A one-dimensional garden lies on the x-axis, starting at point $0$ and ending at point n. There are n + 1 taps positioned at integer points $[0, 1, \ldots, n]$ along the garden.

You are given an integer n and an integer array ranges of length n + 1, where ranges[i] represents the reach of the $i$-th tap. When opened, the $i$-th tap waters the interval $[i - \text{ranges}[i], i + \text{ranges}[i]]$.

Return the minimum number of taps that must be opened to water the entire garden $[0, n]$. If it is impossible to water the entire garden, return $-1$.

Constraints:

• $1 \leq$ n $\leq 10^4$

• ranges.length $==$ n + 1

• $0 \leq$ ranges[i] $\leq 100$

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.