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
import java.util.*;

public class Solution
{
	static long[] a;
	public static void main(String[] args) 
	{
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		a=new long[n+1];
		for (int i=1;i<=n ;i++ ) 
		{
			a[i]=in.nextInt();
			
		}

		for(int i=1;i<=n;i++)
			for(int j=i;j>1;j--)
				if(j%2==0)
				{
					if(a[j]<a[j-1])
					 	swap(j,j-1);
				}
				else
					if(a[j]>a[j-1])
					 	swap(j,j-1);

					 boolean poss=true;

		for(int i=2;i<=n;i++)
		if(i%2==0)
				{
					if(a[i]<a[i-1])
					 	poss=false;
					 	break;
				}
		else
			if(a[i]>a[i-1])
				{
					poss=false;
					 	break;
				}

		if(!poss)System.out.println("Impossible");
		else
		for(int k=1;k<=n;k++)
		System.out.print(a[k]+" ");			
					 

	}

	static void swap(int f,int s)
	{
		long c=a[f];
		a[f]=a[s];
		a[s]=c;
	}
}		