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: Time Limit Exceeded)

program tsundoku
  implicit none
  integer :: n, m, i,j, h = 0, l, r, p
  integer(8) :: k, t
  integer(8), dimension(0:200001) :: a = 0, b = 0, x = 0, y = 0
  read(*,*) n
    do t=1,n
    m=int(sqrt(dble(t)))
    p=0
	do i=1,m
    	do j=1,m
        	do k=1,m
            	if((i*i+j*j+k*k+i*j+j*k+i*k)==t)then
                p=p+1
                end if
            end do
        end do
    end do
    write(*,*)p
    end do
end program tsundoku