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>
#include <vector>
using namespace std;
#define rep(i,n) for(int i=1;i<=(n);i++)
typedef long long ll;
#define ALL(obj) (obj).begin(), (obj).end()

int main() {
 	int n;
  	cin>>n;
  
  	int p[n];
  	rep(i,n)p[i]=0;
  	int x,y,z;
  	
  	int m=sqrt(n)+1;
  
 	for(int x=1;x<m;x++){
     	for (int y=1;y<m;y++){
        	for (int z=1;z<m;z++){
              int f=x*x+y*y+z*z+x*y+y*z+z*x;
              if(f<=n)p[f]++;                   
            }        
        }
    }
   
	rep(j,n)cout<<p[j]<<endl;
}