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: Time Limit Exceeded)

x,y,z = 1,1,1
import math
import itertools
lar_num = int(input())
answer = 0
linum = 0
#最小でn=6で存在
for i in range(1,lar_num + 1):
    if i < 6:
        answer = 0
        print(answer)
    else:
        maxnum = math.ceil(-1+(i-2)**0.5)
        for x in range(1,maxnum+1):
            for y in range(1,x+1):
                for z in range(1,y+1):
                    if x**2 + y**2 + z**2 + x*y + y*z + z*x == i:
                        if x == y:
                            if x == z:
                                linum = 1
                            else:
                                linum = 3
                        elif y == z:
                            linum = 3
                        elif z == x:
                            linum = 3
                        else:
                            linum = 6
                        answer += linum
        linum = 0
        print(answer)
        answer = 0