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 xa, ya, xb, yb, xc, yc, a, A, b;
  cin >> xa >> ya >> xb >> yb >> xc >> yc;
  if ((xa == xb) && (ya == yb))
    cout << "YES";
  else if ((xb == ya) && (yb == -xa))
    cout << "YES";
  else if ((xb == -xa) && (yb == -ya))
    cout << "YES";
  else if ((xb == -ya) && (yb == xa))
    cout << "YES";
  else if (((xc * xc) + (yc * yc)) == 0)
    cout << "NO";
  else {
    A = (xc * xc) + (yc * yc);
    a = (((xb - xa) * xc) + ((yb - ya) * yc));
    b = (((xb - xa) * (-yc)) + ((yb - ya) * xc));
    if ((a % A == 0) && (b % A == 0)) {
      cout << "YES";
      return 0;
    }
    a = (((xb + ya) * xc) + ((yb - xa) * yc));
    b = (((xb + ya) * (-yc)) + ((yb - xa) * xc));
    if ((a % A == 0) && (b % A == 0)) {
      cout << "YES";
      return 0;
    }
    a = (((xb + xa) * xc) + ((yb + ya) * yc));
    b = (((xb + xa) * (-yc)) + ((yb + ya) * xc));
    if ((a % A == 0) && (b % A == 0)) {
      cout << "YES";
      return 0;
    }
    a = (((xb - ya) * xc) + ((yb + xa) * yc));
    b = (((xb - ya) * (-yc)) + ((yb + xa) * xc));
    if ((a % A == 0) && (b % A == 0)) {
      cout << "YES";
      return 0;
    }
    cout << "NO";
  }
  return 0;
}
