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())
ls=list(map(int,input().split()))
ls.sort()
i=0
j=len(ls)-1
lsN=[]
while i<=j:
	if i<j:
		lsN.append(ls[i])
		lsN.append(ls[j])
	elif i==j:
		lsN.append(ls[i])
	i=i+1
	j=j-1
s=''
for i in range(n):
	if i<n-1:
		s=s+str(lsN[i])+' '
	elif i==n-1:
		s=s+str(lsN[i])
print(s)
  		 			  				 		  	 							  	