Role of Lewis acid in synthesis of adamantane from bicyclic species

What is the role of $\ce{AlCl3}$ in the following synthesis of adamantane? I'm guessing it functions as a Lewis acid, but I am unsure how the mechanism of the second step works, as there is no region of high electron density in the bicyclic species. 


If a mechanism for the second step exists, I would greatly appreciate if someone could propose one. 


[![adamantane synthesis](https://i.stack.imgur.com/Mkpsk.png)](https://i.stack.imgur.com/Mkpsk.png)


Image source: Wikipedia


