The number of routes she chooses $f(m, n)$ satisfies $f(m, n) \leqslant 2^{m n}$.
13. Let the set $S=\{1,2,3, \cdots, 1990\}, A \subset S$, and $|A|=26$. If the sum of all elements in $A$ is a multiple of 5, then $A$ is called a 26-element "good subset" of $S$. Find the number of 26-element "good subsets" of $S$.
For $k=0,1,2,3,4$, let $F_{k}=\{A|A \subseteq S| A \mid=26, A$'s element sum $\equiv k$ $(\bmod 5)\}$, if $\left\{x_{1}, x_{2}, \cdots, x_{26}\right\}$ is in $F_{0}$, then $\left\{x_{1}+k, x_{2}+k, \cdots, x_{26+k}\right\}$ is in $F_{k}$ (if $x_{i}+k>1990$, then use $x_{i}+k-1990$ instead), obviously this is a 1-1 mapping from $F_{0}$ to $F_{k}$, therefore $\left|F_{0}\right|=\left|F_{1}\right|=\left|F_{2}\right|=\left|F_{3}\right|=\left|F_{4}\right|$, and $F_{0}, F_{1}, F_{2}, F_{3}, F_{4}$ have no common elements between any two of them, and all 26-element subsets are $C_{1990}^{26}$, hence $\left|F_{0}\right|=\frac{1}{5} C_{1990}^{26}$.