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)

s1 = input().split()
intN = int(s1[0])

i = 1
while i <= intN :
    cnt = 0
    wkX = 1
    while wkX <= i -5 :
        if (wkX * wkX > i -5) : 
            break
        wkY = 1
        while wkY <= i - 5 -wkX +1:
            if (wkY * wkY > i -5 -wkX +1) : 
                break
            if (wkX * wkY > i -5 -wkX +1) : 
               break
            wkZ = 1
            while wkZ <= i - 5 -wkX -wkY + 2 :
                if (wkZ * wkZ > i -5 -wkX -wkY + 2) : 
                   break
                if (wkY * wkZ > i -5 -wkX -wkY + 2) : 
                    break
                if (wkZ * wkX > i -5 -wkX -wkY + 2) : 
                    break
                intFn = wkX * wkX + wkY * wkY + wkZ * wkZ + wkX * wkY + wkY * wkZ + wkZ * wkX
                if (intFn == i) :
                    cnt += 1
                wkZ += 1
            wkY += 1
        wkX += 1
    print(cnt)
    i += 1