2002 AMC 12A Problem 21

Consider the sequence of numbers $4,$ $7,$ $1,$ $8,$ $9,$ $7,$ $6,$ $\ldots$ For $n \gt 2,$ the $n$th term of the sequence is the units digit of the sum of the two previous terms. Let $S_n$ denote the sum of the first $n$ terms of this sequence. The smallest value of $n$ for which $S_n \gt 10{,}000$ is