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.io.*;
import java.util.*;

public class ZSort{
    public static void main(String[] args) throws IOException, InterruptedException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        // int[] freq = new int[(int)1e9];
        int n = Integer.parseInt(br.readLine());
        Integer[] arr = new Integer[n];
        // int ogN = n;
        StringTokenizer st = new StringTokenizer(br.readLine());
        // while(n-->0){
        for(int l = 0; l<n; l++){
            // freq[Integer.parseInt(st.nextToken())-1]++;
            arr[l] = Integer.parseInt(st.nextToken());
        }
        Arrays.sort(arr);
        int i = 0;
        int j = n-1;
        int k = 0;
        int[] res = new int[n];
        while(k<n){
            res[k++] = arr[i++];
            if(k==n) break;
            res[k++] = arr[j--];
        }
        // System.out.println(Arrays.toString(res));
        for(int l = 0; l<n-1; l++)
            System.out.print(res[l]+" ");
        System.out.print(res[n-1]);
    }
}