3279. Maximum Total Area Occupied by Pistons

There are several pistons in an old car engine, and we want to calculate the maximum possible area under the pistons.

You are given:

• An integer height, representing the maximum height a piston can reach.
• An integer array positions, where positions[i] is the current position of piston i, which is equal to the current area under it.
• A string directions, where directions[i] is the current moving direction of piston i, 'U' for up, and 'D' for down.

Each second:

• Every piston moves in its current direction 1 unit. e.g., if the direction is up, positions[i] is incremented by 1.
• If a piston has reached one of the ends, i.e., positions[i] == 0 or positions[i] == height, its direction will change.

Return the maximum possible area under all the pistons.

Example 1:

Example 2:

Constraints:

• 1 <= height <= 106
• 1 <= positions.length == directions.length <= 105
• 0 <= positions[i] <= height
• directions[i] is either 'U' or 'D'.