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
import math


n = int(input())
list = list(map(int, input().split()))
list.sort()

small = list[:int(math.ceil(n / 2))]
big = list[int(math.ceil(n / 2)):]

iter = 0
for i in range(n):
    if i % 2 == 0:
        list[i] = small[iter]
    else:
        list[i] = big[iter]
        iter += 1

flag = True
for i in range(n):
    if i % 2 == 0 and (i > 0 and list[i] > list[i - 1] or i < n - 1 and list[i] > list[i + 1]):
        flag = False
        break

if flag:
    print(' '.join(map(str, list)))
else:
    print(-1)
