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(input())
arr = [int(i) for i in input().split()]

arr.sort()
res = [-1 for i in range(n)]

left, right = 0, n - 1
for i in range(n):
	if (i + 1) % 2 == 1:
		res[i] = arr[left]
		left += 1

	if (i + 1) % 2 == 0:
		res[i] = arr[right]
		right -= 1

for r in res:
	print(r, end=' ')