There are $n$ robots positioned on an infinite number line. You are given two integer arrays position and speed, each of length $n$, where position[i] and speed[i] represent the starting position and constant speed of the $i$-th robot, respectively. You are also given an integer distance.

All robots move in the positive direction. Whenever a robot or a group of robots gets within a distance of at most distance behind another robot or group, they merge into a single group. Once merged, the combined group continues moving with the position and speed of its rightmost robot.

Return the total number of robot groups that will eventually remain.

Constraints:

• $1 \leq$ position.length $=$ speed.length $\leq 10^5$

• $1 \leq$ position[i], speed[i], distance $\leq 10^9$

• position 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.