You are given a two dimensional integer array tiles, where tiles[i] $= [l_i, r_i]$ indicates that each tile from $l_i$ to $r_i$ inclusive is colored white. You are also given an integer carpetLen, representing the length of a carpet that can be positioned anywhere on the line.

Return the maximum number of white tiles that can be covered by the carpet.

Constraints:

• $1 \leq$ tiles.length $\leq 5 imes 10^4$

• tiles[i].length $= 2$

• $1 \leq l_i \leq r_i \leq 10^9$

• $1 \leq$ carpetLen $\leq 10^9$

• The tiles are non overlapping.

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.