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: Accepted)

#include <bits/stdc++.h>
#define all(X) (X).begin(),(X).end()
#define rall(X) (X).rbegin(),(X).rend()
#define pub push_back
#define puf push_front
#define pob pop_back
#define pof pop_front
#define ff first
#define ss second
#define P 1000000007
#define in(x, a, b) (a <= x && x < b)
#define CASET int ___T; scanf("%d", &___T); for(int cs=1;cs<=___T;cs++)

using namespace std;
using ll = long long;
typedef pair<int, int> ii;
typedef vector<ii> vii; 
typedef vector<int> vi;
const ll inf = 1000000001, INF = (ll)1e18 + 1;

void solve() {
	int n;
	cin >> n;
	
	vi ans(n, 0);
	for(int x = 1; x * x <= n; x++) {
		for(int y = 1; y * y <= n; y++) {
			for(int z = 1; z * z <= n; z++) {
				int calc = (x * x + y * y + z * z + x * y + y * z + z * x);
				if(calc <= n) ans[calc]++;
			}
		}
	}
	
	for(int i = 1; i <= n; i++) cout << ans[i] << endl;
}

int main(){
#define MULTITEST 0
#if MULTITEST   
 
    CASET {
        solve();
    }
    
#else

    solve();
    
#endif

    return 0;
}