You are given two integer arrays nums and costs, both of length n, indexed from $0$ to $n - 1$.

You begin at index $0$ and wish to reach index $n - 1$. From a given index i, you are permitted to jump to another index j such that i $<$ j if and only if at least one of the following conditions is satisfied:

• nums[i] $\leq$ nums[j] and nums[k] $<$ nums[i] for every index k where i $<$ k $<$ j.

• nums[i] $>$ nums[j] and nums[k] $\geq$ nums[i] for every index k where i $<$ k $<$ j.

The cost incurred by jumping from index i to index j is equal to costs[j].

Return the minimum total cost required to reach index $n - 1$ starting from index $0$.

Constraints:

• n $==$ nums.length $==$ costs.length

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ nums[i], costs[i] $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.