You are given two arrays of positive integers, boxes and warehouse, representing the heights of various boxes of unit width and the heights of $n$ rooms in a warehouse of unit width, respectively. The warehouse rooms are ordered from left to right, indexed from $0$ to $n - 1$.

Boxes can be pushed into the warehouse from either the left entrance (room $0$) or the right entrance (room $n - 1$). The placement of boxes is subject to the following rules:

• Each room can hold at most $1$ box.

• A box cannot pass through any room that has a height strictly less than the height of the box.

• Once a box is placed in a room, it remains there and cannot be moved, preventing any other boxes from passing through that room.

Return the maximum number of boxes that can be placed in the warehouse.

Constraints:

• n $==$ warehouse.length

• $1 \leq$ boxes.length, warehouse.length $\leq 10^5$

• $1 \leq$ boxes[i], warehouse[i] $\leq 10^9$

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.