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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class ar {

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (final IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (final IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static boolean[] seen;
    static Map<Integer, Integer> map;
    static Map<Long,Long> lmap;
    static Set<Character> charset;
    static Set<Integer> set;
    static int[] arr;
    static int[][] dp;
    static int rem = (int) 1e9 + 7;
    static List<List<Integer>> graph;
    static int[][] kmv = { { 2, 1 }, { 1, 2 }, { 2, -1 }, { -1, 2 }, { -2, 1 }, { 1, -2 }, { -1, -2 }, { -2, -1 } };
    static char[] car;
    static boolean[] primes;
    static int MAX = (int) 1e4 + 1;
    static double[] dar;
    static long[] lar;

    static void Sieve() {
        primes = new boolean[MAX];
        primes[0] = true;
        primes[1] = true;
        for (int i = 2; i * i < MAX; i++) {
            if (!primes[i]) {
                for (int j = i * i; j < MAX; j += i) {
                    primes[j] = true;
                }
            }
        }
    }

    public static void main(String[] args) throws java.lang.Exception {
        FastReader scn = new FastReader();
    int n=scn.nextInt();
    arr=new int[n];
    for(int i=0;i<n;i++)arr[i]=scn.nextInt();
    Arrays.sort(arr);
    // List<Integer> ans=new ArrayList<>();
    int size=1;
    int fno = arr[0];
    StringBuilder ans = new StringBuilder("" + fno);

    // ans.add(fno);

    int p1=1,p2=n-1;

    while(p1<p2){
        ans.append(" "+arr[p2]);
        ans.append(" "+arr[p1]);
        p1++;
        p2--;
        size+=2;
    }
    if(size<n){
        ans.append(" "+arr[p2]);
    }
    System.out.print(ans);
    
        return;
    }
}