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>

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define RREP(i, n) for (int i = (n); i >= 0; --i)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (a); i >= (b); --i)
#define ALL(v) (v).begin(), (v).end()
#define RALL(a) (a).rbegin(), (a).rend()

#define uint8_t unsigned char
#define uint16_t unsigned short
#define uint32_t unsigned int
#define uint64_t unsigned long long

#define int8_t signed char
#define int16_t signed short
#define int32_t signed int
#define int64_t signed long long



using namespace std;
// #define PI 3.14159265358979323846
// cout << fixed << setprecision(20);

int main(int argc, char const* argv[])
{
    int N = 0;
    int f[10001] = {};

    cin >> N;
    for(int x = 1; x <= sqrt(N); x++) {
    for(int y = 1; y <= sqrt(N); y++) {
    for(int z = 1; z <= sqrt(N); z++) {
      	int a = x*x + y*y + z*z + x*y + y*z + z*x;
      	if (a <= N) {
        	f[x*x + y*y + z*z + x*y + y*z + z*x] += 1;
        }
    }
    }
    }

    for(int i = 1; i <= N; i++) {
      cout << f[i] << endl;
    }

    return 0;
}