ELMO SL 2012 C1

Let $n\ge2$ be a positive integer. Given a sequence $\left(s_i\right)$ of $n$ distinct real numbers, define the "class" of the sequence to be the sequence $\left(a_1,a_2,\ldots,a_{n-1}\right)$ , where $a_i$ is $1$ if $s_{i+1} > s_i$ and $-1$ otherwise.

Find the smallest integer $m$ such that there exists a sequence $\left(w_i\right)$ of length $m$ such that for every possible class of a sequence of length $n$ , there is a subsequence of $\left(w_i\right)$ that has that class.

David Yang.