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: Wrong Answer)

def f(xyz)
    xyz[0]*xyz[0] + xyz[1]*xyz[1] + xyz[2]*xyz[2] + xyz[0]*xyz[1] + xyz[1]*xyz[2] + xyz[2]*xyz[0]
end

def countCombination(xyz)
    c = xyz.uniq.size
    if c == 1 then
        return 1
    elsif c == 2 then
        return 3
    else
        return 6
    end
end

n = gets.chomp.to_i
MAX = 10010
ans = Array.new(MAX, 0)
xyz = [1, 1, 1]
res = 0
loop do
    flag = false
    3.times do |i|
        res = f(xyz)
        if res > n then
            flag = true
            break
        end
        ans[res] += countCombination(xyz)
        xyz[i] += 1
    end
    break if flag
end

(1..n).each do |i|
    puts ans[i]
end