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;
int aa(long long x, long long y) {
  x = bx - x, y = by - y;
  if (cx == 0 && cy == 0) {
    if (x == 0 && y == 0) return 1;
    return 0;
  } else if (cx == 0) {
    long long g = x / cy, h = y / cy;
    if (cy * g == x && cy * h == y) return 1;
    return 0;
  } else if (cy == 0) {
    long long g = x / cx, h = y / cx;
    if (cx * g == x && cx * h == y) return 1;
    return 0;
  } else {
    long long tx = x * cy, ty = y * cx;
    long long b = (tx - ty) / (cy * cy + cx * cx);
    if (b * (cx * cx + cy * cy) != (tx - ty))
      return 0;
    else {
      long long a = (x - b * cy) / cx;
      if (a * cx + b * cy == x) return 1;
      return 0;
    }
  }
}
int main() {
  scanf("%lld%lld%lld%lld%lld%lld", &ax, &ay, &bx, &by, &cx, &cy);
  int f = 0;
  if (aa(ax, ay) == 1) f = 1;
  if (aa(-ax, -ay) == 1) f = 1;
  if (aa(-ay, ax) == 1) f = 1;
  if (aa(ay, -ax) == 1) f = 1;
  if (f == 1)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
