Problem Statement

Snuke has read his own fortune for tomorrow, and learned that there are $N$ scenarios that can happen, one of which will happen tomorrow with equal probability. The $i$-th scenario will cost him $A_i$ yen (Japanese currency).

Following this, Snuke has decided to get insurance today. If he pays $x$ yen to his insurance company, he will get compensation of $\min(A_i,2x)$ yen when $A_i$ yen is lost. Here, he can choose any non-negative real number as $x$.

Snuke wants to minimize the expected value of the amount of money he loses, which is $x+A_i-\min(A_i,2x)$. Find the minimized value.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer. Your answer will be judged correct when its absolute or relative error is at most $10^{-6}$.