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