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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class B652 {

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		for (int i = 0; i < arr.length - 1; i++) {
			if (i % 2 == 0 && arr[i] > arr[i + 1]) {
				swap(arr, i, i+1);
			} else if (i % 2 == 1 && arr[i] < arr[i + 1]){
				swap(arr, i, i+1);
			}
		}
		boolean posible = true;
		for (int i = 0; i < arr.length-1; i++) {
			if (i % 2 == 0 && arr[i] > arr[i + 1]) {
				posible = false;
				break;
			} else if (i % 2 == 1 && arr[i] < arr[i + 1]){
				posible = false;
				break;
			}
		}
		if (posible) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			
		} else {
			System.out.println("Impossible");
		}
	}

	public static void swap(int[] arr, int i, int j) {
		int tmp = arr[i];
		arr[i] = arr[j];
		arr[j] = tmp;
	}

	public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(nextToken());
		}

		long nextLong() {
			return Long.parseLong(nextToken());
		}

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

}
