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 ax, ay, bx, by, cx, cy, dx, dy;
long long a1, b1, c1, a2, b2, c2, d;
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  for (int i = 0; i < 4; i++, swap(ax, ay), ax = -ax) {
    dx = bx - ax;
    dy = by - ay;
    a1 = cx;
    b1 = cy;
    c1 = -dx;
    a2 = cy;
    b2 = -cx;
    c2 = -dy;
    d = a1 * b2 - a2 * b1;
    if (dx * dx + dy * dy == 0 ||
        d && (b1 * c2 - b2 * c1) % d == 0 && (c1 * a2 - c2 * a1) % d == 0) {
      puts("YES");
      return 0;
    }
  }
  puts("NO");
  return 0;
}
