Solving Monotonic Functions
------- --------- ---------

The Department of Monotonic Functions (DMF) will, among
other things, solve equations of the form F(x) = 0,
where F is a strictly monotonic function.  `F(x) is
strictly monotonic' means that whenever x < y,
F(x) < F(y).

You are asked to write a program to perform this task
for fairly arbitrary F.  F is input in polish notation.
That is, F(x) is calculated by a stack machine as
follows.

The stack machine has a stack of double precision
floating point numbers.  Initially the stack is empty.

The function is a sequence of symbols and numbers.  A
number means: push the number into the top of the stack.
All numbers begin with a digit: there are no signed
numbers.  The following are the possible symbols and
their meanings:

	x	push x into the stack

	+	pop the top 2 members of the stack,
		and push their sum onto the stack

	-	pop the top 2 members of the stack,
		and push the second value popped minus
		the first value popped onto the stack

	*	pop the top 2 members of the stack,
		and push their product onto the stack

	/	pop the top 2 members of the stack,
		and push onto the stack the second value
		popped divided by the first value
		popped

Thus `2.4 x * 1.2 x / -' represents the monotonic func-
tion

	F(x) = 2.4 * x - 1.2 / x

Input:
-----

							
    For each of several cases, one line containing

    	L H TOKEN ... ;

    where [L,H] is the range of x values over which F(x)
    is monotonic and in which the solution is to be
    found, and `TOKEN ...' is the sequence of symbols
    and numbers representing the function F.  A TOKEN is
    just one symbol or number.  L, H, TOKENs, and ; are
    all separated by spaces or tabs.  There are at most
    80 TOKENs.

    It is guaranteed that F(L) < 0 < F(H) and that no
    value of x in the range [L,H] will cause the
    computation of F to overflow double precision
    floating point arithmetic.

    Input ends with an end of file.

Output:
------

    For each case, a single line containing nothing but
    the value of x such that F(x) = 0.  The value of x
    must be accurate to within 10**-9.

Example Input:
------- -----

1E-9 1E+9 2.4 x * 1.2 x / - ;
1 1E+9 3 x x x * * * 6 x x * * - 4 x * + 10 - ;



Example Output:
------- ------

0.707106781
2.114827162


File:	   monotonic.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Sun Oct 19 08:17:38 EDT 2003

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: 2003/10/19 12:20:29 $
    $RCSfile: monotonic.txt,v $
    $Revision: 1.5 $