You are given two arrays of positive integers, boxes and warehouse, representing the heights of several boxes and the heights of $n$ rooms in a warehouse, respectively. The rooms in the warehouse are indexed from $0$ to $n - 1$ from left to right, where warehouse[i] is the height of the $i^{ ext{th}}$ room.

Boxes can only be moved into the warehouse from left to right. A box can be placed in room $i$ if:

• The height of the box is less than or equal to the height of room $i$, and

• The height of the box is less than or equal to the heights of all preceding rooms from room $0$ to room $i - 1$, since it must pass through them.

Each room can hold at most $1$ box. Once a box is placed in a room, other boxes cannot pass 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] $\leq 10^9$

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