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+--- Day 19: Monster Messages ---
+
+You land in an airport surrounded by dense forest. As you walk to your high-speed train, the Elves
+at the Mythical Information Bureau contact you again. They think their satellite has collected an
+image of a sea monster! Unfortunately, the connection to the satellite is having
+problems, and many of the messages sent back from the satellite have been corrupted.
+
+They sent you a list of the rules valid messages should obey and a list of
+received messages they've collected so far (your puzzle input).
+
+The rules for valid messages (the top part of your puzzle input) are numbered and build
+upon each other. For example:
+
+0: 1 2
+1: "a"
+2: 1 3 | 3 1
+3: "b"
+
+Some rules, like 3: "b", simply match a single character (in this case, b).
+
+The remaining rules list the sub-rules that must be followed; for example, the rule 0: 1 2 means
+that to match rule 0, the text being checked must match rule 1, and the text after the part that
+matched rule 1 must then match rule 2.
+
+Some of the rules have multiple lists of sub-rules separated by a pipe (|). This means that
+at least one list of sub-rules must match. (The ones that match might be different each
+time the rule is encountered.) For example, the rule 2: 1 3 | 3 1 means that to match rule 2, the
+text being checked must match rule 1 followed by rule 3 or it must match rule 3
+followed by rule 1.
+
+Fortunately, there are no loops in the rules, so the list of possible matches will be finite. Since
+rule 1 matches a and rule 3 matches b, rule 2 matches either ab or ba. Therefore, rule 0 matches aab
+or aba.
+
+Here's a more interesting example:
+
+0: 4 1 5
+1: 2 3 | 3 2
+2: 4 4 | 5 5
+3: 4 5 | 5 4
+4: "a"
+5: "b"
+
+Here, because rule 4 matches a and rule 5 matches b, rule 2 matches two letters that are the same
+(aa or bb), and rule 3 matches two letters that are different (ab or ba).
+
+Since rule 1 matches rules 2 and 3 once each in either order, it must match two pairs of letters,
+one pair with matching letters and one pair with different letters. This leaves eight possibilities:
+aaab, aaba, bbab, bbba, abaa, abbb, baaa, or babb.
+
+Rule 0, therefore, matches a (rule 4), then any of the eight options from rule 1, then b (rule 5):
+aaaabb, aaabab, abbabb, abbbab, aabaab, aabbbb, abaaab, or ababbb.
+
+The received messages (the bottom part of your puzzle input) need to be checked against
+the rules so you can determine which are valid and which are corrupted. Including the rules and the
+messages together, this might look like:
+
+0: 4 1 5
+1: 2 3 | 3 2
+2: 4 4 | 5 5
+3: 4 5 | 5 4
+4: "a"
+5: "b"
+
+ababbb
+bababa
+abbbab
+aaabbb
+aaaabbb
+
+Your goal is to determine the number of messages that completely match rule 0. In the
+above example, ababbb and abbbab match, but bababa, aaabbb, and aaaabbb do not, producing the answer
+2. The whole message must match all of rule 0; there can't be extra unmatched
+characters in the message. (For example, aaaabbb might appear to match rule 0 above, but it has an
+extra unmatched b on the end.)
+
+How many messages completely match rule 0?
+
+