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 C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
//#include <iostream>
//#include <math.h>
//#include <vector>
using namespace std;

int f(int n){
    int cnt = 0;
    int m = sqrt(2*n);
    for (int i=2; i<=m; ++i){
        for (int j=2; j<=m; ++j){
            for (int k=2+abs(i-j); k <= i+j-2; ++k){
                if (pow(i,2) + pow(j,2) + pow(k,2) == 2*n) ++cnt;
            }
        }
    }
    return cnt;
}

int main(){
    int N;
    cin >> N;
    int M=0;
    for (int i=1; i<=N; ++i){
        M = f(i);
        cout << M << endl;
    }
    return 0;
}