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 math
from math import floor

number = int(input())
array = input().split()
nArray = []
for i in array:
    nArray.append(int(i))
    
nArray.sort()

oddArray = nArray[0:math.ceil(number/2)]
evenArray = nArray[math.ceil(number/2):number]

resultArray = []

for i in range(0,int(number/2)):
    resultArray.append(oddArray[i])
    resultArray.append(evenArray[i])

if (number%2 != 0):
    resultArray.append(oddArray[int(number/2)])
    
String =""

for i in resultArray:
    String += str(i) + " "
    
print (String)
    