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)

# -*- coding: utf-8 -*-

import math


def g(nx, ny, nz):
    return nx ** 2 + ny ** 2 + nz ** 2 + nx * ny + ny * nz + nz * nx


def is_int(fn):
    return float(int(fn)) == float(fn)


def solve(n):
    min_z = max(1, int(math.sqrt(n) / 3))
    max_z = max(1, int(math.sqrt(n - 2) - 1) if n > 2 else 1)
    max_x = max(1, int(math.sqrt(n / 3) + 1))
    
    counter = 0
    
    for z in range(max(1, min_z), max_z + 1):
        for y in range(1, z + 1):
            for x in range(1, min(y + 1, max_x)):
                if g(x, y, z) == n:
                    counter += 1
    
    counter *= 3
    
    if is_int(math.sqrt(n / 6)):
        counter -= 2
    
    print(counter, flush=True)


N = int(input())

for ni in range(1, N + 1):
    solve(ni)