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


def pattern(x, y, z):
    if x == y == z:
        return 1
    elif x != y and y != z and x != z:
        return 6
    else:
        return 3


def check(ans):
    cnt = 0
    upper = int(math.sqrt(ans))
    for x in range(1, upper):
        if pow(x, 2) > ans:
            break
        for y in range(x, upper):
            if pow(x+y, 2) > ans:
                break
            for z in range(y, upper):
                tmp = x*(x+y+z) + y*(y+z) + z*z
                #tmp = pow(x+y+z, 2) - x*(y+z) - y*z
                if tmp == ans:
                    cnt += pattern(x, y, z)
                elif tmp > ans:
                    break
    print(cnt)


N = int(input())
# x^2 + y^2 + z^2 + x*y + y*z + z*x = n

for i in range(1, N+1):
    #upper_value = int(math.sqrt(i))
    check(i)