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This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

 Goal

When z units of light shine on any side of a mirror with reflectivity r, rz units of light are reflected, and the other (1-r)z units of light pass through the mirror.
There are n mirrors numbered 1...n arranged in a row. Mirror i has reflectivity r_i. Find the total amount of light reflected back to the source when 1 unit of light shines on the first mirror.
Note that light can be reflected multiple times.
----> | | | | |
light 1 2 3 4 5 ...
Input
Line 1: An integer n for the number of mirrors
Line 2: n space-separated floats r for the reflectivity of the mirrors
Output
Line 1: Total reflected light rounded to 4 decimal places
Constraints
1 ≤ n ≤ 10
0 ≤ r ≤ 1
Example
Input
2
0.5 0.500000
Output
0.6667

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