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
def z_sort(chris_christie):
    ted_cruz = [int(x) for x in chris_christie]
    ted_cruz.sort()
    jeb_bush = []
    high = len(ted_cruz) - 1
    low = 0
    jeb_bush = []
    for x in range(0, len(ted_cruz)):
        if (x+1) % 2 != 0: #index is odd
            jeb_bush.append(ted_cruz[low])
            low = low + 1
        else:
            jeb_bush.append(ted_cruz[high])
            high = high - 1
    answer = str(jeb_bush[0])
    for x in range(1, len(jeb_bush)):
        answer = answer + " "
        answer = answer + str(jeb_bush[x])
    return answer
    

n = raw_input()
donald_trump = raw_input().split(' ')
print z_sort(donald_trump)
