Maximize Points by Deleting Values and Their Neighbors

You are given an array of positive integers `nums`. You may repeatedly choose an occurrence of a value `v` that is still present, remove that occurrence, and earn `v` points. That operation also removes every remaining occurrence of `v - 1` and `v + 1`, earning no points for those additional removals. Return the maximum total points you can earn. Other occurrences of `v` remain available unless you choose to remove them in later operations. ### Input - `nums`: an array of positive integers. Duplicate values are allowed. ### Output Return the maximum achievable total score as an integer. ### Constraints and Edge Cases - For this practice version, `1 <= nums.length <= 20000` and `1 <= nums[i] <= 1000000000`. - Input order does not affect which values an operation removes. - Removing an occurrence never earns points for any neighboring values removed as a side effect. - Values need not fill a continuous range, and the largest value can be much larger than the number of elements. - The result may exceed the range of a signed 32-bit integer. Use a numeric representation that holds the total exactly. ### Example 1 ```text nums = [2, 2, 3, 3, 3, 4] output = 9 ``` Choosing the three occurrences of `3` earns `9` points. Choosing both `2` occurrences and the `4` instead earns only `8`. ### Example 2 ```text nums = [1, 1, 3, 1000000000] output = 1000000005 ``` All occurrences can contribute to the score because none of their values differ by one.