Weak in the Middle

You are given an array $A$ with length $N$. On each day, the following process was performed: - a new array $R$ is created; this array contains all elements $A_i$ such that $i=1$, $i=N$ or $\mathop{\rm min}(A_{i-1}, A_{i+1}) \le A_i$ ($2 \le i \lt N$), in the original order - $A$ is replaced by $R$ and $N$ is replaced by the length of $R$ In other words, all elements of $A$ that are between t