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
from collections import deque

def z_sorted(a):
    a = deque(sorted(a))
    j = 0
    b = []
    
    while a:
        v = a.popleft() if (j%2 == 0) else a.pop()
        if j:
            if j%2 == 1:
                if v < b[-1]: return False
            else:
                if v > b[-1]: return False
        b.append(v)
        j += 1
    return b

def is_z_sorted(a):
    for i in range(len(a)):
        if i and i%2 == 1 and a[i] < a[i-1]: return False
        if i%2 == 0 and a[i] > a[i-1]: return False
    return True

if __name__ == "__main__":
    n = int(input())
    a = z_sorted([int(x) for x in input().split()])
    if a and is_z_sorted(a):
        print(' '.join(str(x) for x in a))
    else:
        print('IMPOSSIBLE')
