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 abc9
 implicit none
 integer::N,i,x,y,z,s,t,sa=0,sb=0,sc=0
 read(*,*)N
 do i=1,N
  t=int(sqrt(dble(i))-1)+1
  s=0
  sa=0
  sb=0
  sc=0
  do x=1,t
   do y=x,t
    do z=y,t
     if(x**2+y**2+z**2+x*y+y*z+z*x==i)then
      if(x==y.and.y==z)then
       sb=sb+1
      else if(x==y.or.y==z.or.z==x)then
       sa=sa+1
      else
       sc=sc+1
      end if
     end if
    end do
   end do
  end do
 s=sc*6+sa*3+sb
  print'(i0)',s
 end do
end program abc9