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: Wrong Answer)

def resolve():
    import sys
    sys.setrecursionlimit(10 ** 6)  # 再帰関数の再帰の深さを設定
    to_index = lambda x: int(x) - 1  # 入力した数字に1を引いたものを返す
    print_list_in_2D = lambda x: print(*x, sep="\n")  # リストの要素を改行を挟んで表示する関数

    # 入力を整数に変換して受け取る
    def input_int():
        return int(input())

    def map_int_input():
        return map(int, input())

    MII = map_int_input

    def MII_split():
        return map(int, input().split())

    def MII_to_index():
        return map(to_index, input())

    def MII_split_to_index():
        return map(to_index, input().split())

    # 入力全てを整数に変換したものの配列を受け取る
    def list_int_inputs():
        return list(map(int, input()))

    LII = list_int_inputs

    def LII_split():
        return list(map(int, input().split()))

    # 2次元リスト化
    def LII_2D(rows_number):
        return [LII() for _ in range(rows_number)]

    def LII_split_2D(rows_number):
        return [LII_split() for _ in range(rows_number)]

    import math
    def L(x, y, z):
        return int(x * x + y * y + z * z + x * y + y * z + z * x)

    N = input_int()
    # for n in range(1, N + 1):  # f(n)を計算する仮定でf(n-1)の候補が現れるので...

    ans = [0 for _ in range(N)]
    for x in range(1, 105):
        for y in range(x, 105):
            for z in range(y, 105):
                f = L(x, y, z)
                
                if f <= N:
                    if x == y == z:
                        ans[f - 1] += 1
                    else:
                        ans[f - 1] += 3

    for a in ans:
        print(a)
resolve()