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())
a=list(map(int,input().split()))
a.sort()
if len(a)%2!=0:
    list1=a[1:(len(a)//2)+1]
    list2=a[(len(a)//2)+1:len(a)]
    res=[[]for i in range(n)]
    res[0]=a[0]
    k1=0
    k2=len(list2)-1
    for i in range(2,len(a)+1):
        if i%2!=0:
            res[i-1]=list1[k1]
            k1=k1+1
        if i%2==0:
            res[i-1]=list2[k2]
            k2=k2-1
if len(a)%2==0:
    
    list1=a[0:(len(a)//2)]
    list2=a[(len(a)//2):len(a)]
    res=[[]for i in range(n)]
    res[0]=a[0]
    k1=1
    k2=len(list2)-1
    for i in range(2,len(a)+1):
        if (i)%2!=0:
            res[i-1]=list1[k1]
            k1=k1+1
        if (i)%2==0:
            res[i-1]=list2[k2]
            k2=k2-1  
print(*res)
    