题目链接：

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. ai ≥ ai - 1 for all even i,
2. ai ≤ ai - 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 ai (1 ≤ ai ≤ 109) — the elements of the array a.

Output

If it's possible to make the array a z-sorted print n space separated integers ai — 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：把数列变成要求的那样,太简单就不好说了; AC代码：

/*2014300227    652B - 6    GNU C++11    Accepted    15 ms    2168 KB*/#include 
        
         using namespace std;int a[2000];int main(){    int n;    scanf("%d",&n);    for(int i=1;i<=n;i++)    {        scanf("%d",&a[i]);    }    sort(a+1,a+n+1);    if(n%2==0)    {        for(int i=1;i<=n/2;i++)        {            printf("%d ",a[i]);            printf("%d ",a[n-i+1]);        }    }    else    {        for(int i=1;i<=n/2;i++)        {            printf("%d ",a[i]);            printf("%d ",a[n-i+1]);        }        printf("%d",a[n/2+1]);    }    return 0;}