### Mutant Flatworld Explorers

Time Limit: 1000 ms Memory Limit: 10000 KiB

#### Problem Description

Background

Robotics,  robot motion  planning,  and  machine learning  are  areas
that  cross  the  boundaries  of  many  of  the  subdisciplines  that
comprise Computer Science:   artificial intelligence, algorithms  and
complexity,  electrical and  mechanical engineering  to name  a  few.
In  addition, robots  as  turtles'' (inspired  by work  by  Papert,
Abelson, and diSessa) and as beeper-pickers'' (inspired by  work by

Pattis) have been studied and used by students as an  introduction to
programming for many years.
This  problem  involves  determining  the  position  of   a  robot
exploring a pre-Columbian flat world.

The Problem

Given  the  dimensions  of a  rectangular  grid  and  a  sequence  of
robot positions  and instructions, you  are to  write a program  that
determines for each sequence of robot positions and  instructions the
final position of the robot.

A  robot  position  consists  of a  grid  coordinate  (a  pair  of
integers:  x-coordinate followed by y-coordinate) and  an orientation
(N,S,E,W for  north, south,  east, and  west).   A robot  instruction
is  a string  of  the letters  'L',  'R',  and 'F'  which  represent,
respectively, the instructions:

* Left:   the  robot  turns left  90 degrees  and remains  on  the
current grid point.

* Right:   the robot  turns right  90 degrees and  remains on  the
current grid point.

* Forward:    the  robot  moves forward  one  grid  point  in  the
direction  of  the current  orientation  and mantains  the  same
orientation.

The direction  North corresponds to the direction from grid  point
(x,y) to grid point (x,y+1).
Since  the grid  is rectangular and  bounded, a  robot that  moves

off'' an edge  of the grid is lost  forever.  However, lost  robots
leave a  robot scent'' that prohibits  future robots from  dropping
off the  world at the  same grid  point.   The scent is  left at  the
last grid  position the robot occupied  before disappearing over  the

edge.   An instruction to  move off'' the world  from a grid  point
from which a robot has been previously lost is simply ignored  by the
current robot.

#### Input

The  first  line of  input  is  the upper-right  coordinates  of  the
rectangular world, the lower-left coordinates are assumed to be 0,0.
The  remaining input  consists of  a sequence  of robot  positions
and  instructions (two  lines per  robot).   A  position consists  of
two integers specifying the  initial coordinates of the robot and  an

orientation (N,S,E,W), all separated  by white space on one line.   A
robot instruction  is a string of  the letters 'L',  'R', and 'F'  on
one line.
Each  robot is  processed sequentially,  i.e., finishes  executing
the robot instructions before the next robot begins execution.
Input is terminated by end-of-file.
You  may assume that  all initial robot  positions are within  the
bounds of the specified  grid.  The maximum value for any  coordinate

is 50.  All  instruction strings will be less than 100 characters  in
length.

#### Output

For each robot  position/instruction in the input, the output  should
indicate the final  grid position and orientation  of the robot.   If
a robot falls  off the edge of the  grid the word LOST'' should  be
printed after the position and orientation.

#### Sample Input

5 3
1 1 E
RFRFRFRF
3 2 N
FRRFLLFFRRFLL
0 3 W
LLFFFLFLFL

#### Sample Output

1 1 E
3 3 N LOST
2 3 S