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.chomp.to_i
s = 1
t = 99
arr = Array.new((10 ** 4)*6,0)
(s..t).each do |x|
    (s..t).each do |y|
        (s..t).each do |z|
            ans = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + x * z
            if ans <= 10 ** 4
            arr[ans+1] += 1
            end
        end
    end
end
#p arr[1..20]
arr.shift
#p arr[1..20]
i = 1
#p n
while true
    if i <= n
    puts arr[i]
    elsif i > n
        break
    end
    i += 1
end