Balanced Strings
-------- -------

A balanced string is a string whose parentheses all
match.  Thus

     balanced-string
         ::= empty-string
	   | balanced-string non-parenthesis-character
	   | balanced-string ( balanced-string )

You have been asked to develop a piece of code that
determines whether strings are balanced.

Input
-----

For each string, one line whose contents is the string.
The maximum string length is 80 characters.

The input ends with an end of file.

Output
------

For each string, one line beginning with `String #:' and
ending with either `balanced' or `NOT balanced'.

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

This is (a) very ((bal)(en(ce)d)) st()ring!
But this is (a) bit (un((bal)(en(ce)d)).
And so is) (this).


Note: This sample input is a file with exactly 3 lines.


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

String 1: balanced
String 2: NOT balanced
String 3: NOT balanced



File:	balanced.txt
Author:	Bob Walton <walton@deas.harvard.edu>
Date:	Mon Oct  8 02:39:54 EDT 2001

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: 2001/10/08 07:16:07 $
    $RCSfile: balanced.txt,v $
    $Revision: 1.2 $