Smallest local maximum

A local maximum of an array is an element strictly greater than both of its neighbours. The first and the last elements have only one neighbour, so they are not local maxima.

You are given an array of $n$ numbers. Find the smallest of its local maxima.

The first line contains $n$ ($3 \le n \le 10^5$). The second line contains $n$ integers ($|a_i| \le 10^9$). The array has at least one local maximum.

A single number — the smallest local maximum.

For $i = 2, \ldots, n - 1$ check $a_{i-1} < a_i > a_{i+1}$. In the first example the local maxima are $3$, $6$, $9$ — the smallest is $3$. In the second, $2, 2$ is a flat spot: $2$ is not strictly greater than its neighbour, and the only local maximum is $3$.