Problem Statement

A-kun and B-kun like card games.
The card game is played with 2*N cards, each with one of the numbers from 1 to 2*N written on it, one number per card.
A-kun and B-kun are each dealt N cards.
The game is simple.
Each player freely plays one card, and the player with the larger number wins that match.
A card that has been played once in a match cannot be used again.
A total of N matches are played, and the player with more match wins wins the game.
If A-kun and B-kun have the same number of wins, the game is a draw.
The cards have already been dealt.
Compute the probability that A-kun wins the game when the N matches are over.
Both players play their cards at random, without any strategy.

Input

$N$
$A_0\ A_1\ \dots\ A_{N-1}$
$B_0\ B_1\ \dots\ B_{N-1}$

$N$ is an integer with $1\le N \le 4$.
$A_0,A_1,...,A_{N-1}$ and $B_0,B_1,...,B_{N-1}$ contain the numbers from $1$ to $2*N$.
There are no duplicate numbers among $A_0,A_1,...,A_{N-1}$ and $B_0,B_1,...,B_{N-1}$.

Output

Output the probability that A-kun wins on one line. An error of up to ±0.01 is allowed.
Do not forget the newline at the end.

Sample

2
2 4
1 3

0.5

2
3 4
1 2

1

1
1
2

0

3
6 2 3
1 5 4

0.666667