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>
using namespace std;
bool compare_first(pair<int, int> a, pair<int, int> b) {
  return a.first < b.first;
}
bool compare_second(pair<int, pair<int, int> > a,
                    pair<int, pair<int, int> > b) {
  return a.second.first < b.second.first;
}
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  int arr[n];
  for (int index = 0; index < n; index++) cin >> arr[index];
  sort(arr, arr + n);
  for (int index = 0; index < n / 2; index++)
    cout << arr[index] << " " << arr[n - 1 - index] << " ";
  if (n % 2) cout << arr[n / 2] << endl;
  return 0;
}
