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;
const bool debug = !false;
const double epsilon = 1e-9;
double f(double x) {
  if (x < 0) return -f(-x);
  return int(x + epsilon);
}
bool ok(complex<double> x) {
  if (debug) cerr << x << endl;
  double a = x.imag(), b = x.real();
  return fabs(a - f(a)) <= epsilon && fabs(b - f(b)) <= epsilon;
}
int main() {
  double ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  complex<double> A(ax, ay), B(bx, by), C(cx, cy), i(0, 1);
  if (fabs(cx) < epsilon && fabs(cy) < epsilon) {
    for (int k = 0; k < 4; k++, A *= i)
      if (A == B) {
        cout << "YES" << endl;
        return 0;
      }
    cout << "NO" << endl;
    return 0;
  }
  if (ok((B - A) / C) || ok((B - A * i) / C) || ok((B + A) / C) ||
      ok((B + A * i) / C))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
