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 Pascal (FPC 3.0.4) (judge verdict: Time Limit Exceeded)

Program main;
var
    i, j, k, n : integer;
    sum : int64;
    
function gcd(a, b, c : integer) : int64;
var
    i : integer;
begin
    for i := 1 to n do 
        if (a mod i = 0) and (b mod i = 0) and (c mod i = 0)
            then gcd := i;
end;

begin
    sum := 0;
    readln(n);
    for i := 1 to n do 
        for j := 1 to n do
            for k := 1 to n do 
                sum := sum + gcd(i,j,k);
    writeln(sum);
end.