Minimum Number of Taps to Water the Garden

Given a garden that extends along a one-dimensional x-axis from point 0 to point N, your task is to determine the minimum number of taps needed to water the entire garden. The garden has N+1 taps located at positions [0, 1, 2, ..., N].

Each tap, once opened, waters a range from (i - ranges[i]) to (i + ranges[i]), inclusive. You must find the fewest number of taps required to water every part of the garden from point 0 to point N. Return -1 if it's not possible to water the entire garden.

Input:

Integer T, the number of test cases 
For each test case:
 - Integer N, the range of the garden.
 - Array ranges of size N+1, where ranges[i] indicates the water coverage radius a tap at point i can achieve.

Output:

For each test case, a single integer representing the minimum number of taps required. If the garden cannot be fully watered, return -1.

Example:

Consider an input where T = 1, N = 5, and ranges = [3,4,1,1,0,0].

Input:

T = 1
N = 5
ranges = [3, 4, 1, 1, 0, 0]

Output:

1

Explanation:

By opening the tap at position 1, which covers points from -3 to 5, the entire garden from 0 to 5 is watered.

Constraints:

• 1 <= T <= 10
• 1 <= N <= 104
• 0 <= ranges[i] <= 100
• Time Limit: 1 sec