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: Time Limit Exceeded)

#include <iostream>
#include <stdio.h>
#include <vector>
#include <algorithm>
#include <string>
#include <iomanip>
#define _USE_MATH_DEFINES
#include <math.h>
using namespace std;
#define rep(i,n) for(i=0;i<n;i++)
#define repl(k,n) for(k=0;k<n;++k)

int main() {
	int N;
	cin >> N;
	int i;
	int x;
	int y;
	int z;
	int count=0;
	for (i = 1; i < N + 1;i++) {
		count = 0;
		for (x = 1; x < i/6+2; x++) {
			for (y = 1; y < i/6+2; y++) {
				for (z = 1; z < i/6+2; z++) {
					if (x * x + x * y + x * z + y * y + z * z + y * z == i)count = count + 1;
				}
			}
		}
		cout << count<<"\n";
	}
	return 0;
}