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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.ObjectInputStream.GetField;
import java.util.Arrays;

public class p1 {
static int a [] ; 
static int b ; 
public static void main(String[] args) throws NumberFormatException, IOException {
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in)) ; 
     b =Integer.parseInt( bf.readLine());
     int n =b ;
     String [] s = bf.readLine().split(" ") ;
     a = new int [b] ; 
     int a1[] = new int [b] ; 
     for (int i = 0; i < b; i++) {
		a[i] = Integer.parseInt(s[i]);
	}
     for (int i = 0; i < n; i++) {
    	
    	
		   if(i%2 == 0) {
			a1[i] = getMin() ;
			
		}
		else {
		a1[i] = getMax() ;
		
		}
		   
	}
     boolean flag = true ; 
     for (int i = 0; i < a1.length-1; i++) {
		if((i+1)%2 == 0 ) {
			if(a1[i] < a1[i+1]) {
				flag = false ;
			}
		}
		else {
			if(a1[i]>a1[i+1]){
				flag = false;
			}
		}
	}
     
     
 if(flag) {
	 for (int i = 0; i < a1.length; i++) {
		System.out.print(a1[i]+" ");
	}
 }
 else {
	 System.out.println("Impossible");
 }
}


public static int getMax() { 
	int max = a[0] ; 
	int [] arr = new int [--b] ;
	int j = 0 ;
	for (int i = 1; i < a.length; i++) {
		if(a[i] > max ){
			arr[j++] = max ;
			max = a[i];
		}
		else {
			arr[j++] = a[i] ; 
		}
	}
	a = arr ;
	
	return max ;
}
public static int getMin() { 
	int max= a[0] ; 
	int [] arr = new int [--b] ;
	int j = 0 ;
	for (int i = 1; i < a.length; i++) {
		if(a[i] < max ){
			arr[j++] = max ;
			max = a[i];
		}
		else {
			
			arr[j++] = a[i] ; 
		}
	}
	
	a = arr ;
	
	return max ;
}

}
