Beautiful Array

Array $a$ is beautiful if all $a_i-a_{i-1}$ ($2\le i\le n$) are distinct.

For example, $[1,3,2,9]$ and $[8,4,6,9]$ are beautiful, while $[1,2,3,9]$ and $[1,5,5,9]$ are not.

A sequence of integers $b_1,b_2,\dots ,b_n$ is called a permutation of the sequence $c_1,c_2,\dots ,c_n$ if the number of each unique number in these arrays is the same. For example, $[1,5,3,4,2]$ is a permutation of $[5,2,1,4,3]$, and $[1,3,3,5]$ is a permutation of $[3,5,1,3]$. However, $[1,3,4]$ is not a permutation of $[2,3,4]$ (it doesn't contain $2$, which should appear in the sequence and has $1$, which should not appear).

Sakurako received an array. She wants to find an example of a permutation of the given array which is beautiful.

Input

The first line contains one integer $n$ ($2\le n\le 2\cdot 10^5$) — the length of the array.

The second line contains $n$ integers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le 10^9$) — elements of the array.

It is guaranteed that all numbers in the array are distinct. It is also guaranteed that an answer exists.

Output

Output a beautiful array (which is a permutation of the original array) in one line. If there are multiple solutions, output any.

Examples

Note

In the first example, array $[3,5,4,1,2]$ is beautiful since if we take $a_i-a_{i-1}$ for all $i$, it will be:

• $5-3=2$;

• $4-5=-1$;

• $1-4=-3$;

• $2-1=1$.

As we see, all numbers are distinct.

In the second example, array $[4,2,3]$ is beautiful since if we take $a_i-a_{i-1}$ for all $i$, it will be:

• $2-4=-2$;

• $3-2=1$.

As we see, all numbers are distinct.

Scoring

You will receive at least $16$ points if your solution works correctly for $n\le 10$.

You will receive at least $48$ points if your solution works correctly for $n\le 1000$.