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
count = int(raw_input())
arr = raw_input().split()
arr = [int(x) for x in arr]


flag = False
new_arr = []
for i in xrange(count):
    if i % 2 == 0:
        min1 = min(arr)
        if i == 0 or min1 <= new_arr[-1]:
            arr.remove(min1)
            new_arr.append(min1)
        else:
            flag = True
            break
    else:
        max1 = max(arr)
        if max1 >= new_arr[-1]:
            arr.remove(max1)
            new_arr.append(max1)
        else:
            flag = True
            break

if flag:
    print "Impossible"
else:
    print ' '.join(str(x) for x in new_arr)
