After discovering the normalized probabilities, Kevin Yang was awarded the Nobel Prize for mathematics.

With this discovery, Kevin can solve even more combinatorics problems.

One of the combinatorics problems entails a list of events that each have a normalized probability of occurring.

Since these are normalized probabilities, there are types of probability:

`A`

corresponds to a 100% probability of occurring.`B`

corresponds to an 80% probability of occurring.`C`

corresponds to a 60% probability of occurring.`D`

corresponds to a 40% probability of occurring.`E`

corresponds to a 20% probability of occurring.

Kevin wants to know how likely it is that all these events occur (assuming each event is independent) up to an error of .

#### Constraints

`A`

`B`

`C`

`D`

`E`

#### Input Specification

The first line will contain , the number of independent events.

The next lines will contain , one of the normalized probabilities (`A`

, `B`

, `C`

, `D`

, or `E`

).

#### Output Specification

Output the probability of all events occurring up to an error of .

#### Sample Input 1

```
3
A
B
B
```

#### Sample Output 1

`0.640000`

#### Sample Input 2

```
4
B
C
D
E
```

#### Sample Output 2

`0.038400`

## Comments