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>
using namespace std;
#define REP(i,n) for(int i=0; i<(n); i++)
#define REP2(i,x,n) for(int i=x; i<(n); i++)
#define ALL(n) begin(n),end(n)
struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;
const long long INF = numeric_limits<long long>::max();
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    long long n; cin>>n;
    long long ans[10100];
    memset(ans,0,sizeof(ans));
    for(int x=1; x<=110; x++){
        for(int y=1; y<=110; y++){
            for(int z=1; z<=110; z++){
                long long cnt=x*x+y*y+z*z+x*y+y*z+z*x;
                if(cnt<10100){
                    ans[cnt]++;
                }
            }
        }
    }
    for(int i=1; i<=n; i++){
        cout<<ans[i]<<endl;
    }
    return 0;
}