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문제

Dreamoon, who doesn't have a girlfriend, often goes for a walk along some streets in Taipei while thinking about problems from algorithm competitions. Unfortunately, there are so many couples acting lovey-dovey on the street that Dreamoon can not focus on thinking about those problems.

One day, despite the love birds everywhere, Dreamoon discovered a problem input containing an integer sequence: $a_1, a_2, a_3, \ldots, a_N$.

Dreamoon thought: because I'm single, every pair of consecutive numbers should have a large difference! This is, Dreamoon wants to reorder the sequence to make the value $\min\limits_{i = 2 \ldots N}(|a_i - a_{i-1}|)$ as large as possible.

So Dreamoon turned on Drazil, who does have a girlfriend, and forced Drazil to fulfill the above condition by reordering the integer sequence. Please help poor Drazil $>\_<$

입력

The input consists of two lines. The first line contains an integer $N$. The second line consists of $N$ integers $a_1, a_2, \ldots, a_N$.

출력

Output a single line consisting of $N$ integers, denoting the integer sequence $a$ after reordering. For this reordering, the value $\min\limits_{i = 2 \ldots N}{|a_i - a_{i-1}|}$ must be the largest possible among all reorderings of the input sequence. If there are several possible answers, output any one of them.

제한

  • $2 \le N \le 2 \times 10^5$
  • $-10^9 \le a_i \le 10^9$

예제 입력 1

3
3 1 5

예제 출력 1

3 5 1

예제 입력 2

4
-1 -1 1 1

예제 출력 2

1 -1 1 -1