cx == 0 && cy == 0 && dx == 0 && dy == 0);
  } else {
    return ((det(dx, cy, dy, -cx) % d == 0) && (det(cx, dx, cy, dy) % d == 0));
  }
}
int main() {
  long long ax, ay;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  bool res = false;
  res |= solve(ax, ay);
  res |= solve(ay, -ax);
  res |= solve(-ax, -ay);
  res |= solve(-ay, ax);
  if (res)
    cout << "YES\n";
  else
    cout << "NO\n";
  return 0;
}
