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: Accepted)

# -*- coding: utf-8 -*-


def main():
    import sys
    input = sys.stdin.readline

    n = int(input())
    ans = [0 for _ in range(10 ** 6 + 2000)]
    candidate = 110

    for x in range(1, candidate + 1):
        for y in range(1, candidate + 1):
            for z in range(1, candidate + 1):
                total = 0
                total += (x ** 2) + (y ** 2) + (z ** 2)
                total += (x * y) + (y * z) + (z * x)

                if total < (10 ** 6 + 2000):
                    ans[total] += 1

    for i in range(1, n + 1):
        print(ans[i])


if __name__ == '__main__':
    main()