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 (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>

int main(void){
    int N,x,y,z,cnt;
    double n,lim;
    
    scanf("%d",&N);
    
    for(n=1.0;n<=N;n=n+1.0){
        cnt=0;
        lim=sqrt(n);
        for(x=1;x<=lim;x++){
            for(y=1;y<=lim;y++){
                for(z=1;z<=lim;z++){
                    if(x*x+y*y+z*z+x*y+y*z+z*x==n){
                        cnt++;
                    }
                }
            }
        }
        
        printf("%d\n",cnt);
    }
    
    return 0;
}