Benzene from cyclopropane-1,2,3-triyltrimethanol in acidic medium What is the mechanism of this reaction? After performing $\ce{E1}$ thrice I was expecting 1,2,3-trimethylidenecyclopropane to be formed instead. 



I know it's highly strained but I couldn't adopt any other pathway to reach any other product. 

Is the triene product not formed at all? If cyclopropane-1,2,3-trione can exist I think even the triene product can. 

This reaction is from my exercise book, couldn't find it on orgsyn.org.
I have not written the steps for carbocation formation, simple dehydration.