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Maximum Sum of Balanced Subsequence 🐮

You are given a 0-indexed integer array nums.

A subsequence of nums having length k and consisting of indices i₀ < i₁ < ... < i_k-1 is balanced if the following holds:

nums[i] - nums[i-1] == i - (i-1),

A subsequence of nums having length 1 is considered balanced.

Return an integer denoting the maximum possible sum of elements in a balanced subsequence of nums.

A subsequence of an array is a new non-empty array that is formed from the original array by deleting some (possibly none) of the elements without disturbing the relative positions of the remaining elements.

Example 1:

Input:  nums = [1, 2, 3]
Output: 6 
Explanation:
Explanation not found 👉👈

Example 2:

Input:  nums = [3, 2, 1]
Output: 3 
Explanation:
Explanation not found 👉👈

Constraints:

Constraints not found 👉👈