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())
x=list(map(int,input().split()))
x.sort()
index=0
index2=0
m=[]
check=0
# print(x)
for i in range(n):
  if i%2==1:
        m.append(x[n-index-1])
        if i!=n-1 and m[i]<m[i-1]:
              check=-1
              
              break
        index+=1
        
  else:
        m.append(x[index2])
        if i!=0 and m[i]>m[i-1]:
              check=-1
              
              
              break
        index2+=1
if check==0:
  for i in range(n-1):
    print(m[i],end=' ')
  print(m[n-1])
else:
  print('Impossible')