You are given an integer array monsters and a 2D integer array boosts.

You must defeat all monsters in sequence from index $0$ to monsters.length $- 1$.

Each element in boosts is given as [l_i, r_i, v_i], which grants an additional bonus strength of v_i at every index $k$ satisfying l_i $\leq k \leq$ r_i. If multiple boosts cover the same index, their values accumulate.

Starting with an initial strength, to defeat the monster at index $i$:

1. Your effective strength at index $i$, defined as the sum of your current strength and the total bonus strength at index $i$, must be greater than or equal to monsters[i].

2. After defeating the monster, your current strength decreases by monsters[i], but it cannot drop below $0$. That is, your updated strength becomes $\max(0, \text{current strength} -$monsters[i]$)$.

Return the minimum initial strength required to defeat all monsters in order.

Constraints:

• $1 \leq$ monsters.length $\leq 5 \times 10^4$

• $1 \leq$ monsters[i] $\leq 10^9$

• $0 \leq$ boosts.length $\leq 5 \times 10^4$

• boosts[i] == [l_i, r_i, v_i]

• $0 \leq$ l_i $\leq$ r_i $<$ monsters.length

• $1 \leq$ v_i $\leq 10^9$

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.