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Maximum Sum of Balanced Subsequence

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Problem statement

You are given a 0-indexed integer array nums.

A non-empty subsequence chosen from indices i[0] < i[1] < ... < i[k - 1] is balanced when every adjacent pair of chosen indices satisfies nums[i[j]] - nums[i[j - 1]] = i[j] - i[j - 1]. A subsequence of length one is balanced.

Return the maximum possible sum of a balanced subsequence.

A subsequence is formed by deleting zero or more elements without changing the relative order of the remaining elements.

Function

maxSumOfBalancedSubsequence(nums: int[]) → int

Examples

Example 1

nums = [1, 2, 3]return = 6

For every index i, nums[i] - i = 1. Therefore all three values form a balanced subsequence with sum 1 + 2 + 3 = 6.

Example 2

nums = [3, 2, 1]return = 3

The transformed values nums[i] - i are 3, 1, and -1. No two indices can belong to the same balanced subsequence, so the best choice is the single value 3.

Constraints

1 <= nums.length <= 100000
-10000 <= nums[i] <= 10000