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: Time Limit Exceeded)

num = gets.chomp.to_i
# num = 20 
# 入力値を受けとる



(1..num).each do |n|

    result_count = 0


    pre_arr_x = (1..n).to_a
    pre_arr_y = (1..n).to_a
    pre_arr_z = (1..n).to_a

    total_arr = pre_arr_x.product(pre_arr_y, pre_arr_z)
    # 全ての組み合わせを一つの配列に格納してくれる

    
    total_arr.each do |a|
        x = a[0]
        y = a[1]
        z = a[2]

        if (x + y + z) ** 2 - (x * y + y * z + z * x) === n
            result_count += 1
        end

    end

    p result_count

end