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: Accepted)

(defun func (&rest args)
  (loop for i on args
        sum
        (loop for j in i
              sum (* (car i) j))))

(defun main (n
             &aux
               (ans (make-array (1+ n) :initial-element 0)))
  (labels ((check (&rest args)
             (<= (apply #'func args) n)))
    (loop for i from 1
          while (check i)
          do
             (loop for j from 1
                   while (check i j)
                   do
                      (loop for k from 1
                            while (check i j k)
                            do
                               (incf (aref ans (func i j k))))))
    (cdr (coerce ans 'list))))

(format t "~{~a~%~}"
        (main (read)))