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: Runtime Error)

from collections import deque
from copy import copy

N = int(input())
result = [0]*N

if N < 6:
    for i in range(N):
        print(0)
    exit()

result[5] += 1

coord = deque()
coord.append([[1,1,1], 6, 0])

while len(coord):
    sol, ans, level = coord.popleft()
    for i in range(level, 3):
        new_sol = copy(sol)
        new_sol[i] += 1
        new_ans = ans + sum(sol) + sol[i] + 1
        if new_ans <= N:
            coord.append([new_sol, new_ans, i])
            result[new_ans] += 1

print(*result, sep='\n', end='')