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 xa, ya, xb, yb, xc, yc, xd, yd;
bool getAC() {
  if (xc == 0 && yc == 0) {
    if (xd == 0 && yd == 0) {
      return true;
    } else
      return false;
  } else {
    long long tmp = xc * xc + yc * yc;
    long long t1 = yd * xc - xd * yc;
    long long t2 = yd * yc + xd * xc;
    if (t1 % tmp == 0 && t2 % tmp == 0) {
      return true;
    } else
      return false;
  }
}
int main() {
  cin >> xa >> ya >> xb >> yb >> xc >> yc;
  for (int i = 0; i < 4; i++) {
    if (i == 0) {
      xd = xb - xa;
      yd = yb - ya;
    } else if (i == 1) {
      xd = xb - ya;
      yd = yb + xa;
    } else if (i == 2) {
      xd = xb + xa;
      yd = yb + ya;
    } else if (i == 3) {
      xd = xb + ya;
      yd = yb - xa;
    }
    if (getAC()) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}
