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
2015-10-20 22:43:50
OMG...I have been for 25 minutes watching the formula trying to get a soltuion....I never thought that this probleme is such easy...XDD
2015-10-01 00:09:04
easy
2015-09-20 03:12:23
Please; no java - Problem with " , " comma
2015-09-15 17:47:41 Brett Fazio
AC in second, put "cards(s)" instead of "card(s)"
2015-09-08 11:17:13 mav3n
very simple... got 1 WA because I forgot to append "card(s)" to the answers... why is that required!!!
2015-07-06 16:23:47 Andrzej Stasiak
I agree with John Doe - the formula given in the problem description is wrong.
It allows to get an AC, but it has nothing to do with the real physical problem with cards described above.

Last edit: 2015-07-06 16:24:07
2015-06-20 08:12:40
easiest one...easier than life,universe and everything!!!
2015-06-18 12:15:08 iammangod96
DON'T DO THIS QUESTION VERY EASY AND NOTHING TO LEARN.
2015-06-17 15:23:25
on ideone it shows sucess all time but when i submit here its say WA.somebody help me.
2015-06-04 06:55:36 Aman Kumar
Very easy
AC in 2nd go :( , got one WA due to missing space between the numbers and card(s) in output, foolish mistake

Last edit: 2015-06-04 06:56:15
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