Problem Description

You are given an array weights of n positive integers, representing product weights arranged in a line. The task is to simulate a removal process and calculate a final sum.

The process repeats until no products remain:

1. Selection: Identify the product with the lightest weight among all currently remaining products.
2. Tie-breaking: If there are multiple products with the same minimum weight, choose the one that currently has the smallest index in the line.
3. Accumulation: Add the weight of the chosen product to a running total.
4. Removal: Remove the chosen product. Additionally, remove up to its two immediate neighbors: the one on its left (if it exists) and the one on its right (if it exists). If only one neighbor exists, remove just that neighbor.

Return the final accumulated total.

Example

weights = [4, 3, 2, 1]

1. Initial: [4, 3, 2, 1]
   • Lightest is 1 (at index 3).
   • Total = 1.
   • Remove 1. Left neighbor 2 exists, remove 2. Right neighbor does not exist.
   • Remaining: [4, 3]
2. Next: [4, 3]
   • Lightest is 3 (at current index 1).
   • Total = 1 + 3 = 4.
   • Remove 3. Left neighbor 4 exists, remove 4. Right neighbor does not exist.
   • Remaining: []

Final total = 4.