Refactor and Debug Poorly Written Code

Given a piece of extremely poorly written code, refactor it and debug it.

Asked in the onsite debugging round stage. Your task is to replace the broken implementation with a clean, correct one.

Function Signature

def normalize_and_sum(nums):

Requirements

1. Ignore negative numbers.
2. Remove duplicate non-negative values, keeping the first time each value appears.
3. Return the sum of the remaining values.
4. The solution should run in linear time.