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: Time Limit Exceeded)

from itertools import combinations, combinations_with_replacement
from math import sqrt


n = int(input())
ans = [0] * (n + 1)
for x, y, z in combinations_with_replacement(range(1, int(sqrt(n)) + n // 10), 3):
    i = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
    if i <= n:
        if x == y == z:
            ans[i] += 1
        elif all([not(s != t) for s, t in combinations([x, y, z], 2)]):
            ans[i] += 6
        else:
            ans[i] += 3

for i in range(1, n + 1):
    print(ans[i])