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 Ax, Ay, Bx, By, Cx, Cy, verCx, verCy;
long long sqr(long long x) { return x * x; }
bool check(long long Dx, long long Dy) {
  long long aa = Dx * Cx + Dy * Cy, bb = Dx * verCx + Dy * verCy,
            l2 = sqr(Cx) + sqr(Cy);
  if (l2 == 0) {
    return Dx == 0 && Dy == 0;
  }
  return aa % l2 == 0 && bb % l2 == 0;
}
int main() {
  int i;
  scanf("%I64d%I64d", &Ax, &Ay);
  scanf("%I64d%I64d", &Bx, &By);
  scanf("%I64d%I64d", &Cx, &Cy);
  verCx = -Cy, verCy = Cx;
  for (i = 0; i < 4; i++) {
    swap(Ax, Ay);
    Ax = -Ax;
    if (check(Bx - Ax, By - Ay)) break;
  }
  if (i < 4)
    puts("YES");
  else
    puts("NO");
  return 0;
}
