You are given a $2$D integer array queries, where queries[i] = [l, r].

For each query, an array nums is formed containing consecutive integers from l to r inclusive, such that nums $= [l, l + 1, \dots, r]$.

In a single operation, you can select two distinct indices i and j where nums[i] > 0 and nums[j] > 0, and simultaneously replace nums[i] with $\lfloor ext{nums}[i] / 4 \rfloor$ and nums[j] with $\lfloor ext{nums}[j] / 4 \rfloor$.

Return the sum of the minimum number of operations required to reduce all elements of nums to $0$ for all queries.

Constraints:

• $1 \leq$ queries.length $\leq 10^5$

• queries[i].length $= 2$

• queries[i] $= [l, r]$

• $1 \leq l < r \leq 10^9$

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.