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: Wrong Answer)

#include <bits/stdc++.h>
#define IO std::ios::sync_with_stdio(false),cin.tie(0)

using namespace std;

int fun(int x, int y, int z) {
	return x*x + y*y + z *z + x *z + y *z + x *y;
}

int a[10001];
int main() {
	int n;
	memset(a,0,sizeof(a));
	cin >> n;
	for(int j = 1; j <= 70; j++) {
			for(int k = 1; k <= 70; k++) {
				for(int l = 1; l <= 70; l++) {
					int t = fun(j,k,l);
					if(t <= 10000) a[t]++;
				}
			}
		}
		
	for(int i= 1; i <= n; i++) cout << a[i] << "\n";
	return 0;
}