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 Ruby (2.7.1) (judge verdict: Accepted)

N = gets.to_i

ans = [0]*N

1.upto(N) do |x|
    x2 = x*x
    break if x2>=N
    x.upto(N) do |y|
        y2 = y*y
        break if y2>=N

        xy_same = x==y

        y.upto(N) do |z|
            a = x2+y2+z*z + x*y + y*z + z*x
            break if a > N
            m = 6
            if xy_same then x != z
                m = x==z ? 1 : 3
            elsif x==z || y==z then 
                m = 3
            end
            ans[a-1] += m
        end
    end
end

ans.each do |a|
    p a
end