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)

# -*- coding: utf-8 -*-
import math

# def f2(x, y, z, n):
#     return x*x+y*y+z*z+x*y+y*z+z*x

def f(x, y, z, n):
    if x*x+y*y+z*z+x*y+y*z+z*x == n:
        return True
    else:
        return False
def main():
    N = int(input())
    for n in range(1, N + 1):
        cnt = 0
        for x in range(1, 100):
            if x * x > n:
                break
            for y in range(x, 100):
                if x*x + y*y > n:
                    break
                for z in range(y, 100):
                    if x*x + y*y + z*z > n:
                        break
                    if f(x, y, z, n):
                        # print(x, end=' ')
                        # print(y, end=' ')
                        # print(z)
                        if x == y == z:
                            cnt += 1
                        else:
                            cnt += 3
        # print(n, end=': ')
        print(cnt)
    return
if __name__ == '__main__':
    main()