You are given an integer array power, where power[i] represents the power required to defeat the $i^{ ext{th}}$ monster.

You start with $0$ mana points and have defeated $0$ monsters. Each day:

• You gain $1 + k$ mana points, where $k$ is the number of monsters that have already been defeated.

• Your mana points accumulate from day to day until you choose to defeat a monster.

• You can defeat an undefeated monster $i$ on any day as soon as your total accumulated mana is at least power[i].

• Upon defeating a monster, all accumulated mana points are immediately spent and your mana resets to $0$.

Return the minimum number of days needed to defeat all the monsters.

Constraints:

• $1 \leq$ power.length $\leq 17$

• $1 \leq$ power[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.