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;
template <class T>
bool umin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool umax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
int arr[100009], ans[100009];
int main() {
  int a;
  scanf("%d", &a);
  for (int i = 1; i <= a; i++) scanf("%d", arr + i);
  sort(arr + 1, arr + a + 1);
  int st = 1, en = a;
  for (int i = 1; i <= a; i += 2) ans[i] = arr[st++];
  for (int i = 2; i <= a; i += 2) ans[i] = arr[en--];
  if (a & 1) ans[a + 1] = 2147483647;
  ans[0] = 2147483647;
  for (int i = 1; i <= a; i++) {
    if (i & 1) {
      if (ans[i] > ans[i + 1] or ans[i] > ans[i - 1]) {
        printf("Impossible\n");
        return 0;
      }
    } else {
      if (ans[i] < ans[i + 1] or ans[i] < ans[i - 1]) {
        printf("Impossible\n");
        return 0;
      }
    }
  }
  for (int i = 1; i <= a; i++) printf("%d ", ans[i]);
  printf("\n");
  return 0;
}
