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 zsort(n, A):
    A.sort()
    return [A[-(i+1)//2] if i % 2 else A[i//2] for i in range(n)]


def main():
    n = readint()
    A = readintl()
    print(' '.join(map(str, zsort(n, A))))

##########

import sys


def readint():
    return int(input())


def readinti():
   return map(int, input().split())


def readintl():
   return list(readinti())


def readintll(k):
    return [readintl() for _ in range(k)]


def log(*args, **kwargs):
    print(*args, **kwargs, file=sys.stderr)


if __name__ == '__main__':
    main()
