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 long long inf = 0x3f3f3f3f;
int n;
const int maxn = 1000 + 5;
long long a[maxn];
int main() {
  while (scanf("%d", &n) == 1) {
    memset(a, 0, sizeof(a));
    for (int i = 1; i <= n; i++) scanf("%I64d", a + i);
    sort(a + 1, a + 1 + n);
    for (int i = 1; i < n; i++) {
      if (i % 2 == 0 && a[i] < a[i + 1]) {
        swap(a[i], a[i + 1]);
      }
    }
    for (int i = 1; i <= n; i++) {
      printf("%I64d%c", a[i], i == n ? '\n' : ' ');
    }
  }
  return 0;
}
