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: Accepted)


N=int(input())
for n in range(1,N+1):
    ans=0
    for x in range(1,101):
        tx=x**2
        if tx>n-2*x :
            break
        for y in range(x,101-x):
            ty=tx+y**2+x*y
            if ty>n-x-y :
                break
            ss=(x+y)**2-4*(ty-n)
            if ss<0:
                break
            s=ss**0.5
            if s.is_integer():
                z=int((-1*(x+y)+s)/2)
                if z>=y:
                    
                    if len(set([x,y,z]))==1:
                        ans+=1
                    if len(set([x,y,z]))==2:
                        ans+=3
                    if len(set([x,y,z]))==3:
                        ans+=6
    print(ans)