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
import sys
input = sys.stdin.readline

############ ---- Input Functions ---- ############


def inp():  # integer inputs
    return(int(input()))


def inlt():  # list inputs
    return(list(map(int, input().split())))


def insr():  # string inputs
    s = input()
    return(list(s[:len(s) - 1]))


def invr():  # integer variable inputs
    return(map(int, input().split()))


def main():
    n = inp()
    arr = inlt()
    arr.sort()
    new_arr = []

    index = 0
    forward = False
    while len(new_arr) < n:
        if forward == False:
            new_arr.append(arr[index])
            forward = True
        else:
            forward = False
            new_arr.append(arr[-(index+1)])
            index += 1

    print(" ".join(map(str, new_arr)))


if __name__ == "__main__":
    main()
