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 mod = 1e9 + 7;
const int N = 1e3 + 10;
const int inf = 2e9;
const double eps = 1e-7;
const long long INF = (long long)1e18;
int a[N];
int main() {
  int n;
  scanf("%d", &(n));
  for (int i = 0; i < (n); ++i) scanf("%d", &(a[i]));
  sort(a, a + n);
  int k = n - 1;
  int cnt = 0, i = 0;
  while (cnt < n) {
    cout << a[i++] << " ";
    cnt++;
    if (cnt < n) {
      cout << a[k--] << " ";
      cnt++;
    }
  }
  return 0;
}
