Broppers
--------

On the planet of Pons, the Xflea (rough translation:
bridge hoppers, or colloquially, broppers) hold a race/
contest every Xflit (rough translation, 5 years, 8
months).

The course consists of a isles connected by bridges.
There is a start isle and a finish isle.  A team
consists of broppers who are all initially at the
start isle and who try to get to the finish isle.
Their movements are controlled by a gong; when the
gong sounds, each bropper either stays put or crosses
a bridge.  The team goal is to get as many team
members as possible to the finish.  Being broppers,
a team is of unbounded size, and the team has an
unbounded amount of time to get from start to finish.

Wait, somethings missing.  We forgot to tell you about
the bridges.  Only one bropper can cross a bridge at
a time (i.e., between one gong and the next gong), and
the bridges are all 1-way.  There are two kinds of
bridges, F-bridges and S-bridges.  An F-bridge, or
falling bridge, falls down immediately after it is
crossed, and cannot be used a second time.  However
S-bridges, or synchronized bridges, are another kettle
of brop altogether.  S-bridges do NOT fall down.  But
they can only be used if all S-bridges are crossed
(by different broppers) simultaneously.  That is, if at
a gong some bropper tries to cross every S-bridge, they
all succeed, but if some S-bridge has no bropper trying
to cross it, none of the broppers trying to cross
S-bridges go anywhere.  Also, there no way for broppers
to get from the end of any S-bridge to the beginning of
some S-bridge, so a bropper cannot cross an S-bridge and
then go to the beginning of some S-bridge to help other
broppers across.

The layout of the race/contest is different for every
team.  But this is not as unfair as it seems, as the
course is always very large and random, and teams never
get nearly as many members to the finish as they could
in theory.  Just to prove this, a team is told in
advance the maximum number of members they could get
from start to finish.  And you have been hired to write
a program which will compute this so the contest can be
properly run.


Input
-----

For each of several test cases, one line containing the
test case name, followed by lines that describe bridges.
These have the form

	type begin end

where type is `F' or `S' and begin and end are isle
numbers.  After these lines is a line containing just
`.'.

Isles are numbered 1, 2, 3, ..., N for some N <= 10,000.
The start isle is always isle 1 and the finish is always
isle 2.  No S-bridge begins or ends at the start or
finish isles, and no two S-bridges start at the same
isle or finish at the same isle.  There is at most one
bridge with a given beginning isle and end isle (but
there can be two bridges going in opposite directions
between two isles).  There are no more than 1,000,000
bridges, and no input line is longer than 80 characters.

Input ends with an end of file.


Output
------

For each test case, a copy of the test case name line,
followed by a line containing just the maximum number of
team members who can make it from start to finish.  Note
that a bropper who starts is not required to finish, but
may drop out at any time (e.g., after crossing an
S-bridge).


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

-- SAMPLE 1 --
F 1 3
F 1 5
F 5 2
S 3 4
S 5 6
.
-- SAMPLE 2 --
F 1 3
F 1 5
F 5 2
F 4 2
S 3 4
S 5 6
.
-- SAMPLE 3 --
F 1 3
F 1 5
F 5 2
F 4 2
F 6 2
S 3 4
S 5 6
.

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

-- SAMPLE 1 --
1
-- SAMPLE 2 --
1
-- SAMPLE 3 --
2


Thanks: To the books of Iain M. Banks for stylistic
        guidance.


File:	   broppers.txt
Author:	   Bob Walton <walton@seas.harvard.edu>
Date:	   Wed Oct 10 03:20:56 EDT 2012

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: 2012/10/10 07:23:26 $
    $RCSfile: broppers.txt,v $
    $Revision: 1.10 $