2007 AMC12A 第$$11$$题  A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. For example, such a sequence might begin with the terms $$247$$, $$475$$, and $$756$$ and end with the term $$824$$. Let $$S$$ be the sum of all the terms in the sequence. What is the largest prime factor that always divides $$S$$?  三位数的有限序列具有以下性质：每项的十位和个位分别为下一项的百位和十位，最后一项的十位和个位分别为百位 和第一项的十位数字。 例如，这样的序列可能以 247、$$475$$ 和$$756$$开头，并以$$824$$结尾。 令 S 是序列中所有项的总和。 能被$$S$$整除的最大质因数是什么？
选项为:A:$$3$$  B:$$7$$  C:$$13$$  D:$$37$$  E:$$43$$  请回答其中一个选项.