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.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] arr = new int [n];
		String s = br.readLine();
		StringTokenizer st = new StringTokenizer(s);
		for(int i=0; i<n; i++)
			arr[i]=Integer.parseInt(st.nextToken());
		for(int i = 0; i < n; i++) {
			if(i%2==0)
			{	int minValue = arr[i], minIndex = i;
				for(int j = i + 1; j < n; j++) {
					if(arr[j] < minValue) {
						minValue = arr[j];
						minIndex = j;
					}
				}
				int temp = arr[i];
				arr[i] = minValue;
				arr[minIndex] = temp;
			}
			else
			{
				int maxValue = arr[i], maxIndex = i;
				for(int j = i + 1; j < n; j++) {
					if(arr[j] > maxValue) {
						maxValue = arr[j];
						maxIndex = j;
					}
				}
				int temp = arr[i];
				arr[i] = maxValue;
				arr[maxIndex] = temp;
			}
		}
		for(int i=0; i<n; i++)
		{
			System.out.print(arr[i]);
			if(i!=n-1)
				System.out.print(" "); 
		}
	}

}
			        		 			 		 	  		  	 	