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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Jun 30 11:36:12 2020

@author: shailesh
"""

n = int(input())


a = [int(i) for i in input().split()]


a.sort()

even_positions = a[(n+1)//2:]

odd_positions = a[:(n+1)//2]

l = []
for i in range(len(even_positions)):
    l.append(str(odd_positions[0]))
    l.append(str(even_positions[0]))
    odd_positions.pop(0)
    even_positions.pop(0)

if len(odd_positions)!= 0:
    l.append(str(odd_positions[0]))


print(' '.join(l))