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())
def search(n):
    global N
    for x in range(1, N + 1):
        xx = x*x
        if n - xx <= 0:
            return None
        for y in range(1, N + 1):
            yy = y*y
            xy = x*y
            if n - xx - yy - xy <= 0:
                break
            z = binarySearch(n, x, y, xx + yy + xy)
            if z:
                return (x, y, z)


def binarySearch(n, x, y, t):
    global N
    right = -1
    left = N + 1
    while(abs(right - left) > 1):
        z = left + (right - left) // 2
        l = t + z*z + y*z + z*x
        if l == n:
            return z
        elif l < n:
            right = z
        else:
            left = z
        # print(right, left, z)
    return None

ans = list()
for n in range(1, N+1):
    xyz = search(n)
    if xyz == None:
        ans.append("0")
        continue
    t = len(set(xyz))
    if t == 1:
        ans.append("1")
    elif t == 2:
        ans.append("3")
    else:
        ans.append("6")

print("\n".join(ans))