Educational Codeforces Round 10——B. z-sort

B. z-sort

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

A student of z-school found a kind of sorting called z-sort. The array a with n elements are z-sorted if two conditions hold:

1. a_i ≥ a_i - 1 for all even i,
2. a_i ≤ a_i - 1 for all odd i > 1.

For example the arrays [1,2,1,2] and [1,1,1,1] are z-sorted while the array [1,2,3,4] isn’t z-sorted.

Can you make the array z-sorted?

Input

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of elements in the array a.

The second line contains n integers a_i (1 ≤ a_i ≤ 10⁹) — the elements of the array a.

Output

If it's possible to make the array a z-sorted print n space separated integers a_i — the elements after z-sort. Otherwise print the only word "Impossible".

Examples

input

4
1 2 2 1

output

1 2 1 2

input

5
1 3 2 2 5

output

1 5 2 3 2

题意：给定一个数组是否能组成一个波动序列（这名称很贴切呃）。然后突然想到了双端队列，然后又想到了据说在两端操作时间很快的list类

代码：

 

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转载于:https://www.cnblogs.com/Blackops/p/5356387.html