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.lang.reflect.Array;
import java.util.*;

public class Rough {
	public static void MergeSort(int[] arr, int start, int end) {
		if (start == end)
			return;
		int mid = (start + end) / 2;
		MergeSort(arr, start, mid);
		MergeSort(arr, mid + 1, end);
		merge(arr, start, mid, end);
	}

	public static void merge(int[] arr, int start, int mid, int end) {
		int start1 = start;
		int end1 = mid;
		int start2 = mid + 1;
		int end2 = end;
		int[] temp = new int[end - start + 1];
		int i = 0;
		while (start1 <= end1 || start2 <= end2) {

			if (start1 > end1)
				temp[i++] = arr[start2++];
			else if (start2 > end2)
				temp[i++] = arr[start1++];
			else if (arr[start1] > arr[start2])
				temp[i++] = arr[start2++];
			else
				temp[i++] = arr[start1++];

		}
		for (i = 0; i < temp.length; i++) {
			arr[start++] = temp[i];
		}
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();
		int[] arr = new int[x];
		for (int i = 0; i < arr.length; i++)
			arr[i] = sc.nextInt();
		MergeSort(arr, 0, arr.length - 1);

		int j = arr.length - 1;
		int i = 0;
		while (i <= j) {
			System.out.print(arr[i]+" ");
			i++;
			if(i<=j)
				System.out.print(arr[j] + " ");
			j--;
		}
	}
}