$\log \left(\log _{a b} a+\frac{1}{\log _b a b}\right)$ is $($ where $a b \neq 1)$

If $a, b$ and $c$ are distinct positive numbers, not equal to unity. Such that $a b c=1$, then the value of $\log _b a \cdot \log _c a+\log _c b$ $\cdot \log _a b+\log _a c \log _b c$ is