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: Wrong Answer)

program atcoder
implicit none
integer :: n , x , y , z , i , sum
real :: j
read *,n
sum = 0
j = real(n)
do i = 1 , n
  sum = 0
  do x = int(sqrt(j/6.0)) , int(sqrt(j))+1
    do y = x , int(sqrt(j))+1
      do z = y , int(sqrt(j))+1
        if(x**2 + y**2 + z**2 + x*y + y*z + z*x == i)then
          sum = sum + 1
          if(x == y .and. y == z)goto 10
        end if
      end do
    end do
  end do
  print *, sum * 3
  goto 20
10 print *, sum * 3 - 2
20 end do
end program atcoder