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: Runtime Error)

# vim: fileencoding=utf-8


def main():
    N = int(input())
    for n in range(1, N + 1):
        ans = 0
        if n <= 5:
            print(ans)
            continue

        zMax = int((N + 1) / 6) + 1
        print(f"{n}")
        for x in range(1, int((N + 1) / 6) + 1):
            tx = x ** 2
            if tx + x + 3 >= n or x >= zMax:
                break
            for y in range(x, int((N + 1) / 6) + 1):
                ty = tx + y ** 2 + x * y
                if ty + y + x + 1 >= n or y >= zMax:
                    break
                for z in range(y, int((N + 1) / 6) + 1):
                    print(f"x :{x} y :{y} z :{z}")
                    t = ty + z ** 2 + y * z + z * x
                    if t == n:
                        print(f"ans x :{x} y :{y} z :{z}")
                        if x == y and x == z:
                            ans += 1
                        elif x == y or y == z:
                            ans += 3
                        else:
                            ans += 6
                        if z <= zMax:
                            zMax = z
                        break
                    if t >= n:
                        break
        print(ans)


if __name__ == "__main__":
    main()