Problem B
Bjagað Beðaltal

Image by Randall Munroe, xkcd.com

At the end of every programming contest, statistics and fun facts are collected to show the contestants afterwards. Often average number of solves, or average number of tries to solve a given problem are calculated. Allegedly, someone at the statistics department said that arithmetic averages are very uninteresting. To make the contest data analysis exciting enough for the statisticians the contest hosts have decided to use a new exciting method to calculate averages. Instead of following the good example set by Hölder in how to generalise averages, the example of Randall Munroe is followed instead. That is where the geothmetic meandian comes in. As the image shows, the geothmetic meandian is calculated in the following way:

Let $n$ be an odd number. A sequence of numbers $x_1, x_2, \dots , x_n$ is sorted resulting in the sequence $y_1, y_2, \dots , y_n$. The original sequence is then replaced by the sequence

This is then repeated on the new sequence resulting in another sequence. If the repetition is performed infinitely often the sequence converges to a single repeated value, this repeated value is then the geothmetic meandian.

Input

The input begins with a single odd integer $1 \leq n \leq 10^5$. The next line contains $n$ real values $x_1, \dots , x_n$. For all $i$ it is guaranteed that $0 < x_i \leq 10^9$. All real values have at most $6$ digits after the decimal.

Output

Print the geothmetic meandian of $x_1, \dots , x_n$. The answer is considered correct if its absolute or relative error from the true answer is at most $10^{-5}$.

5
1 1 2 3 5

2.08905794953626

9
1 1.5 2 2.5 3 3.5 4 4.5 5

2.91827409737909