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.awt.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class problem652B {


	static boolean check(int[] arr){
		for(int i=0;i<arr.length-1;i=i+2){
			if(arr[i]>arr[i+1]) return false;
		}
		for(int i=1;i<arr.length-1;i=i+2){
			if(arr[i]<arr[i+1]) return false;
		}
		return true;
	}
	static boolean check(ArrayList<Integer> list){
		for(int i=0;i<list.size()-1;i=i+2){
			if(list.get(i)>list.get(i+1)) return false;
		}
		for(int i=1;i<list.size()-1;i=i+2){
			if(list.get(i)<list.get(i+1)) return false;
		}
		return true;
	}
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] arr = new int[n];
		for(int i=0;i<n;i++) arr[i] = sc.nextInt();
		/*
		for(int i=0;i<n-1;i++){
			for(int j=i+1;j<n;j++){
				int[] newarr = arr.clone();
				int tmp = newarr[i];
				newarr[i] = newarr[j];
				newarr[j] = tmp;
				if(check(newarr)){
					arr = newarr.clone();
					break;
				}
			}
		}
		*/
		Arrays.sort(arr);
		ArrayList<Integer> list1 = new ArrayList<>();
		ArrayList<Integer> list2 = new ArrayList<>();
		for(int i=0;i<n;i++){
			if(n%2==0){
				if(i<n/2) list1.add(arr[i]);
				else list2.add(arr[i]);
			}
			else{
				if(i<n/2+1) list1.add(arr[i]);
				else list2.add(arr[i]);
			}
		}
		ArrayList<Integer> ans = new ArrayList<>();
		for(int i=0;i<list2.size();i++){
			ans.add(list1.get(i));
			ans.add(list2.get(i));
		}
		if(arr.length%2==1) ans.add(list1.get(list1.size()-1));
		
		
		if(check(ans)){
			String str = "";
			for(int i=0;i<n;i++){
				str += ans.get(i)+" ";
			}
			System.out.println(str.substring(0,str.length()-1));
		}
		else System.out.println("Impossible");
		
		/*
		if(check(arr)){
			String str = "";
			for(int i=0;i<n;i++){
				str += arr[i]+" ";
			}
			System.out.println(str.substring(0,str.length()-1));
		}
		else System.out.println("Impossible");
		*/
	}


}
