Buffalo Finder
------- ------

Ranchy Flatman is a buffalo rancher who has lived on the
Plains for decades.  He has a ranch on which he keeps
buffalo in a field with three sides.  Each side is
bounded by a perfectly straight fence which actually
extends in both directions well beyond Ranchy's field,
and which serves as a boundary between various fields
owned by various other people.  In all there are 7
fields, Ranchy's triangular field, and 6 neighboring
fields.

Sometimes Ranchy loses track of a buffalo.  Then he
sends his trusty Beagle Issy (`I Smell You') out to
find the errant buffalo.  Issy wears a GPS receiver and
a radio, and this sends Issy's position back to Ranchy.
When Issy finds the buffalo, she stops, and Ranchy then
knows the buffalo's GPS coordinates.  If the buffalo has
gotten lost in Ranchy's field, Ranchy goes out to find
the buffalo, but if the buffalo is in a neighbor's
field, Ranchy must call up the neighbor who will go with
Ranchy to retrieve the Buffalo and Issy.

In order to make this work, Ranchy's daughter has worked
out the following naming system for fields, and program-
med the family computer to tell Ranchy which field Issy
is in.  The corners of Ranchy's triangular field are
given the names 1, 2, and 3 in clockwise order, and the
fences are given names 12, 23, and 31 in clockwise
order.  A given field can be either to the left or right
of a given fence.  So we can give a field a name of the
form

	D12 D23 D31

where Dxy is `L' if the field is to the left of fence xy
and `R' if the field is to the right of fence xy when
traveling in the direction from x to y.  Thus Ranchy's
triangular field is named RRR and if you cross fence 12
from this field you enter field LRR.

To find out which field Issy is in, the GPS coordinates
of Issy and the corners 1, 2, and 3 are used.  The GPS
coordinates are treated as integer coordinates of points
in a flat plane.

Due to an unfortunate accident, Ranchy's daughter's
computer program has been lost, and as she is off at
college and in the middle of exams, you have been tasked
to replace it.

Input
-----

For each test case, one line of the form

	x1 y1 x2 y2 x3 y3 xi yi

where (x1,y1), (x2,y2), (x3,y3) are the coordinates of
the corners 1, 2, and 3, respectively, and (xi,yi) are
Issy's coordinates.  All coordinates are integers.
Input ends with an end of file.

For simplicity, the input will be such that Issy is
never exactly on a fence.


Output
------

For each test case one line containing just
the name of the field containing Issy.


Sample Input
------ -----
-3 -3 0 6 3 -3 0 0
-3 -3 0 6 3 -3 -5 0
-3 -3 0 6 3 -3 0 10
-3 -3 0 6 3 -3 5 0
-3 -3 0 6 3 -3 10 -4
-3 -3 0 6 3 -3 0 -4
-3 -3 0 6 3 -3 -10 -4


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

RRR
LRR
LLR
RLR
RLL
RRL
LRL


File:	   buffalo.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Wed Oct 15 03:05:19 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 07:06:00 $
    $RCSfile: buffalo.txt,v $
    $Revision: 1.6 $