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 sys
def input():
    return sys.stdin.readline()[:-1]


def main():
    N = int(input())
    ans = [0] * (10 ** 5)
    m = [0] * (10 ** 5)
    M = [0] * (10 ** 5)
    for x in range(1, 101):
        for y in range(1, 101):
            for z in range(1, 101):
                if x <= y and y <= z:
                    n = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
                    if m[n - 1] != min(x, y, z) and M[n - 1] != max(x, y, z):
                        m[n - 1] = min(x, y, z)
                        M[n - 1] =max(x, y, z)
                        if x == y and y == z:
                            ans[n - 1] += 1
                        elif x == y or y == z or z == x:
                            ans[n - 1] += 3
                        else:
                            ans[n - 1] += 6
    s = [print(i) for i in ans[0 : N]]

                    
    
if __name__ == "__main__":
    main()