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>
int cmpfunc(const void* a, const void* b) {
  return (*(long long int*)a - *(long long int*)b);
}
int main() {
  long long int a[10001] = {0};
  int n;
  scanf("%d", &n);
  int i;
  for (i = 0; i < n; i++) scanf("%lld", &a[i]);
  qsort(a, n, sizeof(long long int), cmpfunc);
  int k = (n % 2 == 0) ? n / 2 : (floor)(n / 2);
  if (n % 2 == 0) {
    for (i = 0; i < k; i++) {
      printf("%lld\n", a[i]);
      printf("%lld\n", a[n - i - 1]);
    }
  } else {
    for (i = 0; i < k; i++) {
      printf("%lld\n", a[i]);
      printf("%lld\n", a[n - i - 1]);
    }
    printf("%lld\n", a[k]);
  }
  return 0;
}
