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 n, a;
vector<int> v, vec;
bool check() {
  int pre = vec[0];
  for (int i = 2; i < n; i += 2) {
    if (pre == 1 || pre <= vec[i]) {
      pre = vec[i];
    } else {
      return false;
    }
  }
  pre = vec[1];
  for (int i = 3; i < n; i += 2) {
    if (pre >= vec[i]) {
      pre = vec[i];
    } else {
      return false;
    }
  }
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a;
    v.push_back(a);
  }
  sort((v).begin(), (v).end());
  int N = n;
  while (N--) {
    vec.push_back(v[0]);
    v.erase(v.begin());
    reverse((v).begin(), (v).end());
  }
  if (check()) {
    for (auto v : vec) cout << v << " ";
    cout << endl;
  } else
    cout << "Impossible\n";
  return 0;
}
