Problem Statement

There are $N$ towns in a coordinate plane. Town $i$ is located at coordinates ($x_i$, $y_i$). The distance between Town $i$ and Town $j$ is $\sqrt{\left(x_i-x_j\right)^2+\left(y_i-y_j\right)^2}$.

There are $N!$ possible paths to visit all of these towns once. Let the length of a path be the distance covered when we start at the first town in the path, visit the second, third, $\dots$, towns, and arrive at the last town (assume that we travel in a straight line from a town to another). Compute the average length of these $N!$ paths.

Constraints

• $2 \leq N \leq 8$
• $-1000 \leq x_i \leq 1000$
• $-1000 \leq y_i \leq 1000$
• $\left(x_i, y_i\right) \neq \left(x_j, y_j\right)$ (if $i \neq j$)
• (Added 21:12 JST) All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the average length of the paths. Your output will be judges as correct when the absolute difference from the judge's output is at most $10^{-6}$.