The Mugs Game
-------------

In the mugs game, the player is provided with a set of N
(2 <= N <= 10) empty mugs in a row, numbered 1 to N.
Each mug has a capacity, specified in ounces. The mugs
are in a fixed order. The player then executes a series
of moves, from the following list:

   1. Fill up mug 1 to its capacity.

   2. Pour the contents from some mug x into mug x+1
      until either mug x is empty or mug x+1 is full.
      This operation can only be done from one mug into
      the mug after it, numerically.

   3. Pour the contents of mug N down the drain, so that
      mug N is empty.  Note that this can only be done
      with the last mug N, not with an arbitrary mug.

For example, if there were two mugs of capacities 3 and
2 (in order) the player could execute the following
sequence of moves:

    1. Fill mug one to the top
    2. Pour 2 ounces from mug 1 into mug 2
    3. Pour out the contents of mug 2
    4. Pour 1 ounce from mug 1 to mug 2

The player's goal is to have a specified number of
ounces in each mug.  For example, if the goal were
to have 0 ounces in mug 1 and 1 ounce in mug 2, then
the goal would have been reached after move 4 above.

In order to win the game, the player must have EXACTLY
the amount specified in all mugs simultaneously.

Input
-----

A sequence of cases, each consisting of a sequence of
integers.  The first integer is N, the number of mugs.
The next N integers are the capacities of the mugs in
order.  The following N integers are the goals for each
mug, in order.  This is, for each mug, the EXACT number
of ounces to be left in the mug at the end of the game.

There are 2N+1 integers per test case with N mugs.
Integers are separated by any kind of whitespace, pos-
sibly including tabs and newlines.

Input ends with an end of file.

Output
------

For each test case, output a single line containing just
the minimum number of moves necessary to reach the goal.

However, if it is not possible to reach the goal, output
instead a single line containing nothing but the word
`impossible'.


Example Input
------- -----

2
3 2
0 1

3
4 3 2
0 0 1

3
4 3 2
3 2 2

3
4 3 2
1 2 1


Example Output
------- ------

4
8
13
impossible


File:	   mugs.txt
Author:	   Tom Widland <twidland@fas.harvard.edu>,
	   edited by
	   Bob Walton <walton@deas.harvard.edu>
Date:	   Sun Oct  9 07:03:12 EDT 2005

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2005/10/09 11:03:58 $
    $RCSfile: mugs.txt,v $
    $Revision: 1.3 $