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: Wrong Answer)

"use strict"
function main(arg) {
    let N = arg.trim().split("\n")[0]
    N = Number(N)
    let ans = (new Array(N + 1)).fill(0)
    const MAX = 10e4
    for (let i = 1; i < MAX; i++) {
        let t = fx(i,i,i)
        if (t > N) {
            break
        }
        ans[t] = 1
    }
    for (let i = 1; i < MAX; i++) {
        let j = 1
        for (j = 1; j < MAX; j++) {
            if (i === j) continue
            let t = fx(i,j,j)
            if (t > N) {
                break
            }
            ans[t] = 3
        }
        if (j===1) {
            break
        }
    }
    for (let i = 1; i < MAX; i++) {
        let j = 1
        for (j = 1; j < MAX; j++) {
            if (i === j) continue
            let k = 1;
            for (k = 1; k < MAX; k++) {
                if (k === i || k === j) continue
                let t = fx(i,j,k)
                if (t > N) {
                    break
                }
                ans[t] = 6
            }
            if (k === 1) {
                break
            }
        }
        if (j === 1) {
            break
        }
    }

    ans.shift()
    console.log(ans.join("\n"))
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));

function fx(x,y,z) {
    return x * x  + y * y + z * z + x * y + y * z + z * x 
}