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
# -*- coding: utf-8 -*-
"""
Created on Fri Jan 19 18:32:41 2018

@author: mohammad.daud
"""

import sys
n = int(input())
arr = list(map(int, input().split()))
arr.sort()
answer = [0]*1001
answer[0] = arr[0]
i = 1
j = n-1
iterx = 1
while(iterx < n):
    if((iterx+1) %2 == 0):
        answer[iterx] = arr[j]
        j=j-1
        if(answer[iterx] < answer[iterx-1]):
            print("Impossible")
            sys.exit()
    else:
        answer[iterx] = arr[i]
        i=i+1
        if(answer[iterx] > answer[iterx-1]):
            print("Impossible")
            sys.exit()
    iterx = iterx+1
for diggy in range(0, n):
    print (answer[diggy])
