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 Julia (1.4.0) (judge verdict: Accepted)

quit() = exit(0)
in_1(ch) = parse(Int, take!(ch))
in_a(ch) = parse.(Int, split(take!(ch)))

quit() = exit(0)
in_1() = parse(Int, readline())
in_a() = parse.(Int, split(readline()))

function main()
  K = in_1()
  s = 0
  for a in 1:K
    for b in 1:K
      gcd_ab = gcd(a, b)
      for c in 1:K
        s += gcd(a, b, c)
      end
    end
  end
  println(s)
end

isempty(ARGS) && main()