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 FizzBuzz
      implicit none
      
      integer K,a(3),gcd,Mi,i,j,l
      read(*,*) K
      a=1
      gcd=0
      do i=1,K
        a(0)=i
      do j=1,K
        a(1)=j
      do l=1,K
         a(2)=l
         Mi=min(a(0),a(1),a(2))
         
         1 if (mod(a(0),Mi)==0.and.mod(a(1),Mi)==0.and.mod(a(2),Mi)==0) then
            gcd=gcd+Mi
         else
             Mi=Mi-1
             go to 1
         end if
      end do
      end do
      end do
      
      write(*,'(i0)') gcd
      stop 
      end program FizzBuzz