Sereja and Dividing

题意翻译

现在桌上有n杯水排成一行,第$i$杯水中有$a_i$ 单位体积的水. 他会选择一个区间$[l, r]$,并拿一个初始为空的杯子(杯子的容积无限大),他可以重复无限次以下操作: • 选定任意一杯水$i ∈ [l, r]$. • 使$i$和它拿着的杯子里的水的体积变为它们的平均值. 希望进行若干操作后最大化杯子里的水的体积,设$g(l, r)$为这个最大值. 求:$\sum_{i=1}^{n}\sum_{j=i}^n g(i,j)$

题目描述

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} $ .

输入输出格式

输入格式

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}) $ .

输出格式

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} $ .

输入输出样例

输入样例 #1

5
1 2 3 4 1

输出样例 #1

1.238750000000000