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
n = 0
x=1
y=1
z=1
count=0
N.times do |num|
    count=0
    x=1
    loop do
        y = 1
        loop do
            z = 1
            loop do
                n = x**2+y**2+z**2+x*y+y*z+z*x
    
        
                if n==num+1 then
                    count+=1
                end

                if z>num+1 then
                    break
                end

               if n>num+1 then
                break
               end
                z+=1
            end
            
            y+=1
            if y>num+1 then
                break
            end
        end
        x+=1
        if x>num+1 then
            break
       end
    end
    
    puts count
  
    
end