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 Python (3.8.2) (judge verdict: Accepted)

N = int(input())
n_list = []
count = 1
max_val = 1
res = 0
for x in range(1,100):
    for y in range(x,100):
        for z in range(y,100):
            res = x**2 +y**2 + z**2 + x*y + y*z + z*x
            for i in range(int(x!=y) + int(y!=z) + int(z!=x)-1):
                count *= 3-i
            if max_val < res:
                for i in range(max_val, res+1):
                    if i != res: n_list.append(0)
                    else: n_list.append(count)
                max_val = res+1
            else:
                n_list[res-1] += count
            count = 1

            

for i in range(N):
    print(n_list[i])