Practice Simulation and Mathematics with the exercise "Mirrors"

Learning Opportunities

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

Simulation
Mathematics

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

Solve it

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