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.*;

/**
 *
 * @author ZOGHBI
 */
public class Contest {
    
    public static void quickSort(int[] arr, int low, int high) {
		if (arr == null || arr.length == 0)
			return;
 
		if (low >= high)
			return;
 
		// pick the pivot
		int middle = low + (high - low) / 2;
		int pivot = arr[middle];
 
		// make left < pivot and right > pivot
		int i = low, j = high;
		while (i <= j) {
			while (arr[i] < pivot) {
				i++;
			}
 
			while (arr[j] > pivot) {
				j--;
			}
 
			if (i <= j) {
				int temp = arr[i];
				arr[i] = arr[j];
				arr[j] = temp;
				i++;
				j--;
			}
		}
 
		// recursively sort two sub parts
		if (low < j)
			quickSort(arr, low, j);
 
		if (high > i)
			quickSort(arr, i, high);
	}
    
    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
                
        int [] l= new int[n];
        
        for(int i=0;i<n;i++)
            l[i]=sc.nextInt();
        
        
        int right = n-1;
        quickSort(l, 0, right);        
        
        
        for(int left=0;left<n/2;left++){
            System.out.print(l[left]+ " ");            
            System.out.print(l[(right-left)]+ " ");            
        }
        if(!(n%2 == 0))
            System.out.print(l[(right/2)]);
        
    }
}