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;
bool solve(long long a, long long b, long long c, long long d, long long e,
           long long f) {
  if ((e || f) && (!a && !b && !c && !d)) return false;
  long long det = a * d - b * c;
  if (det == 0) {
    return abs(f * a) == abs(c * e);
  } else {
    return abs(d * e - b * f) % det == 0 && abs(-c * e + a * f) % det == 0;
  }
}
int ax, ay, bx, by, cx, cy;
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  bool flag = false;
  for (int i = 0; i < 4; i++) {
    if (solve(cx, -cy, cy, cx, bx - ax, by - ay)) flag = true;
    swap(ax, ay);
    ax = -ax;
  }
  printf("%s\n", flag ? "YES" : "NO");
}
