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.

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}.

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.

Sample Input 1

3
0 0
1 0
0 1

Sample Output 1

2.2761423749

There are six paths to visit the towns: 1 → 2 → 3, 1 → 3 → 2, 2 → 1 → 3, 2 → 3 → 1, 3 → 1 → 2, and 3 → 2 → 1.
The length of the path 1 → 2 → 3 is $\sqrt{\left(0-1\right)^2+\left(0-0\right)^2} + \sqrt{\left(1-0\right)^2+\left(0-1\right)^2} = 1+\sqrt{2}$.
By calculating the lengths of the other paths in this way, we see that the average length of all routes is:
$\frac{\left(1+\sqrt{2}\right)+\left(1+\sqrt{2}\right)+\left(2\right)+\left(1+\sqrt{2}\right)+\left(2\right)+\left(1+\sqrt{2}\right)}{6} = 2.276142$...

Sample Input 2

2
-879 981
-866 890

Sample Output 2

91.9238815543

There are two paths to visit the towns: 1 → 2 and 2 → 1. These paths have the same length.

Sample Input 3

8
-406 10
512 859
494 362
-955 -475
128 553
-986 -885
763 77
449 310

Sample Output 3

7641.9817824387

见题面 Input 部分

见题面 Output 部分