Simple Skewness

题意翻译

题意:从n个数中选一些数,使得这些数的平均数减去中位数最大

题目描述

Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of $ n $ (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness. The mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.

输入输出格式

输入格式

The first line of the input contains a single integer $ n $ ( $ 1<=n<=200\ 000 $ ) — the number of elements in the list. The second line contains $ n $ integers $ x_{i} $ ( $ 0<=x_{i}<=1000000 $ ) — the $ i $ th element of the list.

输出格式

In the first line, print a single integer $ k $ — the size of the subset. In the second line, print $ k $ integers — the elements of the subset in any order. If there are multiple optimal subsets, print any.

输入输出样例

输入样例 #1

4
1 2 3 12

输出样例 #1

3
1 2 12 

输入样例 #2

4
1 1 2 2

输出样例 #2

3
1 1 2 

输入样例 #3

2
1 2

输出样例 #3

2
1 2

说明

In the first case, the optimal subset is , which has mean $ 5 $ , median $ 2 $ , and simple skewness of $ 5-2=3 $ . In the second case, the optimal subset is . Note that repetition is allowed. In the last case, any subset has the same median and mean, so all have simple skewness of $ 0 $ .