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;
const int maxn = 1000 + 10;
int a[maxn];
int n;
int b[maxn];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", a + i);
  sort(a + 1, a + 1 + n);
  int num = 1;
  int i = 1;
  int j = (n % 2 == 0) ? n / 2 + 1 : n / 2 + 2;
  for (; num <= n; i++, j++) {
    b[num] = a[i];
    num++;
    b[num] = a[j];
    num++;
  }
  int flag = 1;
  for (int i = 2; i <= n; i += 2) {
    if (b[i] < b[i - 1]) {
      flag = 0;
      break;
    }
  }
  if (flag)
    for (int i = 3; i <= n; i += 2) {
      if (b[i] > b[i - 1]) {
        flag = 0;
        break;
      }
    }
  if (flag) {
    for (int i = 1; i <= n; i++) {
      printf("%d", b[i]);
      if (i == n)
        printf("\n");
      else
        printf(" ");
    }
  } else
    printf("Impossible\n");
  return 0;
}
