You are playing a game with n levels, numbered from $0$ to n $- 1$. You are given a $0$ indexed integer array damage of length n, where damage[i] represents the amount of damage you take at level i.

You are also given an integer armor. You may use your armor ability at most once across all levels. When activated at level i, your armor prevents up to armor damage, meaning you will take $\max(0,$ damage[i] $-$ `armor}$)$ damage at that level instead.

To complete the game, your health must remain strictly greater than $0$ at all times.

Return the minimum initial health needed to complete all levels of the game.

Constraints:

• n == damage.length

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ damage[i] $\leq 10^5$

• $0 \leq$ armor $\leq 10^5$

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.