AtCoder Beginner Contest 138
C
Alchemist
AtCoder
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原题
← BD →
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Problem Statement

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You have a pot and $N$ ingredients. Each ingredient has a real number parameter called value, and the value of the $i$-th ingredient $(1 \leq i \leq N)$ is $v_i$.

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When you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be $(x + y) / 2$ where $x$ and $y$ are the values of the ingredients consumed, and you can put this ingredient again in the pot.

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After you compose ingredients in this way $N-1$ times, you will end up with one ingredient. Find the maximum possible value of this ingredient.

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Constraints

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  • $2 \leq N \leq 50$
  • $1 \leq v_i \leq 1000$
  • All values in input are integers.
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Input

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Input is given from Standard Input in the following format:

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N
v_1 v_2 \ldots v_N

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Output

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Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.

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Your output will be judged correct when its absolute or relative error from the judge's output is at most $10^{-5}$.

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样例

Input #1
2
3 4
Output #1
3.5
If you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values $3$ and $4$ is $(3 + 4) / 2 = 3.5$. Printing `3.50001`, `3.49999`, and so on will also be accepted.
Input #2
3
500 300 200
Output #2
375
You start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices: - Use the ingredients of values $500$ and $300$ to produce an ingredient of value $(500 + 300) / 2 = 400$. The next composition will use this ingredient and the ingredient of value $200$, resulting in an ingredient of value $(400 + 200) / 2 = 300$. - Use the ingredients of values $500$ and $200$ to produce an ingredient of value $(500 + 200) / 2 = 350$. The next composition will use this ingredient and the ingredient of value $300$, resulting in an ingredient of value $(350 + 300) / 2 = 325$. - Use the ingredients of values $300$ and $200$ to produce an ingredient of value $(300 + 200) / 2 = 250$. The next composition will use this ingredient and the ingredient of value $500$, resulting in an ingredient of value $(250 + 500) / 2 = 375$. Thus, the maximum possible value of the last ingredient remaining is $375$. Printing `375.0` and so on will also be accepted.
Input #3
5
138 138 138 138 138
Output #3
138
题目信息
题号
abc138_c
时间限制
2 s
内存限制
1024 MB

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