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 a[1111], ans[1111];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int N;
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  sort(a, a + N);
  int j = 0;
  for (int i = 0; i < N; i++) {
    if (i % 2 == 0) {
      ans[i] = a[j];
      j++;
    }
  }
  j--;
  int done_till = j, flag = 0;
  j = N - 1;
  for (int i = 0; i < N; i++) {
    if (i % 2 == 1) {
      ans[i] = a[j];
      j--;
      if (j == done_till) {
        flag = 1;
        break;
      }
    }
  }
  if (flag == 1) {
    int fx = 0;
    for (int i = 0; i < N; i++) {
      if (ans[i] == 0) {
        fx = 1;
        break;
      }
    }
    if (fx == 1)
      cout << "Impossible" << '\n';
    else {
      for (int i = 0; i < N; i++) cout << ans[i] << ' ';
      cout << '\n';
    }
  } else {
    for (int i = 0; i < N; i++) cout << ans[i] << ' ';
    cout << '\n';
  }
  return 0;
}
