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 math
n = int(input())

anslist = [0] * 10**4
for i in range(1, int(math.sqrt(int(10000/3)))+1):
    x = i
    for j in range(i, int(math.sqrt(int((10000-i**2)/2)))+1):
        y = j
        for k in range(j, int(math.sqrt(10000-i**2-j**2))+1):
            z = k
            uhen = x**2 + y**2 + z**2 + x*y + y*z + z*x
            if uhen-1 >= 10**4:
                continue
            if x == y == z:
                anslist[uhen-1] = 1
            elif x != y and x != z and y != z:
                anslist[uhen-1] = 6
            else:
                anslist[uhen-1] = 3


for i in range(n):
    print(anslist[i])