Sum of gcd of Tuples (Easy)

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

inputFormat

Input

Input is given from Standard Input in the following format:

K

outputFormat

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

样例

2

9