You are playing a video game where you must defend a city against a horde of $n$ monsters. You are given two $0$ indexed integer arrays dist and speed, both of length $n$. Here, dist[i] represents the initial distance of the $i^{ ext{th}}$ monster from the city, and speed[i] represents the speed of the $i^{ ext{th}}$ monster.

You possess a weapon that can eliminate one monster at a time. The weapon is fully charged at minute $0$ and takes exactly $1$ minute to recharge after each use. Consequently, you can eliminate a monster at minute $0$, another at minute $1$, and so on.

The monsters move continuously toward the city at their respective speeds. You lose the game if any monster reaches the city (meaning its distance becomes less than or equal to $0$) before you can eliminate it. If a monster reaches the city at the exact same minute you fire at it, you still lose.

Return the maximum number of monsters you can eliminate before losing, or $n$ if you can eliminate all of them.

Constraints:

• n $==$ dist.length $==$ speed.length

• $1 \leq$ n $\leq 10^5$

• $1 \leq$ dist[i], speed[i] $\leq 10^5$

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.