You are given a positive integer array grades representing the scores of students participating in a competition.

You want to organize these students into $k$ consecutive groups such that for every group index $i$ where $1 \leq i < k$:

1. The total sum of grades of students in the $(i + 1)$-th group is strictly greater than the total sum of grades of students in the $i$-th group.

2. The total number of students in the $(i + 1)$-th group is strictly greater than the total number of students in the $i$-th group.

Return the maximum number of groups $k$ that can be formed.

Constraints:

• $1 \leq$ grades.length $\leq 10^5$

• $1 \leq$ grades[i] $\leq 10^5$

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.