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
//package main;

import java.io.*;
import java.util.*;
import java.awt.Point;
import java.math.BigInteger;

public final class Main {
    BufferedReader br;
    StringTokenizer stk;

    public static void main(String[] args) throws Exception {
        new Main().run();
    }
    
    {
        stk = null;
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    
    void run() throws Exception {
        int n = ni();
        int[] a = new int[n];
        for(int i=0; i<n; i++) a[i] = ni();
        
        Arrays.sort(a);
        
        for(int i=1; i<n; i++) {
            if(i % 2 == 0) {
                if(a[i] > a[i - 1]) {
                    int temp = a[i - 1];
                    a[i - 1] = a[i];
                    a[i] = temp;
                }
            } else {
                if(a[i - 1] > a[i]) {
                    int temp = a[i - 1];
                    a[i - 1] = a[i];
                    a[i] = temp;
                }
            }
        }
        
        pl(ok(a) ? string(a) : "Impossible");
    }
    
    boolean ok(int[] a) {
        for(int i=1; i<a.length; i++) {
            if(i % 2 == 0) {
                if(a[i] > a[i - 1]) return false;
            } else {
                if(a[i - 1] > a[i]) return false;
            }
        }
        return true;
    }
    
    String string(int[] a) {
        StringBuilder res = new StringBuilder(a.length << 2);
        for(int num : a) res.append(num).append(" ");
        res.deleteCharAt(res.length() - 1);
        return res.toString();
    }
    
    //Reader & Writer
    String nextToken() throws Exception {
        if (stk == null || !stk.hasMoreTokens()) {
            stk = new StringTokenizer(br.readLine(), " ");
        }
        return stk.nextToken();
    }

    String nt() throws Exception {
        return nextToken();
    }

    String ns() throws Exception {
        return br.readLine();
    }

    int ni() throws Exception {
        return Integer.parseInt(nextToken());
    }

    long nl() throws Exception {
        return Long.parseLong(nextToken());
    }

    double nd() throws Exception {
        return Double.parseDouble(nextToken());
    }

    void p(Object o) {
        System.out.print(o);
    }

    void pl(Object o) {
        System.out.println(o);
    }
}