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-----
2

-----Sample Output-----
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.

见题面

见题面