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
n = int(raw_input())
num = map(int,raw_input().split())
sort = []
sort.append(min(num))
num.remove(sort[0])
for i in xrange(1,len(num)+1):
	if i%2!=0:
		sort.append(max(num))
		num.remove(max(num))
	else:
		sort.append(min(num))
		num.remove(min(num))
find = True
for i in xrange(1,len(sort)):
	if ((i+1)%2==0 and sort[i]<sort[i-1]) or ((i+1)%2!=0 and sort[i]>sort[i-1]):
		find = False
if find:
	print ' '.join(str(x) for x in sort)
else:
	print "Impossible"

