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;
  cin >> n;
  int *v = new int[n];
  for (int i = 0; i < n; i++) cin >> v[i];
  sort(v, v + n);
  int *a = new int[n];
  int l = 0, r = n - 1;
  int c = 0;
  while (l <= r) {
    a[c] = v[l];
    l++;
    c++;
    if (l <= r) {
      a[c] = v[r];
      r--;
      c++;
    }
  }
  bool can = true;
  for (int i = 0; i < n && can; i++) {
    if ((i + 1) % 2 == 0) {
      if (a[i] < a[i - 1]) can = false;
    } else {
      if (i > 0)
        if (a[i] > a[i - 1]) can = false;
    }
  }
  if (can) {
    for (int i = 0; i < n; i++) cout << a[i] << " ";
    cout << endl;
  } else
    puts("Impossible");
  return 0;
}
