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 s[6000];
int a[6000];
int ans[6000], op[6000];
int main() {
  int n, m, j, i, t, k, o, l;
  while (scanf("%d", &n) != EOF) {
    for (i = 1; i <= n; i++) {
      scanf("%d", &a[i]);
    }
    sort(a + 1, a + n + 1);
    m = n / 2;
    if (n & 1)
      m = m + 2;
    else
      m = m + 1;
    j = 1;
    for (i = n; i >= m; i--) op[j++] = a[i];
    for (i = 1; i < m; i++) s[i] = a[i];
    l = o = 1;
    for (i = 1; i <= n; i++) {
      if (i & 1)
        ans[i] = s[l++];
      else
        ans[i] = op[o++];
    }
    for (i = 1; i <= n; i++) printf("%d ", ans[i]);
    printf("\n");
  }
  return 0;
}
