# Colouring

### Memory limit: 32 MB

A number from to is inscribed in each cell of a grid
in such a way that each number appears exactly twice in the grid and each column contains
two different numbers.
An example of such a configuration is depicted below.

We would like to colour each of the cells white or gray in such a way that
cells located in the same column receive different colours and cells
containing same number receive different colours.
An example of such a colouring of the grid from the previous figure
is depicted below.

How many such colourings exist?

## Input

The first line of the standard input contains one integer
().
Each of the following two lines contains integers in the range
, separated by single spaces.
The numbers in these lines represent numbers inscribed in consecutive
cells of the grid.

## Output

The first and only line of the standard output should contain a single
integer - the number of different colourings of the grid with two colours
that fulfill the described conditions.

## Example

For the input data:

5
1 5 3 1 5
4 2 2 4 3

the correct result is:

4

Please note that the example describes the grid from the above figures.

*Task author: Krzysztof Diks.*