There are $n$ robots, each positioned on a one dimensional line. You are given three arrays: positions, healths, and a string directions, where positions[i], healths[i], and directions[i] represent the position, health, and movement direction of the $i^{ ext{th}}$ robot respectively.

All robots start moving simultaneously at the same speed. A robot moves to the left if its direction is 'L' and to the right if its direction is 'R'.

When two robots moving towards each other collide:

• The robot with lower health is destroyed, and the health of the surviving robot decreases by $1$. The surviving robot continues moving in its original direction.

• If both robots have the exact same health, both are destroyed.

Robots moving in the same direction or moving away from each other never collide.

Return an array containing the health of the surviving robots, ordered as they appeared in the initial input.

Constraints:

• $1 \leq$ positions.length $==$ healths.length $==$ directions.length $== n \leq 10^5$

• $1 \leq$ positions[i], healths[i] $\leq 10^9$

• directions[i] $==$ 'L' or directions[i] $==$ 'R'

• All values in positions are distinct

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.