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
// Your code here!

    $N = intval(trim(fgets(STDIN)));
    $count=0;
    //問題文より$X$Y$Zはsqrt($N)を超えることがない。
    for($i=1;$i<=$N;$i++){
        for($x=1;$x<=100;$x++){
            if($x**2+$x+4>$N)goto skipx;
            for($y=$x;$y<=100;$y++){
                if($y**2+$x*$y+$x**2+3>$N)goto skipy;
                for($z=$y;$z<=100;$z++){
                    // echo $x**2 + $y**2 + $z**2 + $x*$y + $y*$z + $z*$x;
                    if((intval($x**2 + $y**2 + $z**2 + $x*$y + $y*$z + $z*$x))>$N)goto skipz;
                    if(intval($x**2 + $y**2 + $z**2 + $x*$y + $y*$z + $z*$x)==$i){
                        if($x==$y && $y==$z){
                            $count++;
                        }else{
                            $count = $count +3;
                            goto skipx;
                        }
                    }
                }
                if((intval($x**2 + $y**2 + $z**2 + $x*$y + $y*$z + $z*$x))>$N)goto skipx;
                skipz:
            }
            if((intval($x**2 + $y**2 + $z**2 + $x*$y + $y*$z + $z*$x))>$N)goto skipx;
            skipy:
        }
        skipx:
        echo $count."\n";
        $count=0;
    }
?>