Preparing NOJ

# Hangover

1000ms 10000K

## Description:

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.

## Sample Input:

1.00
3.71
0.04
5.19
0.00


## Sample Output:

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

Info

Provider POJ

Origin Mid-Central USA 2001

Code POJ1003

Tags

Submitted 3

Passed 2

AC Rate 66.67%

Date 07/22/2019 17:04:20

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