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;
long long int extgcd(long long int a, long long int b, long long int& x,
                     long long int& y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    int g = extgcd(b, a % b, y, x);
    y -= a / b * x;
    return g;
  }
}
long long int hcf(long long int a, long long int b) {
  if (b > a) return (hcf(b, a));
  if (a % b == 0) return b;
  return (hcf(b, a % b));
}
long long int modpow(long long int a, long long int b) {
  long long int res = 1;
  a %= 1000000007;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % 1000000007;
    a = a * a % 1000000007;
  }
  return res;
}
int a[1005];
int main() {
  int n;
  cin >> n;
  for (int i = (int)0; i < (int)n; ++i) cin >> a[i];
  sort(a, a + n);
  int i = 0, j = n - 1;
  while (i <= j) {
    if (i == j)
      cout << a[i];
    else
      cout << a[i] << " " << a[j] << " ";
    --j;
    ++i;
  }
  return 0;
}
