1003143202

What is the total count of all integer solutions of the all following equations? $$\begin{array}{rl}{\log }_{\frac{1}{2}}({\log }_{2}x)& =-1\\ {\log }_5({\log }_{\frac{1}{5}}x)& =0\\ -{\log }_{\frac{1}{3}}({\log }_{\frac{1}{2}}x)& =1\end{array}$$