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.lang.reflect.Array;
import java.util.*;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a  = new int[n];
        for(int i=0; i<n ; i++) {
            a[i] = sc.nextInt();
        }

        Arrays.sort(a);

        int[] out = new int[n];
        int j = n-1;
        int k = 0;
        boolean zSort = true;
        for(int i=0; i< n; i++) {
            if((i+1)%2 == 0) {
                out[i] = a[j--];
            } else {
                out[i] = a[k++];
            }
        }

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



        if(zSort) {
            for(int num: out) {
                System.out.print(num + " ");
            }

        } else {
            System.out.print("Impossible");
        }
    }

}


