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E. Sereja and Dividing

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet'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:

- choose an index of the sequence element
*i*(1 ≤*i*≤ |*a*|); - 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}.

Examples

Input

5

1 2 3 4 1

Output

1.238750000000000

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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