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 input_list():
    s = raw_input()
    s = s.split(' ')
    l = [0 for i in range(len(s))]
    for i in range(len(s)):
        l[i] = int(s[i])
    return l

n = int(raw_input())
##if n == 1:
##    print "Impossible"
a = input_list()
a.sort()
if n % 2 == 0:
    a1 = a[:(n / 2)]
    a2 = a[(n / 2):]
else:
    a1 = a[:(n / 2 + 1)]
    a2 = a[(n / 2 + 1):]
a_z = [0 for i in range(n)]

i = j = k = 0
while i < n:
    if i % 2 == 0:
        a_z[i] = a1[j]
        j += 1
    else:
        a_z[i] = a2[k]
        k += 1
    i += 1

for i in a_z:
    print i,
print
        
