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: Wrong Answer)


n=30000
l=[0 for i in range(n)]
for i in range(2,101):
    for j in range(i,101):
        for k in range(j,101):
            if ((i+j+k)/2>i and (i+j+k)/2>j and (i+j+k)/2>k and (i**2+j**2+k**2)//2==(i**2+j**2+k**2)/2):              
                if i==j==k:
                    l[(i**2+j**2+k**2)//2-1]+=1
                elif (i==j or j==k or k==i):
                    l[(i**2+j**2+k**2)//2-1]+=3
                else:
                    l[(i**2+j**2+k**2)//2-1]+=6

n=int(input())
for i in l[:n]:
    print(i)