How Much Does a Bigger Sample Help?

A research team is arguing about budget. A pilot study surveyed a small number of people; the proposal on the table is to survey a larger number, which costs proportionally more in interviewer time. The finance director wants one number before signing: how much steadier does the study's average actually get?

The quantity being measured has a known population standard deviation, and that does not change between the two designs - only the number of people surveyed does. The same comparison gets rerun for every proposal that crosses her desk.

Task: Print how many times larger the standard error of the mean is under the small design than under the large one - the small study's figure expressed as a multiple of the large study's. Print the raw number; no rounding is asked for.

Input

Three lines: the population standard deviation as a decimal, then the pilot study's sample size, then the proposed sample size. Both sizes are whole numbers of at least 1, and the proposed size is the larger.

Output

One line holding the ratio as a float, printed raw - 2.0, and 1.5811388300841895 when it does not land on a tidy value.

Example:

Input:
20
25
100

Output:
2.0