There are two sequences $h_1\sim h_n$ and $c_1\sim c_n$. $h_1\sim h_n$ is a permutation of $1\sim n$. particularly, $h_0=h_{n+1}=0$.
We define the expression $[condition]$ is 1 when $condition$ is True,is 0 when $condition$ is False.
Define the function $f(h)=\sum_{i=1}^{n}{c_i[h_i>h_{i-1}~~and~~h_i>h_{i+1}]}$
Bo have gotten the value of $c_1\sim c_n$, and he wants to know the expected value of $f(h)$.
This problem has multi test cases(no more than $12$).
For each test case, the first line contains a non-negative integer $n(1\leq n\leq1000)$, second line contains $n$ non-negative integer $c_i(0\leq c_i\leq 1000)$.
For each test cases print a decimal - the expectation of $f(h)$.
If the absolute error between your answer and the standard answer is no more than $10^{-4}$, your solution will be accepted.