$$
\text { 3. } 19 \text { Let } \frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots-\frac{1}{1}}}}=\frac{m}{n} \text {, }
$$

where $m$ and $n$ are coprime natural numbers, and the left side of the equation contains 1988 fraction bars. Calculate the value of $m^{2}+m n-n^{2}$.