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: Wrong Answer)

import sys


def f(i):
    ans = 0
    for x in range(1, 33):
        for y in range(x, 33):
            for z in range(y, 33):
                n = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
                if i == n:
                    a = len(set((x, y, z)))
                    if a == 1:
                        ans += 1
                    elif a == 2:
                        ans += 3
                    elif a == 3:
                        ans += 6
                    break
                elif i < n:
                    break

    return ans

def resolve(in_):
    n = int(in_.readline())
    for i in range(1, n):
        yield f(i)



def main():
    for answer in resolve(sys.stdin.buffer):
        print(answer)


if __name__ == '__main__':
    main()