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
#!/usr/bin/env python3

from __future__ import division, print_function

def solver(ifs):
    n = int(ifs.readline().strip())
    a = list(map(int, ifs.readline().split()))
    a.sort()
    mid = (n+1)//2
    res = [0, ] * n
    pos = 0
    for i in range((n+1)//2):
        res[pos] = a[i]
        pos = pos + 1
        if pos < n:
            res[pos] = a[n-1-i]
            pos = pos + 1
    print(" ".join(str(x) for x in res))


def main():
    import sys
    if sys.version_info.major == 3:
        from io import StringIO as StreamIO
    else:
         from io import BytesIO as StreamIO
    
    with StreamIO(sys.stdin.read()) as ifs, StreamIO() as ofs:
        _stdout = sys.stdout
        sys.stdout = ofs
        solver(ifs)
        sys.stdout = _stdout
        sys.stdout.write(ofs.getvalue())
    return 0

if __name__ == '__main__':
    main()
