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)

import math
N = int(input())

j, k, l, wk = 0,0,0,0
for i in range(1, N+1):
    sum = 0
    while True:
        j += 1
        if j >= math.sqrt(i) and j != 1:
            break
        k = 0
        while True:
            k += 1
            if k >= math.sqrt(i) and k != 1:
                break
            l = 0
            while True:
                l += 1
                if l >= math.sqrt(i) and l != 1:
                    break
                elif (j+k+l) >= math.sqrt(i) and j != 1 and k != 1 and l != 1:
                    break
                if (j**2 + k**2 + l**2 + j*k +k*l + l*j) == i:
                    sum += 1
    j = 0
    wk = 0
    print(sum)