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<stdio.h>

long long n,r[16384]={0};

void rep(long long x,long long y,long long z,long long tg){
  if(x*x+y*y+z*z+x*y+y*z+z*x>n){return;}
  r[x*x+y*y+z*z+x*y+y*z+z*x]++;
  if(tg<=0){rep(x+1,y,z,0);}
  if(tg<=1){rep(x,y+1,z,1);}
  if(tg<=2){rep(x,y,z+1,2);}
}

int main(){
  long long i;
  scanf("%lld",&n);
  rep(1,1,1,0);
  for(i=1;i<=n;i++){printf("%lld\n",r[i]);}
  return 0;
}