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)

n = gets.chomp.to_i
#as = gets.chomp.split.map(&:to_i)

def func(n)
    cnt = 0
    ans = 0
    for x in 1..n do
        ans = x**2
        break if ans >= n
        for y in 1..x do
            ans = x**2 + y**2 + x*y
            break if ans >= n
            for z in y..x do
                ans = x**2 + y**2 + x*y + z**2 + y*z + z*x
                break if ans > n
                if ans == n
                    #puts "#{x} #{y} #{z}"
                    if x == y && y == z 
                        cnt += 1
                    elsif x != y && y != z && x != z
                        cnt += 6
                    else
                        cnt += 3
                    end
                end
            end
        end
    end
    return cnt
end

for i in 1..n do
    #puts "N=#{i}のとき"
    puts func(i)
end