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;
  while (cin >> N) {
    int a[1000] = {0};
    int b[1000] = {0};
    int temp;
    for (int i = 0; i < N; i++) cin >> a[i];
    for (int i = 0; i < N - 1; i++) {
      for (int j = 0; j < N - 1 - i; j++) {
        if (a[j] > a[j + 1]) {
          temp = a[j];
          a[j] = a[j + 1];
          a[j + 1] = temp;
        }
      }
    }
    int j = 0;
    for (int i = 0; i < N; i += 2) {
      b[i] = a[j];
      j++;
    }
    j = N - 1;
    for (int i = 1; i < N; i += 2) {
      b[i] = a[j];
      j--;
    }
    for (int i = 0; i < N; i++) cout << b[i] << " ";
    cout << endl;
  }
  return 0;
}
