Stupid people

The current pandemic has proven (once again) how many stupid people there are. Consider, for instance, the use of face masks, under this simplified model: The length of a face is $\ell$ , with the bottom of the chin at position 0 and the top of the front at position $\ell$ . The bottom of the mouth is at position $m$ , and the top of the nostrils is at position $n$ , with $0 < m < n < \ell$ .

Let us consider that a placement of a mask is defined by two real numbers: its bottom position $b \ge 0$ and its upper position $u \le \ell$ , where $b < u$ . We say that a placement is reasonable if it completely covers the mouth and the nostrils, that is, if $b \le m$ and $u \ge n$ .

A stupid person just choses any possible placement such that $0 \le b < u \le \ell$ uniformly at random. Note that $b$ and $u$ are real numbers with an arbitrary (or infinite) number of decimals. What is the probability that a stupid person wears a mask in a reasonable way?

Input

Input consists of several cases, each with three real numbers $m$ , $n$ and $\ell$ . You can assume $0 < m < n < \ell \le 10^6$ .

Output

For every case, print the probability that a stupid person wears a mask in a reasonable way. Print four digits after the decimal point. The input cases do not have precision issues.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:18:20.049Z