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() {
  int n;
  while (cin >> n) {
    vector<int> vt;
    for (int i = 0; i < n; i++) {
      int k;
      cin >> k;
      vt.push_back(k);
    }
    sort(vt.begin(), vt.end());
    vector<int> ans;
    int m = vt.size() - 1;
    int l = 0;
    int flag = 0;
    for (int i = 1; i <= n; i++) {
      if (i % 2) {
        if (m == l and ans.size() != 0 and vt[m] > ans[ans.size() - 1])
          flag = 1;
        else
          ans.push_back(vt[l++]);
      } else {
        if (m == l and ans.size() != 0 and vt[m] < ans[ans.size() - 1])
          flag = 1;
        else
          ans.push_back(vt[m--]);
      }
    }
    if (flag)
      cout << "Impossible\n";
    else {
      for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
    }
    cout << endl;
  }
}
