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;
vector<int> v, VV, boro, choto;
int main() {
  int n, st;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> st;
    v.push_back(st);
  }
  if (n == 1) {
    cout << v[0];
    return 0;
  }
  sort(v.begin(), v.end());
  if (n % 2 == 0) {
    for (int i = 0; i <= n / 2 - 1; i++) {
      choto.push_back(v[i]);
    }
    for (int i = n / 2; i <= n - 1; i++) {
      boro.push_back(v[i]);
    }
  } else {
    for (int i = 0; i <= n / 2; i++) {
      choto.push_back(v[i]);
    }
    for (int i = n / 2 + 1; i <= n - 1; i++) {
      boro.push_back(v[i]);
    }
  }
  if (n % 2 == 0) {
    for (int i = 0; i <= min(boro.size(), choto.size()) - 1; i++) {
      VV.push_back(choto[i]);
      VV.push_back(boro[i]);
    }
  } else {
    for (int i = 0; i <= min(boro.size(), choto.size()) - 1; i++) {
      VV.push_back(choto[i]);
      VV.push_back(boro[i]);
    }
    VV.push_back(choto[choto.size() - 1]);
  }
  for (int i = 0; i <= VV.size() - 1; i++) {
    if (i == 0)
      continue;
    else if (i % 2 != 0 && VV[i] < VV[i - 1]) {
      cout << "Impossible";
      return 0;
    } else if (i % 2 == 0 && VV[i] > VV[i - 1]) {
      cout << "Impossible";
      return 0;
    } else
      continue;
  }
  for (int i = 0; i <= VV.size() - 1; i++) cout << VV[i] << " ";
  return 0;
}
