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: Accepted)

program main
      implicit none
      integer(4) :: k, a, b, mab, c, mabc
      integer(8) :: cnt

      read *, k
      cnt = 0
      do a = 1, k
        do b = 1, k
          do c = 1, k
            call gcd(a,b,mab)
            call gcd(mab, c, mabc)
            cnt = cnt + mabc
          end do
        end do
      end do
      print *, cnt

      contains

      subroutine gcd(m,n,j)
        implicit none
        integer, intent(in) :: m, n
        integer, intent(out) :: j
        integer :: i, l, x, y

        x = m
        y = n
        do 
          l = mod(x,y)
          if ( l == 0 ) exit
          x = y
          y = l
        end do
        j = y

      end subroutine gcd

end program main