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 PHP (7.4.4) (judge verdict: Accepted)

<?php
list($n) = ints();
$max = (int) (sqrt($n) + 1);
$ans = array_fill(1, $n, 0);
for ($x = 1; $x <= $max; ++$x) {
    for ($y = $x; $y <= $max; ++$y) {
        for ($z = $y; $z <= $max; ++$z) {
            $t = $x ** 2 + $y ** 2 + $z ** 2 + $x * $y + $y * $z + $x * $z;
            if ($t <= $n) {
                $c = count(array_unique([$x, $y, $z]));
                if ($c === 3) $ans[$t] += 6;
                elseif ($c === 2) $ans[$t] += 3;
                else ++$ans[$t];
            }
        }
    }
}
echo implode(PHP_EOL, $ans);
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}