[Usaco2011 Feb]Cowlphabet 奶牛文字

题目描述

Like all bovines, Farmer John's cows speak the peculiar 'Cow'
language. Like so many languages, each word in this language comprises
a sequence of upper and lowercase letters (A-Z and a-z).  A word
is valid if and only if each ordered pair of adjacent letters in
the word is a valid pair.

Farmer John, ever worried that his cows are plotting against him,
recently tried to eavesdrop on their conversation. He overheard one
word before the cows noticed his presence. The Cow language is
spoken so quickly, and its sounds are so strange, that all that
Farmer John was able to perceive was the total number of uppercase
letters, U (1 <= U <= 250) and the total number of lowercase
letters, L (1 <= L <= 250) in the word.

Farmer John knows all P (1 <= P <= 200) valid ordered pairs of
adjacent letters.  He wishes to know how many different valid
words are consistent with his limited data.  However, since
this number may be very large, he only needs the value modulo
97654321.

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输入格式

* Line 1: Three space-separated integers: U, L and P

* Lines 2..P+1: Two letters (each of which may be uppercase or
        lowercase), representing one valid ordered pair of adjacent
        letters in Cow.

  第一行：三个用空格隔开的整数：U，L和P，1≤U．L≤250，1≤P<=200

  第二行到P+1行：第i+l有两个字母，表示第i个词素，没有两个词素是完全相同的

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输出格式

* Line 1: A single integer, the number of valid words consistent with
        Farmer  John's data mod 97654321.
单个整数，表示符合条件的单词数量除以97654321的余数

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样例输入

2 2 7
AB
ab
BA
ba
Aa
Bb
bB

INPUT DETAILS:

The word Farmer John overheard had 2 uppercase and 2 lowercase
letters.  The valid pairs of adjacent letters are AB, ab, BA, ba,
Aa, Bb and bB.

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样例输出

7

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提示

(可能的单词为AabB, Abba, abBA, BAab,BbBb, bBAa, bBbB)

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题目来源

Gold