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

Examples

Input

2

Output

9

Input

200

Output

10813692

见题面

见题面