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
fscanf(STDIN, "%d", $a);


for($i = 1; $i <= $a ; $i++){
    $cnt = 0;
    for($x = 1; $x <= 20 ; $x++){
        for($y = 1; $y <= 20 ; $y++){
            for($z = 1; $z <= 20 ; $z++){
                $ans = ($x * $x) + ($y * $y) + ($z * $z) +($x * $y) + ($y * $z) + ($x * $z);
                if($ans == $i){
                    $cnt++;
                }
            }
        }
    }

    echo $cnt . "\n";
}