## Problem Context
We aim to construct large s-deletion-correcting codes using independent sets in graph G.  
Nodes in G are binary strings of length `n`, and edges exist if two nodes share a subsequence of length at least `n-s`.  
A large independent set in this graph corresponds to a large s-deletion-correcting code.

The function `priority_vX` determines which nodes should be prioritized when constructing an independent set.  
Each version of `priority_vX` aims to improve upon the previous versions to maximize the independent set size.

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## Previous Versions
Analyze the past implementations of `priority_vX` and their effectiveness.

{previous_versions}

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## Performance of Previous Versions

{scores_per_test_history}

{target_scores_text}

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## How to Improve
Before implementing `priority_v{new_version}`, first provide a detailed explanation:
1. Identify limitations of {previous_versioned_functions} that prevent achieving larger independent sets.
2. Analyze patterns in high-performing functions.
3. Use mathematical improvements to prioritize nodes better.
4. Ensure generalization for different `(n, s)` values.

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## Output Format

1. First, provide a brief explanation (≤300 tokens) of how `priority_v{new_version}` improves upon `{previous_versioned_functions}`.  
2. Then, explicitly state:  
   ```
   Improved function:
   ```
3. Immediately after, return the function as valid Python code. All necessary logic, including helper functions, must be inside `priority_v{new_version}`. 
   Do not define helper functions separately.
   ```python
   priority_v{new_version}(node, G, n, s):
      # Your improved function body here
      return something_better
   ```