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;
const int OO = 1000000000;
const int maxn = 1e5 + 5;
string itos(int x) {
  if (x == 0) return "0";
  string xs = "";
  while (x > 0) {
    xs = char(x % 10 + '0') + xs;
    x /= 10;
  }
  return xs;
}
int main(void) {
  int n, num[1005], ans[1005];
  cin >> n;
  for (int(i) = 0; (i) < (n); (i)++) cin >> num[i];
  sort(num, num + n, greater<int>());
  int x = 0;
  for (int i = 1; i < n; i += 2) {
    ans[i] = num[x];
    x++;
  }
  for (int i = 0; i < n; i += 2) {
    ans[i] = num[x];
    x++;
  }
  for (int i = 1; i < n; i++) {
    if ((i % 2 != 0 && ans[i] < ans[i - 1]) ||
        (i % 2 == 0 && ans[i] > ans[i - 1])) {
      cout << "Impossible" << endl;
      return 0;
    }
  }
  for (int(i) = 0; (i) < (n); (i)++) cout << ans[i] << " ";
  return 0;
}
