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>
bool cmp(int a, int b) { return a > b; }
int comp(void const *a, void const *b) {
  int *p, *q;
  p = (int *)a;
  q = (int *)b;
  return (*p - *q);
}
const int N = 3e5 + 2;
const int INF = 0x7FFFFFFF;
using namespace std;
int main() {
  int n, a[1110], aa[1111];
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  sort(a + 1, a + 1 + n);
  int c = 1;
  for (int i = 1; i <= n; i += 2) {
    aa[i] = a[c++];
  }
  for (int i = n / 2 * 2; i >= 1; i -= 2) {
    aa[i] = a[c++];
  }
  for (int i = 1; i < n; i++) cout << aa[i] << " ";
  cout << aa[n] << endl;
  return 0;
}
