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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

var GET = (function () {function f(s) {return new g(s);}function g(s) {this._s = s.trim().split("\n");}g.prototype.getValue = function (n) {return this._s[n];};g.prototype.getArray = function (n) {return this.stoa(this._s[n]);};g.prototype.slice = function (s, limit) {return this._s.slice(s, +limit + s || undefined).map(v => this.stox(v));};g.prototype.sliceArray = function (s, limit) {return this._s.slice(s, +limit + s || undefined).map(v => this.stoa(v));};g.prototype.stoa = function (s) {return s.split(" ").map(v => this.stox(v));};g.prototype.stox = function (v) {var i = +v;return (i === i) ? i : v;};return f;})();
var o = GET(require("fs").readFileSync("/dev/stdin", "utf8"));

console.log(main());
function main(){
    var N = +o.getValue(0);

    var result = Array(N).fill(0);
    for(var x = 1; 100 > x; x++) {
        for(var y = 1; 100 > y; y++) {
            for(var z = 1; 100 > z; z++) {
                var n = x**2 + y**2 + z**2 + x*y + x*z + y*z;
                if (N >= n) {
                    result[n - 1] += 1;
                }
            }
        }
    }

    return result.join('\n');
}