The current selected programming language is CPP$.$ We emphasize the submission of a fully working code over partially correct but efficient code. Once submitted, you cannot review this problem again. You can use cout to debug your code. The cout may not work in case of syntax$/$runtime error. The version of $GCC$ being used is $5\mathrm{.}5\mathrm{.}0.$

An alternate sort of a list consists of alternate elements $($starting from the first position$)$ of the given list after sorting it in an ascending order. You are given a list of unsorted elements. Write an algorithm to find the alternate sort of the given list.

Input

The first line of the input consists of an integer size, representing the size of the given list $($N$).$

The second line consists of $N$ space$-$separated integers $a{r}_0,a{r}_1,$dots... arr $N_N$ representing the elements of input list.

Output

Print space$-$separated integers representing the alternately sorted elements of the given list.

Constraints

$0$ size ${10}^6$

$-{10}^6$arn${10}^6$

$0i$ size

Example

Input:

$8$

$351591026$

Output:

$1359$

Explanation:

After sorting, the list is $1,2,3,5,5,6,9,10.$

$50,$ the alternate elements of the sorted list are $1,3,5,9.$