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 math import ceil
n = int(input())
l = list(map(int,input().split()))

l.sort(reverse = True)
ans = [0] * n

for i in range(0,n//2):   
    ans[i*2+1] = l[i]
    

for i in range(ceil(n/2)):
    ans[2*i] = l[n//2 + i]
    
flag = True

for i in range(n):
    if i % 2 == 1:
        if not(ans[i] >= ans[i-1]):
            flag = False 
            break
    elif i % 2 == 0 and i != 0:
        if not(ans[i] <= ans[i-1]):
            flag = False

if flag:
    print(*ans)
else:
    print("Impossible")