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)

import math




N=int(input())

anslist=[0]*(N+1)
ma=int(math.sqrt(N))+1
for x in range(1,ma):
    for y in range(x,ma):
        for z in range(y,ma):
            n=x**2+y**2+z**2+x*y+y*z+z*x
            if n <=N:
                if x==y and y==z:
                    anslist[n]+=1
                elif x==y or y==z or z==x:
                    anslist[n]+=3
                else:
                    anslist[n]+=6

            
for i in range(1,N+1):
    print(anslist[i])