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: Accepted)

program main;
var 
    i, j, k, n, a, b, t : integer;
    sum : longint;
begin
    readln(n);

    sum := 0;
    for i := 1 to n do
        for j := 1 to n do
            for k := 1 to n do begin
                a := i; b := j;
                while (a <> 0) do begin
                    t := a;
                    a := b mod a;
                    b := t;
                end;

                a := k;
                while (a <> 0) do begin
                    t := a;
                    a := b mod a;
                    b := t;
                end;

                sum := sum + b;
            end;

    writeln(sum);
end.