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 AIsing2020C
    implicit none
    integer(8)::N,i,j,k,A(10000),m
    read*,N
    A=0
 
    do i=1,100
        do j=1,100
            do k=1,100
                m=i**2+j**2+k**2+i*j+j*k+k*i
                if(m<=10000)A(m)=A(m)+1
            end do
        end do
    end do
 
    do i=1,N
        print'(i0)',A(i)
    end do
end program AIsing2020C