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: Time Limit Exceeded)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0].split(" ")[0]);
    
    const map = Array(1e5).fill(0);
    
    for(let i=1; i<=N; i++) {
        for(let j=1; j<=i; j++) {
            for(let k=j; k<=i; k++) {
                const temp = Math.pow(i, 2) + Math.pow(j, 2) + Math.pow(k, 2) + (i * j) + (i * k) + (j * k);
                
                if(i === j && j === k) {
                    map[temp]++;
                } else if(i !== j && j !== k && i !== k) {
                    map[temp] += 6;
                } else {
                    map[temp] += 3;
                }
            }            
        }
    }
    
    let answer = [];
    
    for(let i=1; i<=N; i++) {
        answer.push(map[i]);
    }
    
    console.log(answer.join("\n"));
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));