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 assume every card is perpendicular to the table). With two cards, the top card can overhang the bottom one by half a card length, and the bottom one can overhang the table by a third of a card length, for a total maximum overhang of $\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$ card lengths.

In general, with $n$ cards you can achieve an overhang of

$$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \cdots + \frac{1}{n+1}$$

card lengths: the top card overhangs the second by $\frac{1}{2}$, the second overhangs the third by $\frac{1}{3}$, the third overhangs the fourth by $\frac{1}{4}$, and so on, while the bottom card overhangs the table by $\frac{1}{n+1}$. 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 $5.20$; $c$ always has exactly three significant digits (the form X.YZ).

For each test case, output the minimum number of cards needed to achieve an overhang of at least $c$ card lengths. Print one line per test case in the exact form N card(s), where N is that minimum number of cards.