Score : $200$ points

问题描述

高桥正在参加一场体操比赛。

在比赛中，每位裁判会为高桥的表现打分，他的得分计算方法如下：

• 取消给出最高分的 $N$ 位裁判的评分。
• 取消给出最低分的 $N$ 位裁判的评分。
• 高桥的得分定义为剩余 $3N$ 位裁判评分的平均值。

更正式地，通过以下步骤对包含裁判评分的多重集合 $S$（$|S|=5N$）进行操作来得到高桥的得分：

• 重复以下操作 $N$ 次：选择并移除当前最大元素（如果有多个最大元素，则从中选择一个）。
• 重复以下操作 $N$ 次：选择并移除当前最小元素（如果有多个最小元素，则从中选择一个）。
• 高桥的得分由剩余的 $3N$ 个元素的平均值得出。

第 $i$ 位（$1\leq i\leq 5N$）裁判给高桥的表现打分为 $X_i$ 分。请计算高桥的得分。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is participating in a gymnastic competition.
In the competition, each of $5N$ judges grades Takahashi's performance, and his score is determined as follows:

• Invalidate the grades given by the $N$ judges who gave the highest grades.
• Invalidate the grades given by the $N$ judges who gave the lowest grades.
• Takahashi's score is defined as the average of the remaining $3N$ judges' grades.

More formally, Takahashi's score is obtained by performing the following procedure on the multiset of the judges' grades $S$ ($|S|=5N$):

• Repeat the following operation $N$ times: choose the maximum element (if there are multiple such elements, choose one of them) and remove it from $S$.
• Repeat the following operation $N$ times: choose the minimum element (if there are multiple such elements, choose one of them) and remove it from $S$.
• Takahashi's score is defined as the average of the $3N$ elements remaining in $S$.

The $i$-th $(1\leq i\leq 5N)$ judge's grade for Takahashi's performance was $X_i$ points. Find Takahashi's score.

Constraints

• $1\leq N\leq 100$
• $0\leq X_i\leq 100$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$

$X_1$ $X_2$ $\ldots$ $X_{5N}$

Output

Print Takahashi's score.
Your answer will be considered correct if the absolute or relative error from the true value is at most $10^{-5}$.

Sample Input 1

1
10 100 20 50 30

Sample Output 1

33.333333333333336

Since $N=1$, the grade given by one judge who gave the highest grade, and one with the lowest, are invalidated.
The $2$-nd judge gave the highest grade ($100$ points), which is invalidated.
Additionally, the $1$-st judge gave the lowest grade ($10$ points), which is also invalidated.
Thus, the average is $\displaystyle\frac{20+50+30}{3}=33.333\cdots$.

Note that the output will be considered correct if the absolute or relative error from the true value is at most $10^{-5}$.

Sample Input 2

2
3 3 3 4 5 6 7 8 99 100

Sample Output 2

5.500000000000000

Since $N=2$, the grades given by the two judges who gave the highest grades, and two with the lowest, are invalidated.
The $10$-th and $9$-th judges gave the highest grades ($100$ and $99$ points, respectively), which are invalidated.
Three judges, the $1$-st, $2$-nd, and $3$-rd, gave the lowest grade ($3$ points), so two of them are invalidated.
Thus, the average is $\displaystyle\frac{3+4+5+6+7+8}{6}=5.5$.

Note that the choice of the two invalidated judges from the three with the lowest grades does not affect the answer.

update @ 2024/3/10 12:08:21