Problem:
Score : 300 points

Problem Statement

Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.

Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Constraints

1 \leq K \leq 200

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.

Sample Input 1

2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

200

Sample Output 2

10813692

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program name
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int64)::a, i,j,k,ans
    read*, a

    ans=0
    do i = 1, a-2
        do j = i+1, a-1
            do k = j+1, a
                ans= ans+ gcd(i,gcd(j,k))
            end do
        end do
    end do
    print*, ans*3


contains
recursive function gcd(x,y) result(ret)
    integer(int64):: x,y,ret

    if (mod(x,y) == 0) then
        ret = y
        RETURN
    end if

    ret = gcd(y,mod(x,y))
    
end function
end program name