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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

def main():
        
    import math

    N = int(input())

    for n in range(1, N + 1):
        max_itr = min(45, int(math.sqrt(n)) + 1)
        
        ans_list = []
        ans = 0
        
        for x in range(1, max_itr):
            # for y in range(1, x+1):
            for y in range(1, max_itr):

                # for z in range(1, x+1):
                for z in range(1, max_itr):

                    left_eq = x * x + y * y + z * z + x * y + y * z + z * x
                    if (left_eq == n):
                        ans_list = [x, y, z]
                        ans_len = len(set(ans_list))
                        


                        ans += 1
                        
                        # if (ans_len==3):
                        #     ans += 6
                        # elif (ans_len == 2):
                        #     ans += 3
                        # else:
                        #     ans += 1

        
        
        print(ans)


if __name__ == '__main__':
    main()