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
import sys


def scan():
    return list(map(int, sys.stdin.readline().strip().split()))


def solution():
    n = int(input())
    a = scan()
    b = []
    c = []
    a.sort()
    for i in range(n//2):
        b.append(a[i])
    for j in range(n//2, n):
        c.append(a[j])
    j = 0
    c.reverse()
    for i in range(n//2+1):
        if i < len(b):
            print(b[i], end=' ')
        if i < len(c):
            print(c[i], end=' ')
    # print(b, c)


if __name__ == '__main__':
    solution()
