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 sys,math
sys.setrecursionlimit(10**8)
'''
def fun():
    for i in range(16):
        for j in range(4):
            if i&(1<<j):
                print(j,end='')
        print()
import binarytree
from collections import deque
bst = binarytree.tree(height=4,is_perfect=True)
print(bst)
def s(bst):
    if bst:
        bst.left,bst.right = bst.right,bst.left
        s(bst.right)
        s(bst.left)
s(bst)
print(bst)
'''
n = int(input())
arr = list(map(int,input().split()))
arr.sort()
x = []
z = 1
for i in range(n//2):
    x.append(arr[i])
    x.append(arr[len(arr)-i-1])
if n%2 == 1:
    x.append(arr[(n//2)])
for i in range(n):
    if i%2 == 1:
        if x[i]<x[i-1]:
            print("Impossible")
            z=0
            break
    else:
        if x[i]>x[i-1]:
            print("Impossible")
            z=0
            break
if z!=0:
    print(' '.join(map(str,x)))
