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;
void solve() {
  vector<long long> v, ans;
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) {
    long long q;
    cin >> q;
    v.push_back(q);
  }
  sort(v.begin(), v.end());
  bool cur = 0;
  while (!v.empty()) {
    if (!cur) {
      cout << v.front();
      v.erase(v.begin());
    } else {
      cout << v.back();
      v.erase(v.begin() + v.size() - 1);
    }
    cout << ' ';
    cur = 1 - cur;
  }
}
signed main() {
  long long t = 1;
  while (t--) solve();
}
