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: Time Limit Exceeded)

N = int(input())

for i in range(1,N+1):
  ans = 0
  if i < 6:
    print(ans)
  else:
    for a in range(2,int((2*i)**0.5+1)):
      for b in range(a,int((2*i-a**2)**0.5+1)):
        for c in range(b,int((2*i-a**2-b**2)**0.5+1)):
          #print(a,b,c)
          if a**2 + b**2 + c**2 > 2*i:
            ans = 0
          if a**2 + b**2 + c**2 == 2*i:
            if max(a,b,c) < a+b+c-max(a,b,c):
              if len({a,b,c}) == 1:
                ans = 1
              elif len({a,b,c}) == 2:
                ans = 3
              else:
                ans = 6
              #print(a,b,c)
    print(ans)