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;
set<int> st;
set<int>::iterator it;
map<int, int> mp;
map<int, int>::iterator itr;
queue<int> q;
stack<int> stk;
priority_queue<int> pq;
vector<int> v;
vector<int> v1;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL), cout.tie(NULL);
  long long a, p;
  cin >> a;
  p = a;
  while (a--) {
    int l;
    cin >> l;
    v.push_back(l);
  }
  for (int i = 0; i < p; i += 2)
    for (int j = i + 1; j < p; j++)
      if (v[i] > v[j]) swap(v[i], v[j]);
  for (int i = 1; i < p; i += 2)
    for (int j = i + 1; j < p; j++)
      if (v[i] < v[j]) swap(v[i], v[j]);
  for (int i = 0; i < v.size(); i++) cout << v[i] << " ";
}
