Let $7 \overbrace{5 \ldots 5}^r 7$ denote the $(r+2)$ digit number where the first and the last digits are 7 and the remaining $r$ digits are 5 . Consider the sum $S=77+757+7557+\ldots+7 \overbrace{5 \ldots 57}^{98}$. If $S=\frac{7 \overbrace{5 \ldots 57}^{99}+m}{n}$, where $m$ and $n$ are natural numbers less than 3000 , then the value of $m+n$ is $\_\_\_\_$ .