## SAC '22 Code Challenge 3 Junior P3 - Normal Probabilities

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Points: 3 (partial)
Time limit: 1.0s
Memory limit: 256M

Author:
Problem type

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

ABCDE

#### 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