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.*;
import java.io.*;
import java.math.*;

public class Main {

    static Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws Exception {

        int n = sc.nextInt();
        int[] arr = new int[n];

        for(int i = 0; i < n; ++i)
            arr[i] = sc.nextInt();


        Arrays.sort(arr);
        ArrayDeque<Integer> ad = new ArrayDeque<>();

        for(int x : arr) ad.add(x);

        for(int i= 0; i < n; ++i)
            out.print((i & 1) == 0 ? ad.pollFirst() + " " : ad.pollLast() + " ");


        out.flush();
        out.close();
        sc.close();
    }

    static final int MOD = (int) 1e9 + 7;
    static final double PI = 3.14159265358979323846;

    // takes array input
    public static int[] init(int n) {

        int[] arr = new int[n];

        for (int i = 0; i < n; ++i)
            arr[i] = sc.nextInt();

        return arr;
    }

    // finds GCD of two number
    public static int gcd(int a, int b) {

        if (a == 0) {
            return b;
        }

        return gcd(b % a, a);
    }

    // checks whether a number is prime or not
    public static boolean prime(int n) {

        if (n < 2)
            return false;

        for (int i = 2; i * i <= n; ++i)
            if (n % i == 0)
                return false;

        return true;
    }
}
