Right Hand on the Wall
----- ---- -- --- ----

Karel the Robot lives on a 10x10 board of squares.  Each
boundary line of a square may or may not have a wall.
At any given time, Karel is on one particular square,
and is facing in one of four directions: up, left, down,
or right.

Karel can move forward one square if there is no wall in
front of him.  Alternatively, Karel can turn 90 degrees
clockwise or 90 degrees counter-clockwise.  These are
the only moves Karel can make.  Karel can sense whether
there is a wall in front of him.

In this problem Karel repeats the 'Right Hand on the
Wall' algorithm, which is:

    (1) If there is a wall in front of Karel, Karel
        turns counterclockwise 90 degrees.

    (2) Otherwise if the square in front of Karel is the
        original square on which Karel started, Karel
	stops (WITHOUT moving forward to the original
	square).

    (3) Otherwise Karel moves forward one square and
        turns clockwise 90 degrees;

Starting from an initial position facing a wall, Karel
repeats this algorithm until he stops.

The boundary lines on the edge of the board all have
walls, so Karel can never fall off the edge of the
board, and will always eventually stop.

You are asked to make Karel move according to this
algorithm, and display the results.


Board Display
----- -------

The 10x10 board is displayed in a 21x21 character matrix
that can be printed in 21 lines of 21 columns each.

There is one character position for each square, for
each boundary line of a square, and for each corner of
a square.

The corner character positions hold the `+' character.

The boundary line character positions hold the space
character if there is no wall at the boundary, or `-'
for a horizontal boundary wall, or `|' for a vertical
boundary wall.

A square character position holds the space character if
Karel has never visited the position.  Otherwise it
holds a character showing the direction Karel LAST faced
when he was at that square.  `<' and `>' are used for
`facing left' and `facing right', respectively.  `^' and
`v' are used for `facing up' and `facing down', respec-
tively.  Here `^' is the circumflex and `v' is the lower
case letter.


Input
-----

Each of several test cases.  Each case consists of an
empty line followed by a board display.  On the board
display, Karel is shown as being at one position and
facing in one direction (there is only one `<', `>',
`^', or `v' on the board).  The start position is
always such that Karel is facing a wall, and all the
board edges have walls.

Input ends with an end of file.


Output
------

For each test case, a copy of the input for the test
case, with some board squares changed to hold characters
showing that Karel has been at the square and was facing
in a particular direction when he was last at the
square.

The board should show Karel's movement using the Right
Hand on the Wall algorithm exactly as described above,
starting with the initial situation defined by the input
board.

The empty lines beginning each input test case are
copied to the output, so the first line output is an
empty line.  The output should be an exact copy of the
input except that some square positions are changed to
`>', `^', `<', or `v'.


Sample Input
------ -----

[There is an empty line before each board.]


+-+-+-+-+-+-+-+-+-+-+
|   |               |
+ + + + + + + + + + +
|   |               |
+-+-+ + + + + + + + +
|                   |
+ + + + + + + + + + +
|                   |
+ + + + + + + + + + +
|                   |
+-+-+ + + + + +-+-+-+
|                   |
+-+-+ + + + + + + + +
|                   |
+ + + + + + + +-+-+-+
|             |     |
+ + + + + + + +-+-+-+
|                   |
+ + + + + + + + + + +
|v                  |
+-+-+-+-+-+-+-+-+-+-+

+-+-+-+-+-+-+-+-+-+-+
|       |           |
+ + + + +-+-+-+ + + +
|             |     |
+ + + + + + + +-+-+-+
|                   |
+ + + + + + + +-+-+-+
|             |     |
+-+-+-+-+-+ + + + + +
|             |     |
+ + + + +-+-+-+-+-+-+
|                   |
+ + + + + + + +-+-+-+
|             |     |
+ + + + + +-+-+ + + +
|        >|         |
+-+-+ + + + + + + + +
|   |               |
+ + +-+-+ + + + + + +
|       |           |
+-+-+-+-+-+-+-+-+-+-+


Sample Output
------ ------

[There is an empty line before each board.]


+-+-+-+-+-+-+-+-+-+-+
|   |v < < < < < < <|
+ + + + + + + + + + +
|   |v             ^|
+-+-+ + + + + + + + +
|v < <             ^|
+ + + + + + + + + + +
|v                 ^|
+ + + + + + + + + + +
|> > v       > > > ^|
+-+-+ + + + + +-+-+-+
|> > v       ^ < < <|
+-+-+ + + + + + + + +
|v < <       > > > ^|
+ + + + + + + +-+-+-+
|v           ^|     |
+ + + + + + + +-+-+-+
|v           ^ < < <|
+ + + + + + + + + + +
|> > > > > > > > > ^|
+-+-+-+-+-+-+-+-+-+-+

+-+-+-+-+-+-+-+-+-+-+
|v < < <|           |
+ + + + +-+-+-+ + + +
|v     ^ < < <|     |
+ + + + + + + +-+-+-+
|v           ^ < < <|
+ + + + + + + +-+-+-+
|> > > > > v ^|     |
+-+-+-+-+-+ + + + + +
|v < < < < < ^|     |
+ + + + +-+-+-+-+-+-+
|v     ^ < < < < < <|
+ + + + + + + +-+-+-+
|v       > > ^|v < <|
+ + + + + +-+-+ + + +
|> > v   ^|v < <   ^|
+-+-+ + + + + + + + +
|   |> > ^ <       ^|
+ + +-+-+ + + + + + +
|       |> > > > > ^|
+-+-+-+-+-+-+-+-+-+-+


File:	   handonwall.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Tue Oct 10 02:10:25 EDT 2006

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: 2006/10/10 06:22:07 $
    $RCSfile: handonwall.txt,v $
    $Revision: 1.6 $