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)

n = int(input())

for i in range(1, n+1):
    ans = 0
    for x in range(1, int(n ** 0.5) + 1):
        for y in range(1, x + 1):
            z = 4*i - 3*x**2 - 3*y**2 - 2*x*y
            if z > 0:
                z = z**0.5
                z1 = int(z) - x - y
                z2 = z1 // 2
                
             
                if int(z) == z and z1 // 2 >= 1 and z1 % 2 == 0 and z2 <= y:
                    if x != y and y != z2:
                        ans += 6
                    elif x == y and y == z2:
                        ans += 1
                    else:
                        ans += 3
    print(ans)