Hangover

<P>How far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We're assuming that the cards must be perpendicular to the table.) With two cards you can make the top card overhang the bottom one by half a card length, and the bottom one overhang the table by a third of a card length, for a total maximum overhang of 1/2 <TT>+</TT> 1/3 <TT>=</TT> 5/6 card lengths. In general you can make <I>n</I> cards overhang by 1/2 <TT>+</TT> 1/3 <TT>+</TT> 1/4 <TT>+</TT> ... <TT>+</TT> 1/(<I>n</I> <TT>+</TT> 1) card lengths, where the top card overhangs the second by 1/2, the second overhangs tha third by 1/3, the third overhangs the fourth by 1/4, etc., and the bottom card overhangs the table by 1/(<I>n</I> <TT>+</TT> 1). This is illustrated in the figure below.</P> <br><CENTER><img src="http://poj.org/images/1003/hangover.jpg" width="424" height="115"></CENTER> <br>

The input consists of one or more test cases, followed by a line containing the number 0.00 that signals the end of the input. Each test case is a single line containing a positive floating-point number c whose value is at least 0.01 and at most 5.20; c will contain exactly three digits.

For each test case, output the minimum number of cards necessary to achieve an overhang of at least c card lengths. Use the exact output format shown in the examples.

1.00
3.71
0.04
5.19
0.00

3 card(s)
61 card(s)
1 card(s)
273 card(s)

PKU