Yes or No?

Multiple-choice tests are easy to grade, so they are popular with some teachers. The simplest form is the true/false, or yes/no, question.

You are taking a yes/no test. For each question you have an a priori estimate of how likely each answer is to be correct. For question $i$ you believe the answer is “Yes” with probability $y_i$ and “No” with probability $1 - y_i$.

If the questions were independent you would simply pick whichever of $y_i$ and $1 - y_i$ is larger. However, this teacher dislikes a lopsided answer key, and you know that the number of “Yes” answers is always between $\ell$ and $r$ inclusive, for some $\ell \le r$.

You must therefore decide which questions to answer “Yes” — answering “Yes” at least $\ell$ times and at most $r$ times — so as to maximize the expected number of questions you get right. Output that maximum expected number of correct answers.

The first line contains the number of data sets $K \ge 1$. Then follow $K$ data sets of the following form.

The first line of each data set contains three integers $\ell \le r \le n$, where $n \le 200$ is the total number of questions, $\ell$ is the minimum number of questions answered “Yes”, and $r$ is the maximum.

This is followed by $n$ lines, each containing one fractional number $y_i \in [0, 1]$ for the corresponding question $i$.

For each data set, first output Data Set x: on a line by itself, where $x$ is its number. Then output the maximum expected number of questions you can get right subject to all the constraints, rounded to two decimals.