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 ABC162_C
  integer::G,A,H,I,J,K,L
  read(5,*)K
  A=0
  do I=1,K
     do J=1,K
        do L=1,K
           call gcd(J,L,G)
           call gcd(I,G,H)
           A=A+H
        end do
     end do
  end do
  write(6,*)A
end program ABC162_C

  subroutine gcd(A,B,G)
    integer::A,B,C,G,M
    if(A<B) then
       D=B
       E=A
    else
       D=A
       E=B
    end if
    do while(E/=0)
       M=mod(D,E)
       D=E
       E=M
    end do
    G=D
  end subroutine gcd