You are given a strictly increasing integer array rungs representing the heights of rungs on a ladder, and an integer dist. You start at height $0$ and can climb to the next rung if the difference in height between your current position and the rung is at most dist.

You may add rungs at any positive integer heights.

Return the minimum number of rungs you must add to reach the highest rung.

Constraints:

• $1 \leq$ rungs.length $\leq 10^5$

• $1 \leq$ rungs[i] $\leq 10^9$

• $1 \leq$ dist $\leq 10^9$

• rungs is strictly increasing.

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.