Four. (20 points) Let $a_{1} \in \mathbf{R}_{+}, i=1,2, \cdots, 5$. Find
$$
\begin{array}{l}
\frac{a_{1}}{a_{2}+3 a_{3}+5 a_{4}+7 a_{5}}+\frac{a_{2}}{a_{3}+3 a_{4}+5 a_{5}+7 a_{1}}+ \\
\cdots+\frac{a_{5}}{a_{1}+3 a_{2}+5 a_{3}+7 a_{4}}
\end{array}
$$

the minimum value.