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
from sys import stdin
n = int(stdin.readline())
a = list(map(int, stdin.readline().split()))
a.sort()

half = int(len(a) / 2)
if len(a) % 2 == 1:
    half += 1


odd = sorted(a[:half])
even = sorted(a[half:], reverse=True)

l = zip(odd, even)


next_ind = 0
next_left = 1
while 1:
    if next_left:
        if next_ind >= len(odd):
            break;
        print(odd[next_ind], '', end="")
    else:
        if next_ind >= len(even):
            break;
        print(even[next_ind], '', end="")
        next_ind += 1
    next_left = 1 - next_left