After discovering the ~5~ 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 ~N~ events that each have a normalized probability ~P_i~ of occurring.

Since these are normalized probabilities, there are ~5~ 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 ~N~ events occur (assuming each event is independent) up to an error of ~10^{-6}~.

Constraints

~1 \le N \le 100\,000~

~P_i \in~ ~\{~A~,~B~,~C~,~D~,~E~\}~

Input Specification

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

The next ~N~ lines will contain ~P_i~, one of the normalized probabilities (A, B, C, D, or E).

Output Specification

Output the probability of all ~N~ events occurring up to an error of ~10^{-6}~.

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