The NWRRC security server has a final access check for teams that try to submit their solutions to the secret hidden problem.

To pass the check, the team must enter three passwords $s$, $t$, and $u$ that the system will accept. Each password must be a non-empty string consisting of at most $5000$ lowercase English letters.

The rules of the server are public:

\begin{shortitems}
\item The distance between $s$ and $t$ should be equal to $a$.
\item The distance between $s$ and $u$ should be equal to $b$.
\item The distance between $t$ and $u$ should be equal to $c$.
\end{shortitems}

The \textit{distance} between two strings $s_1$ and $s_2$ is the minimum number of single-character operations (insert one character, remove one character, or replace one character) needed to convert string $s_1$ into string $s_2$. This metric is also known as the Levenshtein distance.

The server gives access to the hidden problem if and only if all described conditions are satisfied. Your goal is to construct a triple of passwords to unlock the hidden problem or determine that it is impossible.