A central sphere of radius R is the set of all points(x, y, z) in 3D space that satisfy the following.
Equation:
x^2+y^2+z^2 = R^2

We say that a set of central spheres covers a set of points if each of the points belongs to one of the spheres.

Assume that the following declartions are given.
struct Point3D {
int x;
int y;
int z;
};

write a function:
int solution (struct Point3D A[], int N);
that, given an array describing of a set of points in 3D space, returns the minimum number of central spheres required to cover them.

For example, given the following array.
A[0].x = 0 A[0].y = 5 A[0].z = 4
A[1].x = 0 A[1].y = 0 A[1].z = -3
A[2].x = -2 A[2].y = 1 A[2].z = -6
A[3].x = 1 A[3].y = -2 A[3].z = 2
A[4].x = 1 A[4].y = 1 A[4].z = 1
A[5].x = 4 A[5].y = -4 A[5].z = 3

The function should return 3, because three central spheres are required to cover these points:

• a central sphere of radius sqrt(3) covers array element A[4],
• a central sphere of radius 3 covers array elements A[1] and A[3],
• a central sphere of radius sqrt(41) covers array elements A[0], A[2] and A[5].

It is impossibel to cover these points with fewer central spheres.

Write an efficient algorithm for the following assumptions:

• N is a integer with in the range [0 ... 100,000];
• the coordinates of each point in array A are integers within the range[-10,000 ... 10, 000].