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', $cnt);
for ($l=1; $l <= $cnt; $l++) {
    $memo = []; 
    $ans = 0;
    for ($i=1; $i <= $cnt; $i++) { 
        for ($j=$i; $j <= $cnt; $j++) { 
            for ($k=$j; $k <= $cnt; $k++) { 
                if ($i != 1 && $j != 1 && $k != 1) {
                    break 3;
                }
                if (in_array("$i-$j-$k", $memo) || in_array("$i-$k-$j", $memo) || in_array("$j-$i-$k", $memo) || in_array("$j-$k-$i", $memo) || in_array("$k-$i-$j", $memo) || in_array("$k-$j-$i", $memo)) {
                    break 3;
                }
                if ($i > $l || $j > $l || $k > $l) {
                    continue 2;
                }
                if ($i * $i + $j * $j + $k * $k + $i * $j + $j * $k + $i * $k == $l) {
                    $ans++;
                    $memo[] = "$i-$j-$k";
                }
            }
        }
    }
    if ($l > 6) {
        $ans *= 3;
    }
    echo $ans."\n";
}