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 i_0 < i_1 < ... < 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.

Constraints

Constraints not found

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