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 Main {
static int inv;
public static void main(String[] args) throws Exception {
Scanner sc = new Scanner(System.in);
PrintWriter out = new PrintWriter(System.out);
int n=sc.nextInt();
int[] arr=new int[n];
for (int i=0;i<n;i++)
	arr[i]=sc.nextInt();
int[] sorted=mergeSort(arr,0,n-1);
int[] ans=new int[n];
int i=0;
for (int j=0;j<n;j++){
	ans[j]=sorted[i];
	++j;
	if (j>=n)
		break;
	ans[j]=sorted[n-1-i];
	++i;
}
for (int j=0;j<n;j++)
	System.out.print(ans[j]+" ");
out.flush();
}

static int[]mergeSort(int[]in,int start,int end){
    if (start==end)return new int[]{in[start]};

    int mid=(start+end)/2;
    int[]left=mergeSort(in,start,mid);
    int[]right=mergeSort(in,mid+1,end);
    int[]res= new int[end-start+1];
    int i=0;
    int j=0;
    int idx=0;
    while (i<left.length&&j<right.length){
        if (left[i]<=right[j]){
            res[idx++]=left[i++];
        }
        else{
            res[idx++]=right[j++];
            inv+=left.length-i;

        }
    }
    while (i<left.length){
        res[idx++]=left[i++];
    }
    while (j<right.length){
     res[idx++]=right[j++];
    }
    return res;
}









static class Scanner
    {
        StringTokenizer st;
        BufferedReader br;
 
        public Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
        public Scanner(String file) throws Exception {br = new BufferedReader(new FileReader(file));}
        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public String nextLine()throws IOException{return br.readLine();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public double nextDouble() throws IOException {return Double.parseDouble(next());}
        public char nextChar()throws IOException{return next().charAt(0);}
        public Long nextLong()throws IOException{return Long.parseLong(next());}
        public boolean ready() throws IOException{return br.ready();}
        public void waitForInput() throws InterruptedException {Thread.sleep(30000);}
    }

}