Difference Row

题意翻译

一串数列的价值是这样计算的： (x[1]-x[2])+(x[2]-x[3])+···+(x[n-1]-x[n]) 这串数列的顺序是可以改变的，试求出价值最大的一种排列（若有多种答案，按字典序最小的一种输出）。

题目描述

You want to arrange $ n $ integers $ a_{1},a_{2},...,a_{n} $ in some order in a row. Let's define the value of an arrangement as the sum of differences between all pairs of adjacent integers. More formally, let's denote some arrangement as a sequence of integers $ x_{1},x_{2},...,x_{n} $ , where sequence $ x $ is a permutation of sequence $ a $ . The value of such an arrangement is $ (x_{1}-x_{2})+(x_{2}-x_{3})+...+(x_{n-1}-x_{n}) $ . Find the largest possible value of an arrangement. Then, output the lexicographically smallest sequence $ x $ that corresponds to an arrangement of the largest possible value.

输入输出格式

输入格式

The first line of the input contains integer $ n $ ( $ 2<=n<=100 $ ). The second line contains $ n $ space-separated integers $ a_{1} $ , $ a_{2} $ , $ ... $ , $ a_{n} $ ( $ |a_{i}|<=1000 $ ).

输出格式

Print the required sequence $ x_{1},x_{2},...,x_{n} $ . Sequence $ x $ should be the lexicographically smallest permutation of $ a $ that corresponds to an arrangement of the largest possible value.

输入输出样例

输入样例 #1

5
100 -100 50 0 -50

输出样例 #1

100 -50 0 50 -100 

说明

In the sample test case, the value of the output arrangement is $ (100-(-50))+((-50)-0)+(0-50)+(50-(-100))=200 $ . No other arrangement has a larger value, and among all arrangements with the value of $ 200 $ , the output arrangement is the lexicographically smallest one. Sequence $ x_{1},x_{2},...\ ,x_{p} $ is lexicographically smaller than sequence $ y_{1},y_{2},...\ ,y_{p} $ if there exists an integer $ r $ $ (0<=r&lt;p) $ such that $ x_{1}=y_{1},x_{2}=y_{2},...\ ,x_{r}=y_{r} $ and $ x_{r+1}&lt;y_{r+1} $ .