Average and Median

AtCoder

IDabc236_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

6
2 1 2 1 1 10

Output #1

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.

Input #2

7
3 1 4 1 5 9 2

Output #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.

API Response (JSON)

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      "content": "We have $N$ cards. The $i$\\-th card $(1 \\leq i \\leq N)$ has an integer $A_i$ written on it.\nTakahashi will choose any number of cards from these. However, for each $i$ $(1 \\leq i \\leq N - 1)$, at leas...",
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Full JSON Raw Segments