The primary carbocation shown can rearrange through successive 1,2-hydride and 1,2-methyl shifts. Count the cation shown together with every distinct secondary or tertiary carbocation reachable in this way (ignore all other primary cations). How many distinct carbocations are there in total? Give the answer as an integer.

The cation shown is the 3-methylbutyl cation. A 1,2-hydride shift from C2 gives the secondary 3-methylbutan-2-yl cation. A second 1,2-hydride shift from C3 gives the tertiary 2-methylbutan-2-yl cation; a methyl shift from the secondary cation just regenerates the same secondary cation. The set is the primary, the secondary and the tertiary cation, so the total is 3.