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 cm
  implicit none
  integer::N
  integer(16)::ANS=0
  integer::i,j,ij,k
read*,N
do i=1,N
  do j=1,N
    ij=gcd(i,j)
    do k=1,N
      ANS=ANS+gcd(ij,k)
    end do
  end do
end do
print"(i0)",ANS
contains
integer recursive function gcd(a, b)result(res)
  integer, intent(in)::a, b
  res=merge(b, gcd(b, mod(a, b)),mod(a, b)==0)
end function
end program cm