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: Wrong Answer)

<?php
$n = trim(fgets(STDIN));
$array = [];
for ($x = 1;$x < 99;++$x) {
    for ($y = 1;$y < 99;++$y) {
        for ($z = 1;$z < 99;++$z) {
            $ans = $x ** 2 + $y ** 2 + $z ** 2 + $x * $y + $x * $z + $y * $z;
            if ($ans <= 10000) {
                @++$array[$ans];
            }
        }
    }
}

for ($i = 1;$i < $n;++$i) {
    if (array_key_exists($i,$array)) {
        echo @$array[$i].PHP_EOL;
    } else {
        echo "0".PHP_EOL;
    }
}