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

n = int(input())

numero = input().split()
for i in range(n):
    numero[i] = int(numero[i])


if n == 1:
    print(numero[0])
else:
    for i in range(1,n):
        if i % 2 != 0 and numero[i] < numero[i-1]:
            auxiliar = numero[i]
            numero[i] = numero[i-1]
            numero[i-1] = auxiliar
        elif i % 2 == 0 and numero[i] > numero[i-1]:
            auxiliar = numero[i]
            numero[i] = numero[i-1]
            numero[i-1] = auxiliar

    respuesta = str(numero[0])
    for i in range(1,n):
        respuesta = respuesta + ' ' + str(numero[i]) 
    print(respuesta)