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: Runtime Error)

import math

N = int(input())

rtn = int(math.sqrt(N)) + 1 

used = []

count = [0] * N


if N <= 5:
    for x in range(N):
        print(count(x))
else:
    for n in range(6,N):
        print(n)
        for x in range(1,rtn):
            xx = x**2
            if xx <= n - 5:
                for y in range(1,rtn):
                    xy = x*y
                    yy = y**2
                    ysum = xx+yy+xy
                    if ysum <= n-3:
                        for z in range(1,rtn):
                            zz = z**2
                            xz = x*z
                            yz = y*z
                            result = ysum+zz+xz+yz
                            if result > n:
                                break
                            if result == n:
                                count[n-1] += 1
    for x in range(N):
        print(count[x])