Bending Deck Boards
-------------------

Robert is building a deck on the side of his house and
has a problem.  He is using `composite boards' for the
floor of the deck, but these, being made of the plastic
polyethylene and wood fiber, expand much more than wood
when the temperature gets hot.  Robert is afraid the
boards will bend, or warp, because of this expansion.
So he does a simple calculation to see how bad the pro-
blem is.  You are being asked to program this calcula-
tion.

A section of board is normally a straight line between
two points, B and C, at which the board is fastened by
screws to joists.  Suppose we have such a section of
length L, that is, the distance from B to C is L.
Suppose the section length changes by expansion to L+y,
where y > 0 is a small number, but the end points of
the section remain anchored at B and C.  The section
must assume a non-straight-line shape.  Assume it
becomes an arc of a perfect circle, with end points
B and C.  Let the circle have radius R.  Note that R
is determined by L and y.

The straight line from B to C is then the chord of the
circle from B to C.  Let x be the maximum distance
between a point on the arc and a point on the chord.
y measures the amount of expansion, and x measures the
amount of bending.

Note that if you change the scale of the situation by
multiplying all distances by a constant C, the circle
remains a circle but now of radius C*R, the chord
remains a chord but now of length C*L, the arc remains
an arc but now of length C*(L+y), and the maximum
distance between a point on the chord and a point on
the arc is now C*x.  Therefore, x/L as a function of
y/L does not depend on L.  So you are asked to find
this function.

Note that given R you can compute x and y.  Also, R
decreases whenever y increases, and y/L as a function
of R/L does not depend on L.  The problem reduces to
computing R/L from y/L by inverting a monotonic func-
tion.


Input
-----

For each of several cases, a line containing a value
for y/L.  No lines contain any spaces.  The input
terminates with an end of file.

Output
------

For each case a line containing in order:

	the value of y/L
	a single space
	the value of R/L
	a single space
	the value of x/L

Print all values with exactly 8 decimal places.  Do not
include any extra spaces.  Use double precision float-
ing point arithmetic for all computations.


Example Input
------- -----

0.01
0.02


Example Output
------- ------

0.01000000 2.06885226 0.06132899
0.02000000 1.48249945 0.08686174


File:	   bending.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Wed Oct 10 07:12:26 EDT 2007

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: 2007/10/10 11:16:42 $
    $RCSfile: bending.txt,v $
    $Revision: 1.3 $