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())
a = map(int, raw_input().split(" "))

# N, a = 4, [1, 2, 2, 1]
# N, a = 5, [1, 3, 2, 2, 5]

# import math

# import random
# N = 51
# a = [random.choice(range(5000)) for i in range(N)]

a.sort()
b = []
if N % 2 == 0:
	for i in range(N // 2):
		b.append(i)
		b.append(i + N // 2)
else:
	for i in range(N // 2):
		b.append(i)
		b.append(i + N // 2 + 1)
	b.append(N // 2)
print " ".join(map(str, [a[i] for i in b]))
				  					 	  	 			  		  				