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 r20711c

implicit none
integer :: x, y, z, n, f, i
integer :: a(1:11000)

a = 0

read *, n
roop: do x = 1, 100
  do y = 1, x
   do z = 1, y
    f = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
    if(f > 11000) then
     exit roop
    end if
    !print '(5(I2, 1x))', i, x, y, z, f
    if(x == y .and. y == z) then
     a(f) = a(f) + 1
    else if(x == y .or. y == z) then
     a(f) = a(f) + 3
    else
     a(f) = a(f) + 6
    end if
   end do
  end do
end do roop

do i = 1, n
 print *, a(i)
end do
   
end program r20711c