Disjoint Regular Expressions

Mark is building a new social network, Facepalm, for the inhabitants of Phobos and Deimos. For each account he wants to suggest a default home asteroid at logon, and he has found that a user's home asteroid can be guessed by analyzing their last name.

Every last name is a non-empty word of lowercase English letters. Last names of users from Phobos match a regular expression $P$, while last names of users from Deimos match a regular expression $D$.

The trouble is that some last names may match both expressions. The two expressions are called disjoint if there is no non-empty string $s$ that matches both of them. Mark believes $P$ and $D$ are disjoint, but he needs you to check.

Given the two regular expressions $P$ and $D$, decide whether they are disjoint. If they are not, find the shortest non-empty string that matches both of them. If several shortest strings exist, output the lexicographically smallest one.

The input consists of two lines. The first line contains the regular expression $P$, and the second line contains the regular expression $D$. Each expression has from $1$ to $100$ characters.

If the two expressions are disjoint, print Correct on a single line.

Otherwise print Wrong on the first line, and on the second line print the shortest non-empty string that matches both expressions; if several shortest strings exist, print the lexicographically smallest one.

Regular expressions and the strings that match them are defined as follows.

• A single lowercase letter $c$ is a regular expression; it matches only the one-character string $c$.
• Alternation: if $P$ and $Q$ are regular expressions, then $(P \mid Q)$ is a regular expression; a string $\alpha$ matches it if $\alpha$ matches $P$ or $\alpha$ matches $Q$.
• Concatenation: if $P$ and $Q$ are regular expressions, then $(PQ)$ is a regular expression; a string $\alpha$ matches it if $\alpha = \beta\gamma$ where $\beta$ matches $P$ and $\gamma$ matches $Q$.
• Kleene star: if $P$ is a regular expression, then $(P^{*})$ is a regular expression; a string $\alpha$ matches it if $\alpha$ can be split into zero or more pieces $\alpha_1\alpha_2\dots\alpha_k$ that each match $P$. The empty string always matches a Kleene star.

In the input, expressions are written with parentheses for grouping and the usual operator precedence: the Kleene star * binds most tightly, then concatenation, then alternation |. For example, a(ab)*b means the letter a, followed by zero or more copies of ab, followed by the letter b.