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 a[1001], res[1001];
int main() {
  int i, n, q, flag;
  while (~scanf("%d", &n)) {
    flag = 1;
    q = 0;
    for (i = 0; i < n; i++) scanf("%d", &a[i]);
    sort(a, a + n);
    for (i = 0; i < n; i += 2) res[i] = a[q++];
    for (i = 1; i < n; i += 2) res[i] = a[q++];
    for (i = 1; i < n; i++) {
      if ((i + 1) % 2 == 0) {
        if (res[i] >= res[i - 1])
          continue;
        else
          flag = 0;
      } else {
        if (res[i] <= res[i - 1])
          continue;
        else
          flag = 0;
      }
    }
    if (flag) {
      for (i = 0; i < n; i++) printf("%d ", res[i]);
      printf("\n");
    } else
      printf("Impossible\n");
  }
  return 0;
}
