First, read a line containing an integer $t$: the number of starting numbers ($1 \le t \le 50$). The jury has $t$ starting numbers $x_0$, selected uniformly and independently at random from the range $\left[2; 10^7\right]$, and you need to turn them all into ones in sequence.

At the beginning of the $i$-th round, read a line containing a single integer $x_0$: the next starting number ($2 \le x_0 \le 10^7$). Then you need to transform the number. After each transformation, if the screen shows the number $x_j$, output a line with either the string ``\texttt{collatz}'' (the letters can be in any case) if you want to replace the number with $x_{j+1} = \mathrm{collatz}{\left(x_j\right)}$, or the string ``\texttt{random}'' (the letters can be in any case) if you want to replace the number with $x_{j+1}$ which is a random integer uniformly selected from the range $\left[3x_j+1; 6x_j\right]$. After printing each line, do not forget to flush the output buffer, otherwise, you will likely receive an error of \texttt{Idleness Limit Exceeded}:
\begin{shortitems}
    \item \texttt{std::cout.flush()} in C++;
    \item \texttt{fflush(stdout)} in C;
    \item \texttt{stdout.flush()} in Python and D;
    \item \texttt{flush(output)} in Pascal and Delphi;
    \item \texttt{System.out.flush()} in Java;
    \item for help with other languages, refer to the documentation.
\end{shortitems}
After that, read a line containing a single integer $x$. The following options are possible:
\begin{shortitems}
    \item if $x = 0$, you have run out of tokens;
    \item if $x = 1$, then $x_{j+1}=1$: you have successfully completed the round, move on to the next round (for which you should start by reading the next starting number $x_0$);
    \item if $x > 1$, then $x_{j+1}=x$: the number on the screen has changed after pressing the button, continue outputting the strings ``\texttt{collatz}'' and ``\texttt{random}''. Note that, during the interaction, $x$ may exceed $2^{64}$ as well as $2^{128}$.
\end{shortitems}
The jury will also send your program the number $0$ if you violate the output format and print any string other than ``\texttt{collatz}'' and ``\texttt{random}''. Upon reading $0$, your program should immediately terminate to receive a \texttt{Wrong Answer} verdict. Otherwise, the verdict can be anything other than \texttt{Accepted}.

After reading the $t$-th number one, terminate the program to receive the \texttt{Accepted} verdict.