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())
ch=input()
d=ch.split()
for i in range(n):
    d[i]=int(d[i])
d.sort()
d1=[]
i=0
j=0
while j<n:
    d1.append(d[i])
    j+=1
    if j<n:
        j+=1
        d1.append(d[n-i-1])
    i+=1
B=False
for i in range(n):
    if d1[i]<d1[i-1] and (i+1)%2==0:
        B=True
    if d1[i]>d1[i-1] and (i+1)%2!=0:
        B=True
if B==False:
    for i in d1:
        print(i,end=" ")
else:
    print( "Impossible")
