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 main() {
  int n;
  int a[1020];
  while (scanf("%d", &n) != EOF) {
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);
    sort(a, a + n);
    int sa[1020];
    memset(sa, 0, sizeof(sa));
    int i = 0, j = 0;
    while (1) {
      sa[i] = a[j];
      i += 2;
      j++;
      if (j >= ((n + 1) / 2)) break;
    }
    i = 1;
    j = j;
    while (1) {
      sa[i] = a[j];
      i += 2;
      j++;
      if (j >= n) break;
    }
    for (i = n; i >= 1; i--) sa[i] = sa[i - 1];
    int flag = 1;
    i = 2;
    while (1) {
      if (i > n) break;
      if (sa[i] < sa[i - 1]) {
        flag = 0;
        break;
      }
      i += 2;
    }
    i = 3;
    while (1) {
      if (i > n) break;
      if (sa[i] > sa[i - 1]) {
        flag = 0;
        break;
      }
      i += 2;
    }
    if (flag == 1) {
      for (i = 1; i <= n; i++) printf("%d ", sa[i]);
      printf("\n");
    } else
      printf("Impossible\n");
  }
  return 0;
}
