Typing Contest

Teacher Docriz is planning to select some students in his class for a typing contest.

There are $n$ students in the class. The $i$-th student has an initial typing speed $s_i$ and a typing noise $f_i$. When several students are selected to compete, their total typing speed is not the sum of their initial speeds. The noise each person makes affects the others.

If students $1, 2, \ldots, k$ form a team, the actual typing speed of student $1$ is

$s_1 \cdot (1 - f_1 f_2 - f_1 f_3 - \ldots - f_1 f_k)$

the actual typing speed of student $2$ is

$s_2 \cdot (1 - f_2 f_1 - f_2 f_3 - \ldots - f_2 f_k)$

and so on.

Teacher Docriz wants to form a team so that the total typing speed is as large as possible. Calculate the maximum total typing speed he can achieve.

The first line contains an integer $T$ ($1 \leq T \leq 2000$), the number of test cases. Then $T$ test cases follow.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 100$), the number of students.

Then $n$ lines follow. Each line contains two numbers $s_i$ and $f_i$ ($1 \leq s_i \leq 10^{12}$, $0 \leq f_i \leq 1$), where $s_i$ is an integer and $f_i$ is a real number with exactly two decimal places.

It is guaranteed that $\sum n \leq 2000$.

For each test case, output a line with a single real number: the maximum typing speed Teacher Docriz can achieve. Print exactly 9 digits after the decimal point. The answer must match the model solution exactly when printed with 9 decimal places.