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

$1\le N\le 100000$

$P_i\in$ $\{$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