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.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class trainswapping {
	static final long INF = Integer.MAX_VALUE;
	static int m = 0;

	static void mergeSort(long[] a, int b, int e) {
		if (b < e) {
			int q = (b + e) / 2;
			mergeSort(a, b, q);
			mergeSort(a, q + 1, e);
			merge(a, b, q, e);
		}
	}

	static void merge(long[] a, int b, int mid, int e) {
		int n1 = mid - b + 1;
		int n2 = e - mid;
		long[] L = new long[n1 + 1], R = new long[n2 + 1];

		for (int i = 0; i < n1; i++)
			L[i] = a[b + i];
		for (int i = 0; i < n2; i++)
			R[i] = a[mid + 1 + i];
		L[n1] = R[n2] = INF;

		for (int k = b, i = 0, j = 0; k <= e; k++)
			if (L[i] <= R[j])
				a[k] = L[i++];
			else {

				a[k] = R[j++];
			}
	}

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

		int n = Integer.parseInt(br.readLine());
		st = new StringTokenizer(br.readLine());
		long[] Arr = new long[n];
		for (int i = 0; i < n; i++) {
			Arr[i] = Long.parseLong(st.nextToken());
		}
		Arrays.sort(Arr);
		long[] Arr1 = new long[n];
		int mid = (n + 1) / 2;
		int k = n;
		int j = 0;
		while (k-- > 0) {
			Arr1[k] = ((k & 1) == 0) ? Arr[j++] : Arr[mid++];

		}
		System.out.print(Arr1[0]);
		for (j = 1; j < n; j++) {
			System.out.print(" " + Arr1[j]);
		}

	}

}
