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;
int main() {
  long long a, b, c, d, x, y;
  cin >> a >> b >> c >> d >> x >> y;
  long long x2[5], y2[5], cx = a, cy = b;
  for (int i = 0; i < 4; i++) {
    x2[i] = c - cx;
    y2[i] = d - cy;
    int tmp = cx;
    cx = -cy;
    cy = tmp;
  }
  long long anum, den, bnum;
  bool ans = false;
  for (int i = 0; i < 4; i++) {
    den = x * x + y * y;
    if (den == 0) {
      if (x2[i] == 0 and y2[i] == 0) {
        ans = true;
        break;
      }
      continue;
    }
    anum = x * x2[i] + y * y2[i];
    bnum = x * y2[i] - y * x2[i];
    if ((anum % den == 0) && (bnum % den == 0)) {
      ans = true;
      break;
    }
  }
  if (ans) {
    cout << "YES\n";
  } else {
    cout << "NO\n";
  }
}
