22701번 - Jaggie Spheres 다국어

Let J(n) be a three-dimensional body that

• is a union of unit cubes whose all vertices lie on integer coordinates,
• contains all points that are closer than the distance of √n to the origin, and
• is the smallest of all such bodies.

The figure below shows how J(1), J(2), and J(3) look.

Figure 1: Jaggie Spheres for n = 1, 2, 3

Your task is to calculate how many faces J(n) have. Here, we define two square belong to the same face if they are parallel and share an edge, but don’t if they share just a vertex.

The input consists of multiple data sets, each of which comes with a single line containing an integer n (1 ≤ n ≤ 1000000). The end of input is indicated by n = 0.

For each data set, print the number of faces J(n) have.