Let's assume that we have a sequence of doubles $*a*_{1}, *a*_{2}, ..., *a*_{|*a*|}$ and a double variable $*x*$. You are allowed to perform the following two-staged operation:

1. choose an index of the sequence element $*i*$ $(1 ≤ *i* ≤ |*a*|)$;
2. consecutively perform assignments: .

Let's use function $*g*(*a*, *x*)$ to represent the largest value that can be obtained from variable $*x*$, using the described operation any number of times and sequence $*a*$.

Sereja has sequence $*b*_{1}, *b*_{2}, ..., *b*_{|*b*|}$. Help Sereja calculate sum: . Record $[*b*_{*i*}, *b*_{*i* + 1}, ..., *b*_{*j*}]$ represents a sequence containing the elements in brackets in the given order. To avoid problems with precision, please, print the required sum divided by $|*b*|^{2}$.

Input

The first line contains integer $|*b*|$ $(1 ≤ |*b*| ≤ 3·10^{5})$ — the length of sequence $*b*$. The second line contains $|*b*|$ integers $*b*_{1}$, $*b*_{2}$, $...$, $*b*_{|*b*|}$ $(1 ≤ *b*_{*i*} ≤ 10^{5})$.

Output

In a single line print a real number — the required sum divided by $|*b*|^{2}$. Your answer will be considered correct if its absolute or relative error won't exceed $10^{ - 6}$.