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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(let* ((n (read))
    (ans (make-array (+ n 1) :initial-element 0)))

    (loop for x from 1 to n do
        (loop for y from 1 to n do
            (loop for z from 1 to n do
                (if (<= (+ (expt x 2) (expt y 2) (expt z 2) (* x y) (* y z) (* z x)) n)
                    (incf (aref ans (+ (expt x 2) (expt y 2) (expt z 2) (* x y) (* y z) (* z x))))
                )
            )
        )
    )
    (loop for i from 1 to n do
        (format t "~D~%" (aref ans i))
    )


)