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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> a(n + 1), b(n + 1);
  for (int i = 1; i <= n; i++) cin >> a[i];
  vector<bool> flags(n + 1);
  for (int i = 1; i <= n; i++) {
    if (i & 1) {
      int mini = 1000000000 + 2;
      int pos = -1;
      for (int j = 1; j <= n; j++) {
        if (flags[j]) continue;
        if (a[j] < mini) {
          mini = a[j];
          pos = j;
        }
      }
      if (pos == -1) {
        cout << "Impossible" << '\n';
        return 0;
      } else {
        b[i] = a[pos];
        flags[pos] = true;
      }
    } else {
      int maxi = -1;
      int pos = -1;
      for (int j = 1; j <= n; j++) {
        if (flags[j]) continue;
        if (a[j] > maxi) {
          maxi = a[j];
          pos = j;
        }
      }
      if (pos == -1) {
        cout << "Impossible" << '\n';
        return 0;
      } else {
        b[i] = a[pos];
        flags[pos] = true;
      }
    }
  }
  for (int i = 1; i <= n; i++) cout << b[i] << " ";
  cout << '\n';
  return 0;
}
