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: Accepted)

n = int(input())

x,y,z =1,1,1
a = 0
for i in range(1,101):
    if i**2+1**2+1**2+i*1+1*1+1*i >n:
        a = i
        break
    

L = {}

for x in range(1,a):
    for y in range(1,a):
        for z in range(1,a):
            b = x**2+y**2+z**2+x*y+y*z+z*x
            if b <= n:
                if b in L:
                    L[b] = L[b] +1
                else:
                    L[b] = 1

#print(L)
            
for i in range(1,n+1):
    if i in L:
        print(L[i])
    else:
        print(0)