[PKU] P1003: Hangover

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.

Hangover

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

Sample Output

Source

Solution:

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