Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in Julia (1.4.0) (judge verdict: Accepted)

function main()
    n = parse(Int, readline())
    ans = Dict{Int, Int}()
    for x in 1:100
        for y in 1:100
            for z in 1:100
                ret = g(x,y,z)
                ret > n && break
                if haskey(ans, ret)
                    ans[ret] += 1
                else
                    ans[ret] = 1
                end
            end
        end
    end

    for i in 1:n
        if haskey(ans, i)
            println(ans[i])
        else
            println(0)
        end
    end
end

g(x,y,z) = x^2 + y^2 + z^2 + x*y + y*z + z*x

main()