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 logging
import copy
import sys

logging.basicConfig(stream=sys.stderr, level=logging.DEBUG)

#def solve(firstLine):
def solve(length, line):
    length = length[0]
    line.sort()
    r = [-1] * length

    for i in range(0,length,2):
        r[i] = line[0]
        del line[0]

    line.sort(reverse=True)

    for i in range(1,length,2):
        r[i] = line[0]
        del line[0]

    resultStr= ' '.join(str(e) for e in r)
    return resultStr

def main():
    firstLine = input().split()
    firstLine = list(map(int, firstLine))
    inputLines = input().split()
    inputLines = list(map(int, inputLines))

        
    #solve(firstLine)
    print(solve(firstLine, inputLines))

def log(*message):
    logging.debug(message)
    
if __name__ == "__main__":
    main()
