HANGOVER - Hangover

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.

Input

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.

Output

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.

Input:
1.00
3.71
0.04
5.19
0.00

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

Added by:Wanderley Guimarăes
Date:2006-06-09
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Mid Central Regionals 2001

hide comments
2016-03-07 08:01:16 giriprasad kemburu
Ac in 1 Go...my 12th :)
2016-02-18 11:26:41
simply use loop
2016-02-09 12:24:09
AC in 1 go
2016-01-31 00:08:45
that series.... Cards will fall :p
2016-01-10 07:00:06
got 2 WA due to spacing btw number and card(s)....seriously hate these mistakes!
2015-12-24 16:38:40 Shreyas Gupta
AC in 2nd go! Got 1 WA for putting "card(s)" instead of " card(s)".
2015-11-16 03:26:51
Did anyone solve this problem in constant time using the relation between logarithm and harmonic numbers?

Last edit: 2015-11-16 03:27:29
2015-11-02 17:31:14 sumit suthar
simple math. Easy one :)
2015-10-30 10:03:42
Got AC in second go .. not attaching card(s) with the output cost me a wrong answer :(
2015-10-24 12:45:20
my first ac in one go!
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