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)

def func(a, b, c):
    return a**2 + b**2 + c**2 + a*b + b*c + c*a

n = int(input())
ans = [0]*(n+1)
x, y, z = (1, 1, 1)
flag = 0
while flag == 0:
    if func(x, 1, 1) <= n:
        for y in range(1, x+1):
            for z in range(1, y+1):
                num = func(x, y, z)
                if num <= n and x == y == z:
                    ans[num] += 1
                elif num <= n and (x == y or y == z or z == x):
                    ans[num] += 3
                elif num <= n:
                    ans[num] += 6
    else:
        flag = 1
    x += 1

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