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

#Created by Minsol Jeong
def L2():
    n = int(input())
    arr = [int(x) for x in input().split()]
    arr.sort()

    zsort = []

    #z sort
    for i in range(n):
        if i % 2 == 0:
            zsort.append(min(arr))
            arr.remove(min(arr))
        else:
            zsort.append(max(arr))
            arr.remove(max(arr))

    # check if it is sorted well
    flag = False
    for i in range(1,n):
        if i %2 ==0:
            if ( zsort[i-2] <= zsort[i-1] >= zsort[i]):
                continue
            else:
                print("Impossible")
                flag = True
                break

    if (flag == False):
        for i in zsort:
            print(i, end= " ")

if __name__ == '__main__':
    L2()
			    		  	 		   	 		  	