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.util.*;
import java.io.*;

public class Main {

	public static void main(String[] args) throws IOException, InterruptedException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);

		int size = Integer.parseInt(br.readLine());

		int[] a = new int[size];
		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int j = 0; j < size; j++) {
			a[j] = Integer.parseInt(st.nextToken());
		}
		mergesort(a, 0, a.length - 1);
		int[] zsort=new int[size];
		int k=0;
		for (int i = 0; i < zsort.length; i+=2) {
			zsort[i]=a[k++];
		}
		for (int i = size-1; i>-1; i--) {
			if(zsort[i]==0)
				zsort[i]=a[k++];
		}
		pw.print(zsort[0]);
		for (int i = 1; i < zsort.length; i++) {
			pw.print(" "+zsort[i]);
		}
		pw.close();
	}

	public static void mergesort(int[] a, int l, int r) {
		if (l == r)
			return;
		int mid = (r + l) / 2;
		mergesort(a, l, mid);
		mergesort(a, mid + 1, r);
		merge(a, l, r);

	}

	public static void merge(int[] a, int l, int r) {
		int m = (l + r) / 2;
		int i = l;
		int j = m + 1;
		int[] tmp = new int[r - l + 1];
		int k = 0;
		// int ans = 0;
		while (i <= m && j <= r) {
			if (a[i] <= a[j])
				tmp[k++] = a[i++];
			else {
				// ans += m - i + 1;
				tmp[k++] = a[j++];
			}
		}
		while (i <= m) {
			tmp[k++] = a[i++];
		}
		while (j <= r) {
			tmp[k++] = a[j++];
		}
		for (int k2 = 0; k2 < tmp.length; k2++) {
			a[l++] = tmp[k2];
		}
		// return ans;
	}

}
 	    	 		 					 	   	 	   	 	