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)

import math
n = int(input())
# ans = [0 for _ in range(n)]
ans = [0] * n

for x in range(1, int(math.sqrt(n+1))):
    x2 = x*x
    for y in range(1, int(math.sqrt(n+1))):
        y2 = y*y
        xy = x * y
        tmp = x2 + y2 + xy
        if tmp >= n:
            break
        for z in range(1, int(math.sqrt(n+1))):
            tmp2 = tmp + z*z + y*z + z*x
            if tmp2 > n:
                break
            try:
                ans[tmp2 - 1] += 1
                print(x, y, z)
            except:
                pass
for i in range(n):
    print(ans[i])