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: Wrong Answer)

#+nil(defparameter *cash* (make-array 1000001))
(defun calc (x y z)
  #+nil(let ((r (aref *cash* (+ (* x 10000) (* y 100) z))))
         (if (zerop r)
             (setf (aref *cash* (+ (* x 10000) (* y 100) z))
                   (+ (* x x)
                      (* y y)
                      (* z z)
                      (* x y)
                      (* y z)
                      (* z x)))
             r))
  (+ (* x x)
     (* y y)
     (* z z)
     (* x y)
     (* y z)
     (* z x)))

(defun f (n)
  (loop with result = 0
        for x from 1
        while (>= n (calc x 0 0))
        do (loop for y from x
                 while (>= n (calc x y 0))
                 do (loop for z from (max y (floor (sqrt (- n (calc x y 0)))))
                          for r = (calc x y z)
                          while (>= n r)
                          when (= n r)
                          do ;;(print (list x y z n (calc x y z)))
                             (incf result (if (= x y)
                                              (if (= y z) 1 3)
                                              (if (= y z) 3 6)))))
        finally (return result)))

(let ((n (read)))
  (loop for i from 1 to n
        do (format t "~A~%" (f i))))