Problems
God! Save me
God! Save me
You are located in a room with $n$ doors. If you open the $i$-th door, in $x_i$ hours you will be either get to a safe place or you will return to the same room again. What is the expected time $P$ (in hours) until you can move to the safe place?
\InputFile
The first line is the number of test cases. The first line of each test case contains the value of $n\:(0 < n < 100)$. Each of the next $n$ lines contains two numbers $x_i\:(0 < | x_i | < 25)$ and $p_i\:(0 \le p_i \le 1)$
\begin{itemize}
\item if $x_i$ is positive, it indicates the time in which you will get to a safe place;
\item if $x_i$ is negative, then $| x_i |$ indicates the time in which you will return to the room;
\end{itemize}
The value of $p_i$ is the probability to open the $i$-th door. The sum of all $p_i$ equals $1$.
\OutputFile
For each test case, first print the serial number of the case, a colon, a space and then print \textbf{“God! Save me”} (without the quotes) if you can't expect to be in the safe place, otherwise print the value of $P$ with $6$ digits after the decimal point.
\includegraphics{https://static.eolymp.com/content/20/20q8vv3mkl1mj6n6ddp1tkmrh4.gif}
Input example #1
3 3 2 0.33 -3 0.33 -5 0.34 3 2 0.34 -3 0.33 -5 0.33 3 10 0.0 -1 0.4 -1 0.6
Output example #1
Case 1: 10.151515 Case 2: 9.764706 Case 3: God! Save me