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)

n = int(input())
for N in range(1,n+1):
    count = 0
    # x = y = zの時
    if ((2*N/3)**0.5).is_integer():
        count +=1
    # x = y 
    nx = int((N/3)**0.5)
    for x in range(1,nx+1):
        nz = int((N-3*x**2)**0.5)
        for z in range(1,nz+1):
            if N == (3*x**2 + 2*x*z + z**2):
                count +=3
                if x == z:
                    count -=3

    for i in range(1,99):
        loca = N/2-i**2-i-3
        if loca < 1:
            continue
        jmax = int((N/2-i**2-i-3)**0.5)
        if i < jmax:
            jmax = i
        for j in range(1,i):
            loc = N-i**2-j**2-i*j-i-j
            if loc < 1:
                continue
            kmax = int((N-i**2-j**2-i*j-i-j)**0.5)
            if j < kmax:
                kmax = j
            for k in range(1,j):
                if 2*N == (i+j)**2 + (j+k)**2 + (k+i)**2:
                    count += 6
                    if  i == k & k ==j:
                        count -=6
                    elif i == k:
                        count -=3
                    elif k == j:
                        count -=3
    print(count)