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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program answer
  implicit none

  integer(8) :: N, i, j, k, count, eg(10000)
  read(*,*) N
  eg=0
  do i = 1, 100
     do j = 1, 100
        do k= 1, 100
           if(i**2+j**2+k**2+i*j+j*k+k*i<=10000) then
              eg(i**2+j**2+k**2+i*j+j*k+k*i)=eg(i**2+j**2+k**2+i*j+j*k+k*i)+1
           end if
        end do
     end do
  end do

 
  do i = 1, N
     write(*,*) eg(i)
  end do
  stop
 end program answer