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 Det(long long a11, long long a12, long long a21, long long a22) {
  return a11 * a22 - a12 * a21;
}
bool HasSolution(long long Ax, long long Ay, long long Bx, long long By,
                 long long Cx, long long Cy) {
  long long d = Det(Cx, Cy, Cy, -Cx);
  long long d1 = Det(Bx - Ax, Cy, By - Ay, -Cx);
  long long d2 = Det(Cx, Bx - Ax, Cy, By - Ay);
  if (d != 0) return d1 % d == 0 && d2 % d == 0;
  return Ax == Bx && Ay == By;
}
int main() {
  int Ax, Ay, Bx, By, Cx, Cy;
  cin >> Ax >> Ay >> Bx >> By >> Cx >> Cy;
  bool t = HasSolution(Ax, Ay, Bx, By, Cx, Cy) ||
           HasSolution(Ay, -Ax, Bx, By, Cx, Cy) ||
           HasSolution(-Ax, -Ay, Bx, By, Cx, Cy) ||
           HasSolution(-Ay, Ax, Bx, By, Cx, Cy);
  cout << (t ? "YES" : "NO") << endl;
}
