Rearrange Ranges

Let $f([x_1,\,x_2,\,\cdots,\,x_k])$ be the minimum number of subarrays such that each $x_i$ belongs to exactly one subarray, and it's possible to arrange the subarrays in a way that makes $x$ increasing. For example, $f([5,\,4,\,1,\,2,\,3]) = 3$ since we can divide $x$ into three subarrays: $[5],\,[4],\,[1,\,2,\,3]$ then rearrange them to $[1,\,2,\,3],\,[4],\,[5]$. You are given a **permutation**