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 prime[1 << 20];
int numofprimes;
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return (a * (b / gcd(a, b))); }
long long POWER(long long x, long long y, long long m) {
  if (y == 0) return 1;
  if (y % 2 == 0) {
    long long temp = POWER(x, y / 2, m);
    temp *= temp;
    temp %= m;
    return temp;
  }
  long long temp = POWER(x, y - 1, m);
  temp *= x;
  temp %= m;
  return temp;
}
long long POWER(long long x, long long y) {
  if (y == 0) return 1;
  if (y % 2 == 0) {
    long long temp = POWER(x, y / 2);
    temp *= temp;
    return temp;
  }
  long long temp = POWER(x, y - 1);
  temp *= x;
  return temp;
}
void runEratosthenesSieve(int upperBound) {
  int upperBoundSquareRoot = (int)sqrt((double)upperBound);
  bool *isComposite = new bool[upperBound + 1];
  memset(isComposite, 0, sizeof(bool) * (upperBound + 1));
  for (int m = 2; m <= upperBoundSquareRoot; m++) {
    if (!isComposite[m]) {
      prime[numofprimes++] = m;
      for (int k = m * m; k <= upperBound; k += m) isComposite[k] = true;
    }
  }
  for (int m = upperBoundSquareRoot + 1; m <= upperBound; m++)
    if (!isComposite[m]) prime[numofprimes++] = m;
  delete[] isComposite;
}
int a[1010];
int main() {
  ifstream fin("ali");
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  for (int i = 0, j = n - 1; i <= j; i++, j--) {
    if (i == j)
      cout << a[i] << '\n';
    else
      cout << a[i] << " " << a[j] << " ";
  }
}
