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.Arrays;

public class ZSort {

	public static void main(String[] args) throws IOException {

		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		
		int size = Integer.valueOf(reader.readLine());
		int[] elements = Arrays.stream(reader.readLine().split(" ")).mapToInt(element -> Integer.valueOf(element)).sorted().toArray();
		
		if (size != elements.length) {
			throw new IllegalStateException("invalid array size");
		}
		
		int[] newArray = new int[elements.length];
		for (int i = 0, firstElementsIndex = 0; i < newArray.length; i += 2, firstElementsIndex++) {
			newArray[i] = elements[firstElementsIndex];
		}
		
		for (int i = 1,lastElementsIndex = newArray.length - 1; i < newArray.length; i += 2, lastElementsIndex--) {
			newArray[i] = elements[lastElementsIndex];
		}

		for (int i = 1; i < newArray.length; i++) {
			if (i % 2 == 0 && newArray[i] > newArray[i - 1]) {
				System.out.println("Impossible");
				return;
			}
			
			if (i % 2 == 1 && newArray[i] < newArray[i - 1]) {
				System.out.println("Impossible");
				return;
			}
		}
		
		for (int i = 0; i < newArray.length; i++) {
			System.out.print(newArray[i]);
			System.out.print(" ");
		}

		
	}

}