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 int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<n;i++)
#define rev(i,n) for(int i=n-1;i>=0;i--)
#define all(v) v.begin(),v.end()
#define P pair<int,int>
#define len(s) (int)s.size()

template<class T> inline bool chmin(T &a, T b){
	if(a>b){a=b;return true;}
	return false;
}
template<class T> inline bool chmax(T &a, T b){
	if(a<b){a=b;return true;}
	return false;
}
template<class T>inline int cmp(vector<T>&v,T &a){
	return lower_bound(all(v),a)-v.begin();
}
constexpr int mod = 1e9+7;
constexpr int inf = 3e18;

int ans[10005];
signed main(){
	int N;
	cin>>N;
	REP(i,101)REP(j,101)REP(k,101){
		int n=i*i+j*j+k*k+i*j+i*k+j*k;
		if(n<=10000)ans[n]++;
	}
	REP(i,N+1){
		cout<<ans[i]<<"\n";
	}
}