652_B. z-sort
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
```python
n = int(input())
a = [int(x) for x in input().split(" ")]
a.sort()

for i in range(n):
    if i%2 == 0:
        firval = a[i]
        secval = a[i-1]
        if i == 0:
            continue
        elif firval > secval:
            a[i],a[i-1] = a[i-1],a[i]
        elif secval >= firval:
            continue
    elif i%2 != 0:
        firval = a[i]
        secval = a[i-1]
        if firval < secval:
            a[i],a[i-1] = a[i-1],a[i]
        elif secval <= firval:
            continue
final = []
for k in a:
    final.append(str(k))
print(' '.join(final))
```