The Two Legged Maze
-------------------

A two legged maze is a board of NxN squares, with each
square labeled by a single lower case letter.  The
problem is to go by a path from a start square to a goal
square.  The path is a sequence of horizontal and verti-
cal moves to adjacent squares.  The path is divided into
two parts, the `first leg' followed by the `second leg'.
Each leg is a sequence of moves.  In the first leg all
moves must be from a square labeled X to a square
labeled Y where Y follows X in the alphabet, or in
short, X<Y.  In the second leg all moves must be from X
to Y where Y precedes X in the alphabet, or X>Y.  Either
leg can have zero moves.

The board columns are numbered 1, 2, ..., N and the
board rows are numbered 1, 2, ..., N.  A square has
coordinates (r,c) where r is the square's row number and
c is its column number, (1,1) is the upper left corner,
and (N,N) is the lower right corner.  The start square
is (sr,sc) and the goal square is (gr,gc).

Diagonal moves are NOT allowed.


Input
-----

For each of several test cases, a single line containing
the 5 numbers

	N sr sc gr gc

where 1 <= N <= 50, followed by N lines each containing
just N lower case letters.  These lines are the rows of
the board, with row 1 first and row N last.  The N lower
case letters on a line are the labels of the squares in
the line's row, with the first letter in the line being
for column 1 and the last being for column N.

An end of file terminates the input.


Output
------

For each case, a single line containing nothing but
the minimum number of moves required by any path from
the start to the goal.  Or if there is no such path,
then the line contains just the word `impossible'.


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

5 1 1 5 5
abcde
fghij
klmno
pqrst
uvwxy
5 1 2 4 5
abken
ywxyz
abekw
yxieb
pqude
5 4 2 5 5
abkzn
ywxyx
abekw
ymief
pqude

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

8
6
impossible


File:	   twolegs.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Wed Oct 15 03:08:09 EDT 2008

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: 2008/10/15 07:08:22 $
    $RCSfile: twolegs.txt,v $
    $Revision: 1.4 $