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>
#pragma comment(linker, "/STACK:65777216")
using namespace std;
int x[3], y[3];
long long det(long long a, long long b, long long c, long long d) {
  return a * d - b * c;
}
int main() {
  for (int i(0); i < (3); i++) cin >> x[i] >> y[i];
  for (int i(0); i < (4); i++) {
    swap(x[0], y[0]);
    y[0] = -y[0];
    int a = x[1] - x[0];
    int b = y[1] - y[0];
    long long d = det(x[2], y[2], y[2], -x[2]);
    long long d1 = det(a, y[2], b, -x[2]);
    long long d2 = det(x[2], a, y[2], b);
    if (d == 0) {
      if (a == 0 && b == 0) {
        puts("YES");
        return 0;
      }
    } else {
      if (d < 0) d = -d;
      if (d1 % d == 0 && d2 % d == 0) {
        puts("YES");
        return 0;
      }
    }
  }
  puts("NO");
  return 0;
}
