Source file: | hangover.{c, cpp, java, pas} |

Input file: | hangover.in |

Output file: | hangover.out |

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 `+` 1/3 `=`
5/6 card lengths. In general you can make *n* cards overhang by 1/2
`+` 1/3 `+` 1/4 `+` ... `+` 1/(*n*
`+` 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/(*n* `+` 1). This is illustrated in the figure below.

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.

**Example input:**

1.00 3.71 0.04 5.19 0.00

**Example output:**

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

*Last modified on October 27, 2001 at 5:20 AM.*