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())
n1=list(map(int,input().split()))
n1.sort()
lst=[]
k=0
for i in range(n//2):
    lst.append(n1[0])
    lst.append(n1[-1])
    n1.remove(n1[0])
    n1.remove(n1[-1])
if(n1!=[]):
    lst.append(n1[0])
for j in range(1,len(lst)-1):
    if((j-1)==0):
        continue
    else:
        if((j)%2==0):
            if(lst[j-1]>=lst[j-2]):
                continue
            else:
                k=k+1
                break
        else:
            if(lst[j-1]<=lst[j-2]):
                continue
            else:
                k=k+1
                break
if(k>0):
    print('IMPOSSIBLE')
else:
    for j in lst:
        print(j,end=' ')

