4. Before the World Cup, the coach of country $F$ plans to evaluate 7 players, $A_{1}$, $A_{2}, \cdots, A_{7}$, by letting them play in 3 training matches (each 90 minutes). Assuming that at any moment during the matches, exactly one of these players is on the field, and the total playing time (in minutes) of $A_{1}, A_{2}, A_{3}, A_{4}$ can all be divided by 7, while the total playing time (in minutes) of $A_{5}, A_{6}, A_{7}$ can all be divided by 13. If there are no limits on the number of substitutions per match, how many different scenarios are there for the total playing time of each player?
(Tip: Let the playing time of the $i$-th player be $x_{i}$ minutes $(i=1,2, \cdots, 7)$. The problem is to find the number of positive integer solutions to the indeterminate equation $x_{1}+x_{2}+\cdots+x_{7}=$ 270, under the conditions $7 \mid x_{i}(1 \leqslant i \leqslant 4)$, and $13 \mid x_{j}(5 \leqslant j \leqslant 7)$. By the conditions, set $x_{1}+x_{2}+x_{3}+x_{4}=7 m$, $x_{5}+x_{6}+x_{7}=13 n(m \geqslant 4, n \geqslant 3)$. Thus, $m$ and $n$ are a set of positive integer solutions to the indeterminate equation $7 m+13 n=270$. $m=\frac{270-13 n}{7} \geqslant 4$, it is easy to get $3 \leqslant n \leqslant 18,(n \in \mathrm{N})$. Solving the system of equations yields a total of $\mathrm{C}_{32}^{3} \mathrm{C}_{2}^{2}+\mathrm{C}_{99}^{3} \mathrm{C}_{9}^{2}+\mathrm{C}_{6}^{3} \mathrm{C}_{16}^{2}=42$ 244 sets of positive integer solutions.)