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.

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}.

Constraints

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

Sample Input 1

3
3 1 4

Sample Output 1

1.83333333333333333333

The optimum choice is x=1.5.
After paying 1.5 yen, one of the following three scenarios will happen with equal probability:

• Scenario 1: Lose 3 yen and get compensation of $\min(3,2x)=3$ yen. After all$, Snuke loses x+A_1-\min(A_1,2x)=1.5+3-3=1.5$ yen.

• Scenario 2: Lose 1 yen and get compensation of $\min(1,2x)=1$ yen. After all$, Snuke loses x+A_2-\min(A_2,2x)=1.5+1-1=1.5$ yen.

• Scenario 3: Lose 4 yen and get compensation of $\min(4,2x)=3$ yen. After all$, Snuke loses x+A_3-\min(A_3,2x)=1.5+4-3=2.5$ yen.

Thus, the expected amount of money lost is $(1.5+1.5+2.5)/3=1.833333\cdots$ yen.

Sample Input 2

10
866111664 178537096 844917655 218662351 383133839 231371336 353498483 865935868 472381277 579910117

Sample Output 2

362925658.10000000000000000000

见题面 Input 部分

见题面 Output 部分