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: Time Limit Exceeded)

<?php
# 整数の入力
fscanf(STDIN, "%d", $n);

for ($i = 1; $i <= $n; $i++) {

    $count = 0;
    $x = 1;
    $y = 1;
    $z = 1;
    for ($x = 1; $x <= $i; $x++) {

        for ($y = 1; $y <= $i; $y++) {

            for ($z = 1; $z <= $i; $z++) {
                $result = ($x ** 2) + ($y ** 2) + (($z + $x) * ($z + $y));
                if ($i == $result) {
                    $count ++;
                }
            }
        }
    }

    echo $count."\n";
}
?>