You are given two integer arrays value and limit, both of length n.

There are n elements indexed from $0$ to $n - 1$. Initially, all elements are available, and no element is active.

You can activate available elements one by one in any order. In each step, you select an available element i and perform the following actions:

1. Add value[i] to the total sum.

2. Add element i to the set of active elements.

3. Let k be the total number of currently active elements. Every element j satisfying limit[j] $\leq k$ becomes inactive, whether it was currently active or available. Inactive elements can never be activated in future steps, and any active element that becomes inactive is removed from the active set.

The process stops when there are no more available elements to activate.

Return the maximum total sum that can be obtained from an optimal activation order.

Constraints:

• $1 \leq n ==$ value.length $==$ limit.length $\leq 10^5$

• $1 \leq$ value[i] $\leq 10^5$

• $1 \leq$ limit[i] $\leq n$

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.