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: Wrong Answer)

#include<stdio.h>
int main()
{
    int N;
    scanf("%d",&N);
    int x,y,z,k,i;

    for(i=1;i<=N;i++)
    {
        for(x=1;x<=101;x++)
        {
            if(x>i)
            {
                printf("0\n");
                break;
            }

            for(y=1;y<=x;y++)
            {
                for(z=1;z<=y;z++)
                {
                    k=(x+y+z)*(x+y+z)-(x*y+y*z+x*z);
                    if(i==k)
                    {
                        if(x==y && y==z) 
                        {
                            printf("1\n");
                            break;
                        }
                        else if(x>y && y>z) 
                        {
                            printf("6\n");
                            break;
                        }
                        else 
                        {
                            printf("3\n");
                            break;
                        }
                    }
                }
                if(i==k) break;
            }
            if(i==k) break;
        }
    }
   
    return 0;
}