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())
b=sorted(a)
ans=[b[0]]
l=1
r=n-1
while l<=r:
    if len(ans)%2==0:
        ans.append(b[l])
        l+=1
    else:
        ans.append(b[r])
        r-=1
poss=True
for i in xrange(1,len(ans)):
    if i%2 and ans[i]<ans[i-1] or i%2==0 and ans[i]>ans[i-1]:
        poss=False
if poss:print ' '.join(map(str,ans))
else:print 'Impossible'
        
