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
def z_sort(s):
    z_seq = []
    m = len(s)/2 if len(s) % 2 == 0 else len(s)/2+1
    s.sort()
    s1 = s[:m]
    s2 = s[m:]
    # print s1, s2

    if len(s1) <= len(s2) + 1:
        for i in range(len(s1)):
            z_seq.append(s1[i])
            try:
                z_seq.append(s2[i])
            except IndexError:
                pass

    return z_seq

n = int(raw_input())
s = [int(i) for i in raw_input().split()]

z_seq = z_sort(s)
if len(z_seq):
    for i in z_seq:
        print i,
else:
    print "Impossible"
