Problem Description
There are two sequences h1∼hn and c1∼cn. h1∼hn is a permutation of 1∼n. particularly, h0=hn+1=0.
We define the expression [condition] is 1 when condition is True,is 0 when condition is False.
Define the function f(h)=∑ni=1ci[hi>hi−1 and hi>hi+1]
Bo have gotten the value of c1∼cn, and he wants to know the expected value of f(h).
Input
This problem has multi test cases(no more than 12).
For each test case, the first line contains a non-negative integer n(1≤n≤1000), second line contains n non-negative integer ci(0≤ci≤1000).
Output
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.
Sample Input
4
3 2 4 5
5
3 5 99 32 12
Sample Output
6.000000
52.833333
