A9068. Difference Row

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.

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

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.

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 $r$ $(0<=r<p)$ such that $x_{1}=y_{1},x_{2}=y_{2},...\ ,x_{r}=y_{r}$ and $x_{r+1}<y_{r+1}$ .