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 num[1111];
int ans[1111];
int main() {
  int n;
  while (~scanf("%d", &n)) {
    for (int i = 1; i <= n; i++) {
      scanf("%d", &num[i]);
    }
    sort(num + 1, num + 1 + n);
    int val = 0;
    int flag = 1;
    for (int i = 1; i <= n; i++) {
      if (flag == 1)
        ans[++val] = num[(val + 1) / 2];
      else
        ans[++val] = num[n - val / 2 + 1];
      flag *= -1;
    }
    for (int i = 1; i <= n; i++) {
      if (i % 2 == 0) {
        if (ans[i] < ans[i - 1]) {
          puts("Impossible");
          return 0;
        }
      } else if (i > 1) {
        if (ans[i] > ans[i - 1]) {
          puts("Impossible");
          return 0;
        }
      }
    }
    for (int i = 1; i <= n; i++) {
      printf("%d ", ans[i]);
    }
    puts("");
  }
}
