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;
void faster() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
const long long INF = 1e18;
const long double pi = acos(-1);
const long long MAXN = 1e5 + 123;
long long n, a[MAXN], b[MAXN];
int main() {
  faster();
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }
  sort(a + 1, a + n + 1);
  int i, j;
  for (i = 1, j = 1; j <= n; ++i, j += 2) {
    b[j] = a[i];
  }
  for (j = 2; j <= n; ++i, j += 2) {
    b[j] = a[i];
  }
  for (i = 1; i <= n; ++i) {
    cout << b[i] << ' ';
  }
  return 0;
}
