Array Sorting

Let $A$ be a permutation of $\{1,2,3, \dots, N\}$. We define a function $f(A)$ as the **minimum** number of **increasing** subarrays into which the permutation $A$ can be [partitioned](https://en.wikipedia.org/wiki/Partition_of_a_set). For example $f(\{5, 1, 4, 2, 3\}) = 3$, as the minimum number of increasing subarrays it can be partitioned into is $3$. The partitions are: $\{5\}, \{1, 4\},$ a