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.

Input

Input is given from Standard Input in the following format:
K

Output

Print the value of $\displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}$.

Constraints

• $1 \leq K \leq 200$
• K is an integer.

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

见题面 Input 部分

见题面 Output 部分