Hannahs Ultimate Challenge

Hannah Baker and Clay Jensen are best friends. One day Hannah decided to give Clay a vector $v = [v_1, v_2, v_3,...,v_n]$ and she defined a function $f(v)$ as the number of pairs of adjacent elements in $v$ which are unequal (In particular if $n = 1$ then $f(v) = 0$). For example if $v = [1, 2, 2, 4]$ then $f(v) = 2$. She wanted to make the task more interesting so she defined another function