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())
X = sorted(list(map(int, input().split())))
i, j = 0, N - 1
Step, Check = 0, True
Answer = []
while Step != N:
    if Check:
        Answer.append(X[i])
        i += 1
    else:
        Answer.append(X[j])
        j -= 1
    Check = not Check
    Step += 1
print(*Answer)

# UB_CodeForces
# Advice: Falling down is an accident, staying down is a choice
# Location: Here in Bojnurd
# Caption: So Close man!! Take it easy!!!!
# CodeNumber: 640
