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 n, a[1100], b[1100];
int main() {
  while (~scanf("%d", &n)) {
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);
    sort(a, a + n);
    for (int i = 0; i < n; i++) {
      if (i & 1) {
        b[i] = a[n - 1 - i / 2];
      } else {
        b[i] = a[i / 2];
      }
    }
    int flag = 0;
    for (int i = 1; i < n; i++) {
      if (i & 1) {
        if (b[i] < b[i - 1]) {
          flag = 1;
          break;
        }
      } else {
        if (b[i] > b[i - 1]) {
          flag = 1;
          break;
        }
      }
    }
    if (flag) {
      printf("Impossible\n");
    } else {
      for (int i = 0; i < n - 1; i++) printf("%d ", b[i]);
      printf("%d\n", b[n - 1]);
    }
  }
  return 0;
}
