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E - Average and Median

Score : $500$ points

Problem Statement

We have $N$ cards. The $i$-th card $(1 \leq i \leq N)$ has an integer $A_i$ written on it.

Takahashi will choose any number of cards from these. However, for each $i$ $(1 \leq i \leq N - 1)$, at least one of the $i$-th and $(i+1)$-th cards must be chosen.

Find the following values.

• The maximum possible average of the integers written on the chosen cards
• The maximum possible median of the integers written on the chosen cards

Here, the median of the $n$ integers is defined to be the $\lceil \frac{n}{2} \rceil$-th smallest of them, where $\lceil x \rceil$ is the smallest integer not less than $x$.

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^{9}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $\ldots$ $A_N$

Output

Print two lines. The first and second lines should contain the maximum possible average and maximum possible median of the integers written on the chosen cards, respectively. For the average, your output will be considered correct when its relative or absolute error from the exact answer is at most $10^{-3}$.

6
2 1 2 1 1 10

4
2

Choosing the $2$-nd, $4$-th, and $6$-th cards makes the average of the written integers $\frac{12}{3} = 4$, which is the maximum possible.

Choosing the $1$-st, $3$-rd, $5$-th, and $6$-th cards makes the median of the written integers $2$, which is the maximum possible.

7
3 1 4 1 5 9 2

5.250000000
4

For the average, your output may contain some degree of error: for example, the output $5.2491$ is still considered correct. For the median, however, the exact value must be printed.