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: Time Limit Exceeded)

x = parse(Int, readline())

function mygcd(a,b,c)
    if(a==b && b==c)
        return a
    end
    max = div(maximum((a,b,c)),2)
    GCD = 0
    for i in [i for i = 1:max]
        if(a%i==0 && b%i==0 && c%i==0)
            GCD = i
        end
    end
    return GCD
end

function mysum(K)
    S = 0
    for a in [i for i = 1:K]
        for b in [i for i = 1:K]
            for c in [i for i = 1:K]
                S = S + mygcd(a,b,c)
            end
        end
    end
    return S
end
println(mysum(x))