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: Runtime Error)

<?php
declare(strict_types=1);
$n = trim(fgets(STDIN));
$ans = array_fill(1, $n, 0);
$x = 1;
while ($x < 100) {
    $y = 1;
    while ($y < 100) {
        $z = 1;
        while ($z < 100) {
            $p = $x * $x + $y * $y + $z * $z + $x * $y + $y * $z + $z * $x;
            if ($p <= $n) {
                ++$ans[$p];
            } else {
                $z = 100;
            }
            ++$z;
        }
        ++$y;
    }
    ++$x;
}
echo join("\n", $ans);