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;
bool check(int ax, int ay) {
  return (cx * ax + cy * ay) % (cx * cx + cy * cy) == 0 &&
         (cx * ay - cy * ax) % (cx * cx + cy * cy) == 0;
}
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (cx == 0 && cy == 0) {
    if ((ax == bx && ay == by) || (ax == -bx && ay == -by) ||
        (ax == -by && ay == bx) || (ax == by && ay == -bx))
      cout << "YES";
    else
      cout << "NO";
    return 0;
  }
  if (cx == 0 && cy == 0) {
    if (ax == 0 && ay == 0)
      cout << "YES";
    else
      cout << "NO";
    return 0;
  }
  if (check(ax - bx, ay - by) || check(ax + bx, ay + by) ||
      check(ax + by, ay - bx) || check(ax - by, ay + bx))
    cout << "YES";
  else
    cout << "NO";
}
