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
#include <bits/stdc++.h>
void lire_input() { freopen("input.txt", "r", stdin); }
void ecrire_output() { freopen("output.txt", "w", stdout); }
using namespace std;
int table[1010];
int ans[1010];
int main() {
  int n, x;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> x;
    table[i] = x;
  }
  sort(table, table + n);
  int indice_min = 0, indice_max = n - 1;
  bool boolean = true;
  for (int i = 0; i < n; i++) {
    if ((i + 1) % 2 == 1) {
      ans[i] = table[indice_min];
      indice_min++;
    } else {
      ans[i] = table[indice_max];
      indice_max--;
    }
    if (((indice_max <= 0) || (indice_min >= n - 1)) && (i < n - 1))
      boolean = false;
  }
  if (boolean == true) {
    for (int i = 0; i < n; i++) cout << ans[i] << " ";
    cout << endl;
  } else
    cout << "Impossible" << endl;
  return 0;
}
