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
# testing
def getArr(f):
    return [f(x) for x in raw_input().strip().split(' ')]

def gi():
    return int(raw_input().strip())

n = gi()
A = getArr(int)
A.sort()

A_ = A[:]
l = 0; r = n-1
ind = 0

while (r >= l):
    A_[ind] = A[l]
    l += 1; ind+=1
    if (r >= l):
        A_[ind] = A[r]
        r -= 1;ind+=1


print ' '.join([str(x) for x in A_])
