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Anna wants to open a marvelous restaurant, “Candy Mountain”, serving only candy kabobs: sticks on which one puts various pieces of food, to be eaten from the tip to the base.
Like other kabob enthusiasts, when Anna eats a pattern of consecutive types of food in a kabob, she expects to eat another pattern later in the kabob. For instance, once she eats a piece of apple immediately followed by a piece of banana, she expects to have a leaf of mint immediately followed by chocolate in the remaining part of the kabob. She is happy if she finds this mint-chocolate pattern anywhere in the remaining kabob pieces.
Here is a kabob that Anna likes:
Anna has written down her perfect set of kabob patterns for the new restaurant, but she worries that these rules would give too many potential kabob types. This set of patterns is written down as a ruleset, where each rule is of the form “b implies e afterwards”, where b and e are non-empty sequences of characters, representing food pieces. A rule of the form b > e with b = b1 . . . bk and e = e1 . . .el means that, if the pattern b is encountered in the kabob, then the kabob should also contain e at some point after. Each bi+1 must immediately follow bi to trigger the rule and similarly each ej+1 must immediately follow ej to satisfy it, but bk and e1 do not need to be consecutive. No food piece can appear more than once in a rule (i.e., there is no i, j such that ej = bi and no i ≠ j with bi = bj or ei = ej) but a food piece can appear in several rules.
Note that if there are several occurrences of the word b in a kabob, they all need to be followed by an e. This can be a single e, as long as this e appears after all the b.
In a ruleset, rules are separated by ‘|’ and are of the form u > v meaning that each pattern u implies a pattern v afterwards. u and v are words composed of alphanumerical characters and no character can appear twice in a rule. For instance, the ruleset “
AB>X|R>A|T>B” describes three rules:
ABthere must be an X afterwards;
Rthere must be an A afterwards; and
Tthere must be a B afterwards.
Using this ruleset, the kabobs
RTABX are valid; but
ABXAB are not.
Anna asks you how many kabobs of a given size are compatible with her ruleset.
The input is such that 1 ≤ K ≤ 500 and 3 ≤ |R| ≤ 60.
One integer: the number of kabobs of length K satisfying all the rules in R, modulo 10 000 000.
4 ABC A>B|B>C|CB>A