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<iostream>
#include<algorithm>
#include<vector>
#include<string>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<numeric>

using namespace std;

#define rep(i, n) for (int i = 0; i < (int)(n); i++)

template<typename A, typename B> bool chmin(A &a, const B &b){ return b < a && (a = b, true); }
template<typename A, typename B> bool chmax(A &a, const B &b){ return a < b && (a = b, true); }

int main () {
  int n;
  vector<int> cnt(1000000);
  cin >> n;
  for (int x = 1; x < 100; x++){
    for (int y = 1; y < 100; y++){
      for (int z = 1; z < 100; z++){
        cnt[x * x + y * y + z * z + x * y + y * z + z * x]++;
      }
    }
  }
  for (int i = 1; i <= n; i++){
    cout << cnt[i] << '\n';
  }  
  return 0;
}