You are given a $0$ indexed integer array nums.

A subsequence of nums with indices $(i_0, i_1, \dots, i_{k - 1})$ of length $k$ is called balanced if:

• $i_0 < i_1 < \dots < i_{k - 1}$

• nums$[i_{j + 1}] -$ nums$[i_j] \geq i_{j + 1} - i_j$ for every $j$ satisfying $0 \leq j < k - 1$

A single element subsequence of length $1$ is always balanced.

Return the maximum possible sum of a balanced subsequence of nums.

Note: A subsequence of an array is a sequence formed by deleting some or no elements without altering the relative order of the remaining elements.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $-10^9 \leq$ nums[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.