Sequence $\displaystyle a_n$, n=1,2,3... is strictly locally monotone if for every integer k>1 either $\displaystyle a_{k-1}$<$\displaystyle a_k$ < $\displaystyle a_{k+1}$ OR $\displaystyle a_{k-1}$> $\displaystyle a_k $> $\displaystyle a_{k+1}$.

Prove every strictly locally monotone sequence is strictly monotone or give counterexample.