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;
inline int Readin() {
  int K = 0;
  char C = ' ';
  while (C < '0' or C > '9') C = getchar();
  while (C <= '9' and C >= '0')
    K = (K << 1) + (K << 3) + C - '0', C = getchar();
  return K;
}
const int MaxN = 1000 + 5;
int N, Nn, A[MaxN];
int main() {
  N = Readin();
  Nn = N >> 1;
  for (register int i = 0; ++i <= N; A[i] = Readin())
    ;
  sort(A + 1, A + 1 + N);
  for (register int i = 1; i <= Nn; ++i) printf("%d %d ", A[i], A[N - i + 1]);
  if (N & 1) printf("%d ", A[Nn + 1]);
  return not printf("\n");
}
