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
/**
 * Created by alanguo on 4/28/16.
 */
import java.util.*;
public class zsort {
    public static void main (String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] arr = new int[n];
        for(int i = 0 ; i < n; i++){
            arr[i] = in.nextInt();
        }
        Arrays.sort(arr);
        for(int i = 1; i < n; i++) {
            if(i%2==0) { //odd
                if(arr[i]>arr[i-1]){
                    int temp = arr[i];
                    arr[i] = arr[i-1];
                    arr[i-1] = temp;
                }
                if(i>=2) {
                    if (!(arr[i - 1] >= arr[i - 2])) {
                        System.out.println("IMPOSSIBLE");
                        return;
                    }
                }
            }
            else if (i%2==1) { //even
                if(arr[i]<arr[i-1]){
                    int temp = arr[i];
                    arr[i] = arr[i-1];
                    arr[i-1] = temp;
                }
                if(i>=2) {
                    if (!(arr[i - 1] <= arr[i - 2])) {
                        System.out.println("IMPOSSIBLE");
                        return;
                    }
                }
            }
        }
        for(int i = 0; i < n; i++){
            System.out.print(arr[i]+" ");
        }
    }
}
