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: Wrong Answer)

N=int(input())
keys=[]
for i in range(10**4):
  keys.append(str(i+1))
values=[0]*(10**4)
d=dict(zip(keys, values))
for x in range(1, 150):
  for y in range(x,150):
    tmp=(x+y)**2
    for z in range(y, 150):
      if (tmp+(y+z)**2+(x+z)**2)%2==1:
        continue
      s=(tmp+(y+z)**2+(x+z)**2)//2
      key=str(s)
      if x==y and y==z:
        v=1
      elif (x==y and y<z) or (x<y and y==z):
        v=3
      else:
        v=6
      d[key]=v

for i in range(N):
  print(d[str(i+1)])