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, i, a[1005], k = 0, b[1005];
  bool flag = 0;
  scanf("%d", &n);
  for (i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
  }
  sort(a, a + n);
  for (i = 0; i < n / 2; ++i) {
    b[k] = a[i];
    b[k + 1] = a[n - 1 - i];
    k += 2;
  }
  if (n % 2 == 1) {
    b[k] = a[n / 2];
    k++;
  }
  for (i = 1; i < k; ++i) {
    if (i % 2 == 1) {
      if (b[i] < b[i - 1]) {
        flag = 1;
      }
    } else {
      if (b[i] > b[i - 1]) {
        flag = 1;
      }
    }
  }
  if (!flag) {
    for (i = 0; i < k; ++i) {
      printf("%d ", b[i]);
    }
  } else {
    printf("Impossible\n");
  }
}
