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: Accepted)

def m():
    N = int(input())
    M = 100
    dp = [[[0] for _ in range(M)] for _ in range(M)]
    ANS = [0] * (N+1)
    for i in range(1, M+1):
        for j in range(1, M+1):
            for k in range(1, M+1):
                a = pow(i,2) + pow(j,2) + pow(k,2)
                b = i*j + j*k + k*i
                tmp = a + b
                if tmp > N:
                    continue
                ANS[tmp] +=1
    for i in range(1, N+1):
        print(ANS[i])
m()