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: Time Limit Exceeded)

def resolve():
    import sys
    import math

    readline = sys.stdin.readline

    N = int(readline())

    for i in range(1, N + 1):
        ans = 0
        li = int(math.sqrt(i))
        for x in range(1, li):
            xx = x * x
            for y in range(1, li):
                yy = y * y
                xy = x * y
                x_y = x + y
                value = (x_y) ** 2 - 4 * (xx + yy + xy - i)
                if value <= 0:
                    continue
                cal = math.sqrt(value)
                z1 = (-(x_y) + cal) / 2
                z2 = (-(x_y) - cal) / 2
                if (1
                        and 1 <= z1
                        and z1 % 1 == 0):
                    ans += 1
                if (1
                        and 1 <= z2
                        and z2 % 1 == 0):
                    ans += 1
        print(ans)


resolve()